Question
Solve only the marked questions
of a horizontal on a frictionless d will break when the tension S. (II) A 0.45-kg ball, attached to the end cord, is rotated in a circle of radius 1.3 m horizontal surface. If the cor in it exceeds 75 N, what is the maximum spee 5-1 to 5-3 Uniform Circular Motion; Highway Curves . (1) A child sitting 1.10 m from the center of a merry-go- round moves with a speed of 1.25 m/s. Calculate (a) the centripetal acceleration of the child, and (b) the net hori maximum speed with which a 1050-kg car turn of radius 77 m on a flat road if the coef can have? zontal force exerted on the child (mass 25.0 kg) 2. (I) A jet plane traveling 1890 km/h (525 m/s) pulls out of . (II) What is the can roun cient of static friction between tires and road is 0.80? Is this result independent of the mass of the car? 11 How large must the coefficie a dive by moving in an arc of radius 6.00 km. What is the plane's acceleration in g's? 3. (1) Calculate the centripetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50 × 1011 m. [Hint: nt of static friction be d if a car is to round a level 0 between the tires and the roa curve of radius 85 m at a speed of 95 km/h? I1. (II) A device for training astronauts and jet fighter pilots rotate a trainee in a horizontal circle of see the Tables inside the front cover of this book )A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at V arm's length) of radius 0.90 m. Calculate the speed of the is designed to radius 12.0 m. If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? scus xpress your answer in both m/s and rev/s. shuttle is in orbit 400 km from the 12. (II) A coin is placed 11.0 cm from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the turntable of variable speed. When the speed of the turntable is slowly increased, the coin remain the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable? s fixed on gravitational acceleration at the Earth's surface. 6. (II) What is the magnitude of the acceleration of a speck f clay on the edge of a potter's wheel turning at 45 rpm (revolutions per minute) if the wheel's diameter is 32 cm? 13. (II) At what minimum speed must a roller coaster be traveling when upside down at the top of a circle (I) A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm, as shown in Fig. 5-33. If its speed is 4.00 m/s and its mass is 0.300 kg. calculate the tension in the string when the ball is (a) at (Fig. 5-34) so that the passengers wil not fall out? Assume a radius of curvature of 7.4 m the top of its path, and (b) at the bottom of its path n2 TI FIGURE 5-34 Problem 13 T2 14. (II) A sports car of mass 950 kg (including the driver) crosses the rounded top of a hill (radius 95 m) at 22 m/s Determine (a) the normal force exerted by the road on the car, (b) the normal force exerted by the car on the 72-kg driver, and (c) the car speed at which the normal force on the driver equals zero. FIGURE 5-33 Problem 7 CHAPTER 5 Circular Motion; Gravitation
Explanation / Answer
1) a) cantripetal acceleration ac = v2 / r
= 1.252 / 1.10 = 1.42 m/s2
b) Net horizontal force F = m v2 / r
= ( 25.0 * 1.252) / 1.10
= 35.5 N
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3) a = 4 pi2 r / T2 = (4 pi2 * 1.5 * 1011) / (365 * 24 * 3600)2
= 5.95 * 10-3 m/s2
F = m a = 5.98 * 1024 * 5.95 * 10-3
= 3.56 * 1022 N
