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The force that is needed to stretch a stiff spring by x metres is F(x) = 50x + 200x³ newtons.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The force that is needed to stretch a stiff spring by metres is newtons. Find the work done in stretching it from 0.1 m to 0.2 m. Check with the formula that you get from integrating by hand.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. The work is the integral of the force over the distance. By hand: .
Check. At 0.2 m the antiderivative is . At 0.1 m it is . The difference is J.
Answer: 0.825 J.
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