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