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Two spheres having masses M (sphere 1) and 2M (sphere 2) and radii R and 2R, respectively, are relea

  1. Nov 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Two spheres having masses M (sphere 1) and 2M (sphere 2) and radii R and 2R, respectively, are released from rest when the distance between their centers is 8R.
    How fast will sphere 1 be moving when they collide? Assume that the two spheres interact only with each other. Enter your answer in units of sqrt(GM/R).
    How fast will sphere 2 be moving when they collide? Enter your answer in units of sqrt(GM/R)
    2. Relevant equations
    -Gmm/r
    (mv^2)/2
    m1v1 + m2v2 = 0 since starts at rest


    3. The attempt at a solution

    Okay.
    So what I did was I first calculated initial PE and Final PE. I then calculated the change in PE which turned out to be -5GM^2/12R
    Then, I equated it to deltaKE = -deltaPE which i got as (Mv1^2)/2 + (2Mv2^2)/2 = 5GM/12R.
    I used conservation of momentum to find out the ratio of V1 to V2 which was V2 = -1/2(V1)
    After that I substituted that to the equation above and solved for V1 as 20GM/36R.
    But it says it is wrong. Any help would be appreciated. Thank you
     
  2. jcsd
  3. Nov 17, 2014 #2

    Simon Bridge

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    Please show your working for the change in potential energy.
     
  4. Nov 17, 2014 #3
    PEi = GM2M/8R = -GM^2/4R and PEf = GM2M/3R = -2GM^2/3R

    delta PE = Final - initial

    make them so that they have common base which is -8GM^2/12R + 3GM^2/12R
     
  5. Nov 17, 2014 #4

    Simon Bridge

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    OK I see ... so for conservaton of energy and momentum respectively you got:

    $$v_1^2 + 4v_2^2 = \frac{10}{12}\frac{GM}{R}\\
    v_1 + 2v_2 = 0$$ ... after dividing through by M in both equations and multiplying through by 2 in the top one.
    That about right?

    After that it is solved by simultaneous equations.
    ... your reasoning seems sound, so you need to check your algebra.
     
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