The cable of an 1800 kg elevator cab snaps. By the time the cab reached the first floor, the cab is falling at 5 m/s, at that moment, when the cab's bottom is a distance d = 4 m above a spring with spring constant k = 5x105 N/m, a safety device is activated which clamps the cab against the guide rails so that a constant friction force of 4400 N is applied to the cab to opposes its motion.
(a). Find the speed of the cab just before it hits the spring.
(b). Find the maximum distance x that the spring is compressed. The friction force from the safely device is still active during this process.
(c). Find the distance that the cab will bounce back up the shaft after its first bounce from the spring. The friction force from the safely device is still active during this process.