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Lesson 3.1: Assignment Questions 51 to 5-3 Uniform Circular Motion 1. (I) A child sitting 1.20 m from the center of a merrygo-round moves with a speed of 1.10 m/s. Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child (mass = 22.5 kg). 3. (I) A horizontal force of 310 N is exerted on a 2.0kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m. Calculate the speed of the ball. 5. (II) A 0.55kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have? 7. (II) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 m. At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling? 9. (ll) What is the maximum speed with which a 1200kg car can round a turn of radius 90.0 m on a flat road if the coefficient of friction between tires and road is 0.65? Is this result independent of the mass of the car? 11. (ll) How many revolutions per minute would a 25mdiameter Ferris wheel need to make for the passengers to feel \"weightless\" at the topmost point? 13. (II) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 539. The circle formed by the tube has a diameter of 1.1 km. What must be the rotation speed (revolutions per day) if an effect nearly equal to gravity at the surface of the Earth (say, 0.90 g) is to be felt? 15. (II) A coin is placed 13.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 38.0 rpm (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable? 17. (ll) Two blocks, with masses mA and ms, are connected to each other and to a central post by thin rods as shown in Fig. 541. The blocks revolve about the post at the same frequencyrevolutions per second) on a frictionless horizontal surface at distances at and n; from the post. Derive an algebraic expression for the tension in each rod. 19. (II) A 975-kg sports car (including driver) crosses the rounded top of a hill (radius = 88.0 m) at 18.0 m/s. Determine (a) the normal force exerted by the road on the car, (b) the normal force exerted by the car on the 62.0-kg driver, and (c) the car speed at which the normal force on the driver equals zero. 13. (II) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 539. The circle formed by the tube has a diameter of 1.1 km. What must be the rota- tion speed (revolutions per day) if an effect nearly equal to gravity at the surface of the Earth (say, 0.90 g) is to be felt? FIGURE 539 Problem 13. 17. (II) Two blocks, with masses mA and ms , are connected to each other and to a central post by thin rods as shown in Fig. 541. The blocks revolve about the post at the same frequency f (revolutions per second) on a frictionless horizontal surface at distances rA and n; from the post. Derive an algebraic expression for the tension in each rod. FIGURES-41 4:_ "'3 Problem 17. ,r' \":u --- __m'-- x r, \" % l {2 r3 I ' \\ x\" '2' I \\ hungII" I, \\'h'h \