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How to derive coefficient of friction?

  1. Oct 2, 2005 #1
    I have a box at rest on a plane raised to the critical angle.

    I need to derive the formula [tex]\mu_s=mgtan(\theta)[/tex]
    I know [tex]f_s/n=\mu[/tex]

    This leaves me with [tex]tan(\theta)=\mu[/tex] cause the mg cancel out.... what did I do wrong?
  2. jcsd
  3. Oct 2, 2005 #2

    Andrew Mason

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    [itex]\mu_s[/itex] is dimensionless so it cannot be equal to [itex]mgtan\theta[/itex]. Your answer is correct.

  4. Oct 2, 2005 #3
    is what you are looking for

    Draw a free body diagram.
    This is only in the limiting case that it is the maximum [tex]\mu_x[/tex] which will let the body rest on the incline of such an angle without sliding. So in this case you can use [tex]Friction=F_n*\mu[/tex]
    And set that equal to the component of the gravitational force pointing down the incline
  5. Oct 2, 2005 #4
    Yes, thats what I managed to get. I think the [tex]mgtan(\theta)[/tex] must be a mistake the teacher made since [tex]\mu[/tex] cannot equal [tex]mgtan(\theta)[/tex] because its dimensionless as AM said.
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