# Elastic Collision of 2 balls

1. Oct 28, 2014

### mshiddensecret

1. The problem statement, all variables and given/known data

Two spheres of mass M1 and M2 are arranged one above the other as shown. They are separated by a fraction of a mm. They are released from rest and allowed to fall to the ground, a distance h = 5.0 m below. Mass M2 collides elastically with the ground and then elastically with mass M1. Calculate the maximum height the center of M1 rises above the ground after the collision. D = 0.20 cm, d = 0.05 cm, M1 = 0.20 kg, M2 = 1.10 kg.

2. Relevant equations

3. The attempt at a solution

so I got the velocity by using vf^2 = 2ad and got 9.89m/s.

I use the collision formula:

(9.89)(1.1)=(.2)(v)

v= 54.337 - 9.89
=44.557 m/s for the smaller ball.

d=101.29 + 5 m = 106m.

Its incorrect.

2. Oct 28, 2014

### Staff: Mentor

It's a bit tricky, so I'd prefer to know the textbook's answer before I venture to offer guidance.

But I think the interaction is between M1 coming down at some speed and colliding with M2 travelling upwards. I think that's what the authors must be intending, anyway.

3. Oct 29, 2014

### rude man

Use potential energy conservation.
(I assume M1 originally sits on top of M2. You should also define d and D though I imagine they are the diameters of M1 and M2 respectively).

4. Oct 29, 2014

### haruspex

I assume that the balls are so small compared to the distance dropped that we can effectively treat them as point masses.
What formula is that, exactly? What does it apply to? What are the velocities of the two balls immediately before they collide?