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Help on a torque question

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 3.0-m-long, 6.6kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 63kg woman lies on the reaction board with her feet over the pivot. The scale reads 23kg .

    What is the distance from the woman's feet to her center of mass?

    2. Relevant equations
    T=F*d

    3. The attempt at a solution
    I know this is a problem that is related to torque, but I'm completely lost. Can someone help me..
     
  2. jcsd
  3. Mar 25, 2015 #2
    Let's say the distance from the woman's feet to her center of mass is d. So now you have Tup=-T down, which tells you
    l(board)*23kg*g=
    -(0.5*l(board)*Fg(board)+d*Fg(woman)
    And then the problem becomes much easier.
     
  4. Mar 26, 2015 #3

    ksj

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    There is a simpler way of doing this without using torque! The formula for finding a center of mass using the reaction board method is:

    x = (r2-r1)/W * d

    where:
    x is the centre of mass
    r2 is the scale after the weight has been added (23kg)
    r1 is the initial scale reading (assuming uniform density, r1 = mass of the board/2)
    W is the weight of the person
    d is the length of the board

    Therefore, your answer is 0.94 m (from her feet)

    The key concept here is that the center of mass is calculated by the formula: x(cm) = x1m1 + x2m2 + x3m3... / m(total)
    Because your question requires you to separate the system (woman + reaction board), you simply subtract the weight of the board.
    The center of mass of the board is exactly at the midpoint, which is why the woman's height is not needed.
     
  5. Mar 26, 2015 #4

    ksj

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    Hope that helps!
     
  6. Mar 26, 2015 #5

    haruspex

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    Rearranging, xW = (r2-r1)d. Looks exactly like the torque equation to me.
    I suggest that the object of the homework exercise is to use the principles of torque to solve it, not to look up some standard solution for reaction boards.
     
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