Collisions

Bell Ringer A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft does what?

Objectives Define inelastic, perfectly inelastic, and elastic collisions. Use conservation of momentum equations to solve for different types of collisions. Determine the relationship between conservation of momentum and conservation of energy.

Introduction For any type of collision, total momentum of the system is conserved. The total kinetic energy on the other hand is generally not conserved. What do you think this energy goes to?

Inelastic Collisions We define an inelastic collision as a collision in which momentum is conserved, but kinetic energy is not. Example: A rubber ball colliding with the floor.

Perfectly Inelastic Collisions When two objects collide and stick together, the collision is said to be perfectly inelastic. Example: Two pieces of clay collide and stick together and move with a common velocity.

Elastic Collisions An elastic collision is defined as one in which both momentum and kinetic energy are conserved.

Perfectly Inelastic Collisions Consider two cars racing to beat the light. They collide (making no sound) and their bumpers stick together, causing them to slide at a common velocity. This is an example of a perfectly inelastic collision

Perfectly Inelastic Collisions Because the total momentum of the two- object isolated system before the collision equals the total momentum of the combined-object system after the collision, we can say that…

Perfectly Inelastic Collision m1v1 + m2 v2 = (m1 + m2) vf

Perfectly Inelastic Collisions When solving for these problems, make sure to pay attention to the signs of the velocity vectors.

Example: SUV vs. Compact An SUV with mass 1,800 kg is traveling eastbound at 15.0 m/s, while a compact car with mass 900 kg is traveling westbound with a velocity of 15.0 m/s. The cars collide head on, becoming entangled.

Continued Find the speed of the entangled cars after the collision. Find the change in velocity for each car

Elastic Collisions Two objects undergo an elastic head on collision. Here, both the momentum and the kinetic energy are conserved.

Elastic Collisions KE I = KE f And pi = pf

Elastic Collisions In a typical problem involving elastic collisions, you will have two unknown values. You will need to use both conservation of momentum and conservation of kinetic energy to solve.

A New Equation A new conservation of energy equation is needed. 𝐯𝟏 − 𝐯𝟐 = − (𝐯𝟏 − 𝐯𝟐) If you are interested in the process to get this equation, look on page 199 of your book.

Example Two billiard balls of identical mass move toward each other. Assume that the collision between them is perfectly elastic. If the initial velocities of the balls are 0.3 m/s and -0.2 m/s, what is the velocity of each ball after the collision?