# Homework Help: 2D Collision b/w two objects, How do I find the speed of the centre of mass?

1. Jan 4, 2010

### TaintedLove

Hi, I was attempting to work through this question.
Anyways, I was working from a graph, so the radius 2.5 cm, the two of them collided, it was an inelastic collision as the two objects did part ways, so how do I find the centre of gravity?
I attempted to calculate it... but if someone could help me out? The masses were 500g and 500g.

So for x and y, would I do:
Xcg = (500)(0.025) + (500)(1.5)(0.025) / 1000 ?
Ycg = (500)(0.025) + (500)(0.025) / 100 ?

That's what I was thinking but I'm not entirely sure.

After this, I also have to find the momentum of the centre of gravity... so for that, I need the masses and the speed.

Even though the objects didn't stick together, would I add the masses when solving for the momentum at the centre of mass?

I was reading on the internet and it said: "The center of mass velocity of a system of particles is the average velocity of all the particles weighted relative to their mass"

but what I'm confused about is, do I add all the velocities... like the velocities of both the masses before and after the collision? So I'd have 4 velocities? But I'd only add the masses twice right? So it would be the velocities / 1000 g

Could someone really help me. Please.

2. Jan 5, 2010

### diazona

It'd be rather easier for all involved if you use the homework question template. Or at least post the exact wording of the problem, followed by your attempt at solving it.

The formula for center of mass is
$$x_\text{CM} = \frac{\sum_i x_i m_i}{\sum_i m_i}$$
and similarly for $y_\text{CM}$. That is, for each particle involved, you multiply its position by its mass, then add up all those products, and finally divide by the sum of all the masses. That would be the average position of all the particles weighted by their masses. You can do the same thing with the velocities of the particles to find the velocity of the center of mass.