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Coefficient of static friction on an inclined plane

  1. Feb 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A dump truck loaded with rock has a coefficient of static friction of 0.4, and a coefficient of kinetic friction of 0.2 between the rock and steel tray. If the truck tilts its bed to 25°, calculate the coefficient of static friction on the load. Hence calculate the angle at which the load begins to slide. The mass of the rock in the truck is 77110kg.

    2. Relevant equations

    Ff = mgsinθ
    FN = mgcosθ
    Ff = μFN

    3. The attempt at a solution

    Ff = μFN


    mgsinθ = μmgcosθ

    Cancelling mg from both sides gives

    sinθ = μcosθ

    μ = (sinθ)/(cosθ)

    μ = tanθ

    μ = tan 25°

    μ = 0.466

    How can this be? How can μ on an inclined plane be greater than μ between the two flat surfaces? Is this saying that the coefficient of friction on the inclined plane is 0.466 x μ given in the question? Which would give a value of μ=0.1864 for the load on the inclined plane?

    Taking this value for μ as 0.466 and using it to determine the angle at which the load begins to slide gives us:

    The load will begin to slide when tanθ > 0.466

    But this gives θ > 25°

    So the load will begin to slide when the tray is tilted to more than 25°?

    I have been through every method I can think of and every time I keep coming back to μ = 0.466 and θ > 25° but I am sure that these values are incorrect.
  2. jcsd
  3. Feb 18, 2013 #2


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    Problem is incorrectly worded. It is given that the static friction coefficient is 0.4, so how can it be calculated if it is given? The rocks will start to slide when tan theta = 0.4 or about 22 degrees. At 25 degrees, they will be sliding.
  4. Feb 18, 2013 #3
    That's exactly what I did in the first place, figured out at what angle tanθ > 0.4, but then I figured it must have been incorrect since it asked me to determine μ.

    Will email the lecturer and clarify what exactly they want us to find, as the problem seems to simple if this is the case.

    Thanks for your help.
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