The cable of the 1800 kg elevator cab in the figure snaps whenthe cab is at rest at the first floor, where the cab bottom is adistance d = 4.9 m above a spring of spring constant k = 0.33 MN/m.A safety device clamps the cab against guide rails so that aconstant frictional force of 3.2 kN opposes the cab's motion. (a)Find the speed of the cab just before it hits the spring. (b) Findthe maximum distance x that the spring is compressed (thefrictional force still acts during this compression). (c) Find thedistance (above the point of maximum compression) that the cab willbounce back up the shaft. (d) Using conservation of energy, findthe approximate total distance that the cab will move before comingto rest.
(Assume that the frictional force on the cab is negligible whenthe cab is stationary.)
