Question

The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is $\mu$. Find the inclination $\theta$ of the plane.

Answer 1

Force required to prevent the body from sliding $\theta$

$F=mg\sin \theta -\mu mg\cos \theta$

force required to just move up the body

$F1=mg\sin \theta +\mu mg\cos \theta$

$F1=2F$

$F1=2fmg\sin \theta +\mu mg\cos \theta =2(mgsin\theta -\mu mg\cos \theta )$

0r$3\mu mg\cos \theta =mg\sin \theta$

$\tan \theta =3\mu$