The document discusses the law of conservation of momentum. It states that momentum cannot be created or destroyed, and the total momentum before a collision equals the total momentum after (momentum in = momentum out). It also defines elastic vs. inelastic collisions. It then works through 4 examples of collisions between objects with different masses and velocities, calculating the velocity of one object before and after collision by applying the law of conservation of momentum.

1. 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.

2. 1. They hit and all the momentum is transferred
Before Collision After Collision
mA = 4 kg mB = 2 kg mA = 4 kg mB = 2 kg
vA = 3 m/s vB = 0 m/s vA = 0 m/s vB = ? m/s
pin = pout
mAvA + mBvB = mAvA + mBvB
(4)(3) + (2)(0) = 4(0) + 2(vB)
vB = 6.00 m/s

3. 2. They hit stick together
Before Collision After Collision
4 kg 2 kg 4 kg 2 kg
3 m/s 0 m/s ? m/s ? m/s
pin = pout
mAvA + mBvB = (mA+mB)vAB
(4)(3) + (2)(0) = (4+2)vB
vAB = 2.00 m/s

4. 3. They hit and bounce away
?
Before Collision After Collision
? ?
4 kg 2 kg 4 kg 2 kg
2 m/s -3 m/s -1 m/s ? m/s
pin = pout
mAvA + mBvB = mAvA + mBvB
(4)(2) + (2)(-3) = (4)(-1) + (2)vB
vAB = 3.00 m/s

5. 3. They hit and bounce away
Before Collision After Collision
? ?
4 kg 2 kg 4 kg 2 kg
2 m/s -3 m/s -1 m/s ? m/s
pin = pout
mAvA + mBvB = mAvA + mBvB
(4)(2) + (2)(-3) = (4)(-1) + (2)vB
vAB = 3.00 m/s

6. 4. Both start with zero velocity
Before Collision After Collision
4 kg 2 kg 4 kg 2 kg
0 m/s 0 m/s ? m/s 20 m/s
pin = pout
mAvA + mBvB = mAvA + mBvB
(4)(0) + (2)(0) = (4)(vA) + (2)(20)
vA = -10.0m/s