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  4. The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If θ is the angle of friction and θ is the angle which the plane makes with the horizontal, then :

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Q. The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\theta$ is the angle of friction and $\theta$ is the angle which the plane makes with the horizontal, then :

Haryana PMTHaryana PMT 2005Laws of Motion

Solution:

Here, $m g(\sin \phi+\mu \cos \phi)=2 m g(\sin \phi-\mu \cos \phi) $
$\Rightarrow $ $\tan \phi=3 \mu$
As $\mu=\tan \theta$
So, $\tan \phi=3 \tan \theta$