GATE 2021 ME (ME1) – Question 63

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

A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4. The magnitude of the torque applied by the brake is _____ N.m (round off to one decimal place).

Clockwise drum of radius 260 mm under a short-shoe lever; pivot-to-shoe and shoe-to-effort distances are each 500 mm and pivot height above drum centre is 310 mm. See the attached source image.

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Correct answer: 199.00 to 201.00

Explanation

The contact lies 310−260=50 mm below the pivot. Clockwise drum motion exerts rightward friction on the shoe; both friction and normal reaction oppose the applied effort’s moment.

Moment balance is $N(500)+0.4N(50)=1000(1000)$ in Nmm. Thus N=1923.077 N and $T=\mu Nr=0.4(1923.077)(0.26)=\mathbf{200.0}$ Nm.