A body of mass 2 kg is placed on a rough inclined plane of inclination 30^ . Find the magnitude of the horizontally applied push necessary to initiate the block's movement up the incline. The coefficient of static friction is 0.2 .

Step-by-step solution

Let P be the magnitude of the horizontally applied push. The forces acting on the block are its weight mg , the normal reaction N , the horizontal push P , and the frictional force f . Resolving the forces perpendicular to the inclined plane, the normal reaction is: N = mg 30^ + P 30^ To initiate movement up the incline, the component of the push along the incline must overcome the downward component of the weight and the limiting static friction: P 30^ = mg 30^ + f Since f = N , we have: P 30^ = mg 30^ + (mg 30^ +