A \(3.0-\mathrm{kg}\) block is attached to one end of a light, unstretchable string that is wrapped securely around a cylinder that has a \(0.30-\mathrm{m}\) radius and a rotational inertia of \(0.80 \mathrm{~kg} \cdot \mathrm{m}^{2}\). The cylinder is free to rotate about an axle aligned along its long axis. The block is held right alongside the cylinder (so there is essentially no unwound string) and then released from rest. As the block falls, it unwinds the string from the cylinder, with no slippage between string and cylinder.

(a) Calculate the magnitude of the block's acceleration.

(b) Calculate the rotational speed of the cylinder after the block has dropped \(1.5 \mathrm{~m}\). (First use the acceleration from part \(a\) to determine the block's speed.)

(c) Use energy methods to obtain the cylinder's rotational speed after the block has dropped \(1.5 \mathrm{~m}\).

(d) Calculate the tension in the string after the block has dropped this distance.

(e) Calculate the instantaneous power delivered by the string and block to the cylinder after the block has dropped this distance.