AP Concepts and Problems

Question 1

Relationships between motion variables (with calculus)

Answer 1

v = dx/dt ; a = dv/dt ; x = ∫vdt ; v = ∫adt

Question 2

Rules for drag force

Answer 2

• Drag force is proportional to just the velocity of the object. Because of it, we can simplify it (though not entirely true) to: F(drag) = kv where k is a constant.
• Drag force is parallel and in the same direction as the relative wind (typically opposite to the opposite direction of the object)
• In reality, drag force is more complex and its formula is given by: F(drag) = (1/2)pCA where p is momentum, C is the drag coefficient, and A is the cross-sectional area.

Question 3

PROBLEM: If you know velocity according to one person what is the velocity according to another person?

Answer 3

V(ac) = V(ab) + V(bc)

Question 4

Equations for object with constant acceleration

Answer 4

Vf^2-Vi^2=2a(xf-xi)
Vf=Vi+a(tf-ti)
(Vf-Vi)/(tf-ti)=a
Xf=xi+vi(tf-ti)+1/2(a(tf-ti)^2)
Change in x=(vf+vi)/2(tf-ti)
(when in more than one dimension, create another exact formula for y direction variables)

Question 5

PROBLEM: Find the final velocity of objects after a totally inelastic collision.

Answer 5

p=mv
p total=m1v1+ m2v2 + …
vf=ptotal/(m1+m2+…)

Question 6

Equations for a projectile

Answer 6

x(t) = xo + vxot
y(t) = yo + vyot + 1/2gt˄2

Question 7

Law of static friction

Answer 7

Static friction opposes the direction of potential sliding. It will keep increasing until its maximum and then become kinetic friction.
(uk)(fN)≤Ffs

Question 8

PROBLEM: A pulley holding up a block with multiple strands of rope

Answer 8

1. Add up all the tensions
2. T = (mg)/2 (If accelerations is 0)
3. Fpull = (mg)/2 (If accelerations is 0)

Question 9

PROBLEM: Find the terminal velocity of an object

Answer 9

Fnet = ma = m(dv/dt)
Fnet = dv/dt = a = 0

Question 10

Relationship between average motion variables (displacement, average velocity, average acceleration)

Answer 10

x(t)=displacememt
v(t)=veolcity
a(t)=acceleration

x’(t)=v(t)
v’(t)=a(t)
x’‘(t)=a(t)

Question 11

Conservation of momentum

Answer 11

Momentum is maintained when there are no external forces.

Elastic collision
m1v1 Initial +m2v2Initial = m1v1 Final+m2v2 Final

Inelastic collision
m1v1 Initial +m2v2Initial = VFinal(m1+m2)

Question 12

PROBLEM: Draw the forces on an object on a ramp and break the forces into components

Question 13

Newton’s 1st law

Answer 13

The default state of objects is constant speed straight line motion.

Question 14

Newton’s 2nd Law for systems

Answer 14

Equation: Fnet(external)= m(total)*a(com)

Question 15

Newton’s 3rd Law

Answer 15

If object A exerts a force on object B, then object B exerts a force on object A with the same magnitude but opposite direction.

Question 17

Relationship between momentum and impulse

Answer 17

△P = J
Change in momentum is equal to impulse.

Question 18

PROBLEM: One block sliding on top of another block with friction

Answer 18

• F(friction) = μ⋅F(normal)
• F(parallel) = mgsin(θ)
• F(perpendicular) = mgcos(θ)
• F(net) = ma
• Use kinematic equations to find whatever you need using a found.

Question 19

PROBLEM: Calculate average force given initial and final velocity of some object

Answer 19

• F(avg) = Δt/Δp
• Δp = m⋅v(final)−m⋅v(initial)
• F(net) = ma

Question 20

PROBLEM: Find the max height a projectile reaches based on its speed

Answer 20

• Y(max) = V(initial)^2*Sin

Question 21

PROBLEM: Find what angle you should launch a projectile at to reach a certain max-height

Answer 21

y = max-height
vᵢ = initial velocity
g = 10 m/s
— — — — — — — — — — — —
0 m/s = (sin(θ)vᵢ)² - 2(10 m/s)y
(sin(θ) * vᵢ)² = 210 m/sy
sin(θ) * vᵢ = √(210 m/sy)
sin(θ) = √(210 m/sy) / vᵢ
arcsin(√(210 m/sy) / vᵢ) = θ

Question 22

PROBLEM: Write the differential equation for an object that feels air resistance

Answer 22

Without gravity:
m * a = Fnet
Fair = bv
mdvdt=-bv

With gravity:
-Fair + mg = m * a
-Fair+mgm = a
dvdt= -Fairm + g
dvdt= -bvm + g