Question

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?

Answer 1

The torque required is the same. Work is torque times angle rotated through.

Since both wrenches rotate the nut 2 pi raidans, the work required is the same. The longer wrench will required less force on the handle of the wrench, because of its longer lever arm.