A block rests on a rough wedge of angle 30^ . The wedge is given a horizontal acceleration of g 3 to the right, and the block is found to be on the verge of sliding up the incline. The minimum coefficient of static friction required to prevent the block from sliding up the wedge is

Step-by-step solution

In the reference frame of the wedge, a pseudo force ma acts on the block horizontally to the left. Resolving the forces perpendicular to the inclined plane, the normal reaction is: N = mg 30^ + ma 30^ Substituting a = g 3 : N = mg ( 3 2 ) + m(g 3 ) ( 1 2 ) = 3 mg The net driving force pushing the block up the incline is: F_ up = ma 30^ - mg 30^ F_ up = m(g 3 ) ( 3 2 ) - mg ( 1 2 ) = 3mg 2 - mg 2 = mg For the block to be on the verge of sliding up, the limiting friction must balance this upward force: F_ up = _s N m