1. Elastic Collisions
SPH4U

2. Elastic Collisions
An interaction in which both momentum and kinetic energy are conserved is called an elastic collision.

3. Elastic Collisions
An interaction in which both momentum and kinetic energy are conserved is called an elastic collision.

4. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?

5. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?
First consider conservation of momentum:

6. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?

7. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?

8. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?

9. Elastic Collisions: Example
A ball of mass 1 kg with an initial velocity of 10 m/s [E] strikes a stationary ball of mass 1 kg in a completely elastic collision. What is the final velocity of both balls?
Now consider conservation of kinetic energy:

10. Elastic Collisions: Example

11. Elastic Collisions: Example

12. Elastic Collisions: Example

13. Elastic Collisions: Example

14. Elastic Collisions: Example
This equation has two solutions:

15. Elastic Collisions: Example
Let’s interpret these solutions

16. Elastic Collisions: Example
Let’s interpret these solutions The second describes a situation in which the first ball passes completely through the second without affecting it. This is not physically possible.

17. Elastic Collisions: Example
Let’s interpret these solutions The first describes a situation in which the first ball stops and the second carries away all the momentum and kinetic energy. This is physically possible.

18. More Practice
“Mini-Build Project: Newton’s Cradle” “More Practice with Elastic Collisions”