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Math Help - Determine the distance of the center of gravity from the end X of the plank

  1. #1
    Member looi76's Avatar
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    Determine the distance of the center of gravity from the end X of the plank

    Question:
    A non-uniform plank of wood XY is 2.50m long and weighs 950N. Force-meters (spring balances) A and B are attached to the plank at a distance of 0.40m from each end, as illustrated in the Figure below

    When the plank is horizontal, force-meter A records 570N
    (i) Calculate the reading on force-meter B
    (ii) Determine the distance of the center of gravity from the end X of the plank.

    Attempt:
    (i) A + B = 950N
    B = 950 - 570 = 380N

    (ii) I don't know how to solve this question, need help!
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  2. #2
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    Quote Originally Posted by looi76 View Post
    ...

    (ii) I don't know how to solve this question, need help![/SIZE][/FONT]
    I've modified your drawing a little bit.

    Use momenti. The turning point of the plank is the point at forcemeter B:

    970\ N \cdot x = 570\  N \cdot 1.7\  m~\implies~x \approx 0.998969...\  m \approx 1\  m

    Therefore the center of mass is 1.4 m from the endpoint Y that means it is 1.1 m from the endpoint X.
    Attached Thumbnails Attached Thumbnails Determine the distance of the center of gravity from the end X of the plank-schwerpunkt_brett.gif  
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