Question

Let's suppose we are pulling a box of mass m along a horizontal floor. All sides of the box have the same type of surface (same coefficient of friction between any side and the floor). In one case, the contact surface is much larger (first picture) and in another, it is much smaller. Will there be any difference in the force of friction? Why?

Answer 1

No, there will be no difference in force of friction with two different surface area provided coefficient of friction between box surface and horizontal floor is same. This is because force of friction is independent of the contact surface area of the two surfaces which are in contact with each other.

Although a large contact area between two surfaces would result in larger frictional forces, simultaneously it also reduces the pressure between the two surfaces for the force holding the two surfaces together (because pressure is force divided by area). Hence the result is, increase in friction generating area is exactly offset by reduction in pressure. Thus the resulting frictional forces only depend on the coefficient of friction and independent of the surface area of the surfaces in contact and the force holding them together.

Thus increasing force would result in increase in frictional forces.