Multiple-Concept Example 12 reviews the concepts that play roles in this problem

Question

Multiple-Concept Example 12 reviews the concepts that play roles in this problem. A block (mass = 1.6 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.5 x 10-3 kg

Multiple-Concept Example 12 reviews the concepts that play roles in this problem. A block (mass = 1.6 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.5 x 10-3 kg·m2), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.038 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.

Explanation / Answer

at Pulley :

torqque = r XF = I * alpha

rT = (I ) (a/r)

T = Ia / r^2 = (1.5 x 10-3)a / 0.038^2 = 1.04a

and on block:

Mg - T = Ma

1.6g - 1.04a = 1.6a

a = 5.95 m/s2

a) angular acc. = alpha = a/r = 5.95 / 0.038 = 156.53 rad/s

b) T = 1.04a = 1.04 x 5.95 =6.19 N

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