Two body final velocities (check this please)

[dean barry]

Homework Statement

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.

Homework Equations

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

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.

 

[sankalpmittal]

Homework Statement

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.

Homework Equations

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

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.

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.