Project ForgeMachine Design
Design Against Static Load
GATE 2023
Medium
A braking system uses a belt to slow down a pulley by application of a force P. The belt wraps around the pulley over an angle α=270 degrees. The coefficient of friction between the belt and the pulley is 0.3. During braking, the ratio of the tensions T1 to T2 in the belt is equal to ______. (Rounded off to two decimal places; take π=3.14)
4.11(± 0.1 accepted)
Explanation
The belt-friction (capstan) equation gives T1/T2=e^(μα), with α in radians. α=270°=270×3.14/180=4.71 rad. μα=0.3×4.71=1.413. T1/T2=e^1.413≈4.11.
Source: GATE ME 2023 Official Paper (2023)
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