Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_139

6/139 The constant tensions of 200 N and 160 N are applied to the hoisting cable as shown. If the velocity \( v \) of the load is 2 m/s down and the angular velocity \( \omega \) of the pulley is 8 rad/s counterclockwise at time \( t = 0 \), determine \( v \) and \( \omega \) after the cable tensions have been applied for 5 s. Note the independence of the results. Given data: Pulley mass, \( m_p = 15 \text{ kg} \) Pulley centroidal radius of gyration, \( \bar{k} = 250 \text{ mm} = 0.25 \text{ m} \) Pulley radius, \( r = 300 \text{ mm} = 0.3 \text{ m} \) Load mass, \( m_L = 20 \text{ kg} \) Tension on left side, \( T_1 = 200 \text{ N} \) (upward) Tension on right side, \( T_2 = 160 \text{ N} \) (upward) Initial velocity of load, \( v_1 = 2 \text{ m/s} \) (downward) Initial angular velocity of pulley, \( \omega_1 = 8 \text{ rad/s} \) (counterclockwise) Time interval, \( \Delta t = 5 \text{ s} \)