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Not calc this time is physics!

  1. Sep 15, 2003 #1
    ok....

    u have built an exact replica of ur favorite sailboat on a scale of 1 to 20. u know that the boat weighs 3050 kg. to wat total weight, in grams, would u have 2 ballast the model so it floats in water like the real thing?

    i thot it would just b 3050/x = 20/1
    then x = 152.5 kg

    but.....thats not the rite answer....as per usual...
    ne1 wanna help me get started on this 1?
     
  2. jcsd
  3. Sep 16, 2003 #2

    HallsofIvy

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    Although you didn't say, I would conclude that your "Scale of 1 to 20" is a LINEAR scale. That is, the model is 1/20 as long as the original sailboat. Since the width of the model would also be 1/20 the width of the actual sailboat, the AREA of the deck of the model, for example, would be (1/20)(1/20)= 1/400 of area of the deck of the actual sailboat.

    Since volume is "length times width time height", that is, 3 lengths multiplied together (hence "cubic feet" or "cubic meters" to measure volume), the volume of the model sailboat would be (1/20)(1/20)(1/20)= 1/8000 of the volume of the actual sailboat.

    Assuming that your model is made of the same material as the actual sailboat (and so has the same density) you would need
    1/8000 of the mass: 3050/x= 8000/1 so x= 3050/8000= 0.38125 kg.
     
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