The first figure gives spring force F x versus position x for the spring–block a

Question

The first figure gives spring force Fx versus position x for the spring–block arrangement of the second figure. The scale is set by Fs = 180 N. We release the block at x = 12.0 cm. How much work does the spring do on the block when the block moves from xi = +8.0 cm to (a) x = +5.0 cm, (b) x = -5.0 cm, (c) x = -8.0 cm, and (d) x = -10.0 cm?

Posted this one before and the answers were incorrect. I already answered (c) correctly, because it's obvious it'll be O J. Please only answer this if you're completely sure you know how to do it correctly.

Explanation / Answer

F = -kx

So, k = -F/x

So, k = -Fs/-2 = 180/2 = 90

a)

Work done by spring = change in spring energy

So, from xi = +8 cm to x= +5 cm,

Work done by spring = 0.5*k*xi^2 - 0.5*kx^2 = 0.5*k*(xi^2 - x^2)

So, W = 0.5*(90)*(0.08^2 - 0.05^2) = 0.1755 J <------answer

b)

W = 0.5*90*(0.08^2 - (-0.05)^2) = 0.1755 J

c)

W = 0

d)

W = 0.5*90*(0.08^2 - 0.10^2) = -0.162 J

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