Understanding the Relationship between Spring Constant and Energy

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Homework Help Overview

The discussion revolves around the relationship between spring constants and elastic potential energy (EPE) in a physics context. The original poster attempts to compare the energy stored in two springs with different spring constants, K and 2K, while questioning the assumptions made regarding their extensions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore whether the extension (x) is the same for both springs and discuss the implications of differing spring constants on energy calculations. There is a focus on the relationship between spring stiffness and extension.

Discussion Status

Some participants have offered guidance by questioning the assumptions made about the extension of the springs. The discussion is ongoing, with participants clarifying expressions used for energy calculations and recognizing potential mistakes.

Contextual Notes

There is a mention of a possible oversight in the energy expression used by the original poster, indicating that assumptions about the extension of the springs may need to be revisited.

ravsterphysics
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Homework Statement



1.JPG

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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