# Friction

#### 716208058

Is there more than one equations to find friction if so what are they?

#### topsquark

Forum Staff
There are two kinds of friction that frequently come up.

The first is "static friction" that does not have a specified value. It occurs when there are two surfaces that are not sliding across from each other. There is a maximum amount of force that can be applied before the surfaces slip and this force is called "the maximum static friction force" and can be calculated by $$\displaystyle f_{smax} = \mu _s N$$ where N is the normal force between the two surfaces and $$\displaystyle \mu _s$$ is the "coefficient of static friction." The coefficient will be the same between any pair of the same surfaces.​

The second is "kinetic friction" and has a specified value. It occurs between two surfaces that are sliding across each other. Again we can calculate it: $$\displaystyle f_k = \mu _k N$$ where N is the normal force between the two surfaces and $$\displaystyle \mu _k$$ is the "coefficient of kinetic friction." The kinetic friction force is constant: we can generally apply any amount of horizontal force between the two moving surfaces. Again, the coefficient will be the same between any pair of the same surfaces.

The coefficients of friction are not to be taken as literal constants. They are sort of an average result of surface features and molecular boundaries and I don't know of any situation where someone has manganed to calculate it.

Occasionally you will hear about "rolling friction." In order for a wheel (for example) to roll without slipping there needs to be friction between the wheel and the surface it's rolling on. Technically this is a case of static friction, but I don't know much about it.

-Dan

• benit13 and chip

#### 716208058

There are two kinds of friction that frequently come up.

The first is "static friction" that does not have a specified value. It occurs when there are two surfaces that are not sliding across from each other. There is a maximum amount of force that can be applied before the surfaces slip and this force is called "the maximum static friction force" and can be calculated by $$\displaystyle f_x = \mu _{max}N$$ where N is the normal force between the two surfaces and $$\displaystyle \mu _{max}$$ is the "coefficient of static friction." The coefficient will be the same between any pair of the same surfaces.

The second is "kinetic friction" and has a specified value. It occurs between two surfaces that are sliding across each other. Again we can calculate it: $$\displaystyle f_k = \mu _k N$$ where N is the normal force between the two surfaces and $$\displaystyle \mu _k$$ is the "coefficient of kinetic friction." The kinetic friction force is constant: we can generally apply any amount of horizontal force between the two moving surfaces. Again, the coefficient will be the same between any pair of the same surfaces.

The coefficients of friction are not to be taken as literal constants. They are sort of an average result of surface features and molecular boundaries and I don't know of any situation where someone has manganed to calculate it.

Occasionally you will hear about "rolling friction." In order for a wheel (for example) to roll without slipping there needs to be friction between the wheel and the surface it's rolling on. Technically this is a case of static friction, but I don't know much about it.

-Dan
Thank you!!

• chip

#### benit13

Just a minor, but important, detail to add to TopSquark's post...

The frictional force always has the following properties:

1. It always resists motion, it never aids it; and
2. It will always equal the pushing force, up to some limiting value.

The formulae provided by Topsquark are the limiting values. In general, $$\displaystyle f_x \le \mu N$$.

To see how this might be important, let's consider a simple example. Consider a box with a weight of 1000N on a horizontal surface with a coefficient of static friction equal to 0.5. Due to Newton's first law, the normal force is equal to the weight.

The limiting frictional force is then:

$$\displaystyle f_x = \mu_{max} N = 0.5 \times 1000 = 500$$N

However, if someone pushes horizontally on the block with a force less than this, say, 200 N, the frictional force will equal it (200N) and will resist the pushing force. The forces are in equilibrium and the box will not accelerate.

Here's a graph showing how, in general, the frictional force varies with applied force. As the applied force is increased, the frictional force increases to match it. Eventually, however, the applied force starts to exceed the limiting value for static friction (point B). For applied forces above this limit, the object will accelerate. The frictional force then dips slightly to the dynamic limit (C) because of the lower coefficient of resistance.

• topsquark