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Is more work required for this spring?

by endeavor
Tags: required, spring, work
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endeavor
#1
Jan11-06, 10:20 PM
P: 176
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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andrewchang
#2
Jan11-06, 10:25 PM
P: 223
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
endeavor
#3
Jan11-06, 10:27 PM
P: 176
but wouldn't it be:
work1 = 1/2 k (10cm)^2
work2 = 1/2 k (20cm - 10cm)^2=work1
?

andrewchang
#4
Jan11-06, 10:57 PM
P: 223
Is more work required for this spring?

no, the work is the difference between energies.

[tex] EPE_i + W = EPE_f [/tex]
[tex] W = EPE_f - EPE_i [/tex]
[tex] W = 0.5kx_f^2 - 0.5kx_i^2 [/tex]
endeavor
#5
Jan11-06, 11:08 PM
P: 176
I remember now...

what does EPE mean?
catalyst55
#6
Jan11-06, 11:18 PM
P: 24
elastic potential energy


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