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THIS EXPERT DOESNOT KNOW ANYTHING...................................For minimum force , F cos a = f [eqn 1] Where F is the force required , a is the optimum angle for min.force f is the friction force
f is related to F and mg by : f = ( mg - F sin a ) k [eqn 2 ] Where k represents the coefficient of friction
Equiting the two equations F cos a = ( mg - F sin a ) k
Solving for F , F = (mgk)/( ( cos a ) + k sin a ) [eqn 3]
For min.force , dF/da = 0 Differentiating equation 3 with respect to a, dF/da = -mgk*([k cos a ] - sin a)/(cos a + k sin a )^2
Solving for a when dF/da equal to 0 , a = 26.5650512° Substituting a into eqn 3 , F = 0.0219 N or 21.9 mN