Question

A block of mass $\eta$. is pulled by mass means of a force $F$ up an inclined plane forming an angle $\theta$ with the horizontal as shown in figure. the coefficient of friction is $\mu$. Find the minimum force required for the block to move up and the angle $\alpha$ at that instant.

Answer 1

Let $F$ is the force to be applied parallel to the inclined planned to prevent the body from sliding down

$F_R=0F-mg(\sin \theta -{\mu }_s\cos \theta )=0$

$F=mg(\sin \theta -{\mu }_s\cos \theta )$

Refer image.

Force ${}^{\prime }{F}^{\prime }$ is required if angle of inclination $\left(\theta \right)$ is greater than angle of repose $\left(\alpha \right)$