# Coefficients of Friction for Wood

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The coefficient of friction is a constant given by the equation µ = f/N, where f is the friction and N is the normal force. It has no units. When the object is not moving there is static friction. Once the object moves, there is kinetic friction. The coefficient of static friction is generally greater than the coefficient of kinetic friction on the same surface.

The procedures for this experiment are as follows:

1. Place the accelerometer onto the surface of the wood (pine) towards one end. Tape it into place.
2. Hook up the accelerometer onto the Vernier Lab Pro. Connect the Lab Pro to the laptop.
3. Open Logger Pro in the laptop.
4. Place the material to be tested on the surface. Slowly lift one end of the surface until the material starts sliding down the incline.
5. The accelerometer will measure the parallel component of the acceleration due to gravity and its recorded results will be displayed graphically in Logger Pro. Note when the object begins to slide. On the graph, it should be the point where the value jumps.
6. Repeat with different objects: a piece of granite, a penny, a piece of paper, and a piece of aluminum foil.

First we must obtain the parallel component of the acceleration due to gravity from Logger Pro for each material.

At an incline, the weight is directed downwards

W = mg

There are two components that make up the weight: the parallel component

W// = mg sin θ

and the perpendicular component

W = mg cos θ

Since the incline angle is the same as the angle between the weight and its perpendicular component, we can say:

sin θ = W///W = a/g (because the masses cancel)

θ = sin-1(a/g) (where g = 9.8 m/s2)

We know the parallel component of the object's weight acts opposite the static friction. We also know that a = 0 because static friction prevents the object from moving. Thus:

Net Force = 0
W//fstatic = 0

Now substitute:

mg sin θ–µstaticmg cos θ = 0

Solving for µstatic we get:

µstatic = tan θ

Material g// (m/s2) θ (°) µs
Granite 1.92 11.30 0.20
Aluminum 2.09 12.31 0.22
Copper 2.43 14.36 0.26
Paper 4.51 27.40 0.52

Gary Louie, Olga Strachna, Dorothy Soo, Diana Kuruvilla -- 2005

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