I don't quite get the point about the algebraic sign. They probably want you to say it is negative because the spring has work done ON it. The person's finger pushing the spring does the positive work.
Anyway, the work done by the pusher of the spring is
(1/2)k[(.0097)^2 - (.0044)^2]
Note that the compression distances has to be converted to meters.
k = 228 N/m
The answer will be in Joules
A pen contains a spring with a spring constant of 228 N/m. Whe the tip of the pen is in its retracted position, the spring is compressed 4.40 mm from its unstrained length. In order to push the tip out and lock it into its writing position, the spring must be compressed an additional 5.30 mm. How much work is done by the spring force to ready the pen for writing? Be sure to include the proper algebraic sign with your answer.
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