Understanding the Relationship between Spring Constant and Energy

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SUMMARY

The discussion centers on the relationship between spring constants and elastic potential energy (EPE) in springs. The equation for EPE is established as EPE = 0.5kx². A participant mistakenly assumed that the extension (x) is the same for two springs with different spring constants, K and 2K. Upon clarification, it was concluded that the stiffer spring (2K) would have half the extension, leading to equal energy stored in both springs when calculated correctly.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with the formula for elastic potential energy (EPE)
  • Basic knowledge of algebra for manipulating equations
  • Concept of spring extension and its relationship to spring stiffness
NEXT STEPS
  • Review the derivation of the elastic potential energy formula EPE = 0.5kx²
  • Explore the implications of varying spring constants on energy storage
  • Investigate practical applications of Hooke's Law in engineering
  • Learn about the behavior of springs in series and parallel configurations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in the principles of spring dynamics and energy storage.

ravsterphysics
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Homework Statement



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Homework Equations

The Attempt at a Solution



EPE is (0.5)kx^2

Let Y have spring constant of K then X has spring constant of 2K

So EPE of Y is (0.50kx^2 which is E

So EPE of X must be (0.5)2kx^2 which is kx^2 which is 2E? But correct answer is E/2??
 
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It looks like you've assumed that x is the same for both springs. Is that going to be the case?
 
gneill said:
It looks like you've assumed that x is the same for both springs. Is that going to be the case?

Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
 
ravsterphysics said:
Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
Check the expression you've just used for the energy. Did you forget something?
 
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gneill said:
Check the expression you've just used for the energy. Did you forget something?

Argh such a silly mistake! Thanks for your help : )
 

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