How are surface area and frictional forces related?
My answer (along with thoughts collected from various internet sources):
Friction is independent of surface area. However, it is dependant on the types of surfaces in contact. A wooden block will experience less frictional force on ice than it would on concrete.
Friction is proportional to the normal force pressing surfaces together. Although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together. Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the FORCE holding them together. If you were to increase the force as you increased the area to keep PRESSURE the same, then increasing the area WOULD increase the frictional force between the two surfaces.
Other
ways to answer:
In general frictional forces are independent of the area of contact although this is an empirical observation not a theory. Consider a metallic brick and a metallic table. The reason that friction is nearly independent of surface area is if the "microscopic" area of contact of the brick to the table is independent of the orientation of the brick. If this is not the case, then friction will have a small dependence on area. In normal circumstances, with the largest surface area of the brick in contact with the table there are a large number of "contact" points that support the load. With the smallest area in contact (brick standing on end) there are fewer contacts but as long as the area of each contact is larger due to the higher pressure (same force, smaller unit area) then there will be no difference in the amount of static friction. Over wide limits, most materials follow this and hence friction is largely independent of surface area. iF you have a situation where the microscopic contact area does not scale in accordance with the pressure, then static friction will depend upon orientation.
In order to answer this, we need to understand what friction is. Friction is a result of the attractive forces between atoms when two materials are placed in contact with each other. Frictional forces are determined by two things, the size of the upward force of the surface on an object, (on a flat, horizontal surface, this would be the same magnitude as the weight in the opposite direction). and the coefficient of friction. The coefficient of friction is a result of the type of surfaces in contact. If you were to look at any surface under a powerful microscope it would not be smooth. In fact it would look much like a mountain range with high peaks and valleys. When we place two surfaces in contact with one another, there are places where the peaks are touching. At these points the material "cold welds" together. It takes a force to break these welds apart. These welds are the reason for friction.
When two surfaces are in contact the places where they actually touch are very small. The area of contact is a very small fraction of the total surface area of the two objects. The coefficient of friction between two objects is determined by experiment and has a couple of interesting characteristics.
First, it appears to be independent of surface area. I conducted a few experiments with a block of wood on various surfaces. Pulling the block across the surfaces with a spring scale and a constant weight on the block, it did not matter whether the smallest block was down or the largest side was down. The frictional force remained fairly constant even though the surface in contact was reduced by more than a third.
The second characteristic was that the amount of force needed to move the block was proportional to the mass being pulled. I did the same experiment again and varied the mass.
These experiments are ones that you can verify in your physics class. I would encourage you to verify my answer to your question. It would appear that friction depends less on area than on the types of material in contact.
Wide
Tires:
Question
As an engineer, I know that friction does not depend upon surface area. As a car nut, I know that wider tires have better traction. How do you explain this contradiction?
Answer
This is a good question and one which is commonly asked by students when friction is discussed. It is true that wider tires commonly have better traction. The main reason why this is so does not relate to contact patch, however, but to composition. Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. softer tires have a larger coefficient of friction, therefore better traction. A narrow, soft tire would not be strong enough, nor would it last very long. Wear in a tire is related to contact patch. Harder compound tires wear much longer, and can be narrower. They do, however have a lower coefficient of friction, therefore less traction. Among tires of the same type and composition, here is no appreciable difference in 'traction' with different widths. Wider tires, assuming all other factors are equal, commonly have stiffer side-walls and experience less roll. This gives better cornering performance.