Physics MCAT notes Flashcards

Question

What is energy?

Answer 1

Energy is a property or characteristic of a system to do work or more broadly, to make something happen. This broad definition helps us understand that different forms of energy have the capacities to do different things. For example, mechanical energy, such as that which Sisyphus transferred to the large rock, can cause things to move or accelerate through the process of work. An ice cube sitting on the kitchen counter at room temperature will eventually melt into water, undergoing the phase transformation from solid to liquid. Internal energy, or what a few textbooks call thermal energy (and what most of us sloppily call “ heat,” even though heat is actually a process of energy transfer, not energy itself), can make the ice cube on the counter melt. any time an object has a velocity, you should think about kinetic energy and the related concepts of work and conservation of mechanical energy

Answer 2

Energy is a property or characteristic of a system to do work or more broadly, to make something happen. This broad definition helps us understand that different forms of energy have the capacities to do different things. For example, mechanical energy, such as that which Sisyphus transferred to the large rock, can cause things to move or accelerate through the process of work. An ice cube sitting on the kitchen counter at room temperature will eventually melt into water, undergoing the phase transformation from solid to liquid. Internal energy, or what a few textbooks call thermal energy (and what most of us sloppily call “ heat,” even though heat is actually a process of energy transfer, not energy itself), can make the ice cube on the counter melt. any time an object has a velocity, you should think about kinetic energy and the related concepts of work and conservation of mechanical energy

Answer 3

• An object with mass is said to have potential energy when it has the potential to do something. Potential energy is another form of energy, and it can come in different types. One type of potential energy is gravitational potential energy, mechanical potential energy, which can be found in, say, a compressed spring, and chemical potential energy (or just chemical energy), which is found in the covalent and ionic bonds holding atoms together in molecules. Gravitational potential energy depends on a body's position with respect to some level identified as “ ground,” or the zero potential energy position. this equation to solve for gravitational potential energy in situations relatively close to the Earth's surface. where U is the potential energy, m is the mass in kg, g is the acceleration due to gravity, and h is the height of the object above the reference level. We see the potential energy is in a direct, linear relationship with all three of the variables, so changing any one of them by some given factor will result in a change in the potential energy by the same factor. Tripling the height of the pencil held in your hand above the floor would increase the pencil's potential energy by a factor of three, and it would most likely require you to stand on the desk in order to do so (thereby also increasing your own potential energy and potential for injury should you lose your balance).

Answer 4

total mechanical energy- sum of an object's potential and kinetic energies. where E is total mechanical energy, U is potential energy, and K is kinetic energy. The first law of thermodynamics states that energy is never created or destroyed. It is merely transferred from one system to another. Yet this does not mean that the total mechanical energy will always remain constant. You'll notice that the total mechanical energy equation accounts for potential and kinetic energies but not for other energies like thermal energy (“ heat” ) that is transferred as a result of friction. If frictional forces are present, some of the mechanical energy will be transformed into thermal energy and will be “ lost” — or, more accurately, not accounted for by the equation. Note that there is no violation of the first law of thermodynamics, as a full accounting of all the energies (kinetic, potential, thermal, sound, light, etc.) would reveal no net gain or loss of total energy, merely the transformation of some energy from one form to another.

Answer 5

Conservation of Mechanical Energy: E = U + K = Constant- Mechanical energy is conserved when no dissipative forces (e.g., friction, air resistance) are present. In the absence of non-conservative forces, such as frictional forces, the sum of the kinetic and potential energies will be constant. Conservative forces are those that have potential energies associated with them. the two most commonly encountered conservative forces are gravitational and electrostatic. The spring system, which is mechanical, can also be approximated to be conservative. a. If the net work done to move a particle in any round-trip path is zero, the force is conservative. b. If the net work needed to move a particle between two points is the same regardless of the path taken, the force is conservative. an object that falls through a certain displacement in a vacuum will lose some measurable amount of potential energy but will gain exactly that same amount of potential energy when it is lifted back to its original height, regardless of whether the return pathway is the same as that of the initial descent. Furthermore, at all points during the fall through the vacuum, there will be a perfect conversion of potential energy into kinetic energy, with no energy lost to nonconservative forces (e.g., friction). Of course, in real life, outside of theoretical situations, nonconservative forces like friction and air resistance are impossible to avoid, and the balls that we throw know all too well the energy impact of nonconservative forces. When the work done by nonconservative forces is zero, or when there are no nonconservative forces acting on the system, the total mechanical energy of the system remains constant. The conservation of mechanical energy. When nonconservative forces, such as friction or air resistance, are present, total mechanical energy is not conserved. where W′ is the work done by the nonconservative forces only. The work done by the nonconservative forces will be exactly equal to the amount of energy “ lost” from the system. Where did this energy go? The first law of thermodynamics tells us that the energy wasn't really lost. It simply was transformed into a form of energy, such as thermal energy, that isn't accounted for in the mechanical energy equation.

Answer 6

• Work- is used to mean another form of energy. Work is not actually a form of energy, but a process by which energy is transferred from one system to another. In fact, it's one of only two ways in which energy can be transferred. The transfer of energy, by work or heat, is the only way in which anything can be done. We are familiar with both processes, each being something we experience every day of our lives, although, arguably, it's easier to “ see” work than it is to “ see” heat. The chemical potential energy in the ATP was harnessed in the “ form” of heat. In fact, at the molecular level, this is no different from work, because it involves the movement of molecules and atoms, and each of them exert forces that do work on other molecules and atoms. Like any transfer of energy, it's not a perfectly efficient process, and some of that energy is “ lost” as thermal energy. Our muscles quite literally “ warm up” when we contract them repeatedly. theta is the angle between the force and displacement vectors.

Answer 7

Calculating work and power- Energy is transferred through the process of work when something exerts forces on or against something else. where W is work, F is the force applied, d is displacement through which the force is applied, and theta is the angle between the applied force vector and the displacement vector. work is a function of the cosine of the angle, which means that only forces (or components of forces) parallel or antiparallel to the displacement vector will do work (i.e., transfer energy). We've already said that the SI unit for work is the joule, a fact suggesting that work and energy are the same thing, but remember they are not: Work is the process by which a quantity of energy is moved from one system to another. It takes force. Not just any force but force in the direction that we want the object to move. Every time we push, pull, tug, kick, or drag an object for the purpose of moving it from one place to another, we do work, and it's not just humans that do work. Any machine designed to apply a force to generate movement is doing work. By pushing straight into the side of the box, meaning pushing parallel to the ground and thus parallel to its displacement, you get the best results. Remembering your trig, the cosine of 0 degrees is 1, meaning that all of the force is going into the work. If you were to change the angle at which you are pushing to 60 degrees (cosine of 60 is 0.5), then only half of your force would be going into the work. In summary, if in both situations you want the box to accelerate a certain distance, it will take double the force to move the box the same distance if the angle is 60 degrees instead of zero, though the same amount of work will be done. . The unit for power, the watt, W. rate at which energy is transferred from one system to another is measured as power. where P is power, W is work, and t is the time over which the work is done. The SI unit for power is the watt (W), which as you can see from the equation is equal to J/s. Power is calculated in many different situations, especially those involving circuits, resistors, and capacitors. Power is always a measure of the rate of energy consumption, transfer, or transformation per unit time.

Answer 8

• Work-energy theorem- energy (the capacity to do something or make something happen). work-energy theorem is a powerful expression of the relationship between work and kinetic energy. In particular, it offers a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy of that object. The net work done on or by an object will result in an equal change in the object's kinetic energy. If you can calculate the change in kinetic energy experienced by an object, then by definition you can determine the net work done on or by an objectbrake pads exert frictional forces against the rotors, which are attached to the wheels. These frictional forces do work against the wheels, causing them to decelerate and bringing the car to a halt. The net work done by all these forces is equal to the change in kinetic energy of the car.

Answer 9

• Momentum (p) is a quality of objects in motion. In classical mechanics, it is defined as the product of an object's mass and velocity. Because it has magnitude and direction, it is a vector quantity, like velocity and acceleration. where p is momentum, m is mass, and v is velocity. For two or more objects, the total momentum is the vector sum of the individual momenta. All of these objects and all objects that have mass also have inertia. Inertia is the tendency of objects to resist changes in their motion and momentum. We can observe the sometimes disastrous results when objects encounter forces that cause them to change their motion• Momentum (p) is a quality of objects in motion. In classical mechanics, it is defined as the product of an object's mass and velocity. Because it has magnitude and direction, it is a vector quantity, like velocity and acceleration. where p is momentum, m is mass, and v is velocity. For two or more objects, the total momentum is the vector sum of the individual momenta. All of these objects and all objects that have mass also have inertia. Inertia is the tendency of objects to resist changes in their motion and momentum. We can observe the sometimes disastrous results when objects encounter forces that cause them to change their motion

Answer 10

• Impulse- As we have seen over and over again, the only manner by which an object's motion can change is when there is net force acting on it to cause it to accelerate. When net force acts on an object, causing it to change its motion, this also results in change to the object's momentum. This change in momentum is called impulse (I) and is a vector quantity. For a constant force applied through a period of time, impulse and momentum are related where I is impulse, F is force, Δ t is time, p is momentum, m is mass, and v is velocity. the setup of a typical momentum problem will involve changes to momentum in only one dimension, which allows us to treat the vectors as scalars along the number line. The variables are assigned positive or negative signs depending on whether the corresponding vectors are in the positive or the negative direction. inverse relationship between force magnitude and time if impulse is constant. In other words, given a particular change in momentum, the longer the period of time through which this impulse is achieved, the smaller the force necessary to achieve the impulse. front and side airbags and crumple zones in the front and rear of the car, are designed to increase the time through which the change in momentum associated with a collision will occur. Prolonging the duration of the collision allows the change in momentum to occur over a longer period of time, and this reduces the magnitude of the forces necessary to achieve the change in momentum. Reducing the forces exerted on the car and its occupants reduces the risk of severe injury or death.

Answer 11

• Conservation of momentum- situation with no external forces acting on a system, or if external forces are present, the vector sum of the external forces acting on that system is zero. In the absence of (nonzero) external forces, or in the case of the external forces canceling each other, the total (vector sum) momentum of a system will be constant.

Answer 12

• Collisions- two or more objects collide in an idealized collision (instantaneous and in a specific location), we can say that momentum is conserved as long as no (net) external forces act on the objects. Conservation of momentum means that the vector sum of the momenta is constant: The total momentum after the collision is equal to the total momentum before the collision. This does not mean that the individual momenta will necessarily be constant. Objects that collide can sometimes experience dramatic changes in their momenta, even as the total momentum of the system is constant. Individual changes in momentum may occur (e.g., objects may experience changes in velocity as a result of the collision), but total momentum is conserved as long as no external forces, such as friction, are present. For a collision between two objects, a and b, this can be expressed. Use this equation for collisions after which the two objects, a and b, bounce apart and do not stick together. where pai and pbi are the momenta before the collision and paf and pbf are the momenta after the collision. Since we've already defined momentum as the product of mass and velocity, we can rewrite the conservation of momentum where vai and vbi are the velocities before the collision and vaf and vbf are the velocities after the collision. one-dimensional problems of collision can be treated as if the vectors were scalars along the number line. The signs on the velocities (and hence on the momenta) will be determined by the direction of the velocity and momentum vectors. You will decide, for each problem, which direction is given the positive sign.If the momentum problem is two-dimensional, then we will have to resolve the momentum vectors into their X and Y components using trigonometry, it's inevitable that things are going to bump against each other. From cars to beams of high-energy particles directed onto thin sheets of gold foil, collisions are inevitable and frequent.In completely elastic collisions (objects don't stick together), we have a perfect collision in which both momentum and kinetic energy are conserved. In both inelastic collisions (objects don't stick together) and completely inelastic collisions (objects stick together), kinetic energy is not conserved, but momentum is. 1. Completely elastic collisions 2. Inelastic collisions 3. Completely inelastic collisions

Answer 13

• Completely Elastic Collisions- Completely elastic collisions occur when two or more objects collide in such a way that both total momentum and total kinetic energy are conserved. This means that no energy of motion was transformed in the instance of the collision into another form, such as thermal, light, or sound. Nor was any energy used to change the shapes of the colliding objects. rarely do collisions occur without sound, light, or heat production or deformation of objects. can be analyzed as an instance of conservation of momentum and kinetic energy. Be careful not to assume that the velocities of the colliding objects remain constant. In fact, it is almost certain that the objects will experience changes in their velocities (magnitude and/or direction) upon impact. In completely elastic collisions, it is the total kinetic energy, not the individual velocities or even the individual kinetic energies of the objects, that remains constant. In equation form, the conservation of momentum. completely elastic collisions are the only type for which kinetic energy is conserved.

Answer 14

Inelastic Collisions- release of a tremendous amount of energy in the form of loud noises, blindingly bright explosions, ferociously hot fires, and/or bone-rattling vibrations. When a collision results in the production of light, heat, sound, or object deformation, there is necessarily a decrease in the total kinetic energy of the system. This type of collision is an inelastic collision and is closer to what we typically observe in everyday life. Momentum is conserved as long as no external forces are present (as in the case of totally elastic collisions) even as kinetic energy is transformed (“ lost” ). The conservation of momentum equation is identical to that displayed in the discussion of completely elastic collisions. However, the final kinetic energy will be less than the initial kinetic energy. change in kinetic energy will be equal to the amount of energy released from the system in the form of heat, light, or sound.

Answer 15

Completely Inelastic Collisions- Use this equation for collisions after which the two objects, a and b, stick together and move as one. not every collision results in mangled metal or mass extinction. Furthermore, we recognize that many collisions are necessary, even for the continuation of life. In fact, if it weren't for completely inelastic collisions, the molecules that make up the matter of our universe would never have formed. In completely inelastic collisions, the objects that collide stick together rather than bouncing off each other and moving apart. When atoms are moving around and colliding with each other, they sometimes stick together to become compounds as the result of formation of covalent or ionic bonds. This is not that much different than the formation of a “ link” between two balls covered in Velcro that are rolled toward each other: Upon collision, they stick together and move as one object. totally inelastic collisions result in conservation of momentum as long as the vector sum of any external forces, such as frictional forces, is equal to zero. This is a variant of the inelastic collision, so total kinetic energy is not conserved. Because the objects stick together upon collision, ight side adds the masses of the two objects together and calculates a single final velocity, which is appropriate given that the objects move as a single mass after the collision.

Answer 16

• Mechanical Advantage- The difference is mechanical advantage. Sloping inclines, such as hillsides and ramps, make it easier for work to be accomplished. For a given quantity of work, any device (such as an inclined plane) that allows for work to be accomplished through a reduced applied force is said to provide mechanical advantage. In addition to the inclined plane, five other devices are considered the classic simple machines designed to provide mechanical advantage: wedge, axle and wheel, lever, pulley, and screw. Of these, the inclined plane, lever, and pulley. Mechanical advantage is the ratio of the force exerted on object by a simple machine (Fout) to the force actually applied on the simple machine (Fin). The mechanical advantage, because it is a ratio, is dimensionless. his reduction in necessary force for the purpose of accomplishing a given amount of work does have a “ cost” associated with it, however, and that is the distance through which the smaller force must be applied in order to do the work. Simple machines may provide mechanical advantage, but they do not violate the fundamental laws of physics! We know that energy can be neither created nor destroyed, merely changed from one form to another: energy “ in” (in one form) must equal energy “ out” (in another form). Inclined planes, levers, and pulleys do not “ magically” change the amount of work necessary to move an object from one place to another. In mechanical terms, that work is defined as the product of the object's displacement and the magnitude of the force vector that is along the displacement vector. isplacement is pathway-independent, and for conservative systems, work doesn't depend upon the actual distance traveled between the final position and the initial position. An inclined plane, as we will see in the following discussion, allows for masses to be displaced through the application of lower force over a greater distance to achieve the change in position. Pulleys and levers “ work,” in principle, in exactly the same way.

Answer 17

Inclined planes- The ramp allows those using it to change their position (that is, achieve a displacement) from the street level to the elevated front door in a gradual manner. This displacement requires a given quantity of work defined, as we've seen, as the product of displacement and the force vector along the displacement. If we ignore friction forces, we can say that it makes no difference whether that displacement occurs in a straight-line pathway or in the back-and-forth pathway of the entrance ramp: The work required is the same. work equation an inverse relationship between applied force and distance for a constant value of work. Because the ramp is longer than a straight-line path from the street to the building door, the distance through which the ultimate displacement will be achieved is greater, and the force necessary to achieve that displacement is reduced. This is the mechanical advantage offered by an inclined plane to anyone using a wheelchair, pushing a baby carriage, or rolling a heavy object.

Answer 18

Pulleys- a reduction of necessary force at the “ cost” of increased distance to achieve a given value of work or energy transference. In practical terms, pulleys allow heavy objects to be lifted using a much-reduced force. Simply lifting a heavy object of mass m to a height of h will require an amount of work equal to mgh. If the displacement occurs over a distance equal to the displacement, then the force required to lift the object will equal mg. the distance through which the displacement is achieved is greater than the displacement, then setting W = Fd = mgh shows us that the applied force will be less than mg. In other words, we've been able to lift this heavy object to the desired height by using a lower force, but we've had to apply that lower force through a greater distance in order to lift this heavy object to its final height. Because the block is not accelerating, it is in translational equilibrium, and the force that the block exerts downward (its weight) is equaled by the sum of the tensions in the two ropes. For a symmetrical system, the tensions in the two ropes are the same and are each equal to half the weight of the block. epresents a heavy crate that must be lifted by a worker in a warehouse. Assuming that the crate is being held momentarily stationary, in midair, we again have a system in translational equilibrium: the weight (the load) is in balance with the total tension in the ropes. The tensions in the two vertical ropes are equal to each other (if they were unequal, the pulleys would turn until the tensions were equal on both sides) and each rope supports one-half of the crate's total weight. Fortunately for the warehouse employee holding onto the free end of the rope, only half the force (the effort) is required to lift the crate to a high shelf. This is the mechanical advantage provided by the pulley, but as we've already discussed, mechanical advantage comes at the expense of distance. To lift an object to a certain height in the air (the load distance), one must pull through a length of rope (the effort distance) equal to twice that displacement. If, for example, the crate must be lifted to a shelf 3 meters above the ground, then both sides of the supporting rope must shorten by 3 meters, and the only way to accomplish this is by pulling through 6 meters of rope.

Answer 19

All simple machines can be approximated as conservative systems if we ignore the usually small amount of energy that would be “ lost” due to external forces, such as friction. The idealized pulley is massless and frictionless, and under these theoretical conditions, the work put into the system (the exertion of force through a distance of rope) will exactly equal the work that comes out of the system (the displacement of the mass to some height). Real pulleys (and all real machines, for that matter) fail to conform to these idealized conditions to one degree or another and, therefore, do not achieve 100 percent efficiency in conserving energy output to input. We can define work input as the product of effort and effort distance; likewise, we can define work output as the product of load and load distance. Comparing the two, as a ratio of work output to work input, defines the efficiency of the simple machine. Efficiencies are often expressed as percentages by multiplying the efficiency ratio by 100 percent. The efficiency of a machine gives a measure of the amount of work you put into the system that “ comes out” as useful work. The corollary of efficiency is the percentage of the work that you put into the system that becomes unusable due to external forces. For every additional pair of pulleys, we can reduce the effort further still. In this case, the load has been divided among six lengths of rope, so the effort required is now only one-sixth the total load. Remember that we would need to pull through a length of rope that is six times the desired displacement, and too much of a good thing has its price. For pulleys, that price is lowered efficiency due to the added weight of each pulley and the additional friction forces.

Answer 20

• Center of Mass- This point, which can be calculated using coordinate geometry, is the point within any two- or three-dimensional object at which the entire object's mass could be represented as a single particle. Each part of the racket moves in its own way, so it's not possible to represent the motion of the whole racket as a single particle. However, one point within the racket moves in a simple parabolic path, very similar to the flight of a ball. It is this point within the racket that is known as the center of mass. For a system of two masses, m1 and m2, lying along the x-axis at points x1 and x2, respectively, the center of mass is… For a system with several masses strung out along the x-axis, the center of mass is… For a system in which the particles are distributed in all three dimensions, the center of mass is defined by the three coordinates:

Answer 21

• center of gravity is the point at which the entire force due to gravity can be thought of as acting. It is found from similar formulas: The center of mass of a uniform object is at the geometric center of the object. Since W = mg, the center of gravity and the center of mass will be the same point as long as g is constant.

Answer 22

•zeroth law is based on a simple observation: When one object is in thermal equilibrium with another object, say a cup of warm tea and a metal stirring stick, and the second object is in thermal equilibrium with a third object, say the metal stirring stick and your hand, then the first and third object are also in thermal equilibrium and when brought into thermal contact (which doesn't necessarily imply physical contact, by the way), no net heat will flow between them. transitive property of thermal equilibrium; if a = b and b = c, then a = c. No heat flows between objects in thermal equilibrium

Answer 23

Temperature- average motional (kinetic) energy the difference in temperatures, determines the direction of heat flow. When allowed, heat moves spontaneously from materials that have higher temperatures to materials that have lower temperatures. Heat (energy) flows from hot to cold. If no net heat flows between two objects in thermal contact, then we can say that their temperatures are equal and they are in thermal equilibrium. Once we start talking about heat flowing from hotter to colder objects, physical property of matter, motional behavior of atoms and molecules making up matter, freezing and boiling temperatures of water are assigned the 0° and 100° values, respectively, for the Celsius scale. In spite of the fact that the Fahrenheit scale is also based on the phase transformations of water, it is clearly not as straightforward.

Answer 24

Kelvin is a scale based around “ absolute zero,” which is the temperature at which all random atomic motion stops. This occurs at zero degrees Kelvin. there are 180 degrees between water's phase changes on the Fahrenheit scale, rather than 100 degrees as on both the Celsius and the Kelvin scales, the size of the Fahrenheit unit is smaller where TC stands for degrees Celsius, TK stands for degrees Kelvin, and TF stands for degrees

Answer 25

* thermal expansion- Length, volume, and even the conductivity of matter change as a function of temperature. The relationship between temperature and a physical property of some matter. The cold temperature caused the mercury to contract, and when the level in the glass tube stabilized at a lower level, he marked this as the zero reference on the scale. He then placed the same mercury thermometer in a mixture of ice and water (that is, at the freezing temperature for water). The slightly warmer temperature of this mixture caused the mercury to rise in the glass column, and when it stabilized at this higher level, Fahrenheit assigned a value of 32° . When he stuck the thermometer under his (or someone else's) tongue, he marked the even higher mercury level as 96°. A change in the temperature of most solids results in a change in their length. Rising temperatures cause an increase in length, and falling temperatures cause a decrease in length. The amount of length change is proportional to the original length of the solid and the increase in temperature. where Δ L is the change in length, L is the original length, and Δ T is the change in temperature. The coefficient of linear expansion α is a constant that characterizes how a specific material's length changes as the temperature changes. This usually has units of K− 1, though it may sometimes be quoted as ° C− 1. * Liquids also experience thermal expansion, but the only meaningful parameter of expansion is volume expansion.

Answer 26

* first law of thermodynamics tells us that an increase in the total internal energy of a system is caused by transferring heat to the system or performing work on the system. The total internal energy of a system will decrease when heat is lost from the system or work is performed by the system. in the absence of friction forces, the sum of kinetic and potential energies is constant in a system. Essentially, the first law states that the change in the total internal energy of a system is equal to the amount of energy transferred in the form of heat to the system, minus the amount of energy transferred from the system in the form of work. The internal energy of a system can be increased by adding heat, doing work on the system, or some combination of both processes. where Δ U is the change in the system's internal energy, Q is the energy transferred through heat to the system, and W is the work done by the system. sign convention: work done by the system is positive, while work done on the system is negative; heat flow into the system is positive, while heat flow out of the system is negative. The first law of thermodynamics is that energy is neither created nor destroyed. This means the energy of a closed system (such as the universe) will always remain constant. * Examination of the first law of thermodynamics revealed that the energy of a closed system (up to and including the universe) is constant, such that the total internal energy of a system (the sum of all its potential and motional energies) equals the heat energy gained by the system minus the work energy done by the system, third law of thermodynamics, which states that absolute zero can never be actually reached,

Answer 27

Systems – object or material to which they are paying attention, everything else outside system is environment. energy is conserved even when friction is present. Energy can be neither created nor destroyed; it can only be changed from one form to another. Because the first law accounts for all work and all heat processes impacting the system, the presence of friction poses no problem, because the energy transfer associated with the friction will be accounted for in the first law equation.W here may be a “ loss” of energy from the car as a result of the friction, but that precise amount of energy can be “ found” elsewhere, as thermal energy in the atoms and molecules of the road and air.

Answer 28

•Heat is the process of energy transfer between two objects at different temperatures and will continue until the two objects come into thermal equilibrium (i.e., reach the same temperature). work and heat are the only two processes by which energy can be transferred from one object to another. Remember what the zeroth law says: Objects in thermal contact are in thermal equilibrium when their temperatures are the same. The corollary of this is the second law of thermodynamics: Objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature (and come to thermal equilibrium). Heat, then, is defined as the process by which a quantity of energy is transferred between two objects as a result of a difference in temperature. heat can never spontaneously transfer energy from a cooler object to a warmer one without work being done on the system. SI unit for heat is the joule (J),

Answer 29

Heat Transfer- energy to be transferred between objects, they must be in thermal contact with each other. Not necessarily physically touching, enery travels distances and doesn’t require a medium in order to move. conduction, convection, and radiation.

Answer 30

Conduction is the direct transfer of energy from molecule to molecule through molecular collisions have to be in physical contact. the particles of the hotter matter transfer some of their motional energy to the particles of the cooler matter through collisions between the particles of the two materials. Metals are described as the best heat conductors because the density of atoms embedded in the “ sea of electrons” that characterizes the metallic bond facilitates the transfer of energy. Gases tend to be the poorest heat conductors because even though gas molecules are free to move around (in fact, the root mean square velocity of air molecules at room temperature and atmospheric pressure is around 500 m/s), there is so much space between individual molecules that energy transferming collisions occure relatively infrequently.

Answer 31

Convection is the transfer of heat by the physical motion of the heated material. Because convection involves flow, only fluids (liquids and gases) can transfer heat by this means. In convection, heated portions of the fluid rise from the heat source, while colder portions sink (because density decreases as temperature increases). Fans with circulating hot air

Answer 32

• Convection is the transfer of heat by the physical motion of the heated material. Because convection involves flow, only fluids (liquids and gases) can transfer heat by this means. In convection, heated portions of the fluid rise from the heat source, while colder portions sink (because density decreases as temperature increases). Fans with circulating hot air

Answer 33

* vacuum. For this reason, the energy from the sun is able to warm the earth * Specific Heat- One calorie (little c) is the amount of heat required to raise 1 g of water one degree Celsius. One Calorie (big C) is the amount of heat required to raise 1 kg of water 1 degree Celsius. heat energy is added or removed from a system, the temperature of that system will change in proportion to the amount of heat, unless the system is undergoing a phase change during which the temperature is constant. This relationship between heat and temperature for a substance is called specific heat (c). The specific heat of a substance is defined as the amount of heat energy required to raise 1 kg of a substance by 1° C or 1 K. with the specific heat for a substance changes according to its phase. where m is the mass of the object and c is the specific heat. Because the unit size for the Celsius and Kelvin scales is the same, the change in temperature will be the same for temperatures measured in Celsius or Kelvin

Answer 34

• Heat of Transformation- a substance is undergoing a phase change, such as from solid to liquid or liquid to gas, the heat that is added or removed from the system does not result in a change in temperature. phase changes occur at constant temperature, and the temperature will not begin to change until all of the substance has been converted from one phase into the other. water melts at 0° C. No matter how much heat is added to a mass of ice at 0° C, the temperature will not rise until all the ice has been melted into liquid water. We've determined that adding heat raises the temperature of a system because the particles in that system now have a greater average kinetic energy, and it's true that molecules have greater degrees of freedom of movement in the liquid state than in the solid state (and even more so in the gas state). However, phase changes are related to changes in potential energy, not kinetic energy.

Answer 35

The molecules of water in ice, for example, aren't “ frozen” in place and unable to move. Actually, there's a lot of movement. The molecules rotate, vibrate, and wiggle around. The bonds within each molecule are also free to bend and stretch. Of course, the molecules are held in relatively stable positions by the hydrogen bonds that form between them, but they still have a fairly significant amount of motional (kinetic) energy. The potential energy, however, is quite low because of the stability provided by the relative closeness of one molecule to another and by the hydrogen bonds. add heat to ice that is at 0° C. The heat energy causes the water molecules to begin to break away from each other by breaking free of the hydrogen bonds between them. Not all of the hydrogen bonds and liquid water molecules still want to form hydrogen bonds, but because the water molecules are being held less rigidly in place, they now have greater degrees of freedom of movement (statistical mechanics says that these contribute to a greater number of “ microstates” ) and their average potential energy increases. However, their average kinetic energy stays the same because they “ redirect” some of their previously limited motion to other directions. Instead of only jumping up and down or swaying side to side, the molecules begin to move forward and backward. Nevertheless, to start moving forward, they have to decrease their up-and-down jumping. In this way, the average motional (kinetic) energy is constant even as the molecules begin to “ enjoy” greater degrees of freedom of movement (a greater number of possible microstates)

Answer 36

Phase changes are sublimation (solid to gas), deposition (gas to solid), fusion (solid to liquid), freezing (liquid to solid), condensation (gas to liquid), and finally vaporization (liquid to gas).

Answer 37

When work is done by a system, the work is said to be positive, and when work is done on a system, the work is noted as negative. From the first law of thermodynamics, you can see that when work is done by the system, the internal energy of the system decreases, and when work is done on the system, the internal energy of the system increases. process of energy transfer by application of force through some distance. pressure can be thought of as an “ energy density.” During any thermodynamic process, a system goes from some initial equilibrium state with an initial pressure, temperature, and volume to some other equilibrium state, which may be at a different final pressure, temperature, or volume. when a gas expands, we say that work was done by the gas and the work is positive; when a gas is compressed, we say that work was done on the gas and the work is negative. There are an infinite number of paths between an initial and final state. Different paths require different amounts of work. You can calculate the work done on or by a system by finding the area under the pressure-volume curve. Note that if volume stays constant as pressure changes (that is, Δ V = Δ x = 0), then no work is done because there is no area to calculate. On the other hand, if pressure remains constant as volume changes (that is, Δ P = Δ y = 0), then the area under the curve is a rectangle of length P and width Δ V (Vf− Vi). For processes in which pressure remains constant,

Answer 38

Ex. When the gas expands, it pushes up against the piston, exerting a force (F = PA), causing the piston to move up and the volume of the system to increase. When the gas is compressed, the piston pushes down on the gas, exerting a force (F = PA), and the volume of the system decreases. Because the volume of the system has changed due to an applied pressure, we can say that work has been done. much more work to change volume at high pressures. This makes sense when you think of pressurized cylinders. To put more gas into an already pressurized cylinder would take an incredible amount of work. Conversely when a pressurized cylinder is broken, it quickly does a lot of work on its environment. takes much more work to change volume at high pressures. put more gas into an already pressurized cylinder would take an incredible amount of work. Conversely when a pressurized cylinder is broken, it quickly does a lot of work on its environment.

Answer 39

closed cycle in which, after certain interchanges of work and heat, the system returns to its initial state. Because work is positive when the gas expands and negative when the gas is compressed, the work done is the area enclosed by the curve.

Answer 40

special cases of the first law of thermodynamics- some physical property is held constant through the process. These processes are isovolumetric (constant volume), adiabatic (no heat exchange), and closed cycle (constant internal energy). Isovolumetric processes are also known as isochoric; closed cycle processes are also known as isothermal, meaning the temperature stays constant.

Answer 41

* Second Law of Thermodynamics and Entropy- Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. second law states that energy will spontaneously disperse. It does not say that energy can never be localized or concentrated * Ex. The chemical energy in the bonds of elemental iron and oxygen is released and disperses as a result of the formation of the more stable (lower energy) bonds of iron oxide (rust). The potential energy of the building is released and dispersed in the form of light, sound, and heat (motional energy) of the ground and air as the building crumbles and

Answer 42

Entropy- measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out or how widely spread out energy becomes in a process. where Δ S is the change in entropy, Q is the heat that is gained or lost, and T is the temperature in Kelvin. When energy is distributed into a system at a given temperature, its entropy increases. When energy is distributed out of a system at a given temperature, its entropy decreases. the entropy of the universe is always increasing. The more space that appears with the expansion of the universe, the more space there is for the entire universe's energy to be distributed and the total entropy of the universe to increase irreversibly. Work must usually be done to concentrate energy. energy in a closed system will spontaneously spread out and entropy will increase if it is not hindered from doing so. the second law ultimately claims that the entropy of the universe is increasing. That is, energy concentrations at any and all locations in the universe are in the process of becoming distributed and spread out.

Answer 43

Ex. hot object is brought into thermal contact with a cold object, the hot object will transfer heat energy to the cold object until both are in thermal equilibrium (that is, at the same temperature). This is a natural process and also one that we would describe as irreversible: unsurprised that the two objects eventually reach a common temperature, but not possible if all of a sudden the hot object became hotter and the cold object became colder.. ice and liquid water in equilibrium at 0° C. If we place this mixture of ice and liquid water into a thermostat that is also at 0° C and allow infinitesimal amounts of heat to be absorbed by the ice from the thermostat so that the ice melts to liquid water at 0° C and the thermostat remains at 0° C, then the increase in the entropy (+Q/T) of the system (the water) will be exactly equal to the entropy decrease (− Q/T) of the surroundings (the thermostat). The net change in the entropy of the system and its surroundings is zero. Under these conditions, the process is reversible. The key to a reversible reaction is making sure that the process goes so slowly— requiring an infinite amount of time— that the system is always in equilibrium and no energy is lost or dissipated (by friction). To be frank, no real processes are reversible; we can only approximate a reversible process. Ice that melts on the warm countertop will not be expected to “ reverse course” and freeze if it remains in the warm environment. The liquid water will need to be placed in an environment that is cold enough to cause the water to freeze, and once frozen in the cold environment, the ice would not be expected to begin melting spontaneously. The freezing and melting of water in real life is essentially an irreversible process. reversible process, the entropy where L is the latent heat (either heat of fusion or heat of vaporization), m is mass, and T is the constant temperature of the system and environment in Kelvin.

Answer 44

• study of stationary charges and the forces that are created by and act upon these charges.

Answer 45

• One, the proton, has a positive charge; the other, the electron, has a negative charge. While opposite charges exert attractive forces (that is, attracting forces), like charges, those that have the same sign, exert repulsive forces (that is, repelling forces). Unlike the force of gravity, which is always an attractive force, the electrostatic force may be repulsive or attractive, depending on the signs of the charges that are interacting. The fundamental unit of charge is e =1.60 × 10− 19 coulombs. A proton and an electron each have this amount of charge; the proton is positively charged (q = +e), while the electron is negatively charged (q = − e). Most matter is electrically neutral: A balance of positive and negative charges ensures a relative degree of stability. When charges are out of balance, the system can become electrically unstable. SI unit of charge is the coulomb, and the fundamental unit of charge. proton and an electron each have this amount of charge, although as we've already stated, the proton is positively charged (q = +e) while the electron is negatively charged (q = − e). Please note that even though the proton and the electron share the same magnitude of charge, they do not share the same mass. The proton has a mass much greater than that of the electron.

Answer 46

Coulomb's Law- Coulomb's law gives us the magnitude of the electrostatic force F between two charges q1 and q2 whose centers are separated by a distance r in meters. direction of the force may be obtained by remembering that unlike charges attract and like charges repel. The force always points along the line connecting the centers of the two charges.

Answer 47

• electric field- Every electric charge sets up a surrounding electric field. Electric fields make their presence known by exerting forces on other charges that move into the space of the field. Whether the force exerted through the electric field is attractive or repulsive depends on whether the stationary test charge qo (i.e., the charge placed in the electric field) and the stationary source charge (i.e., the charge that sets up the electric field) are opposite charges (attractive) or like charges (repulsive). Electric fields are produced by source charges (q). When a test charge (q0) is placed in an electric field (E), it will experience an electrostatic force (F) equal to q0E. where E is the electric field magnitude, F is the force felt by the test charge qo, k is the electrostatic constant, q is the source charge magnitude, and r is the distance between the charges. Electric field is a vector. The first method is to place a test charge qo at some point within the electric field, measure the force that the test charge feels, and define the electric field at that point in space as the ratio of the force magnitude to test charge magnitude. This is F/qo test charge must actually be present in order for a force to be generated (and measured). Sometimes, however, no test charge is actually within the electric field, so we need another way to measure the magnitude of that field because charges produce electric fields whether or not other charges are present to feel them. need to know the magnitude of the source charge and the distance between the source charge and point in space at which we want to measure the electric field. This is kq/r2. Field lines are used to represent the electric field vectors for a charge. They point away from a positive charge and point toward a negative charge. Field lines look like the spokes of a bicycle wheel, and the field lines of a single charge never cross each other. By convention, the direction of the electric field vector is given as the direction that a positive test charge +qo would move in the presence of the source charge. If the source charge is positive, then +qo would experience a repulsive force and would accelerate away from the positive source charge. On the other hand, if the source charge is negative, then +qo would experience an attractive force and would accelerate toward the negative source charge. Therefore, positive charges have electric field vectors that radiate outward (that is, point away) from the charge, whereas negative charges have electric field vectors that radiate inward toward (that is, point to) the charge. representation of the electric field vectors using field lines, also known as lines of force. These are imaginary lines that represent how a positive test charge would move in the presence of the source charge. The field lines are drawn in the direction of the actual electric field vectors. Field lines also indicate the relative strength of the electric field at a given point in the space of the field. The lines are closer together near the source charge and spread out at distances farther from the charge. Where the field lines are closer together, the field is stronger; where the lines are farther apart, the field is weaker. Since every charge exerts its own electric field, a collection of charges will exert a net electric field at a point in space that is equal to the vector sum of all the electric fields. When a test charge is placed in an electric field, a force will be generated on the test charge by the electric field, the magnitude. maintain the sign on the charge so that the direction of the force vector is in the direction of qoE. In other words, if the charge is positive, then the force will be in the same direction as the electric field vector; if the charge is negative, then the force will be in the direction opposite to the field vector.

Answer 48

• Electric Potential Energy- there are different “ flavors” of potential energy; gravitational, chemical, and mechanical are three forms. electric potential energy. In a manner similar to gravitational potential energy, this is a form of potential energy that is related to the relative position of one charge with respect to another charge or to a collection of charges. Just as a ball that is held high above the ground has a relatively large amount of gravitational potential energy, when one charge q is separated from another charge Q by a distance, r, the charges will have an electric potential energy equal to calculate the electric potential energy between two charges separated in space. If the charges are like charges (both positive or both negative), then the potential energy will be positive. If the charges are unlike (one positive and the other negative), then the potential energy will be negative. Remember that work and energy have the same unit (the joule), so we can define electrical potential energy for a charge at a point in space in an electric field as the amount of work necessary to bring the charge from infinity to that point. Electric potential energy is the work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge. and W = Fd, if we define d as the distance r that separates two charges, then. The electric potential energy of a system will increase when two like charges move toward each other or when two opposite charges move apart. Conversely, the electric potential energy of a system will decrease when two like charges move apart or when two opposite charges move toward each other. Opposite charges will have negative potential energy, and this energy will become increasingly negative as the charges are brought closer and closer together. Increasingly negative numbers are actually decreasing, because they are moving farther to the left of 0 on the number line. As like charges, these will exert repulsive forces, and the potential energy of the system will be positive. Since like charges repel each other, the closer they are to each other, the “ unhappier” (that is, less stable) they will be. Remember that unlike gravitational systems, the forces of electrostatics can be either attractive or repulsive. In this case, the like charges will become more stable the farther apart they move. When like charges are moved toward each other, the electric potential energy of the system increases; when like charges move apart, the electric potential energy of the system decreases. When unlike charges move toward each other, the electrical potential energy of the system decreases; when unlike charges are moved apart, the electrical potential energy of the system increases. This is the basic concept; the equation just helps you quantify the energy! This concept also helps you predict the direction of spontaneous movement of a charge: If allowed, a charge will always move in whatever direction results in a decrease in the system's electric potential energy.

Answer 49

• Electric potential- the ratio of the work done to move a test charge from infinity to a point in an electric field surrounding a source charge divided by the magnitude of the test charge. electric potential energy. electric potential is defined as the ratio of the magnitude of a charge's electric potential energy to the magnitude of the charge itself. Electric potential can also be defined as the work necessary to move a charge qo from infinity to a point in an electric field divided by the magnitude of the charge qo. where V is the electric potential measured in volts (V) and 1 volt = 1 joule/coulomb. Even if there is no test charge qo, we can still calculate the electric potential of a point in space in an electric field as long as we know the magnitude of the source charge and the distance from the source charge to the point in space in the field. Electric potential is a scalar quantity whose sign is determined by the sign of the charge qo. For a positive test charge, V is positive, but for a negative test charge, V is negative. For a collection of charges, the total electric potential at a point in space is the scalar sum of the electric potential due to each charge. Since electric potential is inversely proportional to the distance from the source charge, a potential difference will exist between two points that are at different distances from the source charge. If Va and Vb are the electric potentials at points a and b, respectively, then the potential difference, known as voltage, between a and b is Vb– Va. where Wab is the work needed to move a test charge qo through an electric field from point a to point b. The work depends only on the potentials at the two points a and b and is independent of the actual pathway taken between a and b. The “ plus” end of a battery is the high-potential end, and the “ minus” end of a battery is the low-potential end. Positive charge moves (the definition of current) from + to − while negative charge moves from − to +. When a positive charge moves spontaneously though an electric field, it will move from a position of higher electric potential (higher electric potential energy divided by the positive charge) to a position of lower electric potential (lower electric potential energy divided by the positive charge). Positive charge moves spontaneously from high voltage to low voltage. When a negative charge moves spontaneously through an electric field, it will move from a position of lower electric potential (higher electric potential energy divided by the negative charge) to a position of higher electric potential (lower electric potential energy divided by the negative charge). Negative charge moves spontaneously from low voltage to high voltage.

Answer 50

Equipotential Lines- the potential at every point is the same. That is, the potential difference between any two points on an equipotential line is zero. Since the work to move a charge from one equipotential line to another does not depend on the path, we know that we are dealing with conservative forces. In three-dimensional space, these equipotential lines would actually be spheres surrounding the source charge. From the equation for electric potential, you can see that no work is done when moving a test charge qo from one point to another on an equipotential line. Work will be done in moving a test charge qo from one line to another, but the work depends only on the potential difference of the two lines and not on the pathway taken between them. This is entirely analogous to the displacement of an object horizontally above a constant surface. Since the object's height above the surface has not changed (the object has only moved, say, to the left or to the right of its original position), its gravitational potential energy is unchanged. Furthermore, the change in the object's gravitational potential energy will not depend on the pathway taken from one height to another but only on the actual height displacement. One very important equipotential line that you should be aware of is the plane that lies halfway between +q and – q, called the perpendicular bisector of the dipole. Since the angle between this plane and the dipole axis is 90° (and cos 90° = 0), the electric potential at any point along this plane is 0. The electric field produced by the dipole at any point in space is the vector sum of each of the individual electric fields produced by the two charges. Along the perpendicular bisector of the dipole, the magnitude of the electric field can be approximated. The electric field vectors at the points along the perpendicular bisector will point in the direction opposite to p (as defined directionally by physicists).

Answer 51

The electric dipole, which results from two equal and opposite charges being separated a small distance d from each other, can be transient (as in the case of the moment-by-moment changing distribution of electrons in the electron cloud of an atom or molecule) or permanent (as in the case of the molecular dipole of water or the carbonyl functional group). The equal weights on either end of the bar represent the equal and opposite charges separated by a small distance, represented by the length of the bar. charges +q and – q separated by a distance d. Given the dipole, we want to calculate the electric potential P at some point surrounding the dipole. The distance between the point in space and +q is r1; the distance between the point in space and – q is r2; the distance between the point in space and the midpoint of the dipole is r. We know that for a collection of charges, the electric potential P is the scalar sum of the potentials due to each charge at that point. For points in space relatively distant from the dipole (compared to d), the product of r1 and r2 is approximately equal to the square of r, and the r2– r1 is approximately equal to dcosθ. The product of qd is defined as the dipole moment p with SI units of C· m. The dipole moment is a vector. ector along the line connecting the charges (the dipole axis), with the vector pointing from the negative charge toward the positive charge. Chemists usually reverse this convention, having p point from the positive charge toward the negative charge. Sometimes, you'll see chemists draw a crosshatch at the tail end of the dipole vector to indicate that the tail end is at the positive charge. In terms of the dipole moment p, we can rewrite the equation for calculating the potential at a point in space near a dipole. • when the electric dipole is placed in a uniform external electric field (strength of field everywhere the same), each of the equal and opposite charges of the dipole will feel a force exerted on it by the field. Since the charges are equal and opposite, the forces acting on the charges will also be equal and opposite, resulting in a situation of translational equilibrium. where p is the magnitude of the dipole moment (p = qd), E is the magnitude of the uniform external electric field, and theta is the angle the dipole moment makes with the electric field. This torque will cause the dipole to reorient itself by rotating so that its dipole moment, p, aligns with the electric field E.

Answer 52

* Magnetism- the two necessary conditions for the generation of magnetic fields are charge and movement of that charge. Likewise, the two necessary conditions for the generation of magnetic forces are charge and movement of that charge. Both magnetic and electric fields describe the direction a positive charge would travel. If you are ever given a negative charge, continue to solve as if it were a positive test charge. However, flip your answer 180° at the very end. * Any moving charge creates a magnetic field. Magnetic fields may be set up by the movement of individual charges, such as an electron moving through space; by the mass movement of charge in the form of a current though a conductive material, such as a copper wire; or by the “ flow” of charge in permanent magnets. single electron through space or a current through a conductive material, creates a magnetic field. The SI unit of magnetic field is the tesla (T). SI unit of the magnetic field is the tesla (T) for which 1 T = 1 N· s/m· C. The size of the tesla unit is quite large, so small magnetic fields are sometimes measured in gauss, for which 1 T = 104 gauss. For magnetic field vectors that are “ along the plane of the page,” draw field lines as arrows with the tip of the arrow pointing in the direction of the field vector. For magnetic field vectors that are “ coming out of the page,” draw a dot to represent the tip of the field vector (the tip of the arrow). And for magnetic field vectors that are “ going into the page,” draw an X to represent the tail of the field vector (the tail of the arrow). The spacing between magnetic field lines is reflective of the strength of the field at that point in space: The farther out from the moving charge, the weaker the magnetic field, and the further apart the field lines will be spaced. At any point along a field line, the magnetic field vector itself is tangential to the line.

Answer 53

* Magnetic materials include- diamagnetic, paramagnetic, or ferromagnetic. Diamagnetic materials are made of atoms with no unpaired electrons and that have no net magnetic field. Diamagnetic materials will be repelled by either pole of a bar magnet and so can be called weakly antimagnetic. In layperson terms, diamagnetic materials are “ nonmagnetic” and include common materials that you wouldn't ever expect to get stuck to a magnet: wood, plastics, water, glass, and skin, just to name a few. * both paramagnetic and ferromagnetic materials have unpaired electrons, so these atoms do have a net magnetic moment dipole, but the atoms in these materials are usually randomly oriented so that the material itself creates no net magnetic field. Paramagnetic materials will become weakly magnetized in the presence of an external magnetic field, which causes the permanent magnetic dipoles of the individual atoms to align with the external field. Paramagnetic materials will be attracted toward the pole of a bar magnet, so they are sometimes called weakly magnetic. Upon removal of the external magnetic field, the thermal energy of the individual atoms will cause the individual magnetic dipoles to reorient randomly, and the material will cease to be magnetized. Some paramagnetic materials that we commonly work with include aluminum, copper, and gold.

Answer 54

Ferromagnetic materials, like paramagnetic materials, have unpaired electrons and permanent atomic magnetic dipoles that are normally oriented randomly so that the material has no net magnetic dipole. However, unlike paramagnetic materials, ferromagnetic materials will become strongly magnetized when exposed to a magnetic field or under certain temperatures. For all ferromagnetic materials, there is a critical temperature, called the Curie temperature, above which the material is paramagnetic but below which the material is magnetized as a result of a high degree of alignment of the magnetic fields of the individual atoms (which are assembled into large groups of atoms [1012-1018] called magnetic domains). When the ambient temperature (i.e., room temperature) is below the Curie temperature, the material is permanently magnetized. The common metal bar magnet that holds our grocery lists, photos, and holiday cards against the refrigerator door is made of permanently magnetized material, typically including iron. (Interestingly, the thin flexible magnets that have also found a home on your refrigerator are made of ground-up magnetite, a crystalline ferrimagnetic material that is weakly magnetic.) Other ferromagnetic materials are nickel and cobalt. They are sometimes called strongly magnetic because they have a large and positive susceptibility to external magnetic fields, are strongly attracted to magnetic fields, and can retain their magnetic properties for varying amounts of time after the external magnetic field has been removed. Common examples of ferromagnetic items, in addition to the ubiquitous bar magnet, include paper clips, safety pins, and sewing needles. • All bar magnets have a north and south pole. Field lines exit the north pole and enter the south pole. Because magnetic field lines are circular, it is impossible to have a monopole magnet (but it is possible for magnets to have more than two poles). If two bar magnets are allowed to interact, opposite poles will attract each other, while like poles will repel each other.

Answer 55

Current-Carrying Wires- Because any moving charge creates a magnetic field, we would certainly expect that a collection of moving charge, in the form of a current through a conductive material such as a copper wire, would produce a magnetic field in its vicinity. As with the net electric field of multiple charges, the net magnetic field of a current is equal to the vector sum of the magnetic fields of all the individual moving charges that comprise the current. The configuration of the magnetic field lines surrounding a current-carrying wire will depend on the shape of the wire. when two points at different electric potentials are connected with a conductor (such as a copper wire), charge flows between the two points. The flow of charge is called an electric current. The magnitude of the current i is the amount of charge Δ q passing through the conductor per unit time Δ t, and it can be calculated

Answer 56

SI unit of current is the ampere (1 A = 1 coulomb/second). Charge is transmitted by a flow of electrons in a conductor, and because electrons are negatively charged, they move from a point of lower electric potential to a point of higher electric potential (and in doing so reduce their electrical potential energy). By convention, however, the direction of current is the direction in which positive charge would flow from higher potential to lower potential. Thus, the direction of current is opposite to the direction of actual electron flow.

Answer 57

infinitely long and straight current-carrying wire, we can calculate the magnitude of the magnetic field produced by the current i in the wire at a perpendicular distance, r, from the wire. where B is the magnetic field at a distance r from the wire, and μ o is the permeability of free space (4π × 10− 7 tesla · meter/ampere = 1.26 × 10− 6 T · m/A). The equation demonstrates an inverse relationship between the magnitude of the magnetic field and the distance from the current. shape of the magnetic fields surrounding a current is concentric perpendicular circles of magnetic field vectors. To determine the direction of the field vectors, you can use a right-hand rule. This right-hand rule is one of three right-hand rules that you will use in the context of magnetism. In this rule, your right thumb points in the direction of the current. Your other right-hand fingers mimic the circular magnetic field lines, curling around your thumb in the same direction that the magnetic field lines curl around the current. Your fingers show you the direction of the magnetic field lines and the direction of B itself at any point. This right-hand rule works for both a straight-line wire and a circular loop of wire. (You must use your right hand for this and all other right-hand rules.

Answer 58

For a circular loop of current-carrying wire of radius r, the magnitude of the magnetic field at the center of the circular loop. The less obvious difference is that the first expression gives the magnitude of the magnetic field at any perpendicular distance, r, from the current-carrying wire, while the second expression gives the magnitude of the magnetic field only at the center of the circular loop of current-carrying wire with radiusr.

Answer 59

The Magnetic Field Force- magnetic field lines never cross. created by magnets or moving charge, and magnetic fields exert forces only on other moving charges. Charges do not “ sense” their own fields; they only sense the field established by some other charge or collection of charges. That is to say, charges feel forces only from external electric or magnetic fields. presence of a fixed and uniform magnetic field B. This field is produced, of course, by some external source, such as a magnet or arrangement of moving charge (such as a configuration of current-carrying wires), only concerned with the strength and direction of the external field

Answer 60

• Force On A Moving Charge- When a charge moves in a magnetic field, a magnetic force may be exerted on it, the magnitude of which can be calculated. where q is the charge (including the sign of the charge), v is the velocity of the charge, B is the magnitude of the magnetic field, and θ is the smallest angle between the vector qv and the magnetic field vector B. Notice that the magnetic force is a function of the sine of the angle, which means that the charge must have a perpendicular component of velocity in order to experience a magnetic force. If the charge is moving with a velocity that is parallel or antiparallel to the magnetic field vector, it will experience no magnetic force. sin 0° and sin 180° equal zero. This means that any charge moving parallel or antiparallel to the direction of the magnetic fi eld will experience no force from the magnetic fi eld.

Answer 61

• Second right hand rule- To determine the direction of the magnetic force on a moving charge, you must position your right-hand thumb in the direction of the vector qv. The vector qv takes into account not only the direction of the velocity vector but also the sign on the charge. If the charge is positive, then your thumb will point in the direction of v, but if the charge is negative, your thumb will point in the direction opposite to v. Of course, if either q or v is zero, then you have either no charge or stationary charge, your thumb has nowhere to point, and there is no magnetic force to be calculated. Once you've figured out what direction your thumb needs to point, extend your fingers in the direction of the magnetic field. Your fingers should point away from you if the magnetic field vector is going “ into the page” and represented by Xs; they should point toward you if the magnetic field vector is coming “ out of the page” and represented by dots. You may need to rotate your wrist this way or that to get the correct configuration of thumb and fingers. Once your thumb and fingers are in their proper positions, your palm, which has no choice but to face a particular direction, will indicate the direction of the magnetic force vector F on the moving point charge q. has your thumb point in the direction of velocity, your index finger in the magnetic field, and then the palm of your hand in the direction of force. As long as your own method works for you, use it! Charged particles moving perpendicular to a constant, uniform magnetic field travel in uniform circular motion, with constant speed in the plane perpendicular to the magnetic field. For a charge moving in uniform circular motion due to an external magnetic field, a change in the strength of the external magnetic field will result in a change of the radius of the circular pathway of the charged particle but not in the magnitude of its velocity.

Answer 62

third right hand-rule: applies to current-carrying wire placed in an external magnetic field. It's actually the same right-hand rule you will use to determine the force exerted by a magnetic field on a point charge; the only difference is that the right-hand thumb always points in the direction of the current, never opposite to that direction. Because current, by convention, is the direction of movement of positive charge, it makes sense that the thumb will always point in the same direction as current. The other fingers of your right hand are positioned so that they point in the same direction as the magnetic field vector B. The palm of your right hand will automatically be facing in the direction of the magnetic force vector. The force acting on the current-carrying wire will always be perpendicular to the plane defined by B and the direction of the current. Your palm will indicate which of the two perpendicular directions the force is acting.

Answer 63

When a charged particle moves perpendicular to a constant, uniform magnetic field, the resulting motion is circular motion with constant speed in the plane perpendicular to the magnetic field. Charged particles assume circular motion with constant speed when they move into a constant, uniform magnetic field perpendicular to the field vector. A centripetal force is always associated with circular motion. In other words, an external force, which we call the centripetal force, must always be applied to an object demonstrating circular motion since that object must constantly change direction. The centripetal force may be the tension in a string, the restoring force of a spring, gravitational force between a planet and a satellite, or the force of a magnetic field (just to name a few). In this case, the centripetal force is the magnetic force (F = qvB). solve for the orbit radius (r), the magnetic field (B), and the velocity (v). assuming constant mass and charge of the charged particle, both the velocity and radius of the uniform circular motion seem to be a function of the magnetic field. This is to say, it seems to be the case that changing the magnitude of the magnetic field will either result in an increase in the velocity or a decrease in the radius (or some combination of both). We know that work is done when a force is applied through some distance and there is a dependency of work on the cosine of the angle between the force vector and the displacement vector. In circular motion, the centripetal force is always perpendicular to the instantaneous velocity vector (angle equals 90° ; cos 90° = 0); therefore, no work is done by the centripetal force on the moving charged particle. According to the work-energy theorem, if no (net) work is done on an object, its kinetic energy will not change, and there will be no change in the magnitude of the object's velocity. This is exactly what happens in uniform circular motion: The speed of the object is constant as it travels through its circular pathway. For this charged particle, which demonstrates uniform circular motion, it must be the case that the magnitude of its velocity is constant. Thus, a change in the strength of the magnetic field will result in a change in the radius of the circular pathway of the charged particle but not in the magnitude of the velocity.

Answer 64

• Force On Current-Carrying Wire- current-carrying wire placed in a magnetic field may also experience a magnetic force. For a straight wire of length L carrying a current i in a direction that makes an angle θ with a uniform magnetic field B, the magnitude of the magnetic force on the current-carrying wire can be calculated it is a quantity of charge per unit time. And the length of the wire running through the field is measured in meters, so when we put it all together

Answer 65

Circuits- Current- Some materials allow free flow of electric charge within them; these materials are called electrical conductors. Metal atoms can easily lose one or more of their outer electrons, which are then free to move around in the metal, and this makes most metals good electrical conductors. In fact, in bulk metal, metallic bonding results from an equal division of the charge density of the “ free” (conduction) electrons across all of the (neutral) atoms within the metallic mass. This is a correction of the earlier model of the “ metallic bond,” which posited a “ sea of free electrons” flowing over and past a rigid lattice of metal cations. Other materials hold on to electrons more tightly and severely hinder or retard the flow of electrons. These materials are called insulators. Most nonmetals are good insulators, and you are probably quite familiar with the insulating plastic or rubber tubing that surrounds most electrical wires. Glass, wood, air, and even distilled water are good insulators. (Although water has a reputation as a conductor with the ability to “ short-circuit” electrical appliances, it is actually a good insulator as long as the water has no ions in it. Distilled water has a conductivity of almost zero.)

Answer 66

• electric current: the flow of charge between two points at different electric potentials connected by a conductor (such as a copper wire). The magnitude of the current i is the amount of charge Δ q passing through the conductor per unit time Δ t, and it can be calculated. SI unit of current is the ampere (1 A = 1 coulomb/second). Charge is transmitted by a flow of electrons in a conductor, and because electrons are negatively charged, they move from a point of lower electric potential to a point of higher electric potential (and in doing so reduce their electrical potential energy). By convention, however, the direction of current is the direction in which positive charge would flow from higher potential to lower potential. Thus, the direction of current is opposite to the direction of actual electron flow. The two patterns of current flow are direct current (DC), in which the charge flows in one direction only, and alternating current (AC), in which the flow changes direction periodically. Direct current is produced by household batteries, while the current supplied over long distances to homes and other buildings is alternating current. A potential difference (voltage) can be produced by an electric generator, a voltaic (galvanic) cell, a group of cells wired into a battery, or even a potato! When no charge is moving between the two terminals of a cell that are at different potential values, the voltage is called the electromotive force (emf or ε ). Do not be misled by this term; emf is not a force; it is a potential difference (voltage) and as such has units of joules per coulomb (1 V = 1 J/C). You may find it helpful to think of emf as a “ pressure to move” that results in current, in much the same way that a pressure difference bet-ween two points in a fluid-filled tube causes the fluid to flow.

Answer 67

• Circuit Laws- Circuits and currents are governed by the laws of conservation. Charge and energy must be fully accounted for at all times: They can be neither created nor destroyed. An electric circuit is a conducting path that usually has one or more voltage sources (such as a battery) connected to one or more passive circuit elements (such as resistors).

Answer 68

Kirchhoff's Junction Rule- At any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point. This is an expression of conservation of electrical charge. Parallel circuit. There are a certain amount of water molecules in a river, and at any junction, that number has to go in one of the diverging directions; nothing magically appears or disappears. The same holds true for the amount of current at any junction.

Answer 69

Voltaic cells are also called galvanic cells. standard batteries in flashlights and remote controls

Answer 70

• Kirchhoff's Loop Rule- Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops. This is a consequence of the conservation of energy. All the electrical energy supplied by a source gets fully used up by the other elements of the circuit. No excess energy appears, and no energy disappears that can't be accounted for. Of course, energy can be changed from one form to another, so the kinetic energy of the electrons can be converted to heat or light (or sound, etc.) by the particular apparatus that is connected into the circuit. Remember that though Kirchhoff's loop rule is a consequence of the law of conservation of energy, this law is in terms of voltage (joules per coulomb), not just energy (joules). If all of the voltage wasn't “ used up” in each loop of the circuit, then the voltage would build after each trip around the circuit, something that is quite impossible.

Answer 71

Resistance is the opposition within any material to the movement and flow of charge. Electrical resistance can be thought of like friction, air resistance, or fluid resistance: Motion is being opposed. All appliances function as resistors.

Answer 72

Characteristics Of Resistors That Determine Resistance- Materials that offer low resistance are called conductors, and those materials that offer very high resistance are called insulators. Conductive materials that offer amounts of resistance between these two extremes are called resistors. Resistivity of the Conductive Material- some materials better conductors than other, copper better than plastic. The number that characterizes the intrinsic resistance to current flow in a material is called the resistivity (ρ ), for which the SI unit is the ohm-meter (Ω · m). Resistivity is the proportionality constant that relates a conductor's resistance (R) to the ratio of its cross-sectional area (A) to the length of the resistor (L). The equation for resistance

Answer 73

length- resistance is directly proportional to the length of the resistor, long resistor electrons travel greater distance through the material , longer wire greater resistance. Cross sectional area- inversely proportional relationship between resistance and cross-sectional area of the resistor. Basis for decrease in resistance as cross-secitonal area increases is the increased number or pathways, conduction paths, that are available to the moving electron. COmpareing the resistance of two wires, identical in every way except for cross-secitonal area, the thicker the wire, the lesser amount of resistance to the current. Inversely linear relationship, thicker wire with twice the cross-sectional area, half the resistance of the thinner wire.

Answer 74

• Temperature- most conductors have greater resistance at higher temperatures. This is due to increased thermal oscillation of the atoms in the conductive material, which produces a greater resistance to electron flow. Because temperature is an intrinsic quality of all matter, you can think of the resistivity as a function of temperature. A few materials do not follow this general rule, including glass, pure silicon, and most semiconductors. For cars on a highway, a road made of gravel (representing high ρ ) will impede the flow of traffic more than a smooth road (representing low ρ ) a multi-lane highway (representing large A) will allow for an easier flow of traffic than a single-lane highway (representing small A); and any impediments to traffic flow will accumulate more on a longer road (one with large L) than on a shorter road (one with small L).

Answer 75

Ohm’s law- electrical resistance is an energy loss that results in a drop in electric potential. The voltage drop between any two points in a circuit can be calculated according to Ohm's law. where V is the voltage drop, i is the current, and R is the magnitude of the resistance, measured in the SI unit of resistance, the ohm (Ω ). Ohm's law is the basic law of electricity. It states that for a given magnitude of resistance, the voltage drop across the resistor will be proportional to the magnitude of the current. Likewise, for a given resistance, the magnitude of the current will be proportional to the magnitude of the emf (voltage) impressed upon the circuit. The equation applies to a single resistor within a circuit, to any part of a circuit, or to an entire circuit (provided you correctly calculate the resultant resistance from resistors connected in series and/or parallel). As current moves through a set of resistors in a circuit, the voltage changes, dropping some amount as the current encounters each resister in succession; the current (or sum of currents for a divided circuit) is constant. No charge is gained or lost through resistors. If resistors are connected single-file (that is, in series), all current must pass through each resistor.

Answer 76

• Conductive materials, such as copper wires, act as weak resistors themselves, offering some magnitude of resistance to current and causing a drop in electric potential (voltage). Even the very source(s) of emf, such as batteries, have some measurable but small amount of internal resistance rint. As a result of this small internal resistance, the voltage supplied to a circuit is reduced by an amount equal to irint. with the actual voltage supplied by a cell to a circuit equal to. if the cell is not actually driving any current (e.g., when a switch is in the open position), then the internal resistance is zero, and the emf of the cell is the voltage. For cases when the current is not zero and the internal resistance is not negligible, then voltage will be less than emf (V < ε )

Answer 77

cell is discharging, it supplies current, and the current flows from the positive, higher voltage end of the cell to the negative, lower voltage end. (Remember that current, by convention, is the movement of positive charge. Negatively-charged electrons are the particles that are actually in motion, so they flow in the direction opposite to current.) Certain types of cells (called secondary batteries) can be recharged. You'll find one in your cell phone. When these batteries are being recharged, an external voltage is applied in such a way to drive current toward the positive end of the secondary battery.

Answer 78

* Power of resistors- power is the rate at which energy is transferred or transformed. Power is measured as the ratio of energy to time. electric circuits, energy is supplied by the cell that houses a spontaneous redox reaction, which when “ allowed” to proceed (by the closing of a switch, for example), generates a flow of electrons. These electrons, which have electric potential energy, convert that energy into kinetic energy (the energy of their motion), “ motivated” as they are by the emf of the cell. Think of emf as a pressure to move, exerted by the cell on the electrons. Current delivers energy to the various resistors, which convert this energy to heat or some other form, depending on the particular configuration of the resistor. rate at which energy is dissipated by a resistor is the power of the resistor and is calculated. i is the current through the resistor and V is the voltage drop across the resistor. Using Ohm's law (V = iR), the power expression * Because power equals voltage times current, they can manipulate these two values while keeping power constant. One option is to increase current, which results in a decrease in voltage. The other option would be to increase voltage, thus decreasing the current. If you think of actual power lines, remember that they are known as high-voltage lines. The reason power companies use high-voltage lines is to keep the current smaller. Because the amount of power lost in the line is P = i2R, with current is squared in this relationship, having a large current exponentially increases the amount of power lost.

Answer 79

Resistors in series- all current must pass sequentially through each resistor connected in a linear arrangement. Current has no “choice” but to travel through each resistor in order to return to the cell. As electrons flow through each resistor, energy is dissipated with a voltage drop, with each voltage drop additive. The set of resistors wired in series can be treated as a single resistor whose resistance is equal to the sum of the individual resistances (R1, R2,… , Rn). This single, end-result resistor (Rs) is called a resultant resistor.

Answer 80

Resistors in parallel- current will divide to pass through resistors connected in a parallel arrangement. Wired with a common high-potential terminal and a common low-potential terminal. configuration allows charge to follow different, parallel paths between the high-potential terminal and the low-potential terminal. In this arrangement, electrons have a “ choice” regarding which path they will take: Some will choose one pathway, while others will choose a different pathway. No matter which path is taken, however, the voltage drop experienced by each division of current is the same, because all pathways originate from a common point and end at a common point within the circuit. the parallel pathways may differ in the amount of resistance that each offers to the flow of the electrons if the resistor(s) in each branch of the circuit have different values or add up to different values. In this case, electrons embody an old adage you may know: They prefer the path of least resistance. We will see, from the following equations, that there is an inverse relationship between the magnitude of the divided current that travels through a particular pathway and the resistance offered by that pathway. Inverse relationship between the cross-sectional area of a resistor and the resistance magnitude of the resistor. the configuration of resistors in parallel allows for a greater total number of conduction paths, and the effect of connecting resistors in parallel is a reduction in the resultant resistance. In effect, we could replace all resistors in parallel with a single resistor whose resistance is less than the resistance of the smallest resistor (in the circuit), and the circuit as a whole would move the same amount of current. Because the voltage drop across any one circuit branch must be same as the voltage drops across each of the other parallel branches, applying Ohm's law to each branch, we can see that the magnitude of the current in each branch will be inversely proportional to the resistance offered by each branch. So if a circuit divides into two branches and one branch has twice the resistance of the other, the one with twice the resistance will have half the magnitude of current in the lower-resistance division. The sum of the currents going into each division, according to Kirchhoff's junction rule, must equal the total current going into the point at which the current divides. total resistance is halved by wiring two identical resistors in parallel. More generally, when n identical resistors are wired in parallel, the total resistance Note that the voltage across each of the parallel resistors is equal and that, for equal resistances, the current flowing through each of the resistors is also equal (a current of runs through each)

Answer 81

Capacitance and Capacitors- While Defribilator Charges The Electrons Build Up On One Plate Of The Capacitor, When Fully Charged The Charge Released In One Surge Of Power. Even batteries function as a form of capacitor, but with the ability to hold charge for longer periods and release it more slowly.

Answer 82

• Parallal Plate Capactior- two electrically neutral metal plates are connected to a voltage source, positive charge builds up on the plate connected to the positive (higher voltage) terminal, and negative charge builds up on the plate connected to the negative (lower voltage) terminal. The two-plate system stores charge at a particular voltage and is called a capacitor. Charge will collect on the plates of a capacitor anytime there is a potential difference between the plates. The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge stored on one plate (taking the absolute value of the charge) to the total potential difference, voltage, across the capacitor (that is, between the two plates of a parallel plate capacitor). Therefore, if a voltage difference V is applied across the plates of a capacitor and a charge Q collects on it (with +Q on the positive plate and – Q on the negative plate), then the capacitance. SI unit for capacitance is the farad (1 F = 1 coulomb/volt). Because one coulomb is such a large quantity of charge, one farad is a very large capacitance. Capacitances are usually given in submultiples of the farad, such as microfarads (1 μ F = 1 × 10− 6 F) or picofarads (1 pF = 1× 10− 12 F). Be careful not to confuse the farad with the Faraday constant, which is the amount of charge equal to the charge on a mole of electrons (96,485 coulombs/mole e− ). capacitance of a parallel plate capacitor is dependent upon the geometry of the two conduction surfaces. ε o is the permittivity of free space (8.85 × 10− 12 F/m), A is the area of overlap of the two plates, and d is the separation of the two plates. The separation of charges sets up an electric field between the plates of a parallel plate capacitor. The electric field between the plates of a parallel plate capacitor is a uniform field (parallel field vectors) whose magnitude at any point can be calculate. The direction of the electric field at any point between the plates is away from the positive plate and toward the negative plate. If we imagine placing a positively charged particle between the oppositely charged plates, we would expect the particle to accelerate in the direction from the positively charged plate toward the negatively charged plate. Regardless of the particular geometry of a capacitor (parallel plate or otherwise), the function of a capacitor is to store an amount of energy in the form of charge separation at a particular voltage With The Potential Energy Equal To U.

Answer 83

A dielectric material can never decrease the capacitance; thus K can never be less than 1. Insulation- air, glass, plastic, ceramic, or certain metal oxides, is placed between the plates of a charged capacitor, the voltage across the capacitor decreases. This is the result of the dielectric material “ shielding” the opposite charges from each other. Because they feel each other less, the voltage (energy per coulomb) across the capacitor decreases. By lowering the voltage across a charged capacitor, the dielectric has in effect “ made room” for more charge, and the capacitance of the capacitor increases by a factor equal to a dimensionless number called the dielectric constant K, which is a measure of the insulating capability of a particular dielectric material. he dielectric constant for air is about 1, for glass is 4.7, and for rubber is 7. The increase in capacitance due to a dielectric material, where C′ is the new capacitance with the dielectric and C is the original capacitance. All the stored charge (stored energy) on a capacitor won't do any good unless it is allowed to discharge. The charge will be “ released” from its holding plates either by discharging across the plates or through some conductive material with which the plates are in contact. For example, capacitors can discharge into wires, causing a current to pass through the wires in much the same way that batteries cause current to move through a circuit. The paddles of the defibrillator machine, once charged, are placed on either side of a heart that has gone into a life-threatening abnormal rhythm (such as ventricular tachycardia). The sum of the voltage drops across any combination of resistors or capacitors will always equal the voltage of the entire system (the voltage of the battery).

Answer 84

• Capacitors In Series- When capacitors are connected in series, the total capacitance decreases in similar fashion to the decrease in resistance for resistors in parallel. This rule for voltage is similar to that for resistors in series.

Answer 85

Capacitors In Parallel- Capacitors wired in parallel produce a resultant capacitance that is equal to the sum of the individual capacitances. all the capacitors in parallel can be replaced by a single resultant capacitor whose capacitance is equal to the sum of all the capacitances. the wire from one capacitor to the next is a conductor and equipotential surface, the potential of all the plates on one side are the same. Just as we saw with resistors in parallel, the voltage across each parallel capacitor is the same and is equal to the voltage across the entire combination.

Answer 86

Alternating current- is not fundamentally different from direct current. As currents, both are formed by moving electrons from low potential to high potential; therefore, both are motivated by emf. Both conform to Ohm's law and Kirchhoff's laws. The difference is that direct current flows in one direction only, while alternating current, as its name suggests, reverses direction periodically. For the devices that rely on electrical current for energy, the direction of the current makes no difference: Energy will be delivered as long as charge is moving. (P = i2R; by squaring the current, you “ remove” direction from consideration. Power is energy over time, and energy is scalar.) The reason why electricity delivered to buildings is AC is because it is easier to produce than DC and easier to transport over long distances. Because alternating current and voltage can be “ stepped down” or “ stepped up” by transformers it can be transported through wires over long distances at high voltage and low current, which minimizes resistance and energy dissipation, and then delivered into a building at a lower voltage and higher current. most common form of alternating current oscillates in a sinusoidal way, Notice that for half of the cycle, the current flows in one direction, and for the other half of the cycle, the current flows in the opposite direction. where i is the instantaneous current at the time t, Imax is the maximum current, f is the frequency, and ω is the angular frequency ( ω = 2π f).

Answer 87

Rms Current- Energy is dissipated by a resistor carrying alternating current i according to the equation P = i2R. If we want to find the average power in one cycle of alternating current, we must find the average of i2 over one period. This is equal to Irms2 , where Irms is the root-mean-square (rms) current

Answer 88

Rms Voltage- direction of current reverses at some frequency in alternating current, this must mean that the voltage is also reversing direction (remember, current always flows from higher potential to lower potential). You're probably not surprised to learn that the graph of AC voltage is sinusoidal and oscillates at the same frequency as the current for a given alternating current. Mathematically, this again presents the problem of taking the average of AC voltage (which would be zero). The solution is to calculate the root-mean-square voltage(Vrms), using the same form of equation that we used to calculate the root-mean-square current: calculated the values for Irms and Vrms, you can use these values in applications of Ohm's law to AC circuits just as you would use values of current and voltage in applications of Ohm's law to DC circuits.

Answer 89

Simple Harmonic Motion- oscillating systems by their repetitive motion about some point or position. There are many naturally occurring and manufactured oscillating systems, such as water waves, the pendulum of a grandfather clock, swing sets, springs, sound, and light (electromagnetic waves). The repetitive motion of an oscillating system is also called periodic motion, and a very important type of periodic motion is simple harmonic motion (SHM). In SHM, a particle or mass oscillates about an equilibrium position and is subject to a linear restoring force. The name of this force is perfectly descriptive of its function and character. First, it always acts to restore the particle or object to its equilibrium position any time it is displaced. That is, the direction of the restoring force is always toward the equilibrium position. Second, the magnitude of the force is directly proportional to the magnitude of the displacement of the particle or object from its equilibrium position. From Newton's second law, we can predict that the acceleration of the particle or object is always directed toward the equilibrium position and is also proportional to its displacement from the equilibrium position. Two systems that demonstrate simple harmonic motion are springs and pendulums.

Answer 90

Spring- with a mass attached to one end is compressed or stretched and then released, it will oscillate in simple harmonic motion about its equilibrium position (the spring's natural length). The material of the spring itself is responsible for generating the restoring force. F is the restoring force, k is a constant called the spring constant, and x is the displacement of the spring from its equilibrium (natural) length. The spring constant k is a measure of the spring's stiffness. The higher the k value, the stiffer the spring and the greater the magnitude of the restoring force for any given displacement. The negative sign in front of the right side of the equation tells us that the restoring force is always in the direction opposite to the direction of displacement. That is, if the spring is stretched, the restoring force with be directed “ inward” toward the equilibrium position, but if the spring is compressed, the restoring force will be directed “ outward” toward the equilibrium position. The equation F = − kx is called Hooke's law. Angular frequency is measured in radians; one full rotation equals 2π r radians or 360 degrees. acceleration of the spring toward its equilibrium position is, as we've stated, proportional to the restoring force according to Newton's second law and, therefore, also proportional to the displacement of the spring from its equilibrium length. A spring with spring constant k and mass m, having been displaced x meters, will have an acceleration a calculated as a = − ω 2x, where ω is the angular frequency. angular frequency equation tells us the stiffer the spring (the larger the value of k) or the smaller the mass attached, the faster the spring will oscillate. a measure of the rate at which cycles of oscillation are being completed. Frequencyf is measured in hertz (Hz), which is cycles per second. Angular frequency ω is measured in radians per second. As the term suggests, angular frequency is a measure of the rate at which the oscillating object would move through an arc of a particular size if the object were traveling around a perfect circle (for which one revolution around the circle equals one cycle). The size of a radian is equal to 180/π degrees, so a circle (360° ) is equal to 2π radians. The value of 2π is therefore the conversion between frequency and angular frequency: They measure the same thing (the rate at which an oscillating particle or mass completes a cycle) but in different units. The angular frequency equation tells us the stiffer the spring (the larger the value of k) or the smaller the mass attached, the faster the spring will oscillate. The frequency describes the number of oscillations per second. The period (T) describes how many seconds it takes for one oscillation to occur. These two are inverse to each other.

Answer 91

dependency of frequency/angular frequency on the spring constant and mass attached to the spring but not on the displacement x of the spring. Two springs with identical k and m values but stretched to different lengths will have the same frequency of oscillation. Of course, the spring that is stretched out to the greater length (larger displacement x) will generate a larger restoring force Fx, will experience greater acceleration, and will reach greater linear velocity magnitudes, but all of this only means that it will complete a larger cycle in the same amount of time it takes the spring stretched out to the lesser length to complete its smaller cycle. Frequencies measure the rate at which cycles are completed, irrespective of cycle size. Calculating the position of a spring as it moves through its cycle as a function of time. X is the amplitude (maximum displacement from equilibrium), ω is the angular frequency (ω = 2π f = π /T, where T is the period, ,1/f the time to complete one cycle), and t is time. In calculating the displacement as a function of time, we have assumed that the spring has maximum displacement at t = 0.

Answer 92

small oscillations and short periods of time, we can treat springs as conservative systems. Although the energy of the spring will eventually be dissipated in the form of thermal energy as the molecules of the spring bump up against each other, for short periods of time, we can assume that all of the potential energy of the spring will be converted to kinetic energy as it oscillates. When a spring is stretched or compressed from its equilibrium length, the spring has potential energy, where x is the displacement from equilibrium. Upon being released, the spring will accelerate in proportion to the restoring force, and the potential energy will be converted to kinetic energy. spring generates a restoring force for all positions of displacement, it will accelerate continuously as it returns to its equilibrium length, at which point all the potential energy of the spring will have been converted into kinetic energy. The spring will reach its maximum velocity upon its return to its equilibrium length. As the spring moves through the equilibrium length to become displaced in the other direction, the restoring force opposes the spring's velocity and slows it down. The spring has a velocity of zero at its maximum displacement (amplitude), and all of the kinetic energy has been converted back into potential energy.

Answer 93

* simple pendulum- displaced by drawing the distal end of the pendulum, where the mass is located, through some angle from the vertical equilibrium position. The displacement of a pendulum is not linear, but angular, and is measured in degrees. When a pendulum, such as that of a grandfather clock or a child on a swing, is swung back from the vertical position by some angle, the restoring force is generated by gravity and is a component of the weight of the mass attached to the pendulum, m is the mass attached to the end of the pendulum, g is the acceleration of gravity (9.8 m/s2), and θ is the angle between the pendulum arm and the vertical. his is a restoring force, always directed in the direction opposite to the displacement and in the direction of the equilibrium position. or a pendulum with a length L, the angular frequency. only the acceleration of gravity and the length of the pendulum. Neither the mass m attached to the pendulum nor the angular displacement θ determines the angular frequency ω (don't confuse angular frequency and angular displacement!). Therefore, if two pendulums have the same length, they will demonstrate the same angular frequency irrespective of the masses attached to them or their respective initial displacements. As with two identical springs stretched to different lengths with the same angular frequency but different linear velocities, the two pendulums will be traveling at different velocities. This is because the pendulum pulled back at the greater angle will have to travel a longer path to complete its cycle in the same amount of time that the pendulum pulled back at the lesser angle travels its shorter path. pendulum can also be approximated as a conservative system if we discount air resistance and friction between the pendulum and the mechanism supporting the pendulum from above. When a pendulum is pulled back to its maximum displacement, θ , the pendulum has maximum potential energy equal to. h is the vertical height difference between the pendulum's mass in the equilibrium position and the mass at the given angular displacement. When the pendulum is released and allowed to swing, it experiences an acceleration that is a function of the restoring force, and the potential energy is converted to kinetic energy. Like the spring, a pendulum has maximum kinetic energy (and minimum potential energy) at the equilibrium position and maximum potential energy (and minimum kinetic energy) at maximum displacement. The kinetic energy of the mass same as before * Notice how there are only two factors that affect frequency in both situations. In springs, it is mass and the spring constant. In pendulums, it is gravity and the length of the pendulum.

Answer 94

sinusoidal waves: transverse and longitudinal waves- sinusoidal waves with the individual particles oscillating back and forth with simple harmonic moion. Most waves we see are transverse waves (even “ the wave” at sporting events is a transverse wave).

Answer 95

• reason why beach balls bob is that water waves are transverse, a waveform in which the direction of particle oscillation is perpendicular to the movement (propagation) of the wave. Electromagnetic radiation, such as visible light, microwaves, and x-rays, is a transverse waveform. By holding a piece of string that has been secured at the other end, you can make a transverse wave by moving your hand up and down. The string particles oscillate up and down in a manner that is perpendicular to the direction the wave travels through the string from one end (the end you're holding) to the other (the end attached, say, to a doorknob). In any waveform, energy is delivered in the direction of wave travel, so we can say that for a transverse wave, the particles are oscillating perpendicular to the direction of energy transfer. This is why, discounting air currents or undertows, beach balls and swimmers tend to get pushed into shore by waves: Water waves are delivering their energy in the direction of the beach.

Answer 96

The only longitudinal waves we are likely to encounter are sound waves. longitudinal wave is a sinusoidal wave in which the particles of the wave oscillate along the direction of travel of the wave motion; that is, the wave particles are oscillating along the direction of energy transfer. Sound waves are the classic example of longitudinal waves, but since we can't “ see” sound. the longitudinal wave created by the person moving the piston back and forth consists of oscillating air molecules that go through cycles of compression and rarefaction (decompression) along the direction of motion of the wave. If you are having trouble picturing this, think of the way that the bellows of an accordion are compressed and pulled apart by the accordionist.

Answer 97

• Describing Waves- displacement y of a particle in a wave may be plotted at each point x along the direction of the wave's motion. Y is the amplitude (maximum displacement), k is the wavenumber (don't confuse this k, wavenumber, with the spring constant k in Hooke's law!), ω is the angular frequency, and t is the time. You'll notice how similar this equation is to the equation for calculating the displacement of a spring at time t. distance between one maximum (crest) of the wave to the next is the wavelength λ . The frequency f is the number of wavelengths passing a fixed point per second (measured in hertz [Hz] or cycles per second [cps]). wavenumber k and angular frequency ω

Answer 98

• speed of the wave v as it relates to the frequency and wavelength of the wave. ong as velocity remains constant, frequency and wavelength are inverse to each other. A large wavelength will have a small frequency, and a small wavelength will have a large frequency. period T is the time for the wave to move one wavelength

Answer 99

Phase- phase difference, which describes how “ in step” or “ out of step” two waves are with each other. If we consider two waves that have the same frequency, wavelength, and amplitude and that pass through the same space at the same time, we can say that they are in phase if their respective maxima (crests) and minima (troughs) coincide (i.e., they occur at the same point in space). When waves are perfectly in phase, we say that the phase difference is zero. However, if the two waves occupy the same space in such a way that the crests of one wave coincide with the troughs of the other, then we would say that they are out of phase, and the phase difference would be one-half of a wave, or 180° . Of course, waves can be out of phase with each other by any definite fraction of a cycle. f the two waves have different but similar frequencies, they will periodically go in and out of phase, resulting in “ beats,” which will later be discussed

Answer 100

Principle Of Superposition- principle of superposition states simply that when waves interact with each other, the result is a sum of the waves. When the waves are in phase, the amplitudes add together (constructive interference), and the resultant wave has greater amplitude. When waves are out of phase, the resultant wave's amplitude is the difference between the amplitudes of the interacting waves (destructive interference). . If the two waves were exactly 180 degrees out of phase, then the resul-tant wave would have zero amplitude; thus, there would be no wave.

Answer 101

Principle Of Superposition- principle of superposition states simply that when waves interact with each other, the result is a sum of the waves. When the waves are in phase, the amplitudes add together (constructive interference), and the resultant wave has greater amplitude. When waves are out of phase, the resultant wave's amplitude is the difference between the amplitudes of the interacting waves (destructive interference). . If the two waves were exactly 180 degrees out of phase, then the resul-tant wave would have zero amplitude; thus, there would be no wave.

Answer 102

Traveling And Standing Waves- string fixed at one end is moved up and down, a wave will form and travel, or propagate, toward the fixed end. Because this wave can be seen to be moving, it's called a traveling wave. When the wave reaches the fixed boundary, it is reflected and inverted. free end of the string is continuously moved up and down, there will then be two waves: the original wave moving down the string toward the fixed end and the reflected wave moving away from the fixed end. These waves will then interfere with each other. Certain wave frequencies can result in a waveform that appears to be stationary, with the only apparent movement of the string being fluctuation of amplitude at fixed points along the length of the string. These waves are known as standing waves. Points in the wave that remain at rest (i.e., points where amplitude is constantly zero) are known as nodes, and points that are midway between the nodes are known as antinodes. Antinodes are points that fluctuate with maximum amplitude. In addition to strings fixed at both ends, pipes that are open at both ends can support standing waves, and the mathematics relating the standing wave wavelength and the length of the string or the open pipe are similar. Pipes that are open at one end and closed at the other can also support standing waves, but because the open end supports an antinode rather than a node, the mathematics are different. Standing waves in strings and pipes are discussed in more detail next, within the context of sound, because standing wave formation is integral to the formation of sound in musical instruments.

Answer 103

• Resonance- he frequency or frequencies at which an object will vibrate when disturbed is the natural frequency. If the frequency is within the frequency detection range of the human ear, the sound will be audible. The quality of the sound, called timbre, is determined by the natural frequency or frequencies of the object. Some objects vibrate at a single frequency, producing a pure tone, while others vibrate at multiple natural frequencies that are related to each other by whole number ratios, producing a rich tone. natural frequency of most objects can be changed by changing some aspect of the object itself. For example, a set of eight identical goblets can be filled with different levels of water so that each vibrates at a different natural frequency, producing the eight notes of the musical octave. Strings have an infinite number of natural frequencies that depend on the length, linear density, and tension of the string. A pendulum of length L, however, has a single natural frequency, and there is no way to change that except to change the value of g, periodically varying force is applied to a system, the system will then be driven at a frequency equal to the frequency of the force. This is known as forced oscillation. The amplitude of this motion will generally be small. However, if the frequency of the applied force is close to that of the natural frequency of the system, then the amplitude of oscillation becomes much larger. This can easily be demonstrated by a child on a swing being pushed by a parent. If the parent pushes the child at a frequency nearly equal to the frequency at which the child swings back toward the parent, the arc of the swinging child will become larger and larger: The amplitude is increasing because the force frequency is nearly identical to the swing's natural frequency (which, remember, is a function of only the length of the swing and the acceleration of gravity). If the frequency of the periodic force is equal to a natural frequency of the system, then the system is said to be resonating, and the amplitude of the oscillation is at a maximum. If the oscillating system were frictionless the periodically varying force would continually add energy to the system, and the amplitude would increase indefinitely. However, because no system is completely frictionless, there is always some dampening, which results in a finite amplitude of oscillation. Furthermore, many objects cannot withstand the large amplitude of oscillation and break or crumble. A dramatic demonstration of resonance is the shattering of a wineglass by directing toward the glass a sound whose frequency is equal to the natural frequency of the glass. The glass will resonate (oscillate with maximum amplitude) and eventually shatter.

Answer 104

Sound is transmitted by the oscillation of particles along the direction of motion of the sound wave. Therefore, sound waves are longitudinal. Furthermore, sound waves propagate as mechanical disturbances through a deformable medium and can travel through solids, liquids, and gases, but they cannot travel through a vacuum. The speed of sound is inversely proportional to the square root of density but directly proportional to the square root of the bulk modulus. As a result, sound travels fastest through a solid and slowest through a gas. The speed of sound in air at 0° C is 331 m/s. sound waves whose wavelengths and frequencies are within the human range of audible sound. These audible waves have frequencies that range from 20 Hz to 20,000 Hz. Sound waves whose frequencies are below 20 Hz are called infrasonic waves, and those whose frequencies are above 20,000 hz are called ultrasonic waves.

Answer 105

• production of sound- Sound is produced by the mechanical disturbance of the particles of a material, creating oscillations of particle density that are along the direction of movement of the sound wave. Although the particles themselves do not travel along with the wave, they do vibrate or oscillate about an equilibrium position, which causes small regions of compression to alternate with small regions of rarefaction (decompression). These alternating regions of increased and decreased particle density shift linearly through the material, and this is the way that sound waves propagate. Because sound involves vibration of material particles, the source of any sound is ultimately a mechanical vibration of some frequency. They can be produced by the vibration of solid objects or the vibration of fluids, including gases. Solid objects that can vibrate to produce sound include strings (on a piano, violin, guitar, etc.), metal, wood bars (e.g., on a xylophone), or bells. hey are set in motion and vibrate at their natural frequencies. Because the strings are very thin, they are very ineffective in transmitting their mechanical vibrations to the particles of the air, which is necessary for us to hear the sounds produced by the vibrating guitar strings. The strings are locked down to a solid object called the bridge, which transfers the vibrations of the strings to the hollow soundboard, which causes a much larger volume of air to vibrate (at the same frequency as the strings) and is more effective in transmitting the sound. Sound can also be produced by the vibration of fluids, including gases, that are moved through hollow objects or across small openings in objects. human voice is no less a musical instrument than any of those listed above. Sound is created by passing air between the vocal cords, which are a pair of thin membranes stretched across the larynx. As the air moves past the cords, they vibrate like the reed of a clarinet or oboe, causing the air to vibrate at the same frequency. The pitch of the sound is controlled by varying the tension of the cords. Adult male vocal cords are larger and thicker than those of the adult female; thus, the male voice is typically lower in pitch.

Answer 106

Intensity and loudness of sound- loudness of sounds is the way in which we perceive the intensity of the sound waves. Perception of loudness is subjective, but sound intensity is objectively measurable. Intensity is the average rate per unit area at which energy is transferred across a perpendicular surface by the wave. intensity is the power transported per unit area. The SI units of intensity are watts per square meter, W/m2. power delivered across a surface, such as the eardrum, is equal to the product of the intensity I and the surface area A, assuming the intensity is uniformly distributed. amplitude of a sound wave and the intensity of that sound are related to each other: Intensity is proportional to the square of the amplitude. Doubling the amplitude produces a sound wave that has four times the intensity. Intensity is also related to the distance from the source of the sound wave. You can think of sound waves traveling from their source in three-dimensional space as if the waves were pushing up against the interior wall of an ever-expanding spherical balloon. Because the area of a sphere increases as a function of the square of the radius, sound waves transmit their power over larger and larger areas the farther from the source they travel. Intensity, therefore, is inversely proportional to the square of the distance from the source. For example, sound waves that have traveled 2 meters from their source have spread their energy out over a surface area that is four times larger than that for sound waves of the same amplitude and frequency that have traveled 1 meter from their source. sound level (β ), measured in decibels (dB). where Io is a reference intensity set at the threshold of hearing, 1 × 10− W/m2. When the intensity of a sound is changed by some factor, you can calculate the new sound level. ratio of the final intensity to the initial intensity

Answer 107

Frequency and pitch- requency is measured in hertz (Hz) or cycles per second (cps). Angular frequency is related to frequency (ω = 2π f) and is measured in radians. Our perception of the frequency of sound is called the pitch. Lower-frequency sounds have lower pitch, and higher-frequency sounds have higher pitch. Pitch is a subjective quality and cannot be measured with instruments. People who possess absolute pitch, commonly known as perfect pitch, have the ability to identify any pitch played on an instrument or to sing any pitch without an external reference such as a pitch pipe.

Answer 108

• Beats- can be heard as periodic increases in loudness when an orchestra is tuning. When two waves pass through a region of space at the same time, the waves will interact with each other in such a way that their amplitudes will add or subtract to produce a resultant wave whose amplitude is the sum or difference of the original waves. When two sound waves pass through a region of space at the same time, they too will interact resulting in constructive and/or destructive interference. If the two sound waves have nearly equal frequencies in the audible range, the resultant wave will have periodically increasing and decreasing amplitude, which we hear as beats. Because the amplitude, not the frequency, of the resultant wave varies periodically, we perceive this as periodic variation in the loudness, not the pitch. The beat frequency

Answer 109

Doppler Effect- describes the difference between the perceived frequency of a sound and its actual frequency when the source of the sound and the sound's detector are moving relative to each other. If the source and detector are moving toward each other, the perceived frequency f′ is greater than the actual frequency f, but if the source and detector are moving away from each other, the perceived frequency f′ is less than the actual frequency f. v is the speed of sound in the medium, vD is the speed of the detector relative to the medium, and vS is the speed of the source relative to the medium. The upper sign on vD and vS is used when the detector and the source are getting closer together. The lower sign is used when the detector and the source are going farther away from each other. apparent frequency is less than the actual frequency. The apparent (perceived) frequency is found by multiplying the actual frequency by a ratio. If the apparent frequency is lower than the actual frequency, then that means that the ratio must be less than 1. If the apparent frequency is greater than the actual frequency, then the ratio must be greater than 1. approaching the detector and the source separately. Realize that either one moving toward the other will increase the frequency, so you want to see if each object is working toward increasing or decreasing the frequency. Because the detector is in the numerator, if it is working to increase the frequency, then ADD, giving a larger number. Because the source is in the denominator, if it is working to increase the frequency, then subtract, resulting in a larger number after dividing. Practice using this equation with objects moving in both the same and opposite directions. • The Doppler effect works with all waves, including light. This means that if a source of light is moving toward a detector, the observed frequency will increase (blue shift), and if the source is moving away from a detector, the frequency will decrease (red shift). Observing any distant galaxy, we can see that every one is red shifted, meaning that every galaxy is moving away from our own.

Answer 110

• standing waves- constructive and destructive interference of a traveling wave and its reflected wave. More broadly, we can say that a standing wave will form whenever two waves of the same frequency traveling in opposite directions interfere with one another as they travel through the same medium. Standing waves appear to be “ standing still” — that is, not propagating— because the interference of the wave and its reflected wave produce a resultant that fluctuates only in amplitude. As the waves move in opposite directions, they interfere to produce a new wave pattern characterized by alternating points of maximum amplitude displacement (in the positive and negative direction) and points of no displacement. The point(s) in a standing wave with no amplitude fluctuation are called nodes. The points with maximum amplitude fluctuation are called antinodes. boundary conditions are present, not every wavelength of traveling wave will result in standing wave formation. The length of the medium dictates the wavelengths of traveling wave that are necessary for establishing the standing wave. Furthermore, the nature of the boundary dictates the appearance of a node or antinode at the boundary itself. Closed boundaries are those that do not allow oscillation and that support nodes. The closed end of a pipe and the secured ends of a string are both closed boundaries. Open boundaries are those that allow oscillation and support antinodes. The open end of a pipe and the free end of a flag are both open boundaries.

Answer 111

Strings- have fixed rigidity at both ends. string is secured at both ends and therefore immobile, these two points can only support a node of a standing wave. If a standing wave is set up such that there is only one antinode between the two nodes at the end, the length of the string corresponds to one-half the wavelength of this standing wave. (On a sine wave, the distance from one node to the next immediate node is one-half a wavelength.) If a standing wave is set up such that there are two antinodes between the two nodes at the ends and a third node between the antinodes, the length of the string corresponds to the wavelength of this standing wave. (The distance on a sine wave from a node to the second consecutive node is one wavelength.) This pattern suggests that the length L of a string must be equal to some integer multiple of a half-wavelength (e.g., L = The equation that relates the wavelength λ of a standing wave and the length L of a string that supports n is a positive nonzero integer (n = 1, 2, 3,… ). From the relationship where n is a positive nonzero integer (n = 1, 2, 3,… ). The lowest frequency (longest wavelength) of a standing wave that can be supported in a given length of string is known as the fundamental frequency(first harmonic). The frequency of the standing wave given by n = 2 is known as the first overtone or second harmonic. This standing wave has one-half the wavelength and twice the frequency of the first harmonic. All the possible frequencies that the string can support form its harmonic series. The waveforms of the first three harmonics for a string of length L (N stands for node and A stands for antinode.) For strings attached at both ends, the number of antinodes present will tell you which harmonic it is.

Answer 112

Open Pipes- Pipes can support standing waves and produce sound. Many musical instruments are straight or curved pipes or tubes within which air will oscillate at particular frequencies to set up standing waves. The boundary conditions of pipes are either open or closed. If the end of the pipe is open, it will support an antinode, but if it is closed, it will support a node. One end of the pipe must be open at least a little to allow for the entry of air, but sometimes these openings are small and covered by the musician's mouth and function as a closed end. Pipes that are open at both ends are called open pipes, while those that are closed at one end (and open at the other) are called closed pipes. The flute is an open pipe instrument, and the clarinet is a closed pipe instrument. open pipe, being open at both ends, supports antinodes corresponding to the amplitudes of the variation in the movement of the air. At the closed end, there is no variation in the movement of the air (because of the physical boundary), so this is a node. If a standing wave is set up in an open pipe of length L such that there is only one node between the two antinodes at the open ends of the pipe, the length of the pipe corresponds to one-half the wavelength of the standing wave. (The distance from one antinode to the subsequent antinode is one-half the wavelength.) If a standing wave is set up such that there are two nodes between the antinodes at the open ends (with a third antinode between the two nodes), the length of the pipe corresponds to the wavelength of the standing wave. (The distance from one antinode to the second consecutive antinode is one wavelength.) This pattern suggests that the length L of an open pipe must be equal to some integer multiple of a half wavelength (e.g., L = same relationship for strings and standing waves,). equation that relates the wavelength λ of a standing wave and the length L of an open pipe. For pipes with two open ends, the number of nodes present will tell you which harmonic it is. n is a positive nonzero integer (n = 1, 2, 3,… ) and v is the speed of sound in air at room temperature, 344 m/s. Figure 9.7 gives a symbolic representation of the first three harmonics in an open pipe. We use the word symbolic in recognition that the conventional way of diagrammatically representing sound waves is with transverse, rather than longitudinal, waves. pipes with one open end, finding the harmonic works the same way as with pipes with two open ends, though there is one important difference. Because the pipe only has one open end, the sound must go through the pipe, bounce off the wall, and go out again. This means that each sound wave will travel double the length of the pipe. This is why the equations for these pipes have four in the fraction instead of two. Once again, counting the number of nodes the sound wave passes through (accounting for both passes) will tell you which harmonic it is.

Answer 113

Closed Pipes- clarinet or milk jug, closed end support a node, and the open end will support an antinode. The first harmonic in a closed pipe consists of only the node at the closed end and the antinode at the open end. In a sinusoidal wave, the distance from node to antinode is one-quarter of a wavelength. Because the closed end must always have a node and the open end must always have an antinode, there can only be odd harmonics, since an even harmonic is an integer multiple of the half-wavelength and would necessarily have either two nodes or two antinodes at the ends. The first harmonic has a wavelength that is four times the length of the closed pipe, the third harmonic has a wavelength that is four-thirds the length of the closed pipe, the fifth harmonic has a wavelength that is four-fifths the length of the closed pipe, etc. n is odd integers only (n = 1, 3, 5,… ). The frequency of the standing wave in a closed pipe is where n is odd integers only (n = 1, 3, 5, … ) and v is the speed of sound at room temperature, 344 m/s represents the first, third, and fifth harmonics for a closed pipe

Answer 114

exert forces perpendicular to their surface, although only solids can withstand shear (tangential) force. Impose large perpendicular forces, •withstand shear (tangential) force. Impose large perpendicular forces, •Fluid- ability to flow and conform to the shape of its container, liquids and gases. solid- does not flow and its rigidity helps it retain a shape independenet of that of any caontainer.

Answer 115

Density- fluids and solids are characterized by the ratio of their mass to their volume, scalar quantity and therefore has no direction. ρ is the Greek letter rho (not the English letter p) and represents density. The SI units for density are kg/m3, but you may find it convenient to use g/mL or g/cm3. milliliter and the cubic centimeter are the same volume. One mistake that students sometimes make is assuming that if the mL and the cm3 are equivalent, then so must the liter and the m3. 1,000 liters in a cubic meter. One way to help you remember this is that the density of water is 1,000 kg/m3, and one liter of soda (or water) does not come close to having a mass of 1,000 kg. weight of any volume of a given substance with know density can be calculated by multiplying the substance's density and volume, and the acceleration due to gravity.

Answer 116

specific gravity is that if an object's specific gravity is greater than 1, then it is more dense than water. If the specific gravity is less than one, then it is less dense than water.

Answer 117

• Pressure is a ratio of normal force per unit area. P is pressure, F is normal force, and A is area. The SI unit of pressure is the pascal (Pa), which is equivalent to the newton per square meter (1 Pa = 1 N/m2). Other commonly used units of pressure are the atmosphere, torr, and mm Hg. The unit of atmosphere is based on the average atmospheric pressure at sea level. The conversions between Pa, atm, torr, and mm Hg

Answer 118

• All substances— solids and fluids— can exert forces against other substances: Water pushes against a dam, gale-force winds hammer against windows, and spiky high-heeled shoes dig into soft pine wood floors. Pressure is a scalar quantity. It may seem surprising to learn that pressure has magnitude but not direction. pressure is measured as the magnitude of the normal force, F, per unit area and because the normal force is the force perpendicular to the surface, the direction of the normal force is assumed to determine the direction for pressure. However, you need to remember that no matter where we position a given surface, the pressure will be the same. For example, if we placed a surface inside a closed container filled with gas, the individual molecules, which are moving randomly within the space, will exert pressure that is the same at all points within the container. Because the pressure is the same at all points along the walls of the container and within the space of the container itself, pressure applies in all directions at any point and, therefore, is scalar rather than vector. Of course, because pressure is a ratio of force to area, when unequal pressures are exerted against objects, the forces acting on the object will add in vectors, possibly resulting in acceleration. It's this difference in pressure (pressure differential) that causes air to rush into and out of the lungs during respiration, windows to burst outward during a tornado, and the plastic covering a broken car window to bubble outward when the car is moving. At the surface of the water, the absolute pressure is equal to the atmospheric pressure (Po). But if you dive into the pool, the water exerts an extra pressure (ρ gh) on you, in addition to the surface pressure. You feel this extra pressure on your eardrums.

Answer 119

Absolute Pressure- countless trillions of air molecules are exerting tremendous pressure on your body, with a total force of about 200,000 N! Of course, you don't actually feel all this pressure because your internal organs exert a pressure that perfectly balances it. Atmospheric pressure changes with altitude. Residents of Denver (altitude: 5,000 ft above sea level) experience atmospheric pressure equal to 632 mm Hg (which is equal to 0.83 atm), whereas travelers making their way through Death Valley (altitude: 282 ft below sea level) experience atmospheric pressure equal to 767 mm Hg (1.01 atm). Atmospheric pressure impacts everything from hemoglobin's affinity for oxygen to the baking time of a cake. Absolute pressure is the total pressure that is exerted on an object that is submerged in a fluid. Remember that fluids include both liquids and gases. P is the absolute pressure, Po is the pressure at the surface, and ρ gh quantifies the magnitude of pressure that is a function of the weight of the fluid sitting above the submerged object at some height h. Do not make the mistake of assuming that Po always stands for atmospheric pressure. In open air and most day-to-day situations Po is equal to 1 atm, but in other fluid systems, the surface pressure may be lower or higher than atmospheric pressure. In a closed container, such as a pressure cooker, the pressure at the surface may be much higher than atmospheric. This is, in fact, exactly the point of a pressure cooker, whose culinary benefit is that it allows food to cook at a higher temperature (to explain this, think about phase diagrams and what higher pressures do to boiling points), which reduces the cooking time and prevents loss of moisture and nutrients.

Answer 120

Gauge Pressure- gauge pressure, which is the difference between the absolute pressure inside the tire and the atmospheric pressure outside the tire. In other words, gauge pressure is the pressure in a closed space that is at a pressure above atmospheric pressure. Po = Patm, then Pg = P– Po = ρ gh at depth h

Answer 121

Hydrostatics- fluid at rest is in equilibrium. balance of the forces acting on the fluid. When forces act on a fluid such that a pressure differential is created, that fluid will flow or change shape to restore that equilibrium. Hydrostatics is the study of fluids at rest and the forces and pressures associated with standing fluids. air pressure changes above a large body of water, the water level rises or falls to re-establish pressure equilibrium between the air and the water. The surface of a water body directly below a high-pressure air pocket forms a very small but measurable “ valley” of water. A low-pressure air system has the opposite effect, creating a “ hill” of water.

Answer 122

• Pascal's Principle- incompressible fluids, volumes cant be reduced by any significant degree through application of pressure, when a change of pressure applied to an enclosed fluid, pressure change transmitted undiminished to every portion of the fluid and walls of the containing vessel. Hydraulic systems take advantage of the incompressibility of liquids to generate mechanical advantage. on the left side of the lift, there is a piston of cross-sectional area A1. When this piston is pushed down the column, it exerts a force equal to F1 and generates a pressure equal to P1. The piston displaces a volume of liquid equal to A1d1. Because the liquid inside is incompressible, the same volume of fluid must be displaced on the right side of the hydraulic lift, where we find a second piston with a much larger surface area, A2. The pressure generated by piston 1 is transmitted undiminished to all points within the system, including to A2. As A2 is larger than A1 by some factor, the force, F2, exerted against A2 must be greater than F1 by the same factor so that P1 = P2, according to Pascal's principle. hydraulic machines generate “ output” force by magnifying an “ input” force by a factor equal to the ratio of the cross-sectional area of the larger piston to that of the smaller piston. This does not violate the law of energy conservation; an analysis of the input and output work reveals that there indeed is conservation of energy (assuming the absence of frictional forces). The volume of fluid displaced by piston 1 is equal to the volume of fluid displaced at piston 2. Combining the equations for pressure and volume, we can generate an equation for work as the product of pressure and volume change. simplification of the work equation shows us the familiar form of work as the product of force and distance. Because the factor by which d1 is larger than d2 is equal to the factor by which F2 is larger than F1, we see that no additional work has been done or unaccounted for; the greater force F2 is moving through a smaller distance d2. Therefore, an auto mechanic needs only to exert a small force over a small area through a large distance to generate a much larger force over a larger area through a smaller distance. It's simple mechanical advantage. Remember when applying Pascal's principle, the larger the area, the larger the force, though this force will be exerted through a smaller distance.

Answer 123

•Archimedes' Principle- A body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that it displaces. Archimedes' body and his crown caused the water level to rise in the tub, any object placed in a fluid will cause a volume of fluid to be displaced equal to the volume of the object that is submerged. Since all fluids have density, the volume of fluid displaced will correspond to a certain mass of that fluid. The mass of the fluid displaced exerts a force equal to its weight against the submerged object. This force, which is always directed upward, is called the buoyant force. object is placed in a fluid, it will sink into the fluid only to the point at which the volume of displaced fluid exerts a force that is equal to the weight of the object. If the object becomes completely submerged and the volume of displaced fluid still does not exert a buoyant force equal to the weight of the object, the object will sink and accelerate to the bottom. A gold crown will sink to the bottom of the bathtub. On the other hand, an object that is less dense than water, such as a block of wood or a cube of ice, will stop sinking (and start floating) as soon as it displaces a volume of water equal to its own mass. . An object will float, no matter what it is made of and no matter how much mass it has, if its average density is less than or equal to the density of the fluid into which it is placed. Furthermore, if we express the object's specific gravity as a percentage value, this directly indicates the percentage of the object's volume that is submerged. For instance, the density of ice is 0.92 g/cm3, and its specific gravity is 0.92. An ice cube floating in a glass of water has 92 percent of its volume submerged in the water— only 8 percent is sitting above the surface. From this principle follows something you may already know: Any object whose specific gravity is less than or equal to 1 will float in water (specific gravity of exactly 1 indicates that 100 percent of the object will be submerged but it will not sink) and any object whose specific gravity is greater than 1 will sink.

Answer 124

• Molecular Forces on Liquids- Surface tension causes the liquid to form a thin but strong layer like a “ skin” at the liquid's surface. Surface tension results from cohesion, which is the attractive force that a molecule of liquid feels toward other molecules of the same liquid. Imagine molecules of liquid as thousands of tiny Velcro balls that are jostling around in a container, each momentarily sticking to another. The balls in the middle of the bunch are experiencing attractive forces from all sides; these forces balance out. However, on the surface, the balls only feel an attraction to the balls below them; these attractive forces keep pulling the surface balls toward the center. There is tension in the surface due to the pulling forces. When there is an indentation on the surface (say, caused by a water strider's foot) then the cohesion can lead to a net upward force.• Molecular Forces on Liquids- Surface tension causes the liquid to form a thin but strong layer like a “ skin” at the liquid's surface. Surface tension results from cohesion, which is the attractive force that a molecule of liquid feels toward other molecules of the same liquid. Imagine molecules of liquid as thousands of tiny Velcro balls that are jostling around in a container, each momentarily sticking to another. The balls in the middle of the bunch are experiencing attractive forces from all sides; these forces balance out. However, on the surface, the balls only feel an attraction to the balls below them; these attractive forces keep pulling the surface balls toward the center. There is tension in the surface due to the pulling forces. When there is an indentation on the surface (say, caused by a water strider's foot) then the cohesion can lead to a net upward force. Fluid dynamics- fluid in motion,

Answer 125

adhesion, which is the attractive force that a molecule of the liquid feels toward the molecules of some other substance. For example, the adhesive force causes water molecules to form droplets on the windshield of a car even though gravity is pulling them downward. When liquids are placed in containers, a meniscus, or curved surface in which the liquid “ crawls” up the side of the container just a little bit, will form when the adhesive forces are greater than the cohesive forces. A “ backwards” meniscus (with the liquid level higher in the middle than at the edges) occurs when the cohesive forces are greater than the adhesive forces. Mercury, the only metal that is liquid at room temperature, forms a “ backward” meniscus when placed in a container.

Answer 126

Viscosity- Some fluids flow very easily, while others barely flow at all. resistance of a fluid to flow is called viscosity, and it can be thought of as a measure of fluid friction. “ Thin” fluids, like gases, water, and dilute aqueous solutions, have low viscosity and so flow easily. Whole blood, vegetable oil, honey, cream, and molasses are “ thick” fluids and flow more slowly. Low-viscosity fluids have low internal resistance to flow and behave like ideal fluids. Assume conservation of energy in low-viscosity fluids with laminar flow. Lower viscosities are more ideal of fluids, which have no viscosity and are inviscid. viscosity is a measure of a fluid's internal resistance to flow, more viscous fluids will “ lose” more energy to friction. Low-viscosity fluids more closely approximate conservation of energy, Bernoulli's equation is an expression of energy conservation for flowing fluids. SI unit of viscosity is the newton · second/m2 (N· s/m2). Low-viscosity fluids have low internal resistance to flow and behave like ideal fluids. Assume conservation of energy in low-viscosity fluids with laminar flow.

Answer 127

Laminar And Turbulent Flow- laminar or turbulent flow, aminar flow is smooth and orderly. You can imagine it as concentric layers of fluid that flow parallel to each other. The layers will not necessarily have the same linear velocity. For example, the layer closest to the wall of a pipe flows more slowly than the more interior layers of fluid. Turbulent flow is rough and disorderly. Turbulence causes the formation of eddies, which are swirls of fluid of varying sizes occurring typically on the downstream side of an obstacle. In unobstructed fluid flow, turbulence can arise when the velocity of the fluid exceeds a certain critical velocity (vc). This critical velocity depends on the physical properties of the fluid, such as its viscosity and the diameter of the tube. When the critical velocity for a fluid is exceeded, the fluid demonstrates complex flow patterns, and laminar flow occurs only in the thin layer of fluid adjacent to the wall, called the boundary layer. The flow velocity immediately at the wall is zero and increases uniformly throughout the layer. Beyond the boundary layer, however, the motion is highly irregular and turbulent. A significant amount of energy is “ lost” from the system as a result of the increased frictional forces. Calculations of energy conservation, such as Bernoulli's equation, no longer can be applied. Assume nonturbulent flow, luid flowing through a tube of diameter D, the critical velocity, vc, NR is a dimensionless constant called the Reynolds number, η is the viscosity of the fluid, ρ is the density of the fluid, and D is the diameter of the tube.

Answer 128

Streamlines- movement of individual molecules of a fluid is impossible to track with the unaided eye, it is often helpful to use representations of the molecular movement called streamlines. Like the lines of light that are captured in a slow-shutter photograph of moving cars at night, streamlines indicate the pathway followed by tiny fluid elements (sometimes called fluid particles) as they move. The velocity vector of a fluid particle will always be tangential to the streamline at any point. Streamlines never cross each other. tube containing a moving fluid that passes from P to Q. The streamlines indicate some, but not all, of the pathways for the fluid along the walls of the tube. You'll notice that the tube gets wider toward Q, as indicated by the streamlines that are spreading out over the increased cross-sectional area. This leads us to consider the relationship between flow rate and the cross-sectional area of the container through which the fluid is moving. Once again, we can assume that the fluid is incompressible (which means that we are not considering a flowing gas). Because the fluid is incompressible, the rate at which a given volume (or mass) of fluid passes by one point must be the same for all other points in the closed system. This is essentially an expression of conservation of matter: If x liters of fluid pass a point in a given amount of time, then x liters of fluid must pass all other points in the same amount of time. Thus, we can very clearly state, without any exceptions, the volumetric rate of flow (i.e., unit of volume per unit of time) is constant for a closed system and is independent of changes in cross-sectional area. Linear velocity at which fluid flows, the unit are meters per second and are a measure of the linear displacement of the fluid particle in a given amount of time. When we multiply linear velocity by cross-sectional area, An increase in the velocity of the fluid is associated with a decrease in the pressure that the fluid exerts on the walls of the container. One way to think about this is that the fluid is being pushed through the container so quickly that it isn't given enough time to interact with the walls of the container. A great way to conceptualize this is with an approaching tornado. As a tornado approaches a building, the velocity of the air molecules outside of the building increases greatly. This is associated with a significant decrease in the outdoor air pressure, which may result in the windows of the building exploding outward. continuity equation, and it tells us that fluids will flow more quickly through narrow passages and more slowly through wider ones.

Answer 129

Bernoulli's Equation- continuity equation arises from the conservation of mass of fluids. Excluding gases, we can say that all fluids (liquids) are incompressible, so the volumetric rate of flow within a closed space must be constant at all points. The continuity equation shows us that for a constant volumetric flow rate, there is an inverse relationship between the linear velocity of the fluid and the cross-sectional area of the tube: Fluids have higher velocities through narrower tubes. Fluids that have low viscosity and demonstrate laminar flow can also be approximated to be conservative systems. The total mechanical energy of the system is constant if we discount the small friction forces that occur in all real liquids. principles of conservation (of mass and energy), In accordance with Bernoulli's principle, the fast-moving air creates an area of low pressure in the cushion's neck, making it close quickly. However, the neck opens up again a fraction of a second later when more air is pushed out by the weight of the person sitting on the rubber cushion, starting the process again. This rapid, repeated opening and closing of the neck of the whoopee cushion creates sound waves in the surrounding air, creating the gag item's infamous flatulent sound. a conservation of kinetic and potential energy of a moving fluid. Pressure is a ratio of the magnitude of force exerted per unit area. It doesn't seem to have any obvious or direct connection to energy or energy conservation. ratio of newton/square meter by the ratio of meter/meter (which is perfectly “ legal” because multiplying any value by a ratio that reduces to 1 produces the original value), we arrive at newton times meter per cubic meter. As we know well, the newton meter is the joule, the SI unit for energy. Pressure can therefore be expressed as a ratio of energy per cubic meter; that is, as an “ energy density.” Systems at higher pressure contain a greater density of energy than those systems at lower pressure.

Answer 130

• combination of P and ρ gy gives us the static pressure, where P is the pressure at the surface of the fluid. Ignoring the dynamic pressure, you ought to recognize that the sum of P and ρ gy is the expression that we encountered in our discussion of absolute pressure. Bernoulli's expression states, then, that for an incompressible fluid not experiencing friction forces, the sum of the static pressure and dynamic pressure will be constant within a closed container. In the end, Bernoulli's principle is nothing other than a statement of energy conservation: More energy dedicated towards fluid movement means less energy dedicated towards fluid pressure. The inverse of this is also true (less movement means more static pressure). system of fluid moving through a series of horizontal pipes so that the average height of the fluid is constant. In these cases, the ρ gy terms are the same on both sides and can be cancelled out. The resulting simplified expression shows an inverse relationship between the static pressure and the dynamic pressure: When the velocity of the fluid increases (thereby leading to an increase in the dynamic pressure), the static pressure decreases. Another way to think about this is to apply Newton's second law, which relates forces and accelerations: When two points within a fluid are at different static pressures, the fluid will experience a net force from the point of higher pressure to that lower pressure and will flow (and accelerate) in that direction.

Answer 131

Elastic Properties of Solids- Substances are solid when they are rigid enough to retain their unique shape and can withstand tangential (shearing) forces. (In reality, some solid substances— such as glass, mayonnaise, and shaving cream— classified as amorphous solids, can actually defy these principles and will flow under certain conditions. Substances are solid when they are rigid enough to retain their unique shape and can withstand tangential (shearing) forces. (In reality, some solid substances— such as glass, mayonnaise, and shaving cream— classified as amorphous solids, can actually defy these principles and will flow under certain conditions.

Answer 132

• Elasticity- measure o fthe response of a solid to an application of pressure. Depending on the particular way in which the pressure is exerted, the object may experience a change in length, volume, or lateral displacement such as shear. olid's resistance to an applied pressure is measured by ratios known as moduli

Answer 133

• Young's Modulus- stretching (tensile) or pushing (compression) force is exerted against an object, the object will experience a change in length, objects of the same material may require different force magnitudes to effect the same change in lengths. difficult it is to stretch a very thick rubber band than to stretch a thin one— we quantify the relationship not between applied force and length change but between pressure and the change in length per unit length. We call the applied pressure the “ stress,” and the change in length per unit length is called the “ strain.” Young's modulus, Y, is defined, then, as the ratio of stress over strain. Limit to degree an object can be compressed or stretched before deforming and rupturing. elastic limits should be familiar to anyone who has seen a trash compactor in action, chopped a block of wood, or stretched a rubber band past its breaking point. Yield strength is the point of shape change beyond which a material will not return to its original dimensions once the applied force is removed (think of a crumpled piece of paper). If more stress is applied, eventually the ultimate strength will be reached, beyond which point the object will rupture (think of a broken rubber band). Both Young's modulus and the shear modulus represent the same relationship: stress/strain. Both express stress in the same way as pressure (F/A); it is the way they represent strain that distinguishes them.

Answer 134

Shear Modulus- force applied parallel to object’s surface rather than perpendicular to it, the object experiences a shape change, shear. Rather than elongation or compression, lateral shift in the direction of the force. stress is measured, again, as the ratio of force per unit area (i.e., the pressure), the strain is measured as a ratio of the lateral movement (x) in the direction of the force vector per unit height (h). If you were to exert a shear force along the cover of this book from the free edge toward the binding, you would cause the book to shift laterally with respect to its height, just like the block. three moduli, a large number represents a more rigid material, while a small number represents a more malleable material.

Answer 135

• Bulk Modulus- indicates the degree to which a material will experience a change in its volume in realtion to an applied pressure. two moduli, the stress is the applied pressure, and the strain is a ratio of change in dimension per unit dimension. Here, the dimensional change that we are interested in is with respect to the volume, (Δ V/V). Solids and liquids have very large bulk moduli, reflective of the large amounts of pressure that must be applied to effect a change in volume. Remember, we consider liquids and solids to be essentially incompressible. Gases, on the other hand, are easily compressible and so have relatively small bulk moduli . speed of sound in a material is proportional to the square root of the bulk modulus of that material. Because gases have small bulk moduli, liquids have larger bulk moduli, and solids have the largest, sound will travel fastest through solids and slowest through gases. If you were waiting for a train and you wanted to listen for its arrival, you would be able to hear the train sooner if you put your ear to the ground rather than to the wind.

Answer 136

Electromagnetic Spectrum- includes radio waves on one end, long wavelength, low frequency, low energy) and gamma ray having (short wavelength, high frequency, high energy.) lower energy to higher energy, microwaves, infrared, visible light, ultraviolet, and x-rays. This chapter will focus primarily on the range of wavelengths corresponding to the visible spectrum of light (380 nm− 760 nm). • Changing magnetic field can cause a change in the electric field and a changing electric field can cause a change in the magnetic field. Because changing electric fields affect changing magnetic fields that affect changing electric fields (and so on and so on), we can see how electromagnetic waves occur in nature. One field affects the other, totally independent of matter, and electromagnetic waves can even travel through a vacuum. Electromagnetic waves are transverse waves because the oscillating electric and magnetic field vectors are perpendicular to the direction of propagation. Furthermore, the electric field and the magnetic field are perpendicular to each other.

Answer 137

Color and visible spectrum- electromagnetic spectrum is divided into many regions. The only part of the spectrum that is perceived as light by the human eye is named, quite appropriately, the visible region. Within this region, different wavelengths induce sensations of different colors, with violet at one end of the visible spectrum (380 nm) and red at the other (760 nm). Light that contains all the colors in equal intensity is seen as white. The color of an object that does not emit its own light is dependent on the color of light that it reflects. So an object that appears red is one that absorbs all light except red. This implies that a red object receiving green light will appear black, because it absorbs the green light and has no light to reflect. The term blackbody, used to describe an ideal radiator refers to the fact that such an object is also an ideal absorber and would appear totally black if it were at a lower temperature than its surroundings.

Answer 138

Geometrical Optics- light travels through a single homogenous medium , it travels in a straight line, such as rectilinear propagation. behavior of light at the boundary of a medium or interface between two media is described by the theory of geometrical optics with light traveling in a straight-line path, geometrical optics pertain to the behavior of reflection and refraction.

Answer 139

Reflection- Reflection is the rebounding of incident light waves at the boundary of a medium. Light waves are not absorbed into the second medium; rather, they bounce off of the boundary and travel back through the first medium. Law of reflection is where θ 1 is the incident angle and θ 2 is the reflected angle, both measured from the normal. We don't anticipate that you will have any difficulty remembering this particular law of optics. Do note that, in optics, angles are always measured from a line drawn perpendicular to the boundary of a medium, usually referred to as the normal.

Answer 140

Plane mirror reflections- images created by a mirror can be either real or virtual. An image is said to be real if the light actually converges at the position of the image. An image is virtual if the light only appears to be coming from the position of the image but does not actually converge there. Parallel incident light rays remain parallel after reflection from a plane mirror; that is, plane mirrors— being flat reflective surfaces— cause neither convergence nor divergence of reflected light rays. Because the light does not converge at all, plane mirrors always create virtual images. In a plane mirror, the image appears to be the same distance behind the mirror as the object's distance in front of it. plane mirrors create the appearance of light rays originating behind the mirrored surface. Of course, this is a physical impossibility; nevertheless, the appearance is there. Because the reflected light remains in front of the mirror but the image is behind the mirror, the image is virtual. We are very familiar with plane mirrors, as they are the common mirrors found in our homes (bathroom mirrors, full-length mirrors, etc.)

Answer 141

spherical mirrors- can either be concave or conves, small portion of the surface of the mirrored ball (sphere) Spherical mirrors have a center of curvature (C) and a radius of curvature (r) associated with them. The center of curvature is a point on the optical axis located at a distance equal to the radius of curvature from the vertex of the mirror; in other words, where the center of the mirrored sphere would be, were it a complete sphere. inside of a sphere to its surface, you would see a concave surface (concave = looking into a cave). However, if you were to look from outside the sphere, you would see a convex surface. For a convex surface (mirror on the outer curvature), the center of curvature and the radius of curvature are located behind the mirror. For a concave surface (mirror is on inner curvature), the center of curvature and the radius of curvature are in front of the mirror. Concave mirrors are called converging mirrors, and convex mirrors are called diverging mirrors, because they cause parallel incident light rays to reflect convergently and divergently.

Answer 142

The focal point of converging mirrors (and converging lenses) will always be positive. The focal point of diverging mirrors (and diverging lenses) will always be negative. The focal length (f) is the distance between the focal point (F) and the mirror (for all spherical mirrors, where the radius of curvature (r) is the distance between C and the mirror); the distance of the object from the mirror is o; the distance of the image from the mirror is i. applies ot both kinds of mirrors and lenses, If the image has a positive distance, it is a real image, which implies that the image is in front of the mirror. If the image has a negative distance, it is virtual and thus located behind the mirror. Plane mirrors can be thought of as infinitely large spherical mirrors. As such, for a plane mirror, r = f = ∞ , and the equation. Any time the object is at the focal point, the reflected rays will be parallel, and thus, the image will be at infinity with the virtual image at distance behind mirror equal to distance of object in front of mirror)

Answer 143

magnification (m) is a dimensionless value that is the ratio of the image's height to the object's height. orientation of the image compared with the object can also be determined. A negative magnification signifies an inverted image, while a positive value means the image is upright. If |m| < 1, the image is reduced; if |m| > 1, the image is enlarged; and if |m| = 1, the image is the same size as the object.

Answer 144

ray diagrams for a concave spherical mirror with the object at three different points. A ray diagram is useful for getting an approximation of where the image is. ray diagrams will be especially helpful for getting a quick understanding of the type of image (real versus virtual, inverted versus upright, and magnified versus reduced) that will be produced by an object some distance from the mirror (or lens). To find where the image is, draw these rays and find a point where any two intersect. This point of intersection will show you where the image is.

Answer 145

For a concave mirror, a ray that strikes the mirror parallel to the horizontal is reflected back through the focal point. A ray that passes through the focal point before reaching the mirror is reflected back parallel to the horizontal. A ray that strikes the mirror right where the normal intersects it gets reflected back with the same angle (measured from the normal). the object is placed between F and C, and the image produced is real, inverted and magnified. the object is placed at F, and no image is formed because the reflected light rays are parallel to each other. In terms of the mirror equation, we say that the image distance i = ∞ here. , the object is placed between F and the mirror, and the image produced is virtual, upright, and magnified. A single diverging mirror forms only a virtual, upright, and reduced image, regardless of the position of the object, and the further away the object, the smaller the image will be. The only time that the object can be behind the mirror is when the object is the image from another mirror or lens

Answer 146

• Sign Convention for Single Mirrors- simplify sign conventions, just think about if the image is on the side it's supposed to be on or not. Mirrors reflect light back; lenses let light pass through. If the image is on the wrong side, then it is a virtual image.

Answer 147

Refraction is the bending of light as it passes from one medium to another and changes speed. The speed of light through any medium is always less than its speed through a vacuum. the speed of light through air can be approximated as the speed of light through a vacuum (3.00 × 108 m/s).

Answer 148

• The Law of Refraction: Snell's Law- where c is the speed of light in a vacuum, v is the speed of light in the medium, and n is a dimensionless quantity called the index of refraction of the medium. For air, n is essentially equal to 1 because v≈ c. v < c and n > 1. Refracted rays of light obey Snell's law as they pass from one medium to another where n1 and θ 1 are for the medium from which the light is coming and n2 and θ 2 are for the medium into which the light is entering. Note that θ is once again measured with respect to the perpendicular (normal) to the boundary. When light is not in a vacuum, its speed is less than c. sine of 90 degrees equals 1. This is why the second θ simply cancels out. light enters a medium with a higher index of refraction (n2 > n1), it bends towards the normal so that θ 2 < θ 1. Conversely, if the light travels into a medium where the index of refraction is smaller (n2 < n1), the light will bend away from the normal so that θ 2 > θ 1. If the rays you draw do not intersect, reflect the rays back to the side of the lens the light came from, resulting in a virtual image. find where the image is, draw these rays and find a point where any two rays intersect. This point of intersection will show you where the image is.

Answer 149

• Total Internal Reflection- When light travels from a medium with a higher index of refraction (such as water) to a medium with a lower index of refraction (such as air), the refracted angle is larger than the angle of incidence (θ 2 > θ 1); that is, the refracted light ray bends away from the normal. As the angle of incidence is increased, the refracted angle also increases, and eventually, a special incident angle is reached called the critical angleθ c, for which the refracted angle θ 2 equals 90 degrees. At the critical angle of incidence, the refracted light ray passes along the interface between the two media. The critical angle can be found from Snell's law. Total internal reflection, a phenomenon in which all the light incident on a boundary is reflected back into the original material, results for any angle of incidence greater than the critical angle, θ c.

Answer 150

Thin Spherical Lenses- lenses refract light while mirrors reflect it. Two surfaces that affect the light path with the light refracting twice as it passes from air to lens and from lens back to the air. For thin spherical lenses, the focal lengths are equal, so we speak of the focal length with two focal points focal lengths of either direction from its center. Converging lens is always thicker at the center, diverging lens is always thinner at the center. basic formulas for finding image distance and magnification for spherical mirrors (except r = 2f) also apply to lenses. The object distance o, image distance i, focal length f, and magnification m. lenses where the thickness cannot be neglected, the focal length is related to the curvature of the lens surfaces and the index of refraction of the lens by the lensmaker's equation, n is the index of refraction of the lens material, r1 is the radius of curvature of the first lens surface and r2 is the radius of curvature of the second lens surface. sign conventions change slightly for lenses. both lenses and mirrors, positive magnification means upright images, and negative magnification means inverted images. Also, for both lenses and mirrors, a positive image distance means that the image is real and is located on the R side, whereas a negative image distance means that the image is virtual and located on the V side

Answer 151

identify the R side, remember that the R side is where the light really goes after interacting with the mirror or lens. For mirrors, light is reflected and, therefore, stays in front of the mirror. The image may either appear in front of or behind the mirror, but the light rays always remain in front of the mirror. Because the R side is in front of the mirror, the V side is behind the mirror. For lenses, it is different: Light travels through the lens and comes out on the other side. The light really travels to the other side of the lens, and therefore, for lenses, the R side is opposite to the side of the lens from which the light originated; in other words, it is the side to which the light travels after it passes through the lens. In addition, the V side is the side of the lens from which the light originates; in other words, it is the side from which the light passes through the lens. Although the object of a single lens is on the V side, this does not make the object virtual. Objects are real, with a positive object distance, unless they are placed in certain multiple lens systems. Focal lengths have a simple sign convention. For both mirrors and lenses, converging lenses and mirrors have positive focal lengths, and diverging mirrors and lenses have negative focal lengths. For radii of curvature, you have to remember that a lens has two surfaces, each with its own radius of curvature (r1 and r2, where the surfaces are numbered in the order that they are encountered by the traveling light). For both mirrors and lenses, a radius of curvature is positive if the center of curvature is on the R side and negative if the center of curvature is on the V side. power (P). This is measured in diopters, where f (the focal length) is in meters and is given by this equation. P has the same sign as f and is, therefore, positive for a converging lens and negative for a diverging lens. People who are nearsighted (can see near objects clearly) need diverging lenses, while people who are farsighted (can see distant objects clearly) need converging lenses. Bifocal lenses are corrective lenses that have two distinct regions, one that causes convergence of light to correct for farsightedness (hyperopia) and a second that causes divergence of light to correct for nearsightedness (myopia) in the same lens.

Answer 152

* Multiple Lens Systems- Lenses in contact are a series of lenses with negligible distances between them. These systems behave as a single lens with equivalent focal length, the lens of the eye (a converging lens) is in contact with a contact lens (either converging or diverging, depending on the necessary correction), and their focal lengths and powers would be added. * lenses not in contact, the image of one lens is used to make the object of another lens. The image from the last lens is the image of the system. Microscopes and telescopes are good examples of multiple lenses not in contact. The magnification for the system

Answer 153

Dispersion- the speed of light in a vacuum is the same for all wavelengths. However, when light travels through a medium, different wavelengths travel at different velocities. This fact implies that the index of refraction of a medium is a function of the wavelength, because the index of refraction is related to the velocity of the wave. When the speed of the light wave varies with wavelength, a material exhibits dispersion. The most common example of dispersion is the splitting of white light into its component colors using a prism. If a source of white light is incident on one of the faces of a prism, the light emerging from the prism is spread out into a fan-shaped beam, The light has been dispersed into a spectrum. This occurs because violet light experiences a greater index of refraction than red light and so is bent to a greater extent. Because red experiences the least amount of bending, it is always on top of the spectrum; violet, having experienced the greatest amount of bending, is always on the bottom of the spectrum. You can prove this to yourself the next time you see a rainbow (raindrops act as miniature prisms): The outermost band of light will be red, and the innermost band of light will be violet.

Answer 154

Diffraction- when light passes through a narrow opening (an opening whose size is on the order of light wavelengths), the light waves seem to spread out. slit is narrowed, the light spreads out more. This spreading out of light as it passes through a narrow opening is called diffraction. If a lens is placed between a narrow slit and a screen, a pattern is observed consisting of a bright central fringe with alternating dark and bright fringes on each side. he central bright fringe is twice as wide as the bright fringes on the sides, and as the slit becomes narrower, the central maximum becomes wider. The location of the dark fringes is given by the following formula where a is the width of the slit, λ is the wavelength of the incident wave, and θ is the angle made by the line drawn from the center of the lens to the dark fringe and the line perpendicular to the screen. Note that bright fringes are halfway between dark fringes.

Answer 155

• Interference- superposition principle, when waves interact with each other, the amplitudes of the waves add together in a process called interference. famous double-slit experiment, Thomas Young showed that two light waves can interfere with one another, and this finding contributed to the wave theory of light. Light is similar to other wave forms; it observes constructive and destructive interference. This interference is seen as the light and dark fringes. coherent monochromatic light illuminates the slits, an interference pattern is observed on a screen placed behind the slits. (Monochromatic light is light that consists of just one wavelength, and coherent light consists of light waves whose phase difference does not change with time.) Regions of constructive interference between the two light waves appear as regions of maximum light intensity on the screen. Conversely, in regions where the light waves interfere destructively, the light is at a minimum intensity, and the screen is dark. An interference pattern produced by a double slit setup position of maxima and minima on the screen can be found where d is the distance between the slits, θ is the angle between the dashed lines λ is the wavelength of the light, and m is an integer representing the order.

Answer 156

Polarization- Plane-polarized light is light in which the electric fields of all the waves are oriented in the same direction (i.e., their electric field vectors are parallel). It is true that their magnetic fields vectors are also parallel, but convention dictates that the plane of the electric field identifies the plane of polarization. Unpolarized light has a random orientation of its electric field vectors; sunlight and light emitted from a light bulb are prime examples. in the context of optically active organic compounds. The optical activity of a compound, due to the presence of chiral centers, causes plane-polarized light to rotate clockwise or counterclockwise by a given number of degrees. Light waves exist as a wave in all three dimensions, meaning they oscillate in all 360 degrees. Polarizing light limits its oscillation to only two dimensions. Filters polarizers, cameras and sunglasses only allow light whose electric field pointing in particular direction to pass. hold one polarizer in a beam of light, it will let through only that portion of the light that has a given E vector orientation. If you then hold up another polarizer directly above or below the first and slowly turn it, you will see the light transmitted through the two polarizers vary from total darkness to the level of the original polarizer alone. When both polarizers are polarizing in the same direction, all the light that passed through the first also passes through the second. When the second polarizer is turned so that it polarizes in a direction perpendicular to the first, no light gets through at all.

Answer 157

* Thermal Blackbody Radiaiton- Absolute zero is 0 degrees Kelvin. At this temperature, all random atomic movement stops. At any temperature above absolute zero, the particles that make up matter demonstrate some form of movement (vibration, bending, stretching, translation, and rotation) and therefore emit electromagnetic radiation. The amount of radiant energy emitted at a given wavelength depends on the temperature of the emitter. Furthermore, different materials may emit different amounts of radiant energy at a particular wavelength due to the differences in their atomic structure. ideal radiator, known as a blackbody. The term blackbody is used, because an ideal radiator is also an ideal absorber and would appear totally black if it were at a temperature lower than that of its surroundings. This is because it would absorb all wavelengths of electromagnetic radiation, including those corresponding to the visible light range. In practice, a blackbody radiator can be approximated rather closely by radiation produced in a cavity within a hot object, such as an oven with a small hole in the door. Hence, blackbody radiation is approximated by what is called cavity radiation. * physicist Max Planck developed the theoretical derivation of the blackbody spectrum. His radiant spectrum for two blackbodies at different temperatures, In the derivation, Planck used a number that we now know as Planck's constant (h), whose value is which will be provided. blackbody is a theoretical “ ideal emitter,” the graph of blackbody radiation depends only on the temperature of the blackbody and not at all on the body's composition, size, or shape. An analysis of Planck's formula for the blackbody spectrum shows that for a blackbody, there is one wavelength at which the maximum amount of energy is emitted (λ peak). This wavelength depends on the absolute temperature of the blackbody in a relation known as Wien's displacement law, which is expressed mathematically. value of the constant in this law is 2.90 × 10− 3 m· K. Please note that λ peak is the wavelength at which more energy is emitted than at any other wavelength. λ peak does not refer to the maximum wavelength emitted. A blackbody will emit wavelengths that are both greater and lesser than λ peak, but the body will emit less energy at those wavelengths than at λ peak. object A is cooler than object B, and object A radiates less energy than object B. Furthermore, object A has a peak wavelength around 500 nm (visible light), while object B has a peak wavelength at 250 nm (UV). Because the peak wavelength for object B is half the peak wavelength of object A, object B's absolute temperature is twice that of object A according to Wien's displacement law. According to the Stefan-Boltzmann law, the total energy a blackbody emits per second per unit area (W/m2) is proportional to the fourth power of the absolute temperature: where σ is the Stefan-Boltzmann constant (5.67 × 10− 8 J/s· m2· K4).

Answer 158

* Photoelectric effect- When light of a sufficiently high frequency (typically, blue or ultraviolet light) is incident on a metal in a vacuum, the metal atoms emit electrons. This phenomenon, discovered by Heinrich Hertz in 1887, is called the photoelectric effect. The minimum frequency of light that causes this ejection of electrons is known as the threshold frequency fT. The threshold frequency depends on the type of metal being exposed to the radiation. Einstein's explanation of these results was that the light beam consists of an integral number of light quanta, called photons, with the energy of each photon proportional to the frequency f of the light, h is Planck's constant, energy of a photon increases with increasing frequency. The reason that we only discuss electrons (and not protons or neutrons) being ejected from metals is because of the weak hold that metals have on their valence electrons due to their low electronegativities. c is the speed of light (3.00 × 108 m/s). According to these equations, waves with higher frequency have shorter wavelengths and higher energy (toward the blue and ultraviolet end of the spectrum); waves with lower frequency have longer wavelengths and lower energy (toward the red and infrared end of the spectrum). Common units for wavelengths of light include nanometers (1 nm = 10− 9 m) and angstroms (1 Å = 10− 10 m). frequency of a photon incident on a metal is at the threshold frequency for the metal, the electron barely escapes from the metal. However, if the frequency of an incident photon is above the threshold frequency of the metal, the photon will have more than enough energy to eject a single electron, and the excess energy will be converted to kinetic energy in the ejected electron with the maximum kinetic energy of the ejected electron able to be found by. Where W is the work function of the metal, yielding maximum kinetic energy rather than exact kinetic energy because the actual energy of an ejected electron can be from zero to the max, depending upon the subatomic interactions between the photon and metal atom. Kmax is only achieved when all possible energy from the photon is transferred to the ejected electron.) The work function is the minimum energy required to eject an electron and is related to the threshold frequency of that metal * energy of the photon is converted into ejecting the electron (the amount required by the work function will be given in the problem), and any excess energy is converted into the kinetic energy of the electron. photoelectric effect is (for all intents and purposes) an “ all-or-none” response: If the frequency of the incident photon is less than the threshold frequency (f < fT), then no electron will be ejected because the photon doesn't have sufficient energy to dislodge the electron from its atom. But if the frequency of the incident photon is greater than the threshold frequency (f > fT), then an electron will be ejected, and the maximum kinetic energy of the ejected electron will be equal to the difference between hf and hfT. Electrons liberated from the metal by the photoelectric effect will produce a net charge flow per unit time, or current. Provided that the light beam's frequency is above the threshold frequency of the metal, light beams of greater intensity produce larger current in this way. The higher the intensity of the light beam, the greater the number of photons per unit time that fall on an electrode, producing a greater number of electrons per unit time liberated from the metal. When the light's frequency is above the threshold frequency, the magnitude of the resulting current is directly proportional to the intensity of the light beam.

Answer 159

The Bohr Model of the Hydrogen Atom- Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit and that the centripetal force acting on the electron as it revolved around the nucleus was the electrical force between the positively charged proton and the negatively charged electron.

Answer 160

Energy levels- Bohr used Planck's quantum theory to make some corrections to certain assumptions that classical physics made about the pathways of electrons. Classical mechanics postulates that an object, such as an electron, revolving in a circle may assume an infinite number of values for its radius and velocity. The angular momentum (L = mvr) and kinetic energy. h Bohr placed restrictions on the value of the angular momentum of the electron revolving around the hydrogen nucleus. Analogous to the quantized energy of photons, Bohr predicated that the orbital angular momentum of an electron, is quantized according. H. where h is Planck's constant and n is the quantum number, which can be any positive integer (the numbers 1, 2, 3, 4,... but none of the decimal values in between). Because the only variable is the quantum number, n, the angular momentum of an electron changes only in discrete amounts with respect to the quantum number. The higher the principal quantum number, the more energetic the electron. RH is an experimentally determined constant known as the Rydberg constant equal to 2.18 × 10− 18 J/electron. Therefore, like angular momentum, the energy of the electron changes in discrete amounts with respect to the quantum number. Bohr had to resort to new quantum ideas, since a classical model of hydrogen would require the electron to radiate electromagnetic waves continuously, thereby losing energy and spiraling into the proton. Bohr postulated that there were specific stable, or allowed, orbits of quantized (discrete) energy in which electrons did not radiate energy. This led him to deduce the energy level formula. Bohr energy (in electron-volts) corresponding to the closest allowed orbit to the nucleus (ground state; n = 1) is − 13.6 eV. This number is just the Rydberg constant in more convenient units (eV). The energies corresponding to orbits farther away from the nucleus are less negative and therefore greater, and increase until the electron is given so much energy that it is free of the electrostatic (coulombic) pull of the nucleus and can have any positive energy. The quantum energy levels in the Bohr model of the hydrogen atom can be arranged from lowest to highest, each with an associated principle quantum number (n). The energy levels for hydrogen are given in electron-volts.

Answer 161

• state in which the proton and electron are separated completely, meaning that there is no attractive force between them, has an n value of infinity and an En value of 0. Positive energy states have no principle quantum number because the electron is not bound to the proton. Therefore, the electron in any of its quantized states in the atom will have a negative energy as a result of the attractive forces between the electron and proton; hence the negative sign in the energy equation above. The main conceptual point of the energy equation is that the energy of an electron increases the farther from the nucleus the electron is located. As the denominator (n2, in this case) increases, the fraction itself gets smaller, but the negative sign in front means that energy increases as n2 increases. (The absolute values of negative numbers get smaller as they move to the right on the number line, toward zero, so even though the absolute values of the numbers are decreasing— for example, as you move from – 8 to – 6— the value of the negative number as a whole is increasing.)

Answer 162

• Bohr model describes the structure of the hydrogen atom as a nucleus with one proton forming a dense core around which a single electron revolves in a defined pathway with a discrete energy value. Transferring an amount of energy exactly equal to the difference in energy between one pathway, or orbit, and another results in the electron “ jumping” from the one pathway to the higher-energy pathway. These pathways or orbits have increasing radii, and the orbit with the smallest radius in which hydrogen's electron can be found is called the ground state and corresponds to n = 1. When the electron is promoted to a higher-energy orbit (one with a larger radius and n = 2, 3, 4,… ), the atom is said to be in the excited state. An excited state is any orbit higher than the electron's ground state and, thus, has more energy than the ground state. With each electron traveling along a roughly circular pathway at a set distance and energy value with respect to the nucleus.

Answer 163

• Emission and absorption of light- hydrogen atoms radiate light only at particular frequencies, 1. Energy levels of the electron are stable and discrete. They correspond to specific orbits. 2. An electron emits or absorbs radiation only when making a transition from one energy level to another (from one allowed orbit to another). 3. To jump from a lower energy (inner orbit) to a higher energy (outer orbit), an electron must absorb a photon of precisely the right frequency such that the photon's energy (hf) equals the energy difference between the two orbits. 4. When jumping from a higher energy (outer orbit) to a lower energy (inner orbit), an electron emits a photon of a frequency such that the photon's energy (hf) is exactly the energy difference between the two orbits. electron in the lowest allowed energy level (the ground state; n = 1) cannot emit any more energy (although it could absorb radiation and jump to a higher energy level). An electron occupying an excited state can either emit radiation when it jumps down to a lower energy level or absorb radiation when it jumps to an even higher energy level. We can use Bohr's third and fourth postulates to find the frequency of radiation emitted or absorbed by an electron when it jumps from energy level i to energy level f. The change in the electron's energy. (The values of Ei and Ef can be determined by finding the electron's energy at energy levels i and f with the Bohr model's energy equation. Remember that these values will be always be negative.) If Δ E is negative, the electron has jumped from a higher, less negative energy state (less tightly bound state) to a lower, more negative energy state (more tightly bound state). There is therefore an emission of a photon that has a frequency related to the energy change. if Δ E is positive, then the electron has absorbed a photon and jumped from a lower, more negative energy state to a higher, less negative energy state. The absorbed photon has a frequency that is related to the electron's energy change.

Answer 164

Fluorescence- xcite a fluorescent substance, such as a ruby, an emerald, or the phosphors found in fluorescent lights, with ultraviolet radiation, it will begin to glow with visible light. Photons corresponding to ultraviolet radiation have relatively high frequencies (short wavelengths). After being excited to a higher energy state by the ultraviolet radiation, the electron in the fluorescent substance returns to its original state in two or more steps. By returning in two or more steps, each step involves less energy, so at each step, a photon is emitted with a lower frequency (longer wavelength) than the absorbed ultraviolet photon. If the wavelength of this emitted photon is within the visible range of the electromagnetic spectrum, it will be seen as light of the particular color corresponding to that wavelength. The wide range of colors in fluorescent lights, from the whitish-green of office lighting to the glaring colors of neon signs, is the result of the distinct multi-step emissions spectra of different fluorescent materials.

Answer 165

excite a fluorescent substance, such as a ruby, an emerald, or the phosphors found in fluorescent lights, with ultraviolet radiation, it will begin to glow with visible light. Photons corresponding to ultraviolet radiation have relatively high frequencies (short wavelengths). After being excited to a higher energy state by the ultraviolet radiation, the electron in the fluorescent substance returns to its original state in two or more steps. By returning in two or more steps, each step involves less energy, so at each step, a photon is emitted with a lower frequency (longer wavelength) than the absorbed ultraviolet photon. If the wavelength of this emitted photon is within the visible range of the electromagnetic spectrum, it will be seen as light of the particular color corresponding to that wavelength. The wide range of colors in fluorescent lights, from the whitish-green of office lighting to the glaring colors of neon signs, is the result of the distinct multi-step emissions spectra of different fluorescent materials.

Answer 166

Nuclei- center of an atom lies its nucleus, consisting of one or more nucleons (protons or neutrons) held together with considerably more energy than the energy needed to hold electrons in orbit around the nucleus. The radius of the nucleus is about 100,000 times smaller than the radius of the atom. The nucleus can be described by the number of protons and neutrons that it contains. Protons and neutrons have the same mass; the only difference is that protons have a positive charge while neutrons are neutral

Answer 167

``` Atomic number (Z) and mass number (A)- atomic number(Z) is always an integer and is equal to the number of protons in the nucleus. Each element has a unique number of protons; therefore, the atomic number Z identifies the element. Z is used as a presubscript to the chemical symbol in isotopic notation. The chemical symbols and the atomic numbers of all the elements are given in the periodic table. • mass number (A) is equal to the total number of nucleons (neutrons and protons) in a nucleus is represented by the letter A. If we represent the number of neutrons in a nucleus by the letter N, then the equation relating A, N, and Z is simply. ```

Answer 168

isotopic notation, A appears as a presuperscript to the chemical symbol. In other words, immediately to the left of the elemental symbol, the mass number and the atomic number can be read top to bottom, respectively. Remember it this way: From top to bottom, the mass number and the atomic number tell you everything about the nucleus from A to Z. So for an element X, the mass number and atomic number are written in isotopic notation

Answer 169

Isotope- Isotopes are different atoms of the same element, having the same atomic number (hence, occupying the same place on the periodic table of the elements), that have different numbers of neutrons and, therefore, have different mass numbers. Isotopes are referred to by the name of the element followed by the mass number (e.g., carbon-12 has 6 neutrons, carbon-13 has 7 neutrons). isotopes have the same number of protons and electrons, they generally exhibit the same chemical properties. The term radionuclide is a generic term used to refer to any radioactive isotope, especially those used in nuclear medicine.

Answer 170

Atomic mass and atomic weight- Atomic mass is most commonly measured in atomic mass units (abbreviated amu or simply u). The size of the atomic mass unit is defined 1/12, the mass of the carbon-12 atom, approximately 1.66 × 10− 24 g. Because the carbon-12 nucleus has six protons and six neutrons, an amu is really the average of the mass of a proton and a neutron. Because the difference in mass between the proton and the neutron is so small, the mass of the proton and the neutron are each about equal to 1 amu. We essentially discount the mass of carbon's six electrons because they are so tiny— the mass of an electron 1/1836 the mass of a proton. Thus, the atomic mass of any atom is simply equal to the mass number (sum of protons and neutrons) of the atom. • atomic weight. The atomic weight is the mass in grams of one mole of atoms of a given element and is expressed as a ratio of grams per mole (g/mol). A mole is simply the number of “ things” equal to Avogadro's number: 6.022 × 1023. For example, the atomic weight of carbon-12 is 12.0 g/mol, which means that 6.022 × 1023 carbon-12 atoms (1 mole of carbon-12 atoms) have a mass of 12.0 grams. It also follows that one gram is the mass of one mole of amu. Because isotopes exist, atoms of a given element can have different masses. The atomic weight reported on the periodic table refers to a weighted average of the masses of an element. The average is weighted according to the natural abundances of the various isotopic species of an element. That's why the atomic weight that you read off the periodic table may not be a whole number.

Answer 171

Nuclear Binding Energy and Mass Defect- in reality every nucleus (other than protium) has a smaller mass than the combined mass of its constituent protons and neutrons. The difference is called the mass defect. Scientists had difficulty explaining why this mass defect occurred until Einstein discovered the equivalence of matter and energy, embodied by the equation. E is energy, m is mass, and c is the speed of light.The mass defect is a result of matter that has been converted to energy. A very small amount of mass will yield a huge amount of energy. When protons and neutrons come together to form the nucleus, they are attracted to each other by the strong nuclear force, which is strong enough to more than compensate for the repulsive electromagnetic force between the protons. Although the strong nuclear force is the strongest of the four basic forces, it only acts over extremely short distances, less than a few times the diameter of a proton or neutron. The nucleons have to get very close together in order for the strong nuclear force to hold them together. The bound system is at a lower energy level than the unbound constituents, and this difference in energy must be radiated away in the form of heat, light, or other electromagnetic radiation (that is, the system has to cool down) before the mass defect becomes apparent. This energy, called binding energy, allows the nucleons to bind together in the nucleus. Given the strength of the strong nuclear force, the amount of mass that is transformed into the dissipated energy will be a measurable fraction of the initial total mass. (Note: The binding energy per nucleon peaks at iron, which implies that iron is the most stable atom. In general, intermediate-sized nuclei are more stable than large and small nuclei.)

Answer 172

Nuclear Reactions and Decay- Nuclear reactions, such as fusion, fission, and radioactive decay, involve either combining or splitting the nuclei of atoms. Because the binding energy per nucleon is greatest for intermediate-sized atoms (that is to intermediate-sized atoms are most stable), when small atoms combine or large atoms split, a great amount of energy is released.

Answer 173

Fusion occurs when small nuclei combine into a larger nucleus. As an example, many stars (including the sun) power themselves by fusing four hydrogen nuclei to make one helium nucleus. By this method, the sun produces 4 × 1026 joules every second, which accounts for the mass defect that arises from the formation of helium nuclei from hydrogen nuclei.

Answer 174

Fission is a process in which a large nucleus splits into smaller nuclei. Spontaneous fission rarely occurs. However, by the absorption of a low-energy neutron, fission can be induced in certain nuclei. Of special interest are those fission reactions that release more neutrons, because these other neutrons will cause other atoms to undergo fission. This in turn releases more neutrons, creating a chain reaction. Such induced fission reactions power commercial nuclear electric generating plants.

Answer 175

Radioactive decay is a naturally occurring spontaneous decay of certain nuclei accompanied by the emission of specific particles. 1. The integer arithmetic of particle and isotope species 2. Radioactive half-life problems 3. The use of exponential decay curves and decay constants

Answer 176

• 1. Isotope Decay Arithmetic and Nucleon Conservation. X and Y represent nuclear isotopes, parent-daughter isotope

Answer 177

a. Alpha decay is the emission of an α -particle, which is a 4He -nucleus that consists of two protons and two neutrons. The alpha -particle is very massive (compared to a beta particle) and doubly charged. Alpha particles interact with matter very easily; hence, they do not penetrate shielding (such as lead sheets) very extensively. emission of an α -particle means that the daughter's atomic number Z will be 2 less than the parent's atomic number and the daughter's mass number will be 4 less than the parent's mass number

Answer 178

• b. Beta decay is the emission of a β -particle, which is an electron given the symbol e− or β − . Electrons do not reside in the nucleus, but they are emitted by the nucleus when a neutron in the nucleus decays into a proton and a β − (and an antineutrino). Because an electron is singly charged and about 1,836 times lighter than a proton, the beta radiation from radioactive decay is more penetrating than alpha radiation. In some cases of induced decay, a positively charged antielectron known as a positron -is emitted. The positron is given the symbol e+ or β +. β − decay means that a neutron disappears and a proton takes its place. Hence, the parent's mass number is unchanged, and the parent's atomic number is increased by 1. In other words, the daughter's A is the same as the parent's, and the daughter's Z is one more than the parent's.In both types of beta decay, there needs to be conservation of charges. If a negative charge is created, a positive charge must be created as well (via neutron changed into a proton). Conversely, if a positive charge is created, a negative charge must be created as well (via proton changed into neutron). Remember negative beta decay creates a negative beta particle and positive beta decay creates a positive beta particle. In positron decay, a proton (instead of a neutron as in β − decay) splits into a positron and a neutron. Therefore, a β + decay means that the parent's mass number is unchanged and the parent's atomic number is decreased by 1. In other words, the daughter's A is the same as the parent's, and the daughter's Z is one less than the parent's.

Answer 179

c. Gamma decay is the emission of γ -particles, which are high-energy photons. They carry no charge and simply lower the energy of the emitting (parent) nucleus without changing the mass number or the atomic number. In other words, the -daughter's A is the same as the parent's, and the daughter's Z is the same as the parent's

Answer 180

d. Electron capture- Certain unstable radionuclides are capable of capturing an inner (K or L shell) electron that combines with a proton to form a neutron. The atomic number is now one less than the original, but the mass number remains the same. Electron capture is a rare process that is perhaps best thought of as an inverse β − decay.

Answer 181

2. Radioactive Decay Half-Life- In a sample of a great many identical radioactive isotopes, the half-life (T1/2) of the sample is the time it takes for half of the sample to decay.

Answer 182

* 3. Exponential Decay - Let n be the number of radioactive nuclei that have not yet decayed in a sample. It turns out that the rate at which the nuclei decay is proportional to the number that remain (n). where λ is known as the decay constant. The solution of this equation tells us how the number of radioactive nuclei changes with time. The solution is known as an exponential decay where n0 is the number of undecayed nuclei at time t = 0. The decay constant is related to the half-life. * Magnetic field workshops- a magnetic field will usually be uniform. That means that the field will, in the region in question, have constant magnitude and point in one direction. When an arrow points away from us, into the page, we see the feathers in the back; vectors pointing into the page are drawn as an X.

Answer 183

radical(3)/2

Answer 184

radical(2)/2

Answer 185

radical(2)/2

Answer 186

radical(3)/2

Answer 187

frequency of vibration of the membrane determines the frequency of pressure waves in tha air, and so the pitch, changing the density of ar will not change the frequency of vibration of an ideal membrane, speed of sound increases in lower pressure lower densities environments wavelength will increase and the frequency will remain constant with the sound intensity unchanged, as it depends on the distance form the source and amplitude not the speed or medium, amplitude not directly related to medium,

Answer 188

produce beats of higher amplitude by interference at a frequency equal to the difference between their frequencies, the greater the differences in frequencies between the two sounds, the greater the frequency of the beats produced,

Answer 189

overall, so tetrahedral

Answer 190

Force/area

Answer 191

gauge pressure( or calculated) + atmospheric pressure

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