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Simple machine efficiency

  1. Feb 3, 2007 #1
    1. The problem statement, all variables and given/known data

    Could I please have a tutor check my answer and solution?

    question: An effort of 3 kN is required to move a mass of 2000 kg in a certain simple machine. If the mass is raised 1.5 meters while the effort moves 12 meters, find the efficiency?

    2. equations used in solution:

    work output = load x distance moved by load
    work input = effort x distance moved by effort
    efficiency = work output / work input
    3kN = 3000 Newtons

    3. The attempt at a solution

    my solution:

    efficiency = work output / work input

    mass = 2000 kg =19613.3 Newtons x 1.5 meters /

    3000 Newtons x 12 meters

    effort = 29419.95 Nm / 353039.4 Nm

    = 0.817

    Now, is it possible to have such a low efficiency in a machine? What simple machine would this be?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Feb 3, 2007
  2. jcsd
  3. Feb 4, 2007 #2

    Hootenanny

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    Your solution is correct, although you seemed to have used a nonstandard value for the acceleration due to gravity.
    Why do you think that this efficiency is low? What is the maximum theoretically possible efficiency?
     
  4. Feb 4, 2007 #3
    Which nonstandard value did I use?

    Why do you think that this efficiency is low? What is the maximum theoretically possible efficiency? The maximum theoretically possible efficiency would be 100%.

    I think the efficiency is low because we have a number of .817.The efficiency of any machine depends upon the amount of friction and air resistance present. A frictionless machine would have an efficiency of 100%. Here we have .817 for efficiency, so we must have a lot friction or air resistance.
     
  5. Feb 4, 2007 #4

    Hootenanny

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    You used g = 9.80665, which is indeed the standard acceleration due to gravity; however, g is more commonly approximated to 9.81 since the actual value of g varies greatly depending on location. It is not a serious problem though.
    Note here, that 0.817 is not a percentage efficiency.
     
  6. Feb 4, 2007 #5
    Ok, the percentage efficiency is 81.7%. How can I find out what kind of simple machine this would be?
     
  7. Feb 5, 2007 #6

    Hootenanny

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    Correct. Consider what type of machine/system would operate in such a way?
     
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