1. Collisions
To analyze collisions we will consider the conservation of momentum

2. Momentum During Collisions
When the bumper cars collide,
F1 = -F2 so F1t = -F2t, and therefore p1 = -p2 .
The change in momentum for one object is equal and opposite to the change in momentum for the other object.
Total momentum is neither gained nor lost during collisions.
Newton’s 3rd Law and 2nd Law lead to the idea of momentum being conserved in collisions.
The 3rd Law is used in the first step (F1 = -F2).
The 2nd Law is used in the last step (F=p/t or Ft = p).

3. Practice Problem
A 62.0 kg astronaut on a spacewalk tosses a kg baseball at 26.0 m/s out into space. With what speed does the astronaut recoil?
Answer: m/s or cm/s
Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.
Show students that, when the initial momentum = 0, the equation for conservation of momentum simplifies to pf,a= -pf,b.
Note that the recoil speed is quite small, because the mass of the astronaut is much greater than that of the baseball. However, a speed of roughly 6 cm/s is measurable. Ask students what the recoil speed would be if he threw another 62.0 kg astronaut.
Students may have trouble with the idea of recoiling when you throw something because they have not experienced it. You could ask them what happens if they are standing on skates or a skateboard and thrown something forward.
For the pitcher, several factors come into play. First of all, he is moving forward (not at rest) as he throws the ball so the recoil would simply slow him down. Secondly, his feet are pushing against Earth so the force would be transferredto Earth, and the entire Earth would recoil (very slowly).
If the pitcher were on ice skates (frictionless surface) and at rest when throwing, he would recoil backward just as the astronaut does.
Other examples of recoil include firing a rifle and shooting a cannon. Ask students how the old pirate ships dealth with the recoil of the cannon, which was pretty significant. They may recall that the cannons were mounted in such a way that they could slide or roll back after firing. They were not permanently fixed to the boat or the entire boat would have recoiled slightly. More likely, it would have damaged the boat where it was attached.

4. Conservation of Momentum
Total momentum remains constant during collisions
The momentum lost by one object equals the momentum gained by the other object
Conservation of momentum simplifies problem solving.
Using conservation of momentum makes it possible to determine the effect of a force without knowing how much force was involved. Also, the force need not be constant.

5. Perfectly Inelastic Collisions
Two objects collide and stick together.
Two football players
A meteorite striking the earth
Momentum is conserved.
Masses combine.
Ask students to suggest additional examples of perfectly inelastic collisions.

6. An 2. 0 x 105 kg train car moving east at 21 m/s collides with a 4
An 2.0 x 105 kg train car moving east at 21 m/s collides with a 4.0 x 105 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision.
Answer: 7.0 m/s to the east
Practice Problems
Momentum is conserved, and that is the basis for the first problem. (2.0 x 105 kg)(21 m/s) = (6.0 x 105 kg) (v)
Students should find that KE is not conserved. In fact, it is reduced significantly.

7. Practice Problem
Zach is a quarterback and Jake is a defensive lineman. Zach’s mass is 75.0 kg and he is at rest. Jake has a mass of 112 kg, and he is moving at 8.25 m/s when he tackles Zach by holding on while they fly through the air. With what speed will the two players move together after the collision?
Answer: 4.94 m/s

8. Perfectly Elastic Collision
Two objects collide and bounce off each other.
Newton’s Cradle
Billiard Balls
Kicking a Soccer ball
Momentum is conserved.
Masses remain separate.

9. Practice Problem
A 15.0 g marble moving to the right at m/s makes an elastic head-on collision with a 30.0 g shooter marble moving to the left at m/s. After the collision, the smaller marble moves t the left at m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface. What is the velocity of the 30.0 g marble after the collision?
m/s to the right