A block of mass m rests on a smooth inclined plane making an angle with the horizontal. What is the magnitude of the force exerted by the plane on the block?

Step-by-step solution

The forces acting on the block are its weight mg acting vertically downwards and the normal reaction N acting perpendicular to the inclined plane. Resolving the weight mg into two components: mg parallel to the inclined plane and mg perpendicular to the inclined plane. Since there is no motion perpendicular to the inclined plane, the forces in this direction are balanced. Therefore, the normal reaction N exerted by the plane on the block is equal to the perpendicular component of the weight. N = mg Since the plane