A block of mass m rests on a smooth wedge of mass M, which in turn rests on a smooth horizontal surface. The wedge is accelerated horizontally with acceleration
a. Find the normal force acting on the block by the wedge if the wedge makes an angle θ with the horizontal.

To find the normal force N acting on the block by the wedge, consider the forces in a non-inertial frame attached to the accelerating wedge. In this frame, the block is at rest. The forces acting on the block are:

• Gravity (mg) downwards.
• Normal force (N) perpendicular to the wedge's surface.
• Pseudo force (ma) horizontally to the left.

Resolve these forces perpendicular to the surface of the wedge. The components acting perpendicular to the wedge are:

• Component of mg: mgcosθ (into the wedge).
• Component of ma: masinθ (into the wedge).
• Normal force N (out of the wedge).

Since the block is at rest relative to the wedge, the net force perpendicular to the wedge is zero: N−mgcosθ−masinθ=0 Therefore, the normal force is: N = mgcosθ+masinθ N=m(gcosθ + asinθ)