6-3: Elastic and Inelastic Collisions Objectives: Identify different types of collisions Determine the decrease in kinetic energy during perfectly inelastic collisions Compare conservation of momentum and conservation of kinetic energy in perfectly inelastic and elastic collisions Find the final velocity of an object in perfectly inelastic and elastic collisions

Collisions Collisions happen constantly One type is when two objects collide and stick together and travel as one after contact. – Ex. An arrow hits a target. In an isolated system they would continue to travel together with a momentum equal to their combined momentum before the collision. In other collisions, like a tennis racquet and a tennis ball, two objects collide and bounce so that they move away with two different velocities. Total momentum remains constant in any type of collision

Collisions Although momentum is conserved the total kinetic energy is generally not conserved. Some is lost to thermal energy and internal elastic energy when the objects deform.

Perfectly Inelastic Collisions Perfectly inelastic collisions are collisions in which two objects stick together and move with a common velocity after colliding. – Examples The arrow and target from before A meteor slams into earth and buries itself The two objects essentially become one. They will have one velocity and the mass after the collision is the sum of the mass of each object.

Perfectly Inelastic Collisions m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f This shows that momentum is conserved in the collision.

Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? Momentum is conserved from the instant before lunch until the instant after (in so brief an interval, water resistance does not have time to change the momentum).

A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?

Kinetic energy does not remain constant in inelastic collisions Elastic collision means things will keep their original shape, and will not be deformed by the forces of the collisions. Inelastic collisions on the other hand are deformed during the collision and lose some kinetic energy. Objects in perfectly inelastic collisions are joined together as one mass after the collisions.

Kinetic Energy We can calculate the loss of kinetic energy in a collision using the formulas from chapter 5. Kinetic energy can be lost to thermal energy, sound energy, and other forms of energy. KE i = KE 1,i + KE 2,i KE i = ½ m 1 v 1,i 2 + ½ m 2 v 2,i 2 KE= ½ mv 2 Final Kinetic Energy = KE i – KE f

Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The mass of the second ball is kg, and it has an initial velocity of 3.00 m/s to the left. What is the final velocity of the composite ball of clay after the collision? What is the decrease in kinetic energy during the collision?

Elastic Collisions Elastic collisions are when a collision in which the total momentum and the total kinetic energy remain constant. – The objects will also keep their shape A player kicking a soccer ball – Both the foot and the ball will retain their shape – The foot and the ball will move separately after the collision

Most Collisions are neither elastic nor perfectly inelastic Most objects do not collide and travel as one item (Perfectly inelastic). Most elastic collisions will lose energy. They lose energy in the form of thermal, sound, or elastic potential energy. Most collisions fall into a third category called inelastic collisions. We are not going to consider this case in this class.

Kinetic Energy is conserved in elastic collisions Consider figure 6-12 on page 227. The soccer ball moving to the left is moving faster than the ball to the right. The total momentum is conserved after the collision.

Momentum and Kinetic Energy Remain Constant in an Elastic Collisions Conservation of momentum in elastic collisions: m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f Conservation of kinetic energy in elastic collisions: ½ m 1 v 1,i 2 + ½ m 2 v 2,i 2 = ½ m 1 v 1,f 2 + ½ m 2 v 2,f 2 Remember that v is negative when moving to the left.

A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. What is the velocity of the kg marble after the collision?

6-3 Assignment P. 230 Questions 1-5 Vocabulary quiz tomorrow. Write out definitions – Elastic collisions – Impulse – Momentum – Perfectly inelastic collisions