Mastering Momentum and Collisions: Theory and Practice

1. Chapter 6 Momentum and Collisions • Momentum and Impulse • Conservation of Momentum • 1D Collisions • 2D Collisions

2. Momentum • What is momentum? • How do I represent it? • How do I calculate it? • What are the SI units?

3. Impulse • What is impulse? • How do I calculate it? • What are its SI units • Back to Newton’s Second Law

4. Impulse-Momentum Theorem • What is this theorem? • Average force

5. Example – Momentum and Impulse • A 50-g golf ball is struck with a club as shown. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is deformed) and then back to zero when the ball leaves the club. The force-time graph is also shown. Assume the ball leaves the club face with a velocity of +44m/s • Estimate the size and direction of the impulse due to the collision. • Estimate the duration of the collision and the average force on the ball.

6. Injury in Car Collision Data: Survival data for head on collision: Force for bone fracture 90KN, Pressure 1.9x105N/m2 at 60 mi/h resulting in acceleration of 50g’s for 70 ms for an area of 0.7-0.9 m2 Case Data Mp = 75-kg, Vi =60 mi/h (27m/s), tr=0.010 s, Achest+head=0.5 m2 Find F, a, P

7. Air Bags and Seat Belts • The air bag increases the time of the collision • It will also absorb some of the energy from the body • It will spread out the area of contact • decreases the pressure • helps prevent penetration wounds

8. Conservation of Momentum • What is this conservation law? • What do we mean by a system? • What do we mean by an isolated system? • Is contact necessary? • Another way to say the same thing

9. Conservation of Momentum • Is contact necessary? • Another way to write conservation of momentum

10. Types of Collisions • What is Inelastic collision? • What is Elastic collision?

11. Example – Inelastic Collision • A bullet of mass m with a speed v into a wooden block of mass M. Find an expression that gives the initial velocity of the bullet in terms of masses, acceleration due to gravity g and the height h thru which the pendulum is raised.

12. Example – Elastic Collision • A bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. The pendulum bob is suspended by a stiff rod of length l and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? (Find the expression in terms M, m g and l).

13. Glancing Collisions

14. Example – Glancing Collision • A 1500kg car traveling east with a speed of 25 m/s collides at an intersection with a 2500kg van traveling north at a speed of 20 m/s as shown. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that friction between the vehicles and the road can be neglected.