1. Chapter 9 : Linear Momentum 8-8 Power 9-1 Momentum and Its Relation to Force 9-2 Conservation of Momentum 9-3 Collisions and Impulse HW6: Chapter 9: Pb. 10, Pb. 25, Pb. 35, Pb. 50, Pb. 56, Pb. 64- Due Friday Oct 30

2. 8-8 Power Example 8-14: Stair-climbing power. A 60-kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. (a) Estimate the jogger’s power output in watts and horsepower. (b) How much energy did this require?

3. 8-8 Power Example 8-15: Power needs of a car. Calculate the power required of a 1400-kg car under the following circumstances: (a) the car climbs a 10° hill (a fairly steep hill) at a steady 80 km/h; and (b) the car accelerates along a level road from 90 to 110 km/h in 6.0 s to pass another car. Assume that the average retarding force on the car is F R = 700 N throughout.

4. 8-8 Power Power is the rate at which work is done. Average power: In the SI system, the units of power are watts: Instantaneous power:

5. 8-8 Power In the British system, the basic unit for power is the foot-pound per second, but more often horsepower is used: 1 hp = 550 ft·lb/s = 746 W. Power is the rate at which energy is transformed Units: Joules/s or Watts, W Puzzler: kilowatt·hours [kW·h] are units of what quantity?

6. Question In these two cases, the work done in stopping the car is A.positive, with bricks doing more work B.positive, with bricks and balloon doing same work C.negative, with bricks doing more work D.negative, with bricks and balloon doing same work.

7. 9-1 Momentum and Its Relation to Force Example: A system consists of three particles with these masses and velocities: mass 3.0 kg moving west at 5.0 m/s; mass 4.0 kg moving west at 10.0 m/s; and mass 5.0 kg moving east at 20.0 m/s. What is total momentum of the system?

8. 9-1 Momentum and Its Relation to Force Example 9-1: Force of a tennis serve. For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mi/h). If the ball has a mass of 0.060 kg and is in contact with the racket for about 4 ms (4 x 10 -3 s), estimate the average force on the ball. Would this force be large enough to lift a 60-kg person?

9. 9-1 Momentum and Its Relation to Force Example 9-2: Washing a car: momentum change and force. Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it. (That is, we ignore any splashing back.) What is the force exerted by the water on the car?

10. 9-1 Momentum and Its Relation to Force Momentum is the property of a moving object to continue moving Momentum is a vector symbolized by the symbol and is defined as The rate of change of momentum is equal to the net force: This can be shown using Newton’s second law.

11. Momentum, p Vector units: kgm/s Bowling Ball vs. Tennis Ball Mass7 kg57 g Speed9 m/s60 m/s momentum63kg.m/s3.42kg.m/s

12. 9-2 Conservation of Momentum Example 9-4: Rifle recoil. Calculate the recoil velocity of a 5.0- kg rifle that shoots a 0.020-kg bullet at a speed of 620 m/s.

13. 9-2 Conservation of Momentum Problem 12:(I) A 130-kg tackler moving at 2.5m/s meets head-on (and tackles) an 82-kg halfback moving at 5.0m/s. What will be their mutual speed immediately after the collision? (

14. 9-2 Conservation of Momentum During a collision, measurements show that the total momentum does not change:

15. 9-2 Conservation of Momentum Conservation of momentum can also be derived from Newton’s laws. A collision takes a short enough time that we can ignore external forces. Since the internal forces are equal and opposite, the total momentum is constant.

16. 9-2 Conservation of Momentum This is the law of conservation of linear momentum: when the net external force on a system of objects is zero, the total momentum of the system remains constant. Equivalently, the total momentum of an isolated system remains constant.

17. Question If the car rebounds with the same speed that it had before it hit: A.  p=0, W=0 B.  p is non-zero, W=0 C.  p=0, W is nonzero D.  p, W are both nonzero

18. 9-3 Collisions and Impulse Example 9-6: Karate blow. Estimate the impulse and the average force delivered by a karate blow that breaks a board a few cm thick. Assume the hand moves at roughly 10 m/s when it hits the board.