# Is more work required for this spring?

1. ### endeavor

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.

2. ### andrewchang

221
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

3. ### endeavor

176
but wouldn't it be:
work1 = 1/2 k (10cm)^2
work2 = 1/2 k (20cm - 10cm)^2=work1
?

4. ### andrewchang

221
no, the work is the difference between energies.

$$EPE_i + W = EPE_f$$
$$W = EPE_f - EPE_i$$
$$W = 0.5kx_f^2 - 0.5kx_i^2$$

5. ### endeavor

176
I remember now...

what does EPE mean?

6. ### catalyst55

24
elastic potential energy