A block of mass rests on a horizontal rough surface

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A block of mass mm rests on a horizontal rough surface. A force FF is applied at an angle θ\theta above the horizontal so that the block is on the verge of sliding. (a) Express the horizontal component of the applied force and the limiting static friction in terms of FF, θ\theta, mm, gg and μs\mu_s. (b) Derive an expression for FF in terms of mm, gg, μs\mu_s and θ\theta that will just set the block in motion. (c) Obtain the condition on θ\theta for which this FF is minimum, and hence show that the value of θ\theta satisfying this condition is given by tan⁡θ=μs\tan\theta = \mu_s. (d) For μs=0.30\mu_s = 0.30, calculate the optimum angle and the corresponding minimum force for a 12 kg12\,\text{kg} block. Use g=9.8 m s−2g = 9.8\,\text{m s}^{-2}.

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