Two blocks are on a double incline whose surfaces make angles of 45 degree s wit

Question

Two blocks are on a double incline whose surfaces make angles of 45 degree s with the horizontal. Block A on the left is connected to a rope that is wrapped around a pulley. The other end of the rope is connected to Block B on the right. The surfaces are frictionless. The pulley has I = 0.500 kg*m2 with respect to the fixed horizontal axis of rotation through the center marked by the dot. The pulley radius is R = 0.200 m. See labels on the pulley below. The block on the right has mass mB= 5.00 kg. and the block on the left has mass mA = 8.00 kg. Assume the system starts from rest. In the figure below, what direction does the pulley rotate clockwise or counter clockwise? Circle one. Compute the magnitude |a | of the pulley's angular acceleration about the axis shown. Compute the tension magnitude TB in the section of string between the pulley and Block B. Compute the tension magnitude TA in the section of string between the pulley and Block A. Referring to parts (c) and (d), should TB be larger or smaller than TA ? Circle one and explain.

Explanation / Answer

In the drawing clockwise torques are positive Summing forces about the block yields m*g - T = m*a So T = m*g - m*a Summing torques about the cylinder T*r = I*a where I = 1/2*m*r^2 So (m*g - m*a)*r = 1/2*m*r^2*a but a = r*a so m*g*r - m*r^2*a = 1/2*m*r^2*a Therefore (1.5*m*r^2)*a = m*g*r So a = g/(1.5*r)

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