Elastic and Inelastic Collisions

1. Elastic and Inelastic Collisions Chapter 6 Section 3

2. Collisions • There are many different collisions in which two objects collide. • Sports • Vehicles • Arrow and target

3. Kinetic Energy and Collisions • Momentum is always conserved in a collision, but the total kinetic energy is generally not conserved. • Some of the energy is converted to thermal energy (heat) and internal elastic potential energy when the objects deform.

4. Perfectly Inelastic Collisions • Perfectly Inelastic collisions – A collision in which two objects stick together and move with a common velocity after colliding. • Examples: • Arrow hitting a target • Bullet lodging into a wood block • Meteorite colliding with Earth and becomes buried

5. Perfectly Inelastic Collisions m1v1i + m2v2i = (m1+m2)vf • Since the objects stick together after the collision, the masses must be added together for the final velocity.

6. Distinctions Between Collisions • Elastic Collision – Objects maintain their original shape and are not deformed after colliding. • Inelastic Collision – Objects are deformed during the collision and lose kinetic energy. • Perfectly Inelastic Collision – Objects join together after a collision to form one mass.

7. Kinetic Energy Lost • Energy is lost during an inelastic collision and not a elastic collision. • In most cases energy is lost during a perfectly inelastic collision, but not always. • How much deformation and how the objects stick together play a factor.

8. Kinetic Energy Equations KElost = KEi – Kef Kinetic Energy Lost = Initial Kinetic Energy – Final Kinetic Energy

9. Example Problem • A clay ball with a mass of 0.35 kg hits another 0.35 kg ball at rest, and the two stick together. The first ball has an initial speed of 4.2m/s • What is the final speed of the balls? • Calculate the decrease in kinetic energy that occurs during the collision. • What percentage of the kinetic energy is converted to other forms of energy?

10. Example Problem Answers • 2.1m/s • 1.6J • 52%

11. Elastic Collisions • Elastic Collisions – A collision in which the total momentum and the total kinetic energy remains constant. • The objects remain separate after the collision. • Examples: • Kicking a soccer ball with your foot • Hitting a baseball with a bat • Billiards

12. Everyday Collisions • Most collisions are neither elastic or perfectly inelastic in everyday activities. • In most collisions, kinetic energy is lost. • This places them into the category of inelastic collisions.

13. Kinetic Energy and Elastic Collisions • Kinetic energy is conserved in elastic collisions. • The total momentum and the total kinetic energy remain constant through out the collision.

14. Momentum and Kinetic Energy Equations m1v1i + m2v2i = m1v1f + m2v2f • Momentum equation can be used for all collisions. ½m1v1i²+ ½m2v2i²= ½m1v1f²+ ½m2v2f² • Kinetic Energy equation can only be used for elastic collisions.

15. Making Sure Collisions Are Elastic • To check and see if a collision is an elastic collision: • Solve the problem using the conservation of momentum equation. • Plug the velocities into the conservation of kinetic velocity equation and see if the total initial velocity and the total final velocity are equal. • If they are, then it is a true elastic collision.