GATE 2024 ME – Question 59

Machine Design · Brakes and clutches · 2 marks · Numerical answer

A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The maximum braking force ($F$) that can be safely applied is _______ N (*rounded off to the nearest integer*).

A drum turning clockwise with a band round it. The left end of the band is fixed to the pivot of a horizontal lever at its left end. The right end of the band is attached to the lever 200 mm from the pivot. The force F acts downward on the lever 800 mm further to the right.

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Correct answer: 300

Explanation

The drum turns clockwise, so it drags the band down on its right side and that side carries the larger (tight side) tension $T_1$. The right end of the band is joined to the lever 200 mm from the pivot, and the slack side is joined at the pivot, so its tension gives no moment there. Moments about the pivot: $F \times 1000 = T_1 \times 200$, so $F = 0.2T_1$. The band can take 1500 N at most, so $F_{max} = 0.2 \times 1500 = 300$ N.