6 - Circular Motion and Other Applications of Newton's Laws

Complete one orbit is proportional to r 32 58 a penny

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Unformatted text preview: (magnitude and direction) does the seat exert on a rider when the rider is halfway between top and bottom? 8.00 m 2.50 m θ Figure P6.61 Figure P6.59 (Color Box/FPG) 60. A space station, in the form of a large wheel 120 m in diameter, rotates to provide an “artificial gravity” of 3.00 m/s2 for persons situated at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect. 61. An amusement park ride consists of a rotating circular platform 8.00 m in diameter from which 10.0-kg seats are suspended at the end of 2.50-m massless chains (Fig. P6.61). When the system rotates, the chains make an angle 28.0° with the vertical. (a) What is the speed of each seat? (b) Draw a free-body diagram of a 40.0-kg child riding in a seat and find the tension in the chain. 62. A piece of putty is initially located at point A on the rim of a grinding wheel rotating about a horizontal axis. The putty is dislodged from point A when the diameter through A is horizontal. The putty then rises vertically and returns to A the instant the wheel completes one revolution. (a) Find the speed of a point on the rim of the wheel in terms of the acceleration due to gravity and the radius R of the wheel. (b) If the mass of the putty is m, what is the magnitude of the force that held it to the wheel? 63. An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (Fig. P6.63). The coefficient of static friction between person and wall is s , and the radius of the cylinder is R. (a) Show that the maximum period of revolution necessary to keep the person from falling is T (4 2R s /g )1/2. (b) Obtain a numerical value for T Figure P6.63 180 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws if R 4.00 m and s 0.400. How many revolutions per minute does the cylinder make? 64. An example of the Coriolis effect. Suppose air resistance is negligible for a golf ball. A golfer tees off from a location precisely at i 35.0° north latitude. He hits the ball due south, with range 285 m. The ball’s initial velocity is at 48.0° above the horizontal. (a) For what length of time is the ball in flight? The cup is due south of the golfer ’s location, and he would have a hole-inone if the Earth were not rotating. As shown in Figure P6.64, the Earth’s rotation makes the tee move in a circle of radius RE cos i (6.37 106 m) cos 35.0°, completing one revolution each day. (b) Find the eastward speed of the tee, relative to the stars. The hole is also moving eastward, but it is 285 m farther south and thus at a slightly lower latitude f . Because the hole moves eastward in a slightly larger circle, its speed must be greater than that of the tee. (c) By how much does the hole’s speed exceed that of the tee? During the time the ball is in flight, it moves both upward and downward, as well as southward wit...
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