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Homework Help: Block on an Incline with Varying Elevation

  1. Nov 9, 2011 #1
    The problem statement, all variables and given/known data
    Part one: A block is at rest on an inclined plane whose elevation can be varied. The coefficient of static friction is μs= 0.390, and the coefficient of kinetic friction is μk= 0.190. The angle of elevation θ is increased slowly from the horizontal. At what value of θ does the block begin to slide (in degrees)?

    (Hint after getting it incorrect: mass*acceleration = sum of net forces in one direction. Use mu_s to calculate the frictional force for the moment when it starts to slide)

    Part two: Evaluate the acceleration of the block.

    The attempt at a solution


    Ff = μFn
    Fn= mgcosθ
    Fparallel = mgsinθ
    Ff = μ(mgcosθ)

    When the block begins to slide, the force of friction has to be equal to the force parallel, right? You have to overcome the static μ.

    Fparallel = Ff
    mgsinθ = μmgcosθ

    mg's would cancel, so

    sinθ = μcosθ
    sinθ/cosθ = μ
    tanθ = μ

    θ= tan^-1(0.390)

    However, the answer I get is 0.372°, and that isn't correct.

    For the second half,
    ƩFnet = ma
    Fparallel - Ff = ma
    mgsinθ - mgcosθ = ma
    gsinθ - gcosθ = a

    There's a flaw in my method, I just don't know what it is. Anyone know how to help?
  2. jcsd
  3. Nov 9, 2011 #2
    Your answer was right. It's just that you are in radians, rather than degrees.
  4. Nov 9, 2011 #3
    Thank you. I feel like a bit of an idiot, but I guess that's what I get for working with a new calculator.

    Thank you!
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