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Pushing a crate up incline

  1. May 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Crate of mass m is pushed horizontally with force F up an inclined plane of θ from ground. The plane has a friction coefficient of μ.

    a) draw free body diagram of crate
    b) derive expression for normal force
    c) derive expression for acceleration

    *** Use ONLY m, g, F, μ, θ ****
    2. Relevant equations
    ΣF = ma
    |a| = √(ax2+ay2)

    3. The attempt at a solution
    w8KETdD.png

    Included is a picture of the problem with my free body diagram.

    I set the normal as the y axis so that when solving ΣFy=may I can set ay=0.

    ΣFx=max=-μN+Fcosθ-mgsinθ
    ΣFy=may=N-Fsinθ-mgcosθ

    ay=0 so N = Fsinθ+mgcosθ (part b)

    Since ay=0, a=√ax2 = ax. Substituting N into ax:
    max=-μ(Fsinθ+mgcosθ)+Fcosθ-mgsinθ

    is this correct?
     
  2. jcsd
  3. May 25, 2016 #2

    mfb

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    Looks correct.
     
  4. May 25, 2016 #3

    CWatters

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    Looks correct to me as well although I would have drawn the fbd at the same angle. Nothing wrong with yours it just look odd.
     
  5. May 25, 2016 #4
    If you do that then you will have two components of acceleration (in the x AND y direction) and so your definition of N would involve more variables than the ones they allow, or at least would involve a lot more manipulation to isolate N.
     
  6. May 26, 2016 #5

    haruspex

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    mfb was only commenting on the orientation of the FBD. You can draw it with the same orientation as the physical arrangement but still choose the X and Y axes as parallel and normal to the plane.
     
  7. May 26, 2016 #6
    Oh... my bad
     
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