Is more work required for this spring?

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Homework Help Overview

The discussion revolves around the work required to stretch a spring with a force constant of 50 N/m over different intervals. The original poster questions whether the work needed to stretch the spring from 10 cm to 20 cm is greater than from 0 cm to 10 cm, seeking mathematical justification for their reasoning.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between displacement and work done on the spring, with some suggesting that the work should be the same due to equal displacements, while others argue that the work is determined by the difference in elastic potential energy at different positions.

Discussion Status

The discussion is active, with participants providing different interpretations of the work-energy relationship in the context of spring mechanics. Some have offered mathematical expressions for work done, while others are clarifying terms like elastic potential energy (EPE).

Contextual Notes

There is a focus on the mathematical justification for the work done, and some participants are questioning their understanding of the concepts involved, such as the definition of elastic potential energy.

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A spring with a force constant of 50 N/m is stretched continuously from x0=0 to x2=20 cm. Is more work required to stretch the spring from x1=10 cm to x2=20 cm than from x0 to x1? Justify your answer mathematically.

I thought the work required is the same because the displacements are equal for both work equations... but I think I'm wrong.
 
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work = 1/2 kx^2

so then the difference would be greater between 20cm and 10cm

w= EPEf-EPEi = 0.5(k)400-0.5(k)100 = 150k
w0->1 = 0.5(k)(100) - 0.5k(0) = 50k
 
but wouldn't it be:
work1 = 1/2 k (10cm)^2
work2 = 1/2 k (20cm - 10cm)^2=work1
?
 
no, the work is the difference between energies.

EPE_i + W = EPE_f
W = EPE_f - EPE_i
W = 0.5kx_f^2 - 0.5kx_i^2
 
I remember now...

what does EPE mean?
 
elastic potential energy
 

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