The radius of the pulley is R = 100 mm and its moment of inertia is I = 0.1 kg-m2. The mas...

The radius of the pulley is R = 100 mm and its moment of inertia is I = 0.1 kg-m2. The mass m = 5 kg. The spring constant is k = 135 N/m. The system is released from rest with the spring unstretched. What maximum distance does the mass fall before rebounding?

Strategy: Assume that the mass-has fallen an arbitrary distance x. Write the equations of motion for the mass and the pulley and use them to determine the acceleration a of the mass as a function of x. Then apply the chain rule: