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The normal force refers to a force perpendicular to the surface of contact between two bodies.
The weight of a body with mass m is equal to W = m*g where g is the acceleration due to the gravitational force. This is a force that acts vertically downwards. If a body is placed on a level surface parallel to the horizontal, the normal force is equal to the weight of the body, N = m*g.
If the body is placed on a surface that is inclined with angle A formed between the surface and the horizontal, the normal force is given by the expression N = m*g*cos A. This can also be used in the case of a horizontal surface; as A = 0 and cos 0 = 1, N = m*g
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