The motor in Figure P3.11 lifts the mass mL by winding up

Chapter , Problem 3.11

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The motor in Figure P3.11 lifts the mass \(m_{L}\) by winding up the cable with a force \(F_{A}\). The center of pulley B is fixed. The pulley inertias are \(I_{B}\) and \(I_{C}\). Pulley C has a mass \(m_{C}\). Derive the equation of motion in terms of the speed \(v_{A}\) of point A on the cable with the force \(F_{A}\) as the input.

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