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Is my mass calculation method correct?

  1. Dec 10, 2015 #1
    1. The problem statement, all variables and given/known data
    I have an object of a known mass, and known dimension along one axis (length).
    Mass: 10 kg
    Length: 2 meters

    I wish to calculate what the mass of an object that is similarly constituted and shaped will be if it has a greatly expanded length of: 1,000 meters.

    I am seeking to know what the mass of this larger object will be.

    2. Relevant equations
    Volume = Length * Width * Height

    Conversion factor = larger object / smaller object

    { (conversion factor)^3 } * mass of smaller object = mass of larger object
    (The conversion factor is cubed so as to account for all 3 volumetric dimensions of expansion)
    3. The attempt at a solution
    1,000 m / 2 m = 500
    500 = conversion factor
    (500)^3 = 125,000,000

    This 125 million is then multiplied by the original mass of 10 kg, to get an answer of: 1 billion, 250 million kg.

    Does anybody see a problem with my result and/or logic? Reply if you do.
     
  2. jcsd
  3. Dec 10, 2015 #2

    haruspex

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    Looks fine to me.
     
  4. Dec 10, 2015 #3
    You want to make it 500 times longer, wider, and thicker, so it will have a volume that's ##(500)^3## times bigger. Assuming you keep the density of the object the same, the mass will increase by the same factor:$$10 \ \mathrm{kg} \times (500)^3=1.25 \times 10^9 \ \mathrm {kg}$$
     
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