Question

An electric motor develops 5.0-kW at 2000 rpm.The motor delivers its power through a spur gear 20-cm in diameter.If two teeth of the gear system to torque to another gear at the same instant, find the force exerted by each gear tooth.

Answer 1

Power $(P)$ , Speed rpm $(N)$ , Torque $(T)$

$p = \frac {2\pi NT}{60}$

$T = \frac{5000 \times 60}{2\pi\times2000}$

$T = 23.87 Nm$

the force exerted by each gear tooth $(F)$

Diameter $(D) = 20 cm = 0.2 m$

$T = F \times \frac{D}{2}$

$F = \frac{23.87 \times 2}{0.2} = 238.7N$