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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.

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.


 


 


  

Grade:12

1 Answers

Ramesh V
70 Points
11 years ago

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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