Newton’s Second Law
- States that acceleration is directly proportional to Fnet and inversely proportional to mass (a = Fnet/m)
- Heavier objects will need more force (little masses will accelerate more when the same amt of force is applied)
For small mass m…
mg - T = ma
For big mass M…
T = Ma
mg - T + T = ma + Ma
mg = a(m + M)
mg/(m + M) = a
NOTE:
- Both masses have a common acceleration of a.
Newton’s Third Law
- States that when two bodies (a and b) interact, the force that a exerts on b is equal and opposite to the force that b exerts on a (Fab = -Fba)
- Action-reaction pairs always act on different objects (so normal reaction force and weight aren’t one [reaction force that comes from Newton’s Third Law is only a
Friction (Solid)
*Friction that involves only solid objects
The force exerted by a surface on an object as the object moves or makes effort to move; it always opposes motion, and there are two types (static and dynamic friction).
Static Friction (Fs)
- Static as in stationary
- Friction experienced by an object as it makes effort to move
- Always equal to the applied force as long as no movt is involved (arrows equal and opposite [?])—one will increase as the other increases (as long as there’s no movt)—the heavier the object, the more force needed
- Directly proportional to the applied force
Dynamic Friction (Fd)
- Dynamic as in changing (movt involved)
- Friction experienced by an object as it moves
- Less than Fs (max) as soon as object starts to move
- Only sets in when object starts moving
- Constant (no matter the acceleration)
NOTE:
- For an object to experience dynamic friction, its static friction would have reached a max
- Friction is directly proportional to normal reaction force (R)
- Ff = μR, where mu is the coefficient of friction (every material has its own)
- Fsmax ≤ μsR
- Fd = μdR
- W = R when moving horizontally or at rest
*See notes for graph
Momentum (p)
*Linear
- Simply, mass in motion (every moving mass has momentum [p = mv])
- Defined as the product of mass and velocity
- Since mass is constant, if velocity changes then Δp = mΔv (p is directly proportional to v)
- Unit: kgms^(-1)
- Vector (dependent on velocity): has same direction as velocity (changes once the direction of velocity changes)
Relationship between momentum and Newton’s Second Law
Fnet = ma
Fnet = mΔv/t
Fnet = Δp/t
This is another statement of Newton’s Second Law: the net force is directly proportional to the rate of change of momentum.
Impulse (I)
Fnet = mΔv/t
Fnet(t) = mΔv
I = Fnet(t) or I = mΔv
- Unit: kgms^(-1) or Ns
- Area of a force-time graph represents impulse (area below)
- To get same mΔv, force is reduced when impact time is increased (impact time changes force: less time for impact to take place means that the force felt is big [ex. airbag, trampoline—takes a longer time to settle and force felt is smaller])
Law of Conservation of Momentum
- States that when two or more bodies interact, the total momentum of the system stays constant, provided there’s no external force (*)
- For a and b, MaVa(i) + MbVb(i) = MaVa(f) + MbVb(f) (initial and final momentums…)
Relationship between Newton’s laws and momentum conservation
Fa = -Fb (3rd Law)
F = mΔv/t (2nd Law)
…
*See notebook for full (same formula results)
Elastic collisions
- Involved two objects going separate ways after collision
- Momentum conserved (b/c it’s a law [always true])
- KE conserved (still moving their separate ways), and if asked to show, just use KE instead of momentum in formula (we use the same Conservation of Momentum formula)
Inelastic collisions
- Involves the objects sticking together after collision
- Momentum conserved
- KE not conserved (some level of movt is already stopped)
- MaVa(i) + MbVb(i) = (Ma + Mb)Vf (only one final velocity)
Work (W)
- The product of force and displacement in the direction of the force (W = Fd)
NOTE:
- No displacement, no work done (everything w/ work depends on displacement)
- If force is at an angle to the displacement, W = Fdcosθ (see notes for diagram [we were finding the horizontal component])
- Unit: Joules or Nm or kgm^(2)s^(-2)
- Scalar (vector x vector = scalar [two vectors cancel out to be scalar]): interchanged with energy (all forms of which are scalar)
- Can be positive or negative (focusing on displacement only [why we have negative work], but when we look at it fully, two vectors, so cancel out)
- If the applied force leads to displacement in same direction as the force, +; if leads to displacement in opposite direction (of applied force), -
- Area of (below) force-displacement graph represents work done by an object
Other equations (when +/- work [?]):
- W = mgh (when something is lifted vertically)
- W = 1/2[kx^(2)] (when extending/compressing a string)
Energy (E)
- Ability to do work (forms: KE, PE, thermal, nuclear, chemical, solar, etc.)
- Interchanged w/ work (solve for energy, find work done)
- Units: Joules
- Scalar
Law of Conservation of Energy
States that energy can neither be created nor destroyed, but transferred from one form to another (or the total energy in the universe is constant).
Kinetic energy (KE)
- Energy due to motion of an object (KE = 1/2[mv^(2)])
- Directly proportional to velocity (whatever happens to velocity happens to KE)
- Unit: Joules
Gravitational potential energy (gPE)
- Due to the position or height of an object
- gPE = mgh
- Directly proportional to height
- Unit: Joules
Elastic potential energy (EPE)
- Stored in springs
- EPE = 1/2[kx^(2)]
- Directly proportional to extension/displacement
- Unit: Joules
Power (P)
- Rate at which work is done (or the rate at which energy is transferred)
- P = Work/time or P = ΔEnergy/time
- Unit: Js^(-1) or Watt (1 Watt = 1 Js^(-1))
P = W/t
P = Fd/t
P = Fv
NOTE
- Hooke’s Law+?
- No friction = c?
- When looking at the relationship between two variables (out of three), third must be constant
*See problems (notes) - Don’t consider names of forces (?)
- W also acting on the ground b/c you’re touching the ground (acting upwards on the ground would be the other part of the pair?)
- Normal force cannot act on the ground
- Min means subtraction, max means addition (answer can only be between the two)
- Drag in liquids, air resistance in air (gases?)
- Pushing becomes easier (involves molecules at point of contact)
- If initial, final speeds equal, change in v is the same (accel is same)
- Normal static friction before you start increasing the incline
- Circular more complex
- Opposite directions, so m(u + v)
- Rate of = per unit time
- Force directly proportional to time w/ impulse (??)
- *Efficiency…
- Law of Conservation of Energy?
- Constant force = constant accel
- Changing direction means acceleration not constant
- Slope or area
- KE 0 at peak (falling, increases [velocity increases])
- All abt vertical
- Two types of PE
- Ask yourself what can change
- Spring constant varies
