Question

A screwdriver whose handle is 1 m in diameter is used to tighten a bolt which has 24 threads per inch. If the efficiency is 8 percent, find the force exerted on the nut when a force of 3 N is applied to the handle. 

Answer 1

24 threads per inch is 25.4/24=1.06 mm pitch, or 0.00106 m pitch. The applied force to the nut is

$$F_n=\eta F\frac{D}{p}=0.08·3\frac 1{0.00106}=226\text{ N}.$$