Hooke's Law & Energy conservation

AI Thread Summary
An engineer is tasked with designing a spring for an elevator shaft to limit passenger acceleration to 5.0 g in case of cable failure. The discussion revolves around applying Hooke's Law and energy conservation principles to determine the spring constant k. Initially, the engineer derived k as 15mg/(2h) but later corrected the force equation, leading to the correct solution of k = 12mg/h. The importance of accurately applying both force and energy equations in such calculations is emphasized. The engineer successfully resolved the issue and encouraged sharing the mistake for educational purposes.
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Homework Statement



An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should happen to break when the elevator is at a height h above the top of the spring, calculate the value of the spring constant k so that the passengers undergo an acceleration of no more than 5.0 g when brought to a rest. Let M be the total mass of the elevator and passengers.

Homework Equations



F=-kx, Hooke's law
Energy conservation: spring energy, gravitational energy

The Attempt at a Solution



The maximum acceleration will occur at the maximum compression of the spring, because a is proportional to x. Since kx=ma=5mg, k=5mg/x.

I then conserved energy to get 1/2kx^2 - mgx - mgh = 0.

I solved both equations to get k = 15mg/(2h). But my solution key says 12mg/h. What's wrong?

EDIT: Never mind, solved it. My force equation was off.
 
Last edited:
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Well done :)
Perhaps you could show others where you went wrong with the force equation?
 
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