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ilikephysics2

for a spherical object what is its mass in terms of the density of the material, its diameter and any necessary constants?

  • one year ago
  • one year ago

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  1. lgbasallote
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    well volume of a sphere is \[\frac 43 \pi r^3\]

    • one year ago
  2. lgbasallote
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    and then density = mass/volume

    • one year ago
  3. UnkleRhaukus
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    \[\rho=\frac mV\] \[m=V\rho\]

    • one year ago
  4. lgbasallote
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    so you have \[m = \frac 43\rho \pi r^3\]

    • one year ago
  5. lgbasallote
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    where \(\rho\) = density

    • one year ago
  6. ilikephysics2
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    what about its diameter

    • one year ago
  7. lgbasallote
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    change r to d/2

    • one year ago
  8. UnkleRhaukus
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    and \(r\) is the radius (half the diameter) \(r=\frac d2\)

    • one year ago
  9. lgbasallote
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    radius = diameter/2 so just change r to d/2

    • one year ago
  10. ilikephysics2
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    ok so thats the final solution?

    • one year ago
  11. lgbasallote
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    replace r with d/2....

    • one year ago
  12. ilikephysics2
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    ok cool and can i give you guys both metals or does just one of you get it?

    • one year ago
  13. ilikephysics2
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    hey so its (4/3)p(pi)(d/2)^3

    • one year ago
  14. lgbasallote
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    right

    • one year ago
  15. ilikephysics2
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    is that right?

    • one year ago
  16. UnkleRhaukus
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    you can simplify the numbers a bit

    • one year ago
  17. ilikephysics2
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    unkle...it won't let me give you a metal now

    • one year ago
  18. ilikephysics2
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    why cant i give it to both of you

    • one year ago
  19. UnkleRhaukus
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    i dont mind about that

    • one year ago
  20. UnkleRhaukus
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    \[m=\frac43\rho\pi\left(\frac d2\right)^3\] use \[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\]

    • one year ago
  21. ilikephysics2
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    so it simplifies to 4p(pi)(d/2)?

    • one year ago
  22. ilikephysics2
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    i crossed out the 3's

    • one year ago
  23. lgbasallote
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    what he meant was distribute the exponent

    • one year ago
  24. UnkleRhaukus
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    you can not cancel an index with denominator like that

    • one year ago
  25. ilikephysics2
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    oh so whats it turn to?

    • one year ago
  26. UnkleRhaukus
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    \[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\] \[\left(\frac{d}{2}\right)^3=\frac {d^3} {2^3}\]

    • one year ago
  27. ilikephysics2
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    thanks :)

    • one year ago
  28. UnkleRhaukus
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    can you simplify the numbers in the equation now?

    • one year ago
  29. ilikephysics2
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    yes (4/3)p(pi)(d^3/8) ?

    • one year ago
  30. lgbasallote
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    you can simplify it further

    • one year ago
  31. lgbasallote
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    you can multiply the denominators

    • one year ago
  32. ilikephysics2
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    so 4p(pi)(d/8) ? ?

    • one year ago
  33. lgbasallote
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    what happened?

    • one year ago
  34. ilikephysics2
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    can you simplify it?

    • one year ago
  35. lgbasallote
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    you canceled the denominaotr and teh exponent???

    • one year ago
  36. ilikephysics2
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    it can't be simplified?

    • one year ago
  37. lgbasallote
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    it can...you just simplified it wrong....multiply the denominators

    • one year ago
  38. lgbasallote
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    don't touch anything else

    • one year ago
  39. ilikephysics2
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    so it (4/24)p(pi)(d^3) ?

    • one year ago
  40. UnkleRhaukus
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    thats better!

    • one year ago
  41. lgbasallote
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    yes. now express 4/24 in lowest terms

    • one year ago
  42. ilikephysics2
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    ok so 1/6 p(pi)(d^3) ? thats final!!!!

    • one year ago
  43. lgbasallote
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    right!!

    • one year ago
  44. lgbasallote
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    your turn @UnkleRhaukus

    • one year ago
  45. UnkleRhaukus
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    \[\color{red}\checkmark\]

    • one year ago
  46. UnkleRhaukus
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    so the constants necessary to express the volume in terms of diameter are ; the natural number; 6 the density of the material rho; \(\rho\) the geometrical constant pi; \(\pi\) the diameter of the sphere \(d\) and the dimensional constant \(3\)

    • one year ago
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