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.
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:
|F s max = μ s F N|
This equation for maximum static frictional force contains a lot of information, and a few remarks must be made for clarification.
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.
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:
|F k = μ k F N|
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.