Block A and Block B are hanging from a two-radius pulley, as shown. Block A is s

Question

Block A and Block B are hanging from a two-radius pulley, as shown. Block A is suspended by a massless cord that is wrapped around the pulley's smaller circumference (radius rA), and Block B is hanging by a massless cord wrapped around the pulley's larger circumference (radius rB). Radius rB is three times as large as radius rA, and the pulley's moment of inertia about its COM is I = 0.5 kgm2. The masses of the blocks are mA and mB, and the system is Initially held at rest. What should mA be so that the system remains at rest when the blocks are released? Express your answer in terms of mB, for example = 20 mB. (Hint: If the masses are stationary, what do you know about the tensions in the cords? What about the torques due to these tensions?) Suppose now that mA = mB = 1 kg and = 0.2 m. When released from rest, Block B descends and Block A ascends. What is omega of the pulley when Block B has descended a distance hB=0.4 m? (Hint: You should not have to calculate any forces whatsoever for this part.)

Explanation / Answer

a) torque balance ma x ra = mb x rb ma x ra = mb x 3 ra ma = 3 mb b) torque acting = 1 x .6 - 1x.2 = 0.4 Nm inertia = m r^2 = .36 + .04 = 0.4 a = 1 rad/s^2 s = (.4 /.6) x 2 pi = 4.188 ? = v2 x a x s = v 2 x 1 x 4.188 ? = 2.9 rad

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