Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
In belt drive power transmission, the condition for maximum power transmission considering centrifugal tension $T_c$ is:
Options:
(A) $T_c = \frac{1}{2} T_{\max}$
(B) $T_c = \frac{1}{3} T_{\max}$
(C) $T_c = \frac{2}{3} T_{\max}$
(D) $T_c = T_{\max}$
Answer Key:
B
Step-by-Step Solution & Explanation
Power transmitted is $P = (T_1 - T_2)v = T_1 (1 - e^{-\mu\theta})v$. When centrifugal tension $T_c = m v^2$ is considered, the maximum tension is $T_{\max} = T_1 + T_c$, so $T_1 = T_{\max} - m v^2$. Differentiating power with respect to velocity $v$ and setting to zero yields $v = \sqrt{\frac{T_{\max}}{3m}}$, which corresponds to $T_c = \frac{1}{3} T_{\max}$.