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Block on Incline

  1. Mar 4, 2015 #1
    1. The problem statement, all variables and given/known data
    http://i.minus.com/iVbsy2FomprcM.PNG [Broken]
    http://i.minus.com/iVbsy2FomprcM.PNG [Broken]

    2. Relevant equations
    F=ma

    3. The attempt at a solution
    I'm struggling with the normal force and I'm not sure if the component of the force F is the cosine or sine. I see examples where its sine but that doesnt make any sense to me. Isn't the x direction supposed to be cosine?

    Fn = mgsinθ
    81.2cosθ - Fnμ = 9.23
    -Fnμ = -65.897
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Mar 4, 2015 #2

    PhanthomJay

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    For simplicity of the solution, the x axis is chosen to be the axis parallel to the incline, and the y axis is the axis perpendicular to the incline. In this manner, the applied force F is already in the in the x direction, and when you draw your FBD for the forces (you are missing at least one), a bit of geometry/trig and newton 1 in the chosen y direction will you give you the relationship between the normal force and weight. Since the applied force is already in the x direction and the normal force in the y direction, it is the weight force that needs to be broken up into its x and y components before applying Newton's Laws. And no, the x axis is not always the cos, it depends on what angle you are working with and the trig properties of a right triangle.
     
    Last edited by a moderator: May 7, 2017
  4. Mar 4, 2015 #3
    Okay.

    So the normal force is equal to mgsinθ?
     
  5. Mar 4, 2015 #4

    BvU

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    No. If you aren't sure, then you look at a limiting case: let ##\theta## go to zero, and you know that then the normal force is equal to mg. Forces the choice between ##mg\sin\theta## and ##mg\cos\theta## to be the latter because cos(0) = 1.

    The normal force is ##\perp## the incline. In your FBD you should easily see that the angle between mg and the normal force is ##\theta## and not ##{\pi\over 2}-\theta##. So cosine to project mg on the perpendicular.

    Don't associate x with the one and y with the other. Sometimes it's like this, other times it is the other way.
     
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