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Gravity and superpostion of two spheres

  1. Jul 19, 2015 #1
    1. The problem statement, all variables and given/known data
    The figure shows a spherical hollow inside a lead sphere of radius R = 4.6 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 245 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 20 kg that lies at a distance d = 14 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?
    20150719_171355_zps0voqohjg.jpg


    2. Relevant equations


    3. The attempt at a solution
    20150719_194518_zpscns6hjbm.jpg

    when i find the mass of the "hollowed out" sphere its much larger than the larger sphere. I dont know how else to approach this problem.
     
    Last edited: Jul 19, 2015
  2. jcsd
  3. Jul 19, 2015 #2

    mfb

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    The mass of the sphere is inconsistent with its given diameter and the density of lead. I would ignore the given "lead" and calculate the density based on the given size and mass.
     
  4. Jul 19, 2015 #3
    I updated my original photo with my calculations. Would the total force be the force of the full sphere minus the force of the "hollow" sphere? F=F1-F2? I got the wrong answer not sure where i went wrong.
     
  5. Jul 19, 2015 #4

    gneill

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    Your volume and density calculations don't look right to me. Can you recheck them?
     
  6. Jul 19, 2015 #5
    Thank you! I am having problem getting adjusted to an hp 300s+, I often have to double check its picking up all the buttons i press.
     
  7. Jul 20, 2015 #6

    mfb

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    Right (if you take both F1 and F2 to be positive).
    A quick check: is your mass ratio 1 to 8?
    The ratio of forces should be a bit smaller than that (1 to 7.something or 6.something) as the smaller sphere is a bit closer. If that is not true, something is wrong.
     
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