How would you include gravity in a momentum problem?

[Rnotaria]

Homework Statement

Say you have a big ball of mass m1 and a little ball on top of that of mass m2 (assume they are a small distance apart, like 1mm). Now let's drop these from a height of h so that the big ball will bounce off the ground and collide into the little ball in an elastic collision.

Homework Equations

p=mv

The Attempt at a Solution

I know gravity would play a key role in this example but how would you perform calculations with it? I know F=p/t and momentum will not be conserved since there is an external force (gravity) so knowing this, how can you determine how high each ball will rise after the collision? I was thinking of turning the force of gravity into momentum by multiplying with time but that is an unknown variable.

 

[Lucas SV]

Use gravitational potential energy and energy conservation. Consider the two states of the system: the initial state is before collision and the final state is after collision. Use the fact that the collision is elastic to draw conclusions.

What is the actual problem; what are you asked to calculate?

 

[CWatters]

Perhaps break it down into stages. If you have details about the elasticity of the balls it should be straight forward to work out the velocities of both balls just after the larger ball has bounced. eg when the large ball is on the way up and the small ball is still falling. Then with luck you have a simple collision between two balls to solve.