Another quite common force is frictional force. Like the normal
force, it is caused by direct contact between surfaces. However, while
the normal force is always perpendicular to the surface, the frictional
force is always *parallel* to the surface. To fully describe the
cause of friction requires knowledge beyond the scope of classical
mechanics. For our purposes, it is enough to know that friction is caused
by electrical interactions between the two surfaces on a microscopic
level. These interactions always serve to resist motion, and differ in
nature according to whether or not the surfaces are moving relative to
each other. We shall examine each of these cases separately.

###
Static Frictional Forces

Consider the example of two blocks, one resting on top of the other. If
friction is present, a certain minimum horizontal force is required to
move the top block. If a horizontal force less than this minimum force is
applied to the top block, a force must act to counter the applied force
and keep the block at rest. This force is called the static frictional
force, and it varies according to the amount of force applied to the
block. If no force is applied, clearly there is no static frictional
force. As more force is applied, the static frictional force increases
until it reaches a certain maximum value; once the horizontal force
exceeds the maximum frictional force the block begins to move. The
frictional force, defined as *F*_{s}^{max}, is conveniently proportional to
the normal force between the two surfaces:

The constant of proportionality,

*μ*_{s} is called the coefficient of
static friction, and is a property of the materials that are interacting
(i.e. two interacting rough materials will have a higher value of

*μ*_{s}
than two smooth materials).

This equation for maximum static frictional force contains a lot of
information, and a few remarks must be made for clarification.

- The equation seems to be relating two vectors,
*F*_{s}^{max} and *F*_{N}.
This relation is valid only for the magnitudes of the vectors, not the
direction. In fact, the two vectors will always be perpendicular.
- The equation introduces the concept of the coefficient of static
friction. This constant varies from material to material, but does
not depend on the orientation of the material on the surface. For
example, if a block of wood is set on a concrete platform,
*μ*_{s}
is the same whether the block is on its side, its front, or its top.
In other words, the coefficient does *not* change according to the
surface area of contact.
- Since the equation does not specify a direction for the frictional force,
it must be stated and understood that the frictional force always acts in
the opposite direction as the force applied to the object.
- It is
vitally important to remember that this equation only gives the
*maximum* static frictional force, which corresponds to the maximum
force that can be applied to a body before it moves. If a lesser
force is applied to the body, a frictional force less than the maximum
force counteracts the original force.

Though it is rather surprising that frictional force and normal force are
related in such a simple manner, physical intuition tells us that they
should be directly related. Consider again a block of wood on a concrete
platform. The normal force is given by the weight of the wood. If an
additional downward force is applied to the wood (producing a greater
normal force) the surfaces are actually in closer contact than they were
before, and the resulting electrical interactions are stronger. Thus,
intuitively, a greater normal force yields a greater frictional force.
Our intuition agrees with the equation.

###
Kinetic Frictional Forces

Once a force is applied to an object that exceeds *F*_{s}^{max}, the object
begins to move, and static frictional forces no longer apply. The moving
object does still experience a frictional force, but of a different
nature. We call this force the kinetic frictional force. The kinetic
frictional force always counteracts the motion of the object, and is
independent of speed. No matter the speed of the object (as long as *v*≤ 0) it experiences the same frictional force. Also, for the same
reasons as explained with static friction, the kinetic frictional force is
proportional to the normal force:

This equation is of the same form as that for maximum static frictional
force, and defines the coefficient of kinetic friction, *μ*_{k}, which
has the same properties as *μ*_{s}, but a different value. *μ*_{k} is a
property of the interacting materials, and, like *μ*_{s}, is independent
of orientation of the objects. The only significant difference between
the two friction equations is that the first measures the friction between
two stationary objects and its value is dependent on the force applied to
one, while second measures a frictional force that only exists when one of
the objects is moving and which is not depend on the force applied to the
block. Finally, when comparing static with kinetic friction, it must be
noted that *μ*_{s} is always greater in value than *μ*_{k}. Simply
stated, this means that it takes less force to keep a block moving than to
start its motion.

These two types of friction, like the normal force, arise whenever two
objects are in direct contact. Often both kinetic and static friction
apply to a given situation, as an object might start at rest (when static
friction applies) then begin to move (when kinetic friction applies).
Though friction applies in so many situations, it is often ignored in
order to simplify the situation. Unless friction is explicitly stated to
be present in a given problem, in can be ignored. That said, friction
remains one of the most widely used applications of Newton's Laws.