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Homework Help: Finding Lever Lengths With Overall Mechanical Advantage

  1. Sep 6, 2011 #1
    1. The problem statement, all variables and given/known data
    If the mechanical advantage of a lever is, lets say, 10; the forces pushing down on the effort arm equate to 100kg and the forces pushing down on the load arm equate to 1000kg and the lever itself is 5 meters, how do we go about finding the individual arm lengths (i.e. the length of the effort/lever arm).


    2. Relevant equations



    3. The attempt at a solution
    Here's what I'm thinking.
    MA = 10
    Simultaneously,
    MA = Effort Arm / Load Arm
    10 = Effort Arm / Load Arm
    Load Arm * 10 = Effort Arm
    Load Arm + Load Arm * 10 = Effort Arm + Load Arm
    2Load Arm * 10 = 5
    2Load Arm = 5/10
    Load Arm = 0.5

    True or false?
     
    Last edited: Sep 6, 2011
  2. jcsd
  3. Sep 6, 2011 #2

    ehild

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    Homework Helper

    It is correct up to here, but how did you get the following?
    1(load arm)+10 (load arm) = ? (load arm) ?

    If you add one apple to 10 apples will you get 2*10 =20 apples?

    ehild
     
  4. Sep 6, 2011 #3
    Then how would you isolate the load arm?
     
  5. Sep 6, 2011 #4
    11 * load arm = effort arm + load arm?
    load arm = effort arm + load arm / 11?
     
  6. Sep 6, 2011 #5

    ehild

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    Homework Helper

    No, it is wrong. Division by 11 in your formula refers to the load arm only.
    Use parentheses: length of load arm =(length of effort arm+length of load arm)/11, that is, 5/11 m.

    Remember the hierarchy of operations: First perform everything in the parentheses. Otherwise perform multiplication/division first then the addition/subtraction.

    ehild
     
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