AP Concepts and Problems Flashcards

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1
Q

Relationships between motion variables (with calculus)

A

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

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2
Q

Rules for drag force

A
  • 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.
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3
Q

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

A

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

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4
Q

Equations for object with constant acceleration

A

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)

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5
Q

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

A

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

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6
Q

Equations for a projectile

A

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

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7
Q

Law of static friction

A

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

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8
Q

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

A
  1. Add up all the tensions
  2. T = (mg)/2 (If accelerations is 0)
  3. Fpull = (mg)/2 (If accelerations is 0)
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9
Q

PROBLEM: Find the terminal velocity of an object

A

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

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10
Q

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

A

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

x’(t)=v(t)
v’(t)=a(t)
x’‘(t)=a(t)

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11
Q

Conservation of momentum

A

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)

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12
Q

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

A
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13
Q

Newton’s 1st law

A

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

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14
Q

Newton’s 2nd Law for systems

A

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

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15
Q

Newton’s 3rd Law

A

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.

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16
Q
A
17
Q

Relationship between momentum and impulse

A

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

18
Q

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

A
  • 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.
19
Q

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

A
  • F(avg) = Δt/Δp
  • Δp = m⋅v(final)−m⋅v(initial)
  • F(net) = ma
20
Q

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

A
  • Y(max) = V(initial)^2*Sin
21
Q

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

A

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

22
Q

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

A

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

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

23
Q
A