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

# Orbit around the earth at an altitude equal to the

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Unformatted text preview: the same length? (b) What is the centripetal acceleration of the tip of the second hand? A coin placed 30.0 cm from the center of a rotating, horizontal turntable slips when its speed is 50.0 cm/s. (a) What provides the force in the radial direction when the coin is stationary relative to the turntable? (b) What is the coefﬁcient of static friction between coin and turntable? The cornering performance of an automobile is evaluated on a skid pad, where the maximum speed that a car can maintain around a circular path on a dry, ﬂat surface is measured. The centripetal acceleration, also called the lateral acceleration, is then calculated as a multiple of the free-fall acceleration g. The main factors affecting the performance are the tire characteristics and the suspension system of the car. A Dodge Viper GTS can negotiate a skid pad of radius 61.0 m at 86.5 km/h. Calculate its maximum lateral acceleration. A crate of eggs is located in the middle of the ﬂatbed of a pickup truck as the truck negotiates an unbanked 174 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws curve in the road. The curve may be regarded as an arc of a circle of radius 35.0 m. If the coefﬁcient of static friction between crate and truck is 0.600, how fast can WEB the truck be moving without the crate sliding? 12. A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.12. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors i and j. Determine (b) the car’s average speed and (c) its average acceleration during the 36.0-s interval. hump? (b) What must be the speed of the car over the hump if she is to experience weightlessness? (That is, if her apparent weight is zero.) 15. Tarzan (m 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.0 m long, and his speed at the bottom of the swing (as he just clears the water) is 8.00 m/s. Tarzan doesn’t know that the vine has a breaking strength of 1 000 N. Does he make it safely across the river? 16. A hawk ﬂies in a horizontal arc of radius 12.0 m at a constant speed of 4.00 m/s. (a) Find its centripetal acceleration. (b) It continues to ﬂy along the same horizontal arc but steadily increases its speed at the rate of 1.20 m/s2. Find the acceleration (magnitude and direction) under these conditions. y O 35.0° C 17. A 40.0-kg child sits in a swing supported by two chains, each 3.00 m long. If the tension in each chain at the lowest point is 350 N, ﬁnd (a) the child’s speed at the lowest point and (b) the force exerted by the seat on the child at the lowest point. (Neglect the mass of the seat.) 18. A child of mass m sits in a swing supported by two chains, each of length R. If the tension in each chain at the lowest point is T, ﬁnd (a) the child’s speed at the lowest poin...
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