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Calculating coefficient of friction

  1. Sep 20, 2012 #1
    Hi, i have a set up where i have a block of wood with sandpaper on the bottom, and a 500g mass on top. Given the grade of the sandpaper, i know the average particle size on the sandpaper. This set up is placed on top of a piece of MDF. Is there a way I could calculate the coefficient of friction between the sandpaper and the piece of MDF?
  2. jcsd
  3. Sep 20, 2012 #2
    you could do a series of experiments where you angle the piece of MDF (medium density fiberboard? that's what I got when I googled it) and allow the sandpaper to slide down under the influence of gravity because of the mass placed on top of it.

    Do that for some angle, measure the time taken, determine the acceleration and then find the force due to friction and calculate it from that. Do it for a few different angles to get a more precise determination.
  4. Sep 20, 2012 #3
    You should measure the friction at several constant velocities (no acceleration) so that you can can extract the coulomb and viscous friction components. The offset will be your coulomb friction (constant for all velocities), and the increase in friction that is proportional to speed will be your viscous friction. Use a force gauge to determine how much force it takes to pull the block at the constant velocity, and then divide that force by downward (normal) force that gravity exerts on the 500g to get the coefficient.
    Last edited: Sep 20, 2012
  5. Sep 20, 2012 #4
    I actually wanted to know if there was a mathematical way of doing it. I thought I may be able to calculate the pressure of the sandpaper on the MDF (it is medium density fibreboard)

    I thought i might be able to take the average particle size and divide the area of the sandpaper by the particle size to get the number of particles on the sandpaper. If i then said there was a standard area of each particle in contact with the MDF, and then multiplied this by the number of particles to get the area of sandpaper actually in contact with MDF.

    So if I divided the mass of the block by this area to give me the pressure, is there then a way to calculate friction from this pressure? And is this method viable?
  6. Sep 20, 2012 #5
    Hmm, I don't know how to model friction as a function of surface material/microscopic geometry. That is a bit more advanced I think.
  7. Sep 20, 2012 #6
    Well given that F [itex]\leq[/itex] μN where F is frictional force, μ is the coefficient of friction, and N is the magnitude of the normal force. I presume μ is related to pressure, and N is the same as the weight?
  8. Sep 20, 2012 #7
    μ has no units. The pressure and weight are related to the normal force. μ is related to the materials, and it tells the relation of friction force to normal force, depending on the material.
    Last edited: Sep 20, 2012
  9. Sep 20, 2012 #8
    The friction force depends on the normal force and so will depend on the pressure.
    The coefficient of friction is independent on pressure, in first approximation at least.
    It is a material property so you cannot just calculate it from general considerations about particles' size and number.
    Maybe if you know the coefficient of friction between a sand grain (which is still a macroscopic object, I suppose) and the surface you may find the overall effect for the block.
    Is this what you have in mind?
  10. Sep 20, 2012 #9
  11. Sep 20, 2012 #10
    Sorry, my question was addressed to the OP, after his post #6. I saw your post only after I posted myself.
  12. Sep 21, 2012 #11
    yes that is what i had in mind, but i suppose there is no way to calculate the coefficient of friction other than by experimenting.
  13. Sep 21, 2012 #12
  14. Sep 21, 2012 #13


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    In principle you can. But it is a very, very hard problem, and in reality you need a good supercomputer even for very simple systems (I believe people have had some progress modelling AFM tips on a surface).
    In your case there is no way of doing it.
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