Answer to Question #260004 in Physics for Mule

Question

A 10-tooth gear drives a 40-tooth gear with an efficiency of 80 percent. (a) When the input gear turns at 8 rpm, how fast does the output gear turn? (b) When a torque of 30 N · m is applied to the input gear, what is the output torque? 

Answer 1

(a) The output speed of the output gear is

$$n_o=n_i/(z_o/z_i)=8/(40/10)=2\text{rpm}.$$

(b) The output torque is

$$T_o=\eta T_i·(z_o/z_i)=0.8·30(40/10)=96\text{ N}·\text m.$$