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Static Equilibrium Problem

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data

    Two supports, made of the same material and initially of equal length, are 2.0m apart. A stiff
    board with a length of 4.0m and a mass of 10 kg is placed on the supports, with one support
    at the left end and the other at the midpoint. A block is placed on the board a distance of
    0.50m from the left end. As a result the board is horizontal. The mass of the block is:

    A. zero
    B. 2.3kg
    C. 6.6kg
    D. 10 kg
    E. 20 kg

    2. Relevant equations

    ∑F = 0 = N1 + N2 - mg - Mg
    ∑τ = 0 = -1/2 N1 + 1/2 N2 - 1/2 Mg

    3. The attempt at a solution

    Those equations above are a result of a free body diagram I drew. However, if I begin to solve the equation for m, I end up with an expression in terms of N1 (ie. 2N1 = mg). Is there enough information in the question? By the way, I'm calculating torque from the position where the mass is placed.
     
  2. jcsd
  3. Feb 28, 2014 #2

    BvU

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    Could you post the drawing ?
     
  4. Feb 28, 2014 #3
    I think the key to this problem is this: "supports made of the same material and initially of equal length". What that means is that they are not rigid, but elastic, so as they are loaded, they contract and exert Hookean force on the board; these forces and the weights due to the board and the block balance one another so that everything is horizontal.
     
  5. Feb 28, 2014 #4

    BvU

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    Pretty bright, voko. I agree. So youhoo has his/het work cut out.
    And yes, there is enough info in the question (provided you accept voko's deduction -- which I do)
     
  6. Feb 28, 2014 #5
    So if the supports are made of the same material and initially of equal length, then that means that, since the board is horizontal, they compress by the same amount and as a result, apply equal forces?
     
  7. Feb 28, 2014 #6
    Spot on.
     
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