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Homework Help: Moving Wedges

  1. Mar 6, 2007 #1
    1. The problem statement, all variables and given/known data
    A wedge of mass 4kg and angle 30 degrees is at rest on a smooth horizontal table. a mass of 1kg is placed on the smooth inclined face of the wedge and a horizontal force of 10N is applied to towards the vertical face of the wedge. Show that the acceleration of the wedge is

    (40 - root(3g) ) / 17 ~= 1.35m/s.


    Also find the reaction force between the wedge and the mass


    2. Relevant equations



    3. The attempt at a solution

    (from diagrams)

    Equation of wedge horizontally

    4A = 10 - Rsin30 (1)

    Equation of mass horizontally


    A + acos30 = Rsin30
    A = Rsin30 - acos30 (2)



    Equation of mass vertically

    asin30 = g - Rcos30 (3)


    Substitute (2) into (1)

    4(Rsin30 - acos30) = 10 - Rsin30
    5Rsin30 - 4acos30 = 10
    5Rsin30 = 10 + 4acos30
    5R* 1/2 = 4a * root(3)/2 + 10
    5R/2 = 2 root(3)a + 10
    5R = 4root(3)a + 20
    R = ((4root(3)a) / 5) + 4

    Now I have 'R' in terms of 'a', but I'm not sure where to go. My notes on this trail off...I seem to substitute R back into equation (1), along with equation (2) but that will just give me R in terms of a again.
     

    Attached Files:

  2. jcsd
  3. Mar 6, 2007 #2
    it seems you missed a equation.

    you can achieve a=2g-root(3)R from
    asin30 = g - Rcos30 (3)

    then subtitute it to
    5R = 4root(3)a + 20
    it can give you R without a

    besides, i really cann't understand then method you used in this problem and so as what the A stand for.i suggest you consider more ways.
     
  4. Mar 7, 2007 #3
    where does the 'missing equation' come from?
    I can't actually recall why A is there, though I'm sure i need it :/ could it be the force of the mass pushing the wedge back?
     
  5. Mar 7, 2007 #4
    :tongue:

    you missed equation (3)

    just tell me what the A stand for in the picture in order to let me understand it in your way.
     
  6. Mar 8, 2007 #5
    sorry for the delay in replying.

    A represents the acceleration of the wedge.
     
  7. Mar 17, 2007 #6
    really sorry for so many days' delay.

    in my peasonal sense,non-inertial frame will greatly predigest the problem.just use the wedge as frame.
    in addition,you missed a force on wedge in the maps you gave.

    happy new day!
     
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