Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_144

6/144 The grooved pulley of mass \( m \) is acted on by a constant force \( F \) through a cable which is wrapped securely around the exterior of the pulley. The pulley supports a cylinder of mass \( M \) which is attached to the end of a cable which is wrapped securely around an inner hub. If the system is stationary when the force \( F \) is first applied, determine the upward velocity of the supported mass after 3 seconds. Use the values \( m = 40 \text{ kg} \), \( M = 10 \text{ kg} \), \( r_o = 225 \text{ mm} \), \( r_i = 150 \text{ mm} \), \( k_O = 160 \text{ mm} \), and \( F = 75 \text{ N} \). Assume no mechanical interference for the indicated time frame and neglect friction in the bearing at \( O \). What is the time-averaged value of the force in the cable which supports the 10-kg mass?