Answer to Question #260648 in Physics for Mule

Question

The alternator on a truck engine produces 350Wof electric power when it rotates at 4000 rev/min. If it is 95 percent efficient, what should the difference (in newtons) between the tensions in the tight and slack parts of its V-belt drive be? The diameter of the alternator’s pulley is 10 cm.

Answer 1

1) Determine the torque:

$$\tau=\frac P\omega=30/(4000/60)=0.45\text{ N}·\text{m}.$$

2) The tension applied to the pulley:

$$T=\tau/r=0.45/0.05=9\text{ N}.$$

3) The difference is

$$\Delta T=(1-\eta) T=(1-0.95)9=0.45\text{ N}.$$