Is more work required for this spring?

[endeavor]

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.

 

[andrewchang]

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]

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

 

[andrewchang]

no, the work is the difference between energies.

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

 

[endeavor]

I remember now...

what does EPE mean?

 

[catalyst55]

elastic potential energy