How do you find the coefficient of static friction?

Answer 1

Use the formula: FsMAX=μsFN

if you want to do it experimentally, get the two different surfaces, and angle one until the object on top starts moving. take the tangent of the angle that starts the objects sliding past one another, and that is your coefficient of static friction.

Answer 2

Experiments with Friction: Measuring Static Sliding Coefficient of Friction with a Ramp

by Ron Kurtus (revised 3 November 2005)

The goal of this experiment is to measure the static sliding coefficient of friction between two surfaces by using a ramp and measuring its inclination.

The idea is that if you put a solid object on a ramp and start to tilt the ramp upward, there is a point where the object will start to slide. That is the angle where the force of gravity is strong enough to overcome the static friction.

By simply knowing the angle or the inclination, you can then calculate the static sliding coefficient of friction between the two materials. You can cover the ramp with various materials to determine different coefficients.

Materials

1. A flat board to be used as a ramp
2. Optional covering material for the rmap
3. Objects to slide down the ramp

Steps

1. Place the ramp on the ground and put the object on the ramp
2. Slowly raise one end of the ramp until the object starts to slide
3. Measure the height (A) and length (B) of the inclination, as in the drawing below
4. Calculate the coefficient of friction between the surfaces: fr = A / B

Different combinations

You can use different combinations of materials to measure their coefficients of friction. For example, you can use a:

• Wooden board and a brick to calculate the kinetic coefficient of friction between wood and brick material
• Sheet of iron on the board and an iron block to slide down the ramp
• Sheet of iron with film of oil on it and an iron block to slide down the ramp
• Covering of wet linoleum and a shoe to see how slippery a floor can be

There are many combinations that you can measure.

Explanation

Although the equation to find the static coefficent of friction is very simple, the principles behind it require some knowledge of Mathematics.

Physical science background

The coefficient of friction between two surfaces is a number that determines how much force is required to move an object that is held back by friction when the two sufaces are pressed together.

The friction equation is Fr = fr x N, where Fr is the resistive force of friction or the amount of force required to overcome friction, fr is the coefficient of friction between the two surfaces, and N is the normal or perpendicular force pushing the two surfaces together. If the force pushing to surfaces together is gravity, then N equals the weight of the upper object.

Static and kinetic friction

For a sliding object, the static coefficient of friction results in the force required to start the object moving. Once the object is sliding at a steady rate, the kinetic coefficient of friction results in the force required to keep the object moving at that velocity.

Using ramp

A clever way to determine the static coefficient of friction is to start an object sliding down a ramp. The component of gravitational force that causes the object to just start moving is equal to the resistive force to keep the object stationary. That is the static force of friction.

Note that you must record what the two surfaces are. The coefficient of friction is always for two surfaces. For example, you could find the friction between wood and steel, wood on wood, rubber on wet pavement, and so on.

Knowing the force required to overcome the friction and the force pushing the object onto the ramp, will allow you to determine the static coefficient of friction.

Mathematics

The coefficient of friction is calculated using trigonometry. Consider the triangle in the drawing below.

C is the length of your ramp, which is inclined at an angle a and is at a height of A. The length of the sides of the triangle are A, B, and C. The relationship between the sides are the trigonometric functions sine of angle a, which is abbreviated sin(a), cosine of a or cos(a) and tangent of a or tan(a).

Since sin(a) = A / C and cos(a) = B / C, then sin(a) / cos(a) = tan(a).

Components of gravity

When an object that weighs W is on a ramp, the force of gravity can be divided into components in perpendicular directions.

Normal force component

The force pushing the object against the surface of the ramp is reduced because of the incline. The normal force N = W x cos(a), as show in the picture below. In the case where there is no incline, a = 0 degrees and N = W.

Component down the ramp

The component of gravity is pulling the object along the ramp is F = W x sin(a).

Object starts to move

Now when the angle a become steep enough, the object starts to move and F = Fr, which is the force of static friction required to start the object moving.

But you know that Fr = fr x N.

And for the object on the ramp, N = W x cos(a).

Thus W x sin(a) = fr x W x cos(a).

Using a little Algebra, we get fr = sin(a) / cos(a) or fr = tan(a).

Finally, since tan(a) = A / B, we have fr = A / B.

So, all you need to know is the angle the object starts to slide or the lengths of its sides, and you can easily determine the coefficient of friction between the two surfaces.

Experiments with Friction:
Measuring the Coefficient of Friction Using a Scale

by Ron Kurtus (26 January 2001)

Friction is a resistive force caused when two objects are in contact with each other. There are some simple experiments to determine the force of friction and the coefficient of friction.

The coefficient of friction is a number that determines how much force is required to move an object that is held back by friction.

Background

The equation for this is Fr = fr x N, where Fr is the resistive force of friction or the amount of force required to overcome friction, fr is the coefficient of friction between the two surfaces, and N is the normal or perpendicular force pushing the two surfaces together. If the force pushing to surfaces together is gravity, then N equals the weight of the upper object.

Static and kinetic

For a sliding object, the static coefficient of friction results in the force required to start the object moving. Once the object is sliding at a steady rate, the kinetic coefficient of friction results in the force required to keep the object moving at that velocity.

Two surfaces

Note that you must record what the two surfaces are. The coefficient of friction is always for two surfaces. For example, you could find the friction between wood and steel, wood on wood, rubber on wet pavement, and so on.

Method

One way to determine the coefficient of friction between two surfaces is to pull on an object, using a spring scale that is used to measure weight. If you lay an object on another surface and then pull it, you can determine the amount of force required to move the object.

The coefficient is then fr = Fr / W, where W is the weight of the upper object.

First you pull slowly until the object just starts to move. Record the force and calculate the static coefficient of friction.

Then drag the object along at a steady velocity. Record the force on the scale and calculate the kinetic coefficient of friction.

Answer 3

In coefficient of static friction, force is directly proportional to normal reaction, that means:

F=M N (consider M as coefficient of static friction)

now,

M=F/N

If you'll see the unit, then unit of F is Newton and unit of N is also Newton.

Therefore,

M= newton/newton

Therefore, Coefficient of static friction is unitless.