How Surface Area Affects the Force of Friction
The force of friction comes from the surface characteristics of materials that come into contact. How does physics predict those characteristics theoretically? It doesn’t. Detailed knowledge of surfaces that come into contact is something people have to measure themselves (or they can check a table of information after someone else has done all the work).
What you measure is how the normal force (a force perpendicular to the surface an object is sliding on) relates to the friction force. It turns out that to a good degree of accuracy, the two forces are proportional, and you can use a constant,
to relate the two:
Usually, you see this equation written in the following terms:
This equation tells you that when you have the normal force, F_{N}, all you have to do is multiply it by a constant to get the friction force, F_{F}. This constant,
is called the coefficient of friction, and it’s something you measure for contact between two particular surfaces. (Note: Coefficients are simply numbers; they don’t have units.)
Here are a couple of things to remember:

The equation

relates the magnitude of the force of friction to the magnitude of the normal force. The normal force is always directed perpendicular to the surface, and the friction force is always directed parallel to the surface. F_{F} and F_{N} are always perpendicular to each other.

The force due to friction is generally independent of the contact area between the two surfaces. This means that even if you have two heavy objects of the same mass, where one is half as long and twice as high as the other one, they still experience the same frictional force when you drag them over the ground. This makes sense, because if the area of contact doubles, you may think that you should get twice as much friction. But when you double the length of an object, you halve the force on each square centimeter, because less weight is above it to push down. Note that this relationship breaks down when the surface area gets too small, since then the coefficient of friction increases because the object may begin to dig into the surface.