A body of mass 2kg is lying on a rough inclined plane of inclinat… - Vidyadip

Question

A body of mass 2kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the force parallel to the incline needed to make the block move:

Up the incline
Down the incline. Coefficient of static friction = 0.2.

✓

Answer

To make the block move up the incline, the force should be equal and opposite to the net force acting down the incline $=\mu\text{R}+2\text{g}\sin30^{\circ}$
$=0.2\times(9.8)\sqrt{3}+219.8\times\Big(\frac{1}{2}\Big)$ [from(1)]
$=3.39+9.8=13\text{N}$
With this minimum force the body move up the incline with a constant velocity as net force on it is zero.

Net force acting down the incline is given by,

$\text{F}=2\text{g}\sin30^{\circ}-\mu\text{R}$
$=2\times9.8\times\Big(\frac{1}{2}\Big)-3.39=6.41\text{N}$
Due to F = 6.41N the body will move down the incline with acceleration.
No external force is required.
$\therefore$ Force required is zero.

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