Determine the mass M of the hanging block shown in the figure that will prevent the smaller block from slipping over the triangular block. Assume all surfaces are frictionless and that the string and pulley are light.

Step-by-step solution

Let the acceleration of the system be a to the right. For the smaller block of mass m to not slip over the triangular block, it must move with the same horizontal acceleration a as the triangular block. Considering the free body diagram of the smaller block m from the ground frame, the forces acting on it are its weight mg downwards and the normal reaction N perpendicular to the inclined surface. Resolving the normal reaction N into horizontal and vertical components: Vertical equilibrium: N = mg Horizontal acceler