# How are frictional forces measured?

Aug 2, 2015

The force of friction occurs when one not ideally smooth object slides against another one. This force always directed against the movement and, in absence of other forces, slows down the sliding.

The force of friction depends, mainly, on two factors: material the objects are made of (more or less smooth) and how tightly they are pushed against each other. Typical textbook problem in physics is to determine the force of friction when one object (say, a wooden block) slides horizontally across some surface (like a table) and it's pushed against this surface by its weight (force of gravity). A variation is a similar problem, but the surface is not horizontal, but is a slope of some angle.

While the measure of how tightly the objects are pushed against each other is easily measured using the pressure force, the factor of material objects are made of is not so easily accounted for. For this physicists are using the coefficient of friction, which measures the force of friction between two objects made of certain materials per unit of pressure. It's determined experimentally.

Now, knowing the pressure ${F}_{p}$ from the physical composition of an experiment and the coefficient of friction ${\mu}_{f}$ of materials involved, we can calculate the force of friction ${F}_{f}$ as their product:
${F}_{f} = {\mu}_{f} \cdot {F}_{p}$

So, to determine the force of friction theoretically, we have to know the coefficient of friction of materials involved and the pressure between them.

If we don't know the coefficient of friction, we can determine the force of friction experimentally in many different ways. Here is an example.

Assume you want to measure the force of friction between a wooden block of mass $M$ ($k g$) with the area of its base $S$ (${m}^{2}$) that slides across a wooden table. We can start moving this block at some initial speed $V$ ($\frac{m}{\sec}$) and then let it go by itself until the friction stops it. For instance, the block stops after time $T$ ($\sec$) after we let it go.

It stops because the friction force $F$ stops it acting against the movement, decelerating from speed $V$ to $0$ during time $T$. We can now determine the degree of deceleration $a$ from the initial speed to zero:
$a = \frac{V}{T}$

Now, knowing the deceleration and mass of the block, we determine the friction force:
$F = M \cdot a = M \cdot \frac{V}{T}$

Since we know the mass and area of the base of our block, we can determine the pressure on the table $P$ (weight per unit of area):
$P = \frac{M \cdot g}{S}$

Finally, we can determine the friction coefficient (the friction force per unit of pressure):
$\mu = \frac{F}{P} = \frac{M \cdot V \cdot S}{T \cdot M \cdot g} = \frac{V \cdot S}{T \cdot g}$

Incidentally, the coefficient of friction under these conditions does not depend on the mass of the block. The above obtained coefficient of friction is called kinetic since it was measured during the movement of one object against another.

Another type of the coefficient of friction is static, it measures the initial force of friction when the object starts the movement and it's usually greater than kinetic, it's more difficult to start the movement then to continue. The static friction coefficient also can be determined experimentally, but this is a different story.