Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
In an open flat belt drive, if the coefficient of friction is $\mu$ and the angle of lap is $\theta$ radians, the ratio of tight side tension ($T_1$) to slack side tension ($T_2$), neglecting centrifugal tension, is given by:
Options:
(A) $T_1 / T_2 = e^{\mu \theta}$
(B) $T_1 / T_2 = e^{-\mu \theta}$
(C) $T_1 / T_2 = \mu \theta$
(D) $T_1 / T_2 = \ln(\mu \theta)$
Answer Key:
A
Step-by-Step Solution & Explanation
For a flat belt drive on the verge of slipping, the limiting tension ratio is derived from Euler's belt friction equation as:
$\frac{T_1}{T_2} = e^{\mu \theta}$