Hooke's Law & Energy conservation

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SUMMARY

The discussion centers on the application of Hooke's Law and energy conservation principles in calculating the spring constant (k) for a spring designed to safely decelerate an elevator. The engineer initially derived the equation k = 15mg/(2h) based on maximum acceleration and energy conservation, but later corrected the mistake to k = 12mg/h as per the solution key. The error was identified in the force equation used in the calculations, highlighting the importance of accurate force representation in such problems.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Knowledge of energy conservation principles in physics
  • Familiarity with basic calculus for solving equations
  • Ability to apply Newton's second law (F = ma)
NEXT STEPS
  • Study the derivation of Hooke's Law and its applications in engineering
  • Explore energy conservation in mechanical systems, focusing on potential and kinetic energy
  • Learn about the implications of maximum acceleration in safety engineering
  • Investigate common mistakes in force calculations and how to avoid them
USEFUL FOR

Engineering students, physics enthusiasts, and professionals involved in mechanical design and safety analysis will benefit from this discussion.

Ampere
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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:
Physics news on Phys.org
Well done :)
Perhaps you could show others where you went wrong with the force equation?
 

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