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A lamb grows with its mass proportional

  1. Feb 24, 2014 #1
    A lamb grows with its mass proportional to the cube of its length. When the lambs length changes by 15.8% its mass increases by 17.3kg. Find the final mass.

    Really stumped thanks for any help

    mf=kxf3
    length change by 15.8%
    xi+.158xi=xf
    xf=1.158xi

    mf=k(1.158x)3
    mf=1.55kx3

    I couldnt get the right answer because at this point, my book shows kx3 turning into mi and continuing the problem from there. Why?

    kx3=mi
    mf=1.55mi
    mi=mf/1.55
     
  2. jcsd
  3. Feb 25, 2014 #2

    haruspex

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    The information given is more general than that. It tells you m=kx3. In particular, mi=kxi3 and mf=kxf3.
    You dropped the subscript on the x. Based on your equations to this point, it should be mf=k(1.158xi)3
     
  4. Feb 25, 2014 #3
    It was a little confusing ill try to make it more clear.
    Need to find the value of m at the end of this process.

    m = kx3

    length change by 15.8%
    xi+.158xi = xf
    xf = 1.158xi

    mass increase of 17.3kg
    mf = mi+17.3

    mf = kxf3
    mf = k(1.158xi)3
    mf = 1.55kxi3

    The solutions manual does something here I dont understand
    mf = 1.55(kxi3)
    mf = 1.55mi
    mi = mf/1.55

    Why does kxi3 = mi
    k and xi3 just dissapear and mi shows up
    I got 109kg from 2 different methods which is incorrect and the manual isnt helping much on this one.
     
    Last edited: Feb 25, 2014
  5. Feb 25, 2014 #4

    D H

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    The answer should be staring you in the face. It's because #m=kx^3##.
     
  6. Feb 25, 2014 #5
    Lol gotcha, subscripts were throwing me, gotta remember that m=kx^3 can take any x value whether its initial/final/middle. Thanks
     
  7. Feb 25, 2014 #6
    You have it and you don't know it:

    1.55mi-mi=17.3
     
  8. Feb 25, 2014 #7

    D H

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    Except he's been asked to solve for mf, not mi. It's better to eliminate mi rather than mf so you can solve for mf directly.
     
  9. Feb 25, 2014 #8
    Potatoes, Potahtoes. I thought it would be easier for him to see it that way. I would have done it your way.

    Chet
     
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