A mass of 200 kg is resting on a rough inclined plane of . if the coefficient of friction is √ . find the least and the greatest forces acting parallel to the plane to keep the mass in equilibrium.
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The least force required to keep the mass in equilibrium is 0 N.
The weight of the force which will act in downward direction parallel to the plane
w=mgsinθ
The friction force which will act in the opposite direction of the movement of the block is given as
f_friction=μmgcosθ
Therefore the net force on the body
F=mgsinθ-μmgcosθ
Plugging the values in the above equation
F=200*9.81*sin30-(1/√3)*200*9.81*cos30
=0 N.
This means that the inclination of the plane is not enough to move the block, and block itself will be in equilibrium, there is no need to apply external force.
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