Question

A body of mass 2 kg is lying on a rough inclined plane of inclination ${30}^{\circ }$.. Find the magnitude of the force parallel to the incline needed to make the block move (a) up the incline (b) down the incline, coefficient of static friction = 0.2

Answer 1

(a) To make the block up the incline, force should be equal and opposite to the net force acting down the incline.
Force $=\mu R+2g\sin {30}^{\circ }$
$=0.2\times \left(9.8\right)\sqrt{3}+2\times 9.8\times \left(\frac{1}{2}\right)3.39+9.8=13N$

with this minimum force th body moves up the incline with a constant velocity as net force on it is zero.
(b) Net force acting down the incline is given by,
$F=2g\sin {30}^{\circ }-\mu R=2\times 9.8\times \frac{1}{2}-3.39=6.41N$
Due to F = 6.41 N, the bodyi will move down the incline with acceleration, hence the force required is zero.