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Homework Help: Mass density of a sphere

  1. Aug 18, 2009 #1
    Air in a sphere has density "x" kg/m3

    If radius is halved and air is compressed... does density double? ("2x" km/m3)
  2. jcsd
  3. Aug 18, 2009 #2


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    One thing at a time. Suppose only one of these happened. Say the radius is halved. Does the density increase or decrease and by what factor? Once you figure that out, compress the air some more and see what happens to the final density relative to the initial.
  4. Aug 24, 2009 #3
    Radius halved - density would increase.

    I don't know by what factor though...

    I have the Q&A ... initial is 1.4 kg/m3 and once radius is halved, density is 11 kg/m3.

    I have to show working and I just can't figure it out.

    Multiplying 1.4 by 7.9 gives me the answer, but I don't understand.
  5. Aug 24, 2009 #4
    What's the magical 7.9? Or did you just do 11 kg/m3 / 1.4kg/m3
  6. Aug 24, 2009 #5
    yes, just the 11 / 1.4.

  7. Aug 24, 2009 #6
    What all are you given in the problem?
  8. Aug 24, 2009 #7
    This is the question from the textbook:

  9. Aug 24, 2009 #8
    What happens to the volume of a sphere if the radius is halved?
  10. Aug 24, 2009 #9
    let say: D = Density
    m = mass
    v = volume

    D1 = 1.4 kg/m3

    mass is constant since the air will only be compressed.

    D = m/v yielding m = Dv

    Therefore, D1v1=D2v2

    but v of sphere is (3*pi*r3)/4

    and r2=r1/2

    You can get it now.
    Last edited: Aug 24, 2009
  11. Aug 24, 2009 #10
    Minor correction: volume of a sphere is [tex]V = \frac{4\pi r^{3}}{3}[/tex]
  12. Aug 24, 2009 #11
    Sorry. I interchanged 3 and 4.
  13. Aug 24, 2009 #12
    got your back ;)
  14. Aug 24, 2009 #13
  15. Aug 24, 2009 #14


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    A intuitive way to think about this: Think about a cube. If you cut the side lengths in half, what happens to volume? Halve one dimension and volume halves. Halve the second and volume decreases by a factor of 4. Halve the third and volume goes down how many times?

    The same thing happens to a sphere.
  16. Aug 24, 2009 #15

    Thank you, that really helped!
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