3. Two blocks are on a double incline whose surfaces make angles of 45 degrees w

Question

3. Two blocks are on a double incline whose surfaces make angles of 45 degrees 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. (a) In the figure below, what direction does the pulley rotate, clockwise or counter clockwise? Circle one. (b) Compute the magnitude |? | of the pulley

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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