Question

Neglect the weight and friction of the pulley system in Fig. Determine the velocity of the block E, if the pulley A moves with velocity v,-4m/s to downward VA

Answer 1

If we consider all the (Block + Pulley + string) as one system then tension becomes internal force, and we know that work done by internal force is zero. Implies sigma T middot X = 0 Implies Let a block A, is connected at pulley 'A' which is moving with velocity 4 m/ s downward. Implies Let A_1 moved x_1 distance and 'E' moved x_2 distance Implies work done by block A_1 = T middot x_1 Implies work done by block A_2 = 2T middot x_2 Implies work done by Pulley 'A', using FBD Implies [T - (7/2 + T/2)] middot x_1 = 0 Similarly work done by Pulley B, C and D = 0 Implies sigma T middot X = 0 Implies T middot x_1 - 2T middot x_2 + 0 = 0 Implies x_1 - 2 x_2 = 0 Implies V_A_1 - 2V_E = 0 After differentation Implies V_E = V_r/2 = 4/2 = 2 m/s V_E = 2 m/s