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if the minimum horizontal force required to drag a heavy body on a rough horizontal surface be n times its magnitude, when it be inclined to the horinzontal at the angle of friction. find coefficient of friction.
The free body diagram is shown below:
on balancing forces we have
F and R are forces and u (=tan x) is coeff of friction
N1 =mg and F = f1 = uN1 =umg
N2 = mg.cosx
f2=uN2=umgcos x
R=f2+mgsinx
R = mg(u cosx+sinx)
also given : R = nF
so, nu.mg = mg(u cosx+sinx)
also tanx =u
so , n = 2 (1+ u2 )-1/2
so coeff of friction: u = (1 -(4/n2) )1/2
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