1. Impulse, Momentum and Collisions

2. Interactions and Impulse From –an expertly placed shot in a soccer match –to the violent tug-of- war between galaxies it all boils down to interactions and impulse

3. Collisions What happens when two bodies collide? The two bodies exert equal and opposite forces on each other and for equal amounts of time. They exert equal and opposite impulses.

4. Impulse Impulse is the simple combination for Force and Time. We can express this as A simpler way to understand this is to recognize that impulse appears as the area under a Force- Time graph. go to the MAP pages on Impulse and Collisions

5. Conservation of Momentum and Impulse It is easy to see how the idea of “equal and opposite impulses” (just and extension of Newton’s Third Law) leads naturally to the idea of momentum and the Law of Conservation of Momentum. go to the MAP pages on Collisions and Conservation of Momentum

6. Something’s Missing? Let’s try applying Conservation of Momentum to a number of 1D collisions… go to the MAP pages on Collisions in One Dimension

7. Combining Momentum and Energy For any isolated system: Momentum is ALWAYS conserved Kinetic Energy may or may not be conserved.

8. Classifying Collisions… If kinetic energy is completely conserved then the collision is perfectly elastic If the maximum amount of kinetic energy energy is lost during the collision then the collision is perfectly inelastic. “in between” these extremes we consider the collision to be inelastic.

9. Exploring Perfectly Elastic Collisions This type of collision is governed by two conditions: –Conservation of Momentum: –Conservation of Energy

10. Coefficient of Restitution A very simple but powerful idea is that of coefficient of restitution. It is actually an energy condition (in cognito)

11. Example:1D Collision - Graphical m1 = 2 kg, m2 = 1 kg v1 = 3 m/s, v2 = -4 m/s Initial velocities Final velocities

12. Example:1D Collision - Algebraic Conservation of Momentum: Conservation of Energy: or