Consider the pulley shown in the figure, which has a radius of 10 cm and a moment of inertia of 0.5 kg-m ^2 about its axis. Assuming that the inclined planes are frictionless, determine the acceleration of the 4.0 kg block.

Step-by-step solution

Let a be the acceleration of the blocks, T₁ be the tension in the string attached to the 2.0 kg block, and T₂ be the tension in the string attached to the 4.0 kg block. The equations of motion for the blocks along the incline are: For the 4.0 kg block (moving downwards): m₂ g 45^ - T₂ = m₂ a 4g 45^ - T₂ = 4a For the 2.0 kg block (moving upwards): T₁ - m₁ g 45^ = m₁ a T₁ - 2g 45^ = 2a For the rotation of the pulley: (T₂ - T₁)R = I Since the string does not slip, = a R . T₂ - T₁ = I R^2 a Given I = 0.5 kg-m ^2 and R