the wheel to come to rest when a force of isapplied to the handle. The coefficient of kinetic frictionbetween the belt and the wheel rim is . (Hint:Recall from the statics text that the relation of the tensionin the belt is given by , where is the angle ofcontact in radians.) •19–13.The 200-lb flywheel has a radius of gyration aboutits center of gravity Oof .If it rotatescounterclockwise with a constant angular velocity ofbefore the brake is applied, determine therequired force Pthat must be applied to the handle to stopthe wheel in 2 s. The coefficient of kinetic friction betweenthe belt and the wheel rim is . (Hint: Recall from thestatics text that the relation of the tension in the belt is givenby , where is the angle of contact in radians.)bTB=TCembmk=0.31200 rev>minkO=0.75 ftbTB=TCembmk=0.3P=200 lb1200 rev>minkO=0.75 ft19–11.A motor transmits a torque of tothe center of gear A. Determine the angular velocity of eachof the three (equal) smaller gears in 2 s starting from rest.The smaller gears (B) are pinned at their centers, and themasses and centroidal radii of gyration of the gears aregiven 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 fromrest. The mass of the gear is 50 kg, and it has a radius ofgyration about its center of mass Oof .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 velocityof the 20-kg gear rack in 4 s, starting from rest. The mass ofthe gear is 50 kg and it has a radius of gyration of. Assume that the contact surface betweenthe gear rack and the horizontal plane is smooth.kO=125 mmP=150 NkO=125 mmP=150 N2.5 ft1.25 ft1 ftPOABvCProbs. 19–12/13200 mmC500 mm500 mm400 mmP(N)52APBt(s)Prob. 19–1419–14.The 12-kg disk has an angular velocity of. If the brake ABCis applied such that themagnitude of force Pvaries with time as shown, determinethe time needed to stop the disk. The coefficient of kineticfriction at Bis . Neglect the thickness of the brake.mk=0.4v=20rad>s
19.2PRINCIPLE OFIMPULSE ANDMOMENTUM51319•19–17.The 5-kg ball is cast on the alley with a backspinof , and the velocity of its center of mass Ois. Determine the time for the ball to stop backspinning, and the velocity of its center of mass at thisinstant.The coefficient of kinetic friction between the balland the alley is .mk=0.08v0=5 m>sv0=10 rad>s*19–16.If the boxer hits the 75-kg punching bag with animpulse of , determine the angular velocity ofthe bag immediately after it has been hit. Also, find thelocationdof point B, about which the bag appears to rotate.Treat the bag as a uniform cylinder.