A block of mass m slides down a wedge of mass M. Find the minimum coefficient of friction required between the wedge and the ground so that the wedge does not move.

Question

G1 Physics · Accepted Answer

For the wedge to remain fixed, ground friction must balance the horizontal component of the contact force exerted by the sliding block. Using N = mg cosθ and resolving the block's contact force on the wedge gives horizontal demand mg sinθ cosθ and ground normal (M + m cos²θ)g. Therefore μₘᵢₙ = m sinθ cosθ/(m cos²θ + M).