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Superposition of 3 point masses

  1. Jan 16, 2015 #1
    1. The problem statement, all variables and given/known data
    In the figure below, three 2.00 kg spheres are located at distances d1 = 0.300 m and d2 = 0.400 m. What are the magnitude and direction of the net gravitational force on sphere B due to spheres A and C?

    13-33.gif

    2. Relevant equations
    F = GMm/r^2


    3. The attempt at a solution
    F=sqrt((4G/0.4^2)^2 + (4G/0.3^2)^2)
    F = 3.0E-9

    But that answer is wrong. Is there a mistake in my arithmetic? Of am i missing another term?
     
  2. jcsd
  3. Jan 16, 2015 #2

    haruspex

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    Yes. please post all steps.
     
  4. Jan 16, 2015 #3
    F (B->C) = G(2)(2)/(0.4^2) = 4G/0.16
    F (B->A) = G(2)(2)/(0.3^2) = 4G/0.09

    F (B->net) = F(B->C) + F(B->A)
    Can't add these together since they aren't the same direction, so use Pythagoras' theorem:

    F^2 (B->net) = F^2(B->C) + F^2(B->A) = sqrt((4G/0.16)^2 + (4G/0.09)^2)
     
  5. Jan 16, 2015 #4

    haruspex

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    Yes, I understand you're doing that, but your result is inaccurate (not wildly wrong). I can't tell where the inaccuracy comes in unless you post all steps.
     
  6. Jan 16, 2015 #5

    haruspex

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    Just had a thought... is this what you meant to post, or have you left out a digit?
     
  7. Jan 16, 2015 #6
    Im sorry, I don;t understand what you mean by "Post all steps", these are all the steps I have done. What more is there?
     
  8. Jan 16, 2015 #7
    3.0E-9 is the result my calculator gives me, although the numbers may be cut-off since the calculator display is limited to 10 digits. I'll use an online calculator and see if it makes a difference
     
  9. Jan 16, 2015 #8
    wolfram alpha gives 3.40125... × 10^-9 , so that might be the problem. Can you verify that the way I did the question is indeed correct?
     
  10. Jan 16, 2015 #9

    haruspex

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    Here are my steps (spreadsheet)
    d1= 0.3
    d2= 0.4
    1/d1^4= 123.46
    1/d2^4= 39.06
    sum= 162.52
    sqrt(sum)= 12.75
    G= 6.67E-011
    m*m= 4
    *G*m*m= 3.40E-009
     
  11. Jan 16, 2015 #10
    3.40125 × 10^-9 is indeed the correct answer! It was my calculator that ran out of displaying digits to properly show the number. Thank you for your time.
     
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