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First Year Work and Energy

  1. Apr 9, 2012 #1
    1. The first problem statement, all variables and given/known data

    A crane rated at 2.5x105 W can lift a load of 1.5x104 kg vertically with a speed of 1.6 m/s. Determine the efficiency of the crane. Express your answer as a percentage.

    2. Relevant equations

    p=mv

    efficiency=(Pout/Pin)*100%

    3. The attempt at a solution

    I first use the momentum equation, P=mv, to solve for the output power. P=15000Jx1.6m/s=24000W. Now, I divide my output power by the input power and times by 100% to get my efficiency. efficiency=(Pout/Pin)x100%=(24000/250000)x100%=9.6%.

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    1. The second problem statement, all variables and given/known data

    Imgur Link

    2. Relevant equations

    W+Ep1+Ek1=Ep2+Ek2+Hf

    d=vi+1/2at2

    3. The attempt at a solution

    First Height(h):

    W+Ep1+Ek1=Ep2+Ek2+Hf
    Ep1=Ek2
    mgh=1/2mv22
    Therefore, v2=√(19.6h)
    Assume height is 1 and I get a speed of 4.427188724
    v=d/t, therefore my base value of d is 4.427188724

    Second Height(2h):

    W+Ep1+Ek1=Ep2+Ek2+Hf
    Ep1=Ek2
    mg2h=1/2mv22
    Therefore, v2=√(39.6h)
    Assume height is 1 and I get a speed of 6.292853089
    v=d/t, therefore my base value of d is 6.292853089

    Now I divide both to get the difference and get 1.421410625, which is √2d and thus the answer is B.
     
  2. jcsd
  3. Apr 10, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The solution of the second problem is correct.

    As for the first problem, P is power, and it is not the same as the momentum p.

    Do you know how the power is related to force and velocity?


    ehild
     
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