How to Derive the Coefficient of Friction
- 1). Place the object on the surface so that you are able to tilt the surface at a steadily increasing angle from the horizontal and measure the angle.
- 2). Slowly tilt the surface until the object begins to slide down the surface. Measure the angle.
- 3). Take the tangent of the angle using a scientific calculator. Make sure your calculator is using degrees for angle measurement. Most work with degrees or radians. It doesn't matter which you work with, but if you measure your angle in degrees, use degrees on the calculator. Most default to using degrees rather than radians. The result is the coefficient of static friction between the object and the surface. The coefficient of kinetic friction is usually slightly less than this figure. It can be determined more precisely with a slightly more complex experimental procedure.
- 1). Measure the mass of the object. Multiply this by the acceleration due to gravity which is 9.8 m/sec^2. This is the normal reaction force. If the object were one kilogram, the normal force would be 9.8 m kg / sec^2 or 9.8 Newtons.
- 2). Apply a force to the object to move it horizontally across the surface. Measure the amount of force applied when the object is moving at a constant velocity. The object is not accelerating, so the frictional force is exactly equal to the force pushing the object.
- 3). Divide the frictional force by the normal reaction force. The result is the kinetic coefficient of friction. Suppose the 1-kilogram object moves at a constant velocity when you apply five Newtons of force. 5/9.8 = .51. The kinetic coefficient of friction between the object and the surface is .51
Coefficient of Static Friction
Coefficient of Kinetic Friction
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