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Classical Mechanics

18. A 0.20-kg billiard ball traveling at a speed of 15 m/s strikes the side rail of a pool table at an angle of 60 degrees. If the ball rebounds at the same speed and angle, what is the change of momentum?

34. When bunting, a baseball player uses the bat to change both the speed and direction of the baseball. (a) Will the magnitude of the change in momentum of the baseball before and after the bunt be (1) greater than the magnitude of the of the momentum of the baseball either before or after the bunt, (2) equal to the difference between the magnitudes of momenta of the baseball before and after the bunt, or (3) equal to the sum of the magnitudes of momenta of the baseball before and after the bunt? Why? (b) The baseball has a mass of 0.16 kg; its speeds before and after the bunt are 15 m/s and 10 m/s, respectively; and the bunt lasts 0.025 s. What is the change in momentum of the baseball? (c) What is the average force on the ball by the bat?

54. Two identical cars hit each other and lock bumpers. In each of the following cases, what are the speeds of the cars immediately after coupling bumpers? (a) A car moving with a speed of 90 km/h approaches a stationary car; (b) two cars approach each other with speeds of 90 km/h and 120 km/h, respectively; (c) two cars travel in the same direction with speeds of 90 km/h and 120 km/h, respectively.

28. A race car makes two and a half laps around a circular track in 3.0 min. What is the car's average angular speed?

36. A medical centrifuge is rated at 15 000 rpm. How long will it take the centrifuge to make one revolution?

56. A jet pilot puts an aircraft with a constant speed into a vertical circular loop. (a) Which is greater, the normal force exerted on the seat by the pilot at the bottom of the loop or that at the top of the loop? Why? (b) If the speed of the aircraft is 700 km/h and the radius of the circle is 2.0 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. Express your answer in terms of the pilot's weight mg.

72. A student investigating circular motion places a dime 10 cm from the center of a 33 1/3 -rpm record on a turntable. The record player can accelerate at 1.42 rad/s2. The student notes that the dime slides outward 2.25 s after she has switched on the turntable. (a) Why does the dime slide out-ward? (b) What is the coefficient of static friction between the dime and the record?

100. Circular disks are used in automobile clutches and transmissions. When a rotating disk couples to a stationary one through frictional force, the energy from the rotating disk can transfer to the stationary one. (a) Is the angular-speed of the coupled disks (1) greater than, (2) less than, or (3) the same as the angular speed of the original rotating disk? Why?

(b) If a disk rotating at 800 rpm couples to a stationary disk with three times the moment of inertia, what is the angular speed of the combination?

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