Is more work required for this spring?

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The discussion centers on calculating the work required to stretch a spring with a force constant of 50 N/m from different positions. It is clarified that the work done is not the same for equal displacements due to the nature of elastic potential energy (EPE). The work is calculated using the formula W = EPE_f - EPE_i, leading to a greater amount of work required to stretch the spring from 10 cm to 20 cm compared to 0 cm to 10 cm. The participants emphasize that the work is determined by the difference in energy states rather than just the distance moved. The conversation concludes with a reminder that EPE stands for 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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