Velocity of two spheres under gravitational attraction

[Jimmy Jazz]

Homework Statement

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

Homework Equations

density =mass/volume
F=GMm/r^2

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.

 

[haruspex]

This force changes with distance, so how would I take account of this in my solution?

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?

 

[Jimmy Jazz]

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