# Rusted bolts

**Classical Mechanics**Level 2

We use a wrench to turn nuts on bolts because they require less force. Consider a hexagonal nut \(1~\mbox{cm}\) in diameter. We can tighten this nut with one of two wrenches, wrench A with lever arm \(10~\mbox{cm}\) and wrench B with lever arm \(20~\mbox{cm}\). 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?