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Resultant force projected along a line

  1. Aug 27, 2012 #1
    1. The problem statement, all variables and given/known data

    (i) Find the resultant force acting at point D and write it in Cartesian form. (Note that CD is parallel to the y-axis, the 40N force acts parallel to the z-axis and the 30N force is parallel to the x-axis.)

    (ii) Find the magnitude of the projected component of the resultant force acting along the line AD.

    Image of problem is attached.

    2. Relevant equations

    (i) Unsure about calculating resultant force
    (ii) Find Unit vector of UAD and find the dot product of UAD and FR from (i)

    3. The attempt at a solution

    (i) Unsure if resultant force at point D is simply F1= (-30i) and F2= (-40k) so FR= (-30i - 40k) (Magnitude 50N) ?

    (ii) UAD = (-0.2/0.245)i + (-0.1/0.245)j + (0.1/0.245)k

    Then F.UAD = (Fi)(-0.2/0.245) + (Fj)(-0.1/0.245) + (Fk)(0.1/0.245)

    Thanks for your help,

    Tim
     

    Attached Files:

    Last edited: Aug 27, 2012
  2. jcsd
  3. Aug 27, 2012 #2

    gabbagabbahey

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    You have a sign error in your unit vector UAD, and I would recommend you include the units (Newtons in this case) in your expression for force and use exact numbers in your calculations. I get [itex]\frac{1}{\sqrt{6}}(2\mathbf{i}+\mathbf{j}-\mathbf{k})[/itex] for UAD.
     
  4. Aug 27, 2012 #3
    How did you calculate this?

    I have used u = F(Coord)/F(magnitude) = (Fx/F)i + (Fy/F)j + (Fz/F)k

    F (aka RDA) = (XA-XD)+(YA-YD)+(ZA-ZD)
    = (0-0.2)+(0-0.1)+(0-(-0.1))
    = -0.2i - 0.1j + 0.1k
    magnitude = √0.06

    Which is how I have got:

    UDA = (-0.2/0.245)i + (-0.1/0.245)j + (0.1/0.245)k


    Could you please outline the approach/steps that you believe I should take to solve the problem so I can get a better understanding.

    Thanks for your reply,

    Tim
     
  5. Aug 30, 2012 #4
    Just on top of that, you have the same answers 2/√6 = .2/√.06

    except in the drawing it shows that the pipe is +ve 0.2m (where you have -0.2m) and that if the line is in fact A to D then does it not share this property?
     
  6. Aug 30, 2012 #5

    gabbagabbahey

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    Notice first that [itex]\sqrt{0.06} = \frac{1}{10}\sqrt{6}[/itex]. Next, consider that UAD usually means "the unit vector from A to D". By using RDA as F, instead of RAD, you've calulated the opposite and hence have a sign error.
     
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