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Velocity of two spheres under gravitational attraction

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  1. Dec 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Two solid copper spheres of radii 1 and 2 cm are released from rest in free space, their centers being 20 cm apart. Estimate the velocity with which they collide

    2. Relevant equations
    density =mass/volume
    F=GMm/r^2

    3. The attempt at a solution
    Find mass of each from density of copper and volume.
    With mass and separation I can find force and initial acceleration towards each other.
    This force changes with distance, so how would I take account of this in my solution?

    Many thanks for any prompts.
     
  2. jcsd
  3. Dec 9, 2014 #2

    haruspex

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    The short answer is to write down and solve a differential equation, but there is an easier way. What conservation law can you apply usefully?
     
  4. Dec 9, 2014 #3
    Thanks for responding so I can equate the loss in potential energy with the gain in kinetic energy?
    I am just going to look at the formulas for this now
     
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