# The wheel to come to rest when a force of is applied

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the wheel to come to rest when a force of is applied to the handle. The coefficient of kinetic friction between the belt and the wheel rim is . ( Hint : Recall from the statics text that the relation of the tension in the belt is given by , where is the angle of contact in radians.) •19–13. The 200-lb flywheel has a radius of gyration about its center of gravity O of . If it rotates counterclockwise with a constant angular velocity of before the brake is applied, determine the required force P that must be applied to the handle to stop the wheel in 2 s. The coefficient of kinetic friction between the belt and the wheel rim is . ( Hint : Recall from the statics text that the relation of the tension in the belt is given by , where is the angle of contact in radians.) b T B = T C e mb m k = 0.3 1200 rev > min k O = 0.75 ft b T B = T C e mb m k = 0.3 P = 200 lb 1200 rev > min k O = 0.75 ft 19–11. A motor transmits a torque of to the center of gear A . Determine the angular velocity of each of the three (equal) smaller gears in 2 s starting from rest. The smaller gears ( B ) are pinned at their centers, and the masses and centroidal radii of gyration of the gears are given in the figure. M = 0.05 N # m •19–9. If the cord is subjected to a horizontal force of , and the gear rack is fixed to the horizontal plane, determine the angular velocity of the gear in 4 s,starting from rest. The mass of the gear is 50 kg, and it has a radius of gyration about its center of mass O of . 19–10. If the cord is subjected to a horizontal force of , and gear is supported by a fixed pin at O , determine the angular velocity of the gear and the velocity of the 20-kg gear rack in 4 s, starting from rest. The mass of the gear is 50 kg and it has a radius of gyration of . Assume that the contact surface between the gear rack and the horizontal plane is smooth. k O = 125 mm P = 150 N k O = 125 mm P = 150 N 2.5 ft 1.25 ft 1 ft P O A B v C Probs. 19–12/13 200 mm C 500 mm 500 mm 400 mm P (N) 5 2 A P B t (s) Prob. 19–14 19–14. The 12-kg disk has an angular velocity of . If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is . Neglect the thickness of the brake. m k = 0.4 v = 20 rad > s
19.2 P RINCIPLE OF I MPULSE AND M OMENTUM 513 19 •19–17. The 5-kg ball is cast on the alley with a backspin of , and the velocity of its center of mass O is . Determine the time for the ball to stop back spinning, and the velocity of its center of mass at this instant. The coefficient of kinetic friction between the ball and the alley is . m k = 0.08 v 0 = 5 m > s v 0 = 10 rad > s *19–16. If the boxer hits the 75-kg punching bag with an impulse of , determine the angular velocity of the bag immediately after it has been hit. Also, find the location d of point B , about which the bag appears to rotate. Treat the bag as a uniform cylinder.
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