Elevator falling and bouncing back from a spring

Thread starter jolly_math
Start date Oct 24, 2022
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Elevator Falling Spring

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The discussion centers on the differences between two scenarios involving an elevator and a spring. In part c, the elevator is still airborne after compressing the spring and will descend again until all energy is dissipated. In contrast, part d likely involves a different outcome or behavior after the spring's compression. The key distinction lies in the elevator's motion and energy state post-compression. Understanding these dynamics is crucial for grasping the overall mechanics involved.

Oct 24, 2022

jolly_math

Homework Statement: The cable of a 4000-lb elevator snaps when the elevator is at rest at the first floor so that the bottom is a distance d = 12.0 ft above a cushioning spring whose force constant is k = 10,000 lb/ft. A safety device clamps the guide rails, removing 1000 ft-lb of mechanical energy for each 1.00 ft that the elevator moves.
(a) Find the speed of the elevator just before it hits the spring.
(b) Find the distance that the spring is compressed.
(c) Find the distance that the elevator will bounce back up the shaft.
(d) Calculate approximately the total distance that the elevator will move before coming to rest. Why is the answer not exact?

Relevant Equations: U(x) (gravity) = mgh
U(x) (spring) = (1/2)kx^2
KE = (1/2)mv^2

I don't understand the difference between part c and d. After compressing the spring, the elevator bounds back and moves before coming to rest in both cases. What is the difference? Thank you.

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Oct 24, 2022

BvU

Science Advisor

Homework Helper

Hi,

Well, after c, the thing is still up in the air and will start to go down again, etc, until all energy has been dissipated.

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