Help with spring stiffness calculation (k)

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of spring stiffness (k) based on a scenario where a steel ball is released from a compressed spring. The focus is on the application of Hooke's Law and the potential need for energy conservation principles in the calculation.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a solution using Hooke's Law, calculating the spring stiffness based on the force exerted by the mass of the steel ball.
  • Another participant questions the interpretation of the term "initially," suggesting it may indicate that the compression described is not the equilibrium position but rather the lowest point reached by the weight.
  • A suggestion is made to apply conservation of energy principles as an alternative approach to solve the problem.
  • Units of measurement are briefly discussed, with one participant confirming that they included units in their coursework despite omitting them in the forum post.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the correct approach to the problem, with differing interpretations of the spring's compression and the applicability of energy conservation versus Hooke's Law.

Contextual Notes

The discussion highlights potential ambiguities in the problem statement, particularly regarding the definition of "initially" and its implications for the spring's compression state. There are also unresolved aspects regarding the application of energy conservation in this context.

imd25
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Hi

I was given the following problem in my coursework:

Homework Statement


"A spring is initially compressed by 50mm when a steel ball of mass 2kg is released from just being in contact with the uncompressed spring. Determine the spring stiffness (k) of the spring."

Homework Equations


F = mg
Restorative force F = -kx

The Attempt at a Solution


I gave the answer below, but the teacher has marked it as wrong. Can anyone shed any light on where I may have made a mistake? I thought it was just a simple application of Hooke's Law.

F = mg
F = 2 x -9.81
F = -19.62 N

F = -kx
19.62 = -k(-0.05)
19.62 = 0.05k
k = 19.62/0.05
k = 392.4

Thanks, any insight gratefully received.
 
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Units?
 
Thanks for your reply Bystander,

I did actually include the units (N/m) in my coursework - sorry, I omitted them in my original post by accident.
 
I think the inclusion of "initially" implies the compression given is the lowest point the weight reaches rather than the equilibrium position that your solution assumes.
Try applying conservation of energy to solve.
 

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