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

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Solution

Let $F$ is the force to be applied parallel to the inclined planned to prevent the body from sliding down
$F_{R} = 0 F - m g (sin θ - μ_{s} cos θ) = 0$
$F = m g (sin θ - μ_{s} cos θ)$
Refer image.
Force $^{'} F^{'}$ is required if angle of inclination $(θ)$ is greater than angle of repose $(α)$

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A block of mass η. is pulled by mass means of a force F up an inclined plane forming an angle θ with the horizontal as shown in figure. the coefficient of friction is μ. Find the minimum force required for the block to move up and the angle α at that instant.

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