Static friction is the force that holds two objects that are touching each other at rest. Kinetic friction is the force between two objects that are touching each other but are in motion. The coefficient of friction is a measurement of the amount of friction. We can easily measure the coefficient of static friction.
We will place a plastic car with its wheels removed on a board. Raise the board until the car begins to move. Measure the height of the end of the board and use the pythagorean theorem to calculate the angle of the board in relation to the floor when the car begin to move. Also use a protractor to measure the angle as a check on your calculations. Calculate the coefficient of friction.
Perform the test again with a light weight in the car and again with the heavier weight in the car. Perform all three tests again with different materials attached to the board. We used wax paper, .aluminum foil, and two grades of sandpaper.
Rank the materials in order of their coefficients of friction. The material with the lower coefficient is more slippery. The sandpaper is abrasive. It has a high coefficient of friction.
How do you calculate the friction? The gravitational force that runs parallel to an inclined surface is equal to the weight of the object times the sine of the incline angle. The gravitational force that runs perpendicular to the incline surface is equal to the weight of the object times the cosine of the incline angle. The normal force of the board pushing up against the car offsets the force of the car pushing down on the board. Therefore the frictional force that is offset when the car begins to move is equal to the coefficient of friction times weight times the cosine of the angle. The force that keeps the car from sliding down the board is equal to the weight times the sine of the angle. Since these forces are equal until the car begins to slide, the coefficient of friction times weight times cosine of the angle equals weight times sine of the angle. The coefficient equals the weight times sine divided by weight times cosine. The weight cancels out! The coefficient of friction is equal to the sine divided by the cosine of the angle or more simply the tangent of the angle. Putting weight in the car does not affect the coefficient of static friction. None of this applies to the coefficient of kinetic friction that will be addressed in a future chapter of the book.
Another way to calculate the angle is to take the inverse sine of the height divided by the length of the board. Use this calculation to check the angle measured by the protractor.
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