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Name:  Kenn P.
Status: other
Age: 50s
Location: N/A
Country: N/A
Date: 2000-2001


Question:
I am the Mathematics Test Specialist for GED Testing Service, the organization that develops the High School Equivalency Exam. One of my Item Writers submitted a question in which she stated that the coefficient of friction was equal to the tangent of the angle of inclination at which one surface begins to move across another. I seem to recall from my high school physics class (in 1963) that such a statement was made, but perhaps that explanation is out of date. I would appreciate any attempt to verify the accuracy of the statement.


Replies:
Tipler's Physics text (Worth, 1976) shows how this result derives from Newton's equation. (It's the coefficient of static friction they're talking about, of course.)

Tim Mooney


Kenn,

This statement is true for the coefficient of STATIC friction. The coefficient of DYNAMIC friction is smaller.

Consider an object on a ramp, just starting to overcome static friction. If we let "A" be the angle of the ramp, the force of gravity pulling the object down the ramp is scaled by sin(A): F=mg.sin(A). The normal force between the object and ramp, how hard they are pressed together, is scaled by cos(A): N=mg.cos(A). As e-mail doesn't deal well with Greek symbols, we will use "u" as the coefficient of static friction. At the point of just overcoming friction, the force down the ramp equals the frictional force. The frictional force is "u" times the normal force.
F = u.N

mg.sin(A) = u.mg.cos(A)

divide out mg

sin(A) = u.cos(A)

sin(A) / cos(A) = tan(A)

tan(A) = u

Dr. Ken Mellendorf
Illinois Central College



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