We wrap a light, nonstretching cable around a $9\mathrm{.}00$ kg solid cylinder with diameter of $20\mathrm{.}0$ cm$.$The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a $14\mathrm{.}0$ kg block and release the block from rest. As the block falls, the cable unwinds without stretching or slipping. $1.$ How far will the mass have to descend to give the cylinder $550$ J of kinetic energy?