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Homework Help: How can the coefficient of friction change? Does it?

  1. Oct 25, 2016 #1
    1. The problem statement, all variables and given/known data
    The coefficient of static and kinetic friction is constant for a specific surface. On an incline plane s and k are both equal to tan of the inclined angle. If the angle increases then tan changes which means the coefficient of friction changes. How is this so?

    2. Relevant equations
    Fs = s x Fn
    s = tan

    3. The attempt at a solution
    Attached picture

    Attached Files:

  2. jcsd
  3. Oct 25, 2016 #2


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    The coefficients are considered to be constants, independent of the angle of incline. However, you could have a particular situation where the angle of the incline happens to be such that the tangent of the angle equals the coefficient of friction. If you changed the angle, then the tangent of the angle would no longer equal the coefficient.
  4. Oct 25, 2016 #3
    No it does not change as the angle changes: the friction coefficient only depends on the nature of the materials in contact.
    When you say μ=tanθ you have to remind that θ is the maximun angle for which the body is still at rest.
    So if α is your actual angle, you have no motion until α<θ: if the relation you used was correct it would mean that μ=tanα is increasing as α is increasing from 0 to π/2 and you would have infinite friction as α approaches π/2, and i'm sure you agree that would make no sense
  5. Oct 25, 2016 #4


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    The coefficient of static friction allows you to calculate the max force that is needed to overcome friction. If the applied force is lower then the friction force will also be lower.
  6. Oct 25, 2016 #5


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    No, it is constant for a specific combination of two surfaces in contact.
    Others have answered this in various ways. Here's another.
    It is merely that you are used to questions in which either the object is about to slip (μs=tan θ) or is slipping at constant speed (μk=tan θ). I.e., the angle is just that angle which achieves the relevant condition, given the coefficient.
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