1. Conservation of Momentum
Physics 11

2. First a quick reminder…
What is momentum?
The product of mass and velocity.
What is the formula for momentum?
p = mv (don’t use P!!! Power!)
What are the units for momentum?
kg m/s

3. First let’s look back… What is impulse?
Impulse is the product of force and the time interval during which that force acts.
What is the formula for momentum?
j = Ft (don’t use J!!! Joules)
What are the units for momentum? Ns

4. First let’s look back… How are impulse and momentum related?
Impulse is like momentum except we use it for sudden changes in momentum, like for collisions, explosions, etc.
Impulse is the change in momentum (not just the momentum)

5. Law of Conservation of Momentum
Within a closed, isolated system, the net change in momentum is zero.
The final momentum of the system equals the initial momentum of the system:
pA + pB = p’A + p’B
p = p’
This means that if two objects collide, the total momentum before the collision of the 2 objects is the same as the total momentum after the collision.

6. Example
Two freight cars each have a mass of 3.0 x 105 kg. Car B is moving at +2.2 m/s and car A is at rest.
When the two cars collide, they act as one (“couple”) and move away together. Find the final velocities of A and B.

7. Answer pA + pB = p’A + p’B mAvA + mBvB = m’Av’A + m’Bv’B
(300000)(0) + (300000)(2.2) = (300000)(v’A) + (300000)(v’A)
66000 = (v’A)
v’A= +1.1 m/s
They both travel at 1.1 m/s in the same direction as car B.

8. Example 2
You are playing pool with a friend. The 0.17 kg cue ball hits a stationary numbered ball (mass 0.15kg) with a velocity of 3.2 m/s. Assuming the cue ball stops once it hits the numbered ball and the other ball moves in the direction of the hit, what is the velocity of the numbered ball?

9. Answer pA + pB = p’A + p’B mAvA + mBvB = m’Av’A + m’Bv’B
v’B= +3.6 m/s
The numbered ball moves at a velocity of 3.6m/s. This makes sense as it has less mass so the same momentum will make it move faster.

10. Recoil
Recoil is the interaction that occurs when two stationary objects push against each other and then move apart.
This means there is no initial momentum and therefore no final momentum… HOW IS THIS POSSIBLE???
Examples: Guns cause recoil

11. Example 3 - Recoil
A Winchester .308 cartridge launches a bullet of mass 64.8 mg. The rifle has a mass of 3.8kg. What is the final velocity of the cartridge assuming the velocity of the gun’s recoil is -2.2m/s?

12. Answer pA + pB = p’A + p’B mAvA + mBvB = m’Av’A + m’Bv’B
v’A= m/s = +1.3 x 105 m/s
The bullet moves at a velocity of +1.3 x 105 m/s. This makes sense as it has less mass so the same momentum will make it move faster.

13. Practice
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