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Applying Newton's Three Laws

The Normal Force

Terms and Formulae

Problems

Of all physical forces in everyday life, perhaps the most common is the normal force. The normal force comes into play any time two bodies are in direct contact with one another, and always acts perpendicular to the body that applies the force. The simplest example of the normal force can be seen in the situation of a man standing on a platform. Clearly a gravitational force acts on the man, pulling him down, perpendicular to the platform; but since the man is not moving, another force must act to counteract the gravitational force. This force is applied by the platform, and is called the normal force, and is referred to as F N .

The normal force can also be seen as a direct consequence of Newton's Third Law. Continuing with the example of the man on the platform, his weight, due to the gravitational force, pushes down on the platform. Newton's third law predicts that this force on the platform must be accompanied with an equal and opposite force applied to the man by the platform. This force is precisely the normal force.

Since the normal force is a reactive force, its magnitude is independent of the nature of the force causing it. The most common normal force is caused by gravity, as seen in the man on the platform. However, there can be additional forces that also cause a normal force.

Consider a block on a platform with weight 10 N. In addition, someone pushes downward on the block with an additional force of 15 N. The platform thus experiences a total force of 25 N, and reacts with a normal force of 25 N, keeping the block in equilibrium. Thus, in the situation of a horizontal object, the normal force is simple: it is merely equal in magnitude and opposite in direction to all forces applied to the surface.

The Normal Force on an Inclined Plane

The normal force becomes more complex, however, in situations where forces are not perpendicular to the plane. Consider the case of a block resting on an inclined plane, or a ramp. In this instance, the gravitational force on the block is not perpendicular to the plane. In order to calculate the normal force for this situation we must find the component of the gravitational force that is perpendicular to the plane. We do so by breaking down the force vector into two components (see Vectors, Heading ): one parallel to the plane and one perpendicular to the plane. The normal force thus has equal magnitude and opposite direction of the component of the gravitational force that is perpendicular to the inclined plane. Using a free body diagram, all of these forces can be displayed, and the resultant motion can be predicted:

Figure %: Free Body Diagram of an Inclined Plane

What does our free body diagram predict? To find out we analyze all forces acting upon the object. The perpendicular gravitational force ( F cosθ ) cancels exactly with the normal force ( F N ), as we expected, and we are left with one force, the parallel gravitational force ( F sinθ ), which points down the plane. Thus the block will accelerate down the incline. Such a prediction seems to fit with our intuition: a block placed on an inclined plane will simply slide down the plane.

The normal force thus applies to a variety of situations. Though most commonly used with flat and inclined planes, the normal force applies in any situation in which a force is exerted on an object by direct contact from another object.

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