The cable of the 1600 kg elevator cab in the figure snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 3.1 m above a spring of spring constant k = 0.24 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 2.1 kN opposes the cab's 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 frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) 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. (Assume that the frictional force on the cab is negligible when the cab is stationary.)

The cable of the 1600 kg elevator cab in the figure snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 3.1 m above a spring of spring constant k = 0.24 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 2.1 kN opposes the cab's 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 frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) 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. (Assume that the frictional force on the cab is negligible when the cab is stationary.)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter9: Energy In Nonisolated Systems

Section: Chapter Questions

Problem 28PQ

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