GATE 2018 ME (ME1) – Question 51
The slider–crank shown has crank angle 45°, crank length 30 mm and connecting rod length 70 mm. A 40 N leftward force acts on the slider. Neglect gravity, friction and inertia. Crankshaft torque magnitude for equilibrium, to two decimals, is ______ N m.
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Correct answer: 1.00 to 1.20
Explanation
Slider coordinate is $x=r\cos\theta+\sqrt{l^2-r^2\sin^2\theta}$. Virtual work gives torque magnitude $F|dx/d\theta|$. Differentiation and substitution of r = 0.03 m, l = 0.07 m, θ = 45° and F = 40 N give 1.1184 N m, rounded to 1.12 N m.