Friction is a special kind of force. Unlike other forces, friction can only act to oppose motion. No matter what direction an object is moving, friction will produce a force in a direction opposite to the motion. Friction can be a nuisance, as in an automobile engine, but it can also be essential. Driving a car on icy roads is difficult because there is very little friction between the tires and the road.

The exact cause of friction is rather complicated and not even fully understood, but we can use a simplified model of friction that works fairly well. Just remember that these formulas are an oversimplification and not all matter really acts like this (plastics and rubber, in particular, deviate significantly from this model.)

The essential features of this simplified model are:

  • The frictional force does not depend on the size of the contact area. This means that if you set your book flat on the table or stand it up an its end, it will still take the same amount of force to slide it across the table.
  • The frictional force depends only on the composition of the materials, and the force pressing them together.

    To use the same example, the force needed to slide your book across the table will only depend on the ‘slipperiness’ of the table surface and the book cover, and how much the book weighs.

We recognize two distinct types of frictional forces. Static friction refers to the force that keeps things stuck together when they are not moving relative to each other. Kinetic friction is the friction between two surfaces that are sliding with respect to each other. When you stand on sloping ground, it is static friction that keeps you from sliding downhill. If you do start sliding, then it is kinetic friction that tries to slow you down.

Generally, static friction can exert a stronger force than kinetic friction. Imagine trying to push a heavy box across the floor. It is usually more difficult to get an object break free from rest than it is to keep it moving.

When an object is at rest, there must be zero net force acting on it. When you exert a force on it, the static friction produces a force exactly equal and opposite to the applied force. As the applied force increases, the static friction force increases right along with it, keeping the net force equal to zero. However, there is a limit to how much force can be produced by static friction. When the applied force exceeds this maximum, the object will start sliding. As soon as the object starts moving, the kinetic friction force takes over and produces a force opposing the motion. The following pictures illustrate this sequence of increasing applied force.

Static Friction

If the applied force is less than the maximum static friction force, then the static friction force is just the opposite of the applied force:

Fs = Fapplied

up to a maximum static friction force of

Fmax = Nms

where ms is the coefficient of static friction, a number that depends on the materials, and N is the normal force. The word normal is used to mean perpendicular. What this means is that if the applied force happens to be at an angle, then only the vector component in the direction that is actually pressing the surfaces together will contribute to the friction. For example, if an object is resting on an inclined plane, the force of gravity will not be pulling it perpendicularly to the plane:

Kinetic Friction

The formula for the force of kinetic friction looks just like the formula for the maximum static friction:

Fk = Nmk

The difference is that the coefficient mk is the coefficient of kinetic friction, which is different from ms, the coefficient of static friction.