Unit XI
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 a 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?
Examples:

An object having a mass of 10 kg has
its velocity change from 8 m/s to 3
m/s east. Find the object’s change in
momentum.

A 12kg object has a momentum of
20kg-m/s towards the east. What is
the object’s speed in m/s?

What is the momentum of a 70 kg
runner traveling at 10 m/s?

What is the momentum of a 800 kg
car traveling at 20 m/s?
Example:

What is the change in momentum of a
950 kg car that travels from 40 m/s
to 31 m/s?
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
Minimize the Force
Increase
Dt
 Catching
a ball
 Bungee jumping
Dt
F
Example:

How much impulse is applied by a 25 N
force in 30 seconds?

What will be the change in velocity of
a 850 kg car if a force of 50,000 N is
applied to it for 0.5 seconds?

A 50,000 kg train is rolling on its own
down the track at 5 m/s. You grab the
rope trailing behind it, and exert a
stopping force of 2000 N. How long
does it take to stop the train?
Impulse-Momentum Theorem

What average braking force is
necessary to stop a 1000-kg motorbike
traveling with an initial velocity of
10m/s for 20 seconds?

How long would it take for a net
upward force of 125 N to increase the
speed of a 65kg object from 75m/s to
80m/s?
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  m2u 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
On to problems...