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 FN.
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
(Fcosθ) cancels exactly with the normal force (FN), as we
expected, and we are left with one force, the parallel gravitational force
(Fsinθ), 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.
