The cable of the 1900 kg elevator cab shown the figure snaps when the cab is at

Question

The cable of the 1900 kg elevator cab shown the figure snaps when the cab is at rest at the first floor, where the cab bottom is a distance

above a spring of spring constant

A safety device clamps the cab against guide rails so that a constant frictional force of 4.0 kN opposes the cab's motion. (Assume that the frictional force on the cab is negligible when the cab is stationary.)

(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 frictional force still acts during this compression).

(c) Find the distance that the cab will bounce back up the shaft.

(d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest.

Explanation / Answer

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The cable of the 1800 kg elevator inFigure 8-56 snaps when the elevator is at rest at the first floor,where the cab bottom is a distance d = 3.7 m above a cushioning spring whose spring constantis k = 0.15 MN/m. A safety deviceclamps the elevator against guide rails so that a constantfrictional force of 4.4 kN opposes themotion of the elevator.

(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 frictional force still acts during this compression).

(c) Find the distance that the cab will bounce back up the shaft.

(d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest.

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