Collisions &

Conservation of Momentum

There are 2 types of collisions that can occur :

Elastic Collisions Inelastic CollisionsWhen two object collide with each other and bounce apart without sticking to each other.

When two objects collide with each otherAnd stick or stay together after the collision.

Think about a baseball colliding with a catcher’s mitt. After the collision the ball and mitt are still in contact with each other. This is an inelastic collision.

Think about two or more pool balls striking each other. After the collision, the balls are separate from each other just as they were before the collision. This is an elastic collision.

Most collisions in life are a combination of both Elastic and Inelastic collisions.

Try to put these collisions in one of the following categories:ElasticInelasticMixture of both Elastic AND Inelastic

1. A soccer player’s foot colliding with a soccer ball. 2. Two cars colliding head-on at high speed.3. A bowling ball striking the pins.4. A ball of clay thrown against a concrete wall.5. A skydiver WITHOUT a parachute colliding with the ground below.6. A snowball thrown at a stop sign.7. A rubber ball thrown against a concrete wall.8. A football defensive linebacker tackling a running back.

Whether a collision is Elastic or Inelastic, the TOTAL MOMENTUM of the

system is CONSERVED.

This means that the momentum lost by one object will be gained by another.

The TOTAL momentum of the two objects will ALWAYS be the same after the collision as before

the collision.

Consider a game of billiards (pool). A cue ball with a mass of 0.5kg and moving at 6m/s strikes the stationary 8-ball which also with a mass of 0.5kg.

-With how much momentum did the cue ball collide with the 8-ball? (This is the cue ball’s initial momentum)-What was the 8-ball’s initial momentum? (Why?)-What was the TOTAL Momentum of the two balls? (This is called a system)-After the collision, the cue ball STOPPED. What was the cue ball’s final momentum?-What happened to the cue ball’s momentum

(Where did it go?)-What was the 8-ball’s momentum after the collision?

(This is the 8-ball’s final momentum)-Based on the 8-ball’s mass, what was its velocity after the collision?

EXAMPLE:

Let’s consider another example:

A 100kg defensive lineman running at 4m/s tackles an 80kg quarterback standing in the pocket. After the tackle the lineman slows down to 1m/s.

-With how much momentum did the lineman collide with the quarterback? (This is the lineman’s initial momentum)-What was the quarterback’s initial momentum? (Why?)-What was the TOTAL Momentum of the two players? (This is called a system)-After the collision, what was the lineman’s final momentum?-What happened to the rest of the lineman’s momentum?

(Where did it go?)-What was the quarterback’s momentum after the collision?

(This is the quarterback’s final momentum)-Based on the quarterback’s mass, what was his velocity after the collision?

When you solve Conservation of Momentum problems,It is good to set up a chart like this:

Before the CollisionObject #1: p1=m*v

p1=___*____

Object #2: p2=m*vp2=___*____

After the collision

TOTAL momentum BEFOREp=p1+p2

Object #1: p1=m*vp1=___*____

Object #2: p2=m*vp2=___*____

TOTAL momentum AFTERp=p1+p2

These have to be

the SAME !

Whenever two or more objects collide, the TOTAL momentum of the objects cannot change !

Remember:

Now, the chart will help you remember how you will use Conservation of Momentum to solve problems.But, here is an easier equation that you can use on a daily basis:

m1*v1i + m2*v2i = m1*v1f + m2*v2f

Try problems on your own in your notebook:

Two objects collide. Object 1 has a mass of 50kg and is initially traveling at 6m/s. Object 2 has a mass of 20kg and is initially traveling at 8m/s. After they collide, object 2 is now traveling at 11m/s. How fast does object 1 travel after the collision?

An accident investigator analyses a collision of a motorcycle and a car. He sees that after the collision the motorcycle (mass=550kg) moved at 10m/s and the car(mass=1000kg) moved at 8m/s. A witness says that before the accident the motorcycle was traveling at 7m/s. If you are the investigator, how fast do you think the car was traveling BEFORE the accident?