GATE 2023 ME – Question 34

Engineering Mechanics · Friction and its applications: belts, brakes, clutches, screw jack, wedge · 1 mark · Numerical answer

The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle $\alpha = 270$ degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible.

During braking, the ratio of the tensions $T_1$ to $T_2$ in the belt is equal to __________. (Rounded off to two decimal places)
Take $\pi = 3.14$.

a pulley with a belt wrapped over it and pulled by the two tensions $T_1$ and $T_2$ at the lower end, attached to a lever with a force P.

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Show answer and explanation

Correct answer: 4.09 to 4.13

Explanation

For a belt on a pulley with friction, $\frac{T_1}{T_2} = e^{\mu\alpha}$ where $\alpha$ is in radians: $\alpha = 270° = 1.5\pi = 4.71$ rad. So $\frac{T_1}{T_2} = e^{0.3 \times 4.71} = e^{1.413} = 4.11$.