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Chapter 8
Impulse and Momentum
Momentum and Collisions

This chapter is concerned with
inertia and motion. Momentum helps
us understand collisions.

Elastic Collisions - objects rebound

Inelastic Collisions - object stick
together an usually become
distorted and generate heat
Momentum



Momentum = mass  velocity
p = mv
Momentum is a vector quantity.
Large Momentum Examples

Huge ship moving at a small velocity
P = Mv

High velocity bullet
P = mv
Momentum Examples

A large truck has more momentum
than a car moving at the same speed
because it has a greater mass.

Which is more difficult to slow
down? The car or the large truck?
Impulse

Newton’s Second Law can read
SF = ma
= m(Dv/Dt)
= (Dmv)/(Dt)
= (Dp/ Dt)
Rearranging,
Impulse = Dp = FDt
When Force is Limited

Apply a force for a long
time.

Examples:
Follow through on a golf swing.
 Pushing a car.

F
Dt
Make it Bounce
Dp = p2 - p1 = -p1 - p1
= -2p1
p1
p2 = -p1
Minimize the Force
Increase
Dt
 Catching
a ball
 Bungee jumping
Dt
F
Maximize Momentum Change
Apply a force for a short time.

Examples:


Boxing
Karate
F
Dt
Conservation of Momentum
This means that the momentum
doesn’t change.
 Recall that SF t = D(mv), so SF = 0
 In this equation, F is the "external
force."
 Internal forces cannot cause a
change in momentum.

Examples
Example 1: a bullet fired from a
rifle
 Example 2: a rocket in space

Collisions
Before

u1
m1

u2
m2

v1
After
m1

v2
m2




m1u1  m2 u 2  m1v1  m2 v2
v = 10
v=0
M
M
Before Collision
p = Mv
v’ = 5
M
M
Mv = 2Mv’
v’ = ½ v
After Collision
p = 2Mv’
Conserve Energy and Momentum
Before Collision
Case 1:
Equal masses
Case 2:
M>M
Case 3:
M<M
Coefficient of Restitution
v 2  v1
e
u 2  u1
For perfectly elastic collisions e = 1.
 If the two object stick together, e = 0.
 Otherwise 0 < e < 1.

Center of Mass
x cm
 x i mi

 mi
On to problems...