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Two body final velocities (check this please)

  1. Jul 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Two masses m1 & m2 in free space are released from rest at a distance D and draw together under gravity to a distance d, calculate the final velocity of each mass.


    2. Relevant equations
    Final total KE of both bodies at d from :
    KE (t) = ( ( G * m1 * m2 ) / d ) - ( ( G * m1 * m2 ) / D )
    (Joules)



    3. The attempt at a solution
    Split the KE (t) by mass ratio, so :
    KE (m1) = ( m2 / ( m1 + m2 ) ) * KE (t)
    KE (m2) = ( m1 / ( m1 + m2 ) ) * KE (t)

    The final velocities from :
    v (m1) = sqrt ( ( KE ( m1 ) ) / ( ½ * m1 ) )
    v (m2) = sqrt ( ( KE ( m2 ) ) / ( ½ * m2 ) )

    The final momentums are equal, suggesting a good process, comments please.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 4, 2014 #2
    Ratio of kinetic energies of two particles is NOT the same as ratio of their masses.

    Use following laws:

    1. Conservation of linear momentum
    2. Conservation of mechanical energy.

    CONCEPT of LOST MASS might also be useful.
     
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