Momentum is the product of an object's mass and velocity. It is a vector quantity meaning its direction is important. Impulse is equal to the change in momentum and is calculated by multiplying force by time. During collisions, the total momentum before the collision (momentum in) equals the total momentum after the collision (momentum out) according to the law of conservation of momentum. There are four types of collision problems involving conservation of momentum: 1) all momentum is transferred, 2) objects stick together after collision, 3) objects bounce away after collision, 4) objects start with zero velocity.

1. Momentum
Chapter 6

2. Momentum (Symbol = p) [Unit = kg m/s]
 Inertia in motion 
Momentum = Mass • Velocity
p = M • V
Newton’s 2nd Law
F = ma a= ∆v = v f − vi
t t
v f − vi
F = m( ) = mv f − mvi
t
Ft = Impulse
Impulse (Symbol = I)[Unit = Nsec]
 A force in a certain time
Concept: In order to change momentum,
we need a force in a certain amount of time!

3. I = Ft = ∆p = mv − mv f i
Changing Momentum
mV - 0 = T
F
mV - 0 = Ft
Momentum is a vector, so direction is important!
How is impulse affected when an object bounces?
Impulse is greater!
Why? Takes more to “catch” & “throw” than to just
“catch”

4. A 4.0 x 104 N rocket is at rest when it fires its thrusters.
If the thrusters put out an average force of 5.0 x 10 3 N
over 20 sec, then
(a) What is the impulse the rocket experiences?
(b) What is the rocket’s final velocity?
(a) Impulse
I=Ft
I = 5000 (20)
I = 100,000 Nsec
(b) v
I = ∆p = mvf – mvi
100,000 = 4080 V – 4080(0)
v = 24.5 m/s

5. collisions

6. Conservation of Momentum
Law of Conservation of Momentum
 Momentum cannot be created or destroyed
Momentum In = Momentum out
pin = pout
This is for
2 Types of Collisions Collisions!
Elastic  Energy is conserved
Inelastic  Energy is lost to heat, sound, etc.
Since we work in a happy, ideal world, we will deal with all elastic collisions.

7. 4 Types of Problems
1. They hit and all the momentum is transferred.
Before After
A B A B
MA = 4.0 kg MB = 2.0 kg VA = 0 VB = ?
VA = 3.0 m/s VB = 0 m/s
pin = pout
MA VA + MB VB = MA VA + MB VB
(4)(3) + 2(0) = 4(0) + 2 VB
VB = 6.00 m/s

8. 2. They hit and stick together.
Before After
4 2 4 2
4.0 m/s -2.0 m/s VAB = ?
p in = p out
mv + mv = mv + mv = (m + m)v
(4)(4) + 2(-2) = (4 + 2) VAB
VAB = 2.00 m/s

9. 3. They hit and both bounce away with a velocity
Before After
? ?
4 2 4 2
2.0 m/s -3.0 m/s -1.0 m/s VB = ?
p in = p out
mv + mv = mv + mv
(4)(2) + 2(-3) = 4(-1) + 2 VB
VB = 3.0 m/s

10. 4. They both start with zero velocity
Before After
4 2 4 2
v=0 ? m/s VB = 20
p in = p out
mv + mv = mv + mv
0 = 4(v) + 2 (20)
v = -10.0 m/s