Physics chapter 1-3

Question 1

What are the four basic types of motion?

Answer 1

linear, circular, projectile, and rotational.

Question 2

What is similar between linear, circular, and projectile motion?

Answer 2

the object moving through space is called translational motion and follows a trajectory.

Question 3

What makes rotational motion different?

Answer 3

movement, but object doesnt change position.

Question 4

What does a swinging pendulum, a vibrating guitar string, a sound wave, and jiggling atoms in a crystal have in common?

Answer 4

each is an example of a system moving back and forth around an equilibrium position.

Question 5

define modeling

Answer 5

stripping away the details to focu on essential features

Question 6

define a model

Answer 6

highly simplified picture of reality, one that still captures the essence of what needs to be studied.

Question 7

what are the two types of models?

Answer 7

descriptive - essential characteristics
explanatory - have predictive powers, test using experimental data

Question 8

define a particle model

Answer 8

an object that can be represented as mass at a single point in space.
has no size, no shape, no distinction b/w top and bottom or b/w front and back.

Question 9

What an example of something that cannot be modeled using the particle?

Answer 9

a rotating gear

Question 10

What are needed to make a motion diagram?

Answer 10

objects position (where) and time (when).

Question 11

How can you gather position measurements?

Answer 11

laying a coordinate-system grid over the motion diagram, then measure (x,y) coordinates.

Question 12

what does “t=0” mean?

Answer 12

the origin

Question 13

Why is negative time allowed?

Answer 13

they locate an event in space or time relative to an origin - they could represent earlier instances.

Question 14

What is a position vector?

Answer 14

another way to locate a point, an arrow from the origin to the point given by –>r

Question 15

define scalar

Answer 15

a single number with a unit that describes a physical qaunity it can be pos, neg, or zero.
r or A

Question 16

define a vector

Answer 16

a qaunity having both size and direction.
has arrow on top

Question 17

what is the size and length of a vector called?

Answer 17

magnitude

Question 18

how to illistrate displacement?

Answer 18

draw a vector from two points given by The Greek letter delta r (with an arrow)

Question 19

how to illistrate vector sums

Answer 19

draw an arrow to one from the origin, draw an arrow to the other, connect into a triangle

Question 20

How to draw a motion diagram

Answer 20

When an object either starts from rest or ends at rest, the initial or final dots are as close together as you can draw the displacement vector arrow connecting them. In addition, just to be clear, you should write “Start” or “Stop” beside the initial or final dot. It is important to distinguish stopping from merely slowing down.

Question 21

define average speed

Answer 21

the ratio of distance traveled/time interval spent traveled
ex./ speed

Question 22

Why is displacement important?

Answer 22

a vector that tells us not only the distance traveled by a moving object, but also the direction of motion

Question 23

define avg velocity

Answer 23

delta r arrow/delta t
. The average velocity of an object during the time interval , in which the object undergoes a displacement , is the vector (v arrow)
An object’s average velocity vector points in the same direction as the displacement vector . This is the direction of motion.

Question 24

What is the direction of motion?

Answer 24

direction of avg velocity and displacement

Question 25

What is the important difference between speed and velocity in physics?

Answer 25

In particular, speed is simply “How fast?” whereas velocity is “How fast, and in which direction?”

Question 26

the velocity vector...

Answer 26

points in the same direction as the displacement , and the length of is directly proportional to the length of displacement .

Question 27

what does the length of a velocity vector represent?

Answer 27

The length of a velocity vector represents the average speed with which the object moves between the two points. Longer velocity vectors indicate faster motion.

Question 28

what are two factors that could change velocity?

Answer 28

The magnitude can change, indicating a change in speed; or The direction can change, indicating that the object has changed direction.

Question 29

define avg acceleration

Answer 29

(delta a arrow) = delta v arrow / delta t points in the same direction as delta v arrow Notice that the acceleration vector goes beside the middle dot, not beside the velocity vectors. This is because each acceleration vector is determined by the difference between the two velocity vectors on either side of a dot each acceleration vector is determined by the difference between the two velocity vectors on either side of a dot. The length of arrow a does not have to be the exact length of arrow v it is the direction of arrow a that is most important.

Question 30

3 main ways to describe an objects motion

Answer 30

position, velocity, and acceleration (all vectors)

Question 31

what is uniform motion?

Answer 31

motion with constant velocity displacements are exactly the same position-versus-time graph is a straight line.

Question 32

Position is graphed...

Answer 32

on vertical axis

Question 33

what does the average velocity represent?

Answer 33

the slope of the position-versus-time-graph

Question 34

What are units for velocity?

Answer 34

length per time and miles per hour.

Question 35

define an objects speed

Answer 35

how fast its going, independent of the direction, aka the magnitude || or abs value of the objects velocity.

Question 36

Bob leaves home in Chicago at 9:00 a.m. and drives east at 60 mph. Susan, 400 miles to the east in Pittsburgh, leaves at the same time and travels west at 40 mph. Where will they meet for lunch?

Answer 36

1. solve for t1 = 400mi/60mph-(-40)mph = 4.0 hours 2. 60 mph x 4 hours = 240 miles 3. They meet 240 miles east of Chicago

Question 37

define instantaneous velocity

Answer 37

speed and direction—as its velocity at a single instant of time. limit delta t --> 0 aka the derivative ds/dt

Question 38

steeper slope

Answer 38

...larger magnitude of velocity

Question 39

A particle’s position is given by the function x(t) = -t^3+3t m, where t is in s. (a)What are the particle’s position and velocity at t=2 s?

Answer 39

(a) -2^3 +(3)(2) = -8 + 6 = -2m velocity = -3t^2 +3 m/s at 2 s = -9

Question 40

What is delta s?

Answer 40

the objects displacement/position where (Greek sigma) is the symbol for summation. delta s = lim delta t->0 sigma (vs) k delta (t) = area of small rectangle - The limit of this sum as delta t -> 0 is the total area enclosed between the t-axis and the velocity curve. This is called the “area under the curve.” (review 2.3!!!)

Question 41

A bicyclist has a velocity of 6 m/s and a constant acceleration of 2 . What is her velocity 1 s later? 2 s later?

Answer 41

An acceleration of 2 means that the velocity increases by 2 m/s every 1 s. If the bicyclist’s initial velocity is 6 , then 1 s later her velocity will be 8 . After 2 s, which is 1 additional second later, it will increase by another 2 to 10 . After 3 s it will be 12 . Here a positive is causing the bicyclist to speed up.

Question 42

A bicyclist has a velocity of and a constant acceleration of 2 . What is his velocity 1 s later? 2 s later?

Answer 42

If the bicyclist’s initial velocity is a negative -6m/s but the acceleration is a positive 2 m/s, then 1 s later his velocity will be -4 m/s . After 2 s it will be -2 m/s, and so on. In this case, a positive ax is causing the object to slow down (decreasing speed ). This agrees with the rule from Tactics Box 1.3: An object is slowing down if and only if and have opposite signs.

Question 43

A rocket sled’s engines fire for 5.0 s, boosting the sled to a speed of 250 m/s. The sled then deploys a braking parachute, slowing by 3.0 m/s per second until it stops. What is the total distance traveled?

Answer 43

1. solve for boost-phase acceleration a0 = 250 m/s/5.0 s = 50 m/s^2 2. how far the sled travels while rocket is firing 1/2(50 m/s)(5.0s)^2 = 625 m 3. solve for displacement including breaking 625 m + (0-250 m/s)^2/(2(-3.0 m/s^2) = 11,000 m

Question 44

Fred is driving his Volkswagen Beetle at a steady 20 m/s when he passes Betty sitting at rest in her Porsche. Betty instantly begins accelerating at 5.0 m/s^2. How far does Betty have to drive to overtake Fred?

Question 45

define free fall

Answer 45

the motion of an object moving unswe the influence of gravity - only occurs in a vacuum

Question 46

What is explained by galileo's model for motion in abstance of air resistance?

Answer 46

any two objects in free fall, regardless of their mass, habe the same acceleration

Question 47

Is the value for acceleration the same for all free fall?

Answer 47

No, Careful measurements show that the value of varies ever so slightly at different places on the earth, due to the slightly nonspherical shape of the earth and to the fact that the earth is rotating.

Question 48

define the free-fall acceleration

Answer 48

the length, or magnitude, of the aceleration vector and is represented by the symbol g (also known as the acceleration due to gravity)

Question 49

can g be negative?

Answer 49

g is always positive - simply magnitude

Question 50

global average g (free-fall acceleration)

Answer 50

9.80 m/s^2

Question 51

is free fall restricted to objects that are falling?

Answer 51

Despite the name, free fall is not restricted to objects that are literally falling. Any object moving under the influence of gravity only, and no other forces, is in free fall. This includes objects falling straight down, objects that have been tossed or shot straight up, and projectile motion.

Question 52

A rock is dropped from the top of a 20-m-tall building. What is its impact velocity?

Answer 52

Although the rock falls 20 m, it is important to notice that the displacement is -20 m (y1-y0) - then use kinematic eqaution to find the time sqrt(-2gdeltay) - determine if neg or pos > The velocity vector points down, so the sign of is negative (-20 m/s -> 40 mph)

Question 53

how many mph are in 1 m/s?

Answer 53

~2

Question 54

A springbok goes into a crouch to perform a pronk. It then extends its legs forcefully, accelerating at for 0.70 m as its legs straighten. Legs fully extended, it leaves the ground and rises into the air. How high does it go?

Answer 54

1. For the first part of the motion, pushing off, we know a displacement but not a time interval: v1y^2 = v0y^2 +2aoydeltay = 2(35 m/s^2)(.70 m) = 49 m^2/s^2 - take the sqaure root sqrt(49 m^2/s^2 = 7 m/s = velocity 2. make use of velocity-displacement eqaution v2y^2 = 0 = v1y^2 +2a1ydeltay = v1y^2 - 2g(y2-y1) where y2 = v1y^2/2g = (7.0 m/s)^2/2(9.80 m/s^2) = 2.5 m ~ 8 ft

Question 55

How do we put “How high?” into symbols?

Answer 55

The clue is that the very top point of the trajectory is a turning point, and we’ve seen that the instantaneous velocity at a turning point is v2y =0.

Question 56

how to represent the one-dimensional acceleration?

Answer 56

aS = + or - gsintheta

Question 57

Finally, we can determine that the cart’s acceleration

Answer 57

ax = m/2

Question 58

define the instantaneous acceleration (as)

Answer 58

the slope of the line that is tangent to the velocity-versus-time curve at time t. as = dvs/dt

Question 59

finding velocity

Answer 59

vfs = vis + integral (ti,tf) as dt

Question 60

particle with an initial velocity of 10 m/s. What is the particle’s velocity at t = 8s?

Answer 60

vs (8) = 10 m/s + 4m/s^2 (4s) +1/2(4 m/s^2)(4s) = 34 m/s

Question 61

With v(max) = 15 m/s and T= 8 s realistic values for city driving, we find

Answer 61

amax = 2vmax/T = 2(15 m/s)/8 s = 3.75 m/s^2 xT = 1/3amaxT^2 = 1/3(3.75 m/s^2)(8.0s)^2 = 80 m

Question 62

what is a vector?

Answer 62

a qaunirt with both a size (magnitude) and a direction. - include position, displacement, velocity, acceleration, force, and momentum.

Question 63

How are vectors added?

Answer 63

tip to tail - order of addition does not matter

Question 64

how to subtract vectors

Answer 64

turn subtraction into addition by writting A - B = A + (-B) - (-B) is the same length as B, but in the opposite direction

Question 65

what is a unit vector?

Answer 65

magnitude 1 no units simply points

Question 66

what are components of vectors?

Answer 66

pieces of vectors parallel to the coordinate axes - in the direction of unit vectors. We write: E = Exi + Eyj (components simplify vector math) - used

Question 67

define scalar

Answer 67

described by a single number such as mass, temperature, volume, and energy m for mass, T for temperature, V for volume, E for energy

Question 68

define magnitude

Answer 68

term for the length or size of vector - use absolute value sign (||) magnitude of velocity is |v| = 5 m/s which is speed. - is scalar, cannot be negative or zero

Question 69

displacement vectors...

Answer 69

are straight lines, remain the same no matter the page placement

Question 70

define the resultant vector

Answer 70

C = A + B where a + b are two different displacement vectors from start to end also known as net displacement - you can add vectors in any order - the length of C can be given using the Pythagorean thereom: C = sqrt(A^2+B^2)

Question 71

how do you find the angle used to describe the direction of C (resultant vector)?

Answer 71

theta = arctan(B/A) = degrees

Question 72

A bird flies 100 m due east from a tree, then 50 m northwest (that is, 45 degrees north of west). What is the bird’s net displacement?

Answer 72

C^2 = A^2 + B^2 - 2ABcos(45) C^2 = (100 m)^2 + (50m)^2 - 2(100m)(50m)cos(45) = 5430 m^2 C = sqrt(5430 m^2) = 74m theta = arccos[A^2+C^2-B^2/2AC] = 29 degrees C = (74 m, 29)

Question 73

Carolyn drives her car north at 30 km/h for 1 hour, east at 60km/h for 2 hours, then north at 50 km/h for 1 hour. What is Carolyn’s net displacement?

Answer 73

r1 = (1hr)(30km/h, north) = (30km, north) r2 = (2hr)(60 km/h) = (120 km, east) r3 = (1hr)(50km/h, north) = (50 km, north) rnet = r1+r2+r3 rnet = sqrt((120km)^2 +(80km)^2) = 144km theta = arctan(80km/120km) = 34 degrees rnet = (144km, 34 degrees north of east)

Question 74

define a coordinate system

Answer 74

A coordinate system is an artificially imposed grid that you place on a problem in order to make quantitative measurements. You are free to choose: Where to place the origin, and How to orient the axes.

Question 75

define component vectors

Answer 75

define two new vectors parallel to the axes that we call the component vectors A = Ax + Ay (decomposition)

Question 76

Seen from above, a hummingbird’s acceleration is ( 60 m/s^2, 30 degrees south of west). Find the x- and y-components of the acceleration vector .

Answer 76

ax = -acos(30) = -(6 m/s^2)cos(30) = -5.2 m/s^2 ay = -asin(30) = -(6 m/s^2)sin(30) = -3 m/s^2 The units of ax and ay are the same as the units of vector a. Notice that we had to insert the minus signs manually by observing that the vector points left and down.