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We use a wrench to turn nuts on bolts because they require less force. Consider a hexagonal nut 1 cm in diameter. We can tighten this nut with one of two wrenches, wrench A with lever arm 10 cm and wrench B with lever arm 20 cm. Both wrenches have a very small mass, so you may neglect their masses in this problem. What is the ratio of the total work it would take to tighten the nut one full turn with wrench A to the total work it would take with wrench B?

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closed as too localized by Mark Eichenlaub, Waffle's Crazy Peanut, akhmeteli, David Z Mar 6 '13 at 19:22

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Could you show what you have tried already to solve the question?! –  Michiel Mar 6 '13 at 11:21
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1 Answer 1

Assuming it requires the same torque to tighten the nut then the work done will be the same. Work done in a rotational situation is $$ Wd = \int \tau \rm{d}\alpha. $$

Both wrenches will turn the same $\alpha$ in one rotation and so the work done is the same.

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