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Calculating Tension in a Two Pulley Atwood Machine

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Calculate the force of tension in the string of an Atwood machine with masses (1 - on right) 69.95 grams, (2 - middle) 80.11 grams, and (3 - on right) 60.28 grams. When this value is determined, verify that the net force in the atwood machine is equal to zero.


    .........\........|......../
    .....44º.\.46º.|.60º./.30º
    ----------------------------- (all angles are measured from this line, x components)
    .......|..........|...........|
    .......|..........|...........|
    .....m1.......m2........m3



    2. Relevant equations

    Fg = mg
    Fnet = Fg + Ft (Fnet should equal approx. 0)

    3. The attempt at a solution

    First, calculating the force of gravity on each of the masses:

    Fg1 = (0.06995)(9.8)
    = 0.68 N

    Fg2 = (0.08011)(9.8)
    = 0.79 N

    Fg3 = (0.060280)(9.8)
    = 0.59 N


    Secondly, using the angles measured and the forces of gravity determined, solve for the x and y components.


    y1 = 0.68 N
    y2 = 0.59N


    x1/sin 46 = 0.68/sin 44
    x1 = 0.70 N

    x2/sin 60 = 0.59/sin 30
    x2 = 1.02 N


    Writing Fnet statements for both x and y components produces:

    Fnet(x) = 0.70 N + 1.02 N
    = 1.72 N

    Fnet(y) = 0.68 N + 0.79 N + 0.59
    = 2.06 N


    Finally:
    Fnet = Fx + Fy
    Fnet = 1.72 - 2.06
    Fnet = 0.34 N


    The sum of each of these Fnet statements is supposed to be approximately zero. I understand why this should be so (as it is a static equilibrium), however I do not not know how to achieve that answer, or what I am doing wrong. I do not believe that 0.34 N is a relatively close answer.

    These angles were calculating in a lab, so is it possible that I have done everything right and simply measured the angles wrong?

    I understand some of the values are to be negative, but I am unaware of which (I think it is gravity?). My teacher is no help, so I would really appreciate someone explaining how to fix this. Thank you.
     
    Last edited: Oct 14, 2007
  2. jcsd
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