Ch.9 Momentum and Its Conservation

1. Ch.9 Momentum and Its Conservation

2. 9.1 Impulse and Momentum • Momentum (p): the product of the mass (m) of an object and its velocity (v) p= mv An object has a greater momentum if: • it has a greater mass • it has a greater velocity

3. Example Problem • A 5 kg hockey puck has a momentum of 10 kg* m/s. What is the speed of the hockey puck? • A ball has a momentum of 50 kg*m/s and is thrown at a speed of 10 m/s, what is the ball’s mass?

4. Impulse • Impulse: Force times change in time • Impulse = FΔt • Is the result of force acting on an object over time • Greater force = Greater impulse • Greater time = Greater impulse Which would have a greater impulse, pushing the car for 2 seconds, or pushing the car for 30 seconds? Which would have a greater impulse, one person pushing a car, or 3 people pushing a car?

5. Impulse-Momentum Relationship • The greater the impulse, the greater the change in momentum. Impulse = change in momentum FΔt=mΔv Impulse and the change in momentum are ALWAYS linked! Furthermore, Δv = v2 – v1 so the impulse-momentum theorem says we can write the equation as follows' FΔt = p2 – p1

6. Would you rather… • Drive your car into a brick wall, or into a pile of hay? WHY? • Both would have the same change in momentum to bring your car to a stop…BUT: • The brick wall has a greater force over a smaller period of time • The hay has a smaller force over a greater period of time Change in momentum = Ft Change in momentum = Ft

7. Impulse-Momentum Relationship in Sports Dancers like to have a wooden floor with some “give,” which increases the time of impact whenever a dancer lands. This reduces the chance of injury. Boxers “ride” or “roll” with punches to reduce the force during impact by moving with the punch. A karate expert can break a stack of bricks by reducing the time that the hand is in contact with the bricks, which increases the force.

8. Egg Demo! • http://youtu.be/lPzGSjIoW7c

9. Example Problem • A 5.0-kg ball has a velocity of 10 m/s downward just before it strikes the ground and bounces up with a velocity of 10 m/s upward. What is the change in momentum of the ball?

10. Example Problem pg. 203 • A 2200-kg sport utility vehicle traveling at 94 km/h (26 m/s) can be stopped in 21 s by gently applying the brakes, in 5.5 s in a panic stop, or in 0.22 s if it hits a concrete wall. What average force is exerted on the vehicle in each of these stops?

11. Sec. 9.2 Conservation of Momentum • Law of Conservation of Momentum: • In the absence of an external force, the momentum of a system remains unchanged. The momentum gained by the cannonball, is equal and opposite to the momentum gained by the cannon. So the system has not gained or lost momentum.

12. Conservation of MomentumCollisions Net Momentum before collision = Net Momentum after collision • Elastic Collision: A collision in which colliding objects rebound without lasting deformation or generation of heat • Ex: molecules of gas, billiard ball • Inelastic Collision: A collision in which colliding objects become distorted, generate heat, and possibly stick together. • Ex: One car hitting another

13. Elastic or Inelastic? Elastic or Inelastic? Elastic Inelastic If the problem does not state object stick together or it’s an inelastic collision always assume an ELASTIC collision occurred.

14. Guide to solving ANY collision problem • DRAW A PICTURE • USE The Law of Conservation of Momentum Total Momentum Before Collision = Total Momentum After Collision pbefore = pafter

15. Example Problem pg. 209 • A 2275-kg car going 28 m/s rear-ends an 875-kg compact car going 16 m/s on ice in the same direction. The two cars stick together. How fast does the wreckage move immediately after the collision?

16. Example Problem • A 10.0-kg cart moving to the right with a speed of 2.0 m/s has a head-on collision with a 15.0-kg cart that is initially moving to the left with a speed of 5 m/s. After the collision, the 10.0-kg cart is moving to the left with a speed of 2.0 m/s, what is the final velocity of the 15.0-kg cart?

17. Example Problem pg. 212 • An astronaut at rest in space fires a thruster pistol that expels 35 g of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing the pistol?

18. 2- Dimensional Collisions The Law of Conservation of Momentum still applies

19. Example Problem pg. 215 • A 2.00-kg ball, A, is moving at a speed of 5.00 m/s. It collides with a stationary ball, B, of the same mass. After the collision, A moves off in a direction of 30.0 degrees to the left of its original direction. Ball B moves off in a direction 90.0 degrees to right of ball A’s final direction. How fast are they moving after the collision?

20. Angular Momentum • The product of a rotating object’s moment of inertia and angular speed about the same axis. L= mvr (for a point mass) • Conservation of Angular Momentum = the net external torque acting on an object or objects is zero, the angular moment of the object does not change

21. Angular Momentum Demo • http://youtu.be/WnS2d24HCK0