Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]
    [tex]n=f_y=mgcos(\theta)[/tex]
    [tex]f_s=f_x=mgsin(\theta)[/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

    User Avatar
    Science Advisor
    Homework Helper

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

    AM
     
  4. Oct 2, 2005 #3
    [tex]\mu_s=tan(\theta)[/tex]
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook