- #1
Rats_N_Cats
- 15
- 0
Homework Statement
Say, there are two bodies, mass m1 and m2, initially at rest at infinite separation. They start accelerating towards each other because of gravity. Express the relative velocity of approach as a function of the distance between the two bodies.
Homework Equations
Laws of Motion, Law of Universal Gravitation, Conservation of Momentum and Energy.
The Attempt at a Solution
I thought the loss of gravitational potential energy should equal the gain in kinetic energy of the two bodies, so [itex]\frac{1}{2}(m_1 v_1^2 + m_2 v_2^2) = \frac{Gm_1 m_2}{r}[/itex]. Also, because of conservation of momentum, m1v1 = m2v2, because the two objects have zero initial momentum. But I can't figure out the velocities from these two; and I think that's what i need.