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

[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.

 

[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.

 

[kerimek]

I would first like to clarify that the term "centre of gravity" is often used interchangeably with "centre of mass" but they are not exactly the same thing. The centre of gravity refers to the point at which the weight of an object can be considered to act, while the centre of mass refers to the point at which the mass of an object can be considered to be concentrated. In most cases, these two points coincide, but they can differ in certain situations, such as when an object is on an incline or in a non-uniform gravitational field. For the purpose of this question, I will assume that we are dealing with a flat surface and a uniform gravitational field, so the centre of mass and centre of gravity can be considered the same point.

Now, to answer your question about finding the speed of the centre of mass after a 2D collision between two objects, there are a few steps you can follow:

1. First, you will need to calculate the total mass of the system by adding the masses of the two objects. In this case, it would be 1000g or 1kg.

2. Next, you will need to calculate the total momentum of the system before the collision. This can be done by multiplying the mass of each object by its initial velocity (which can be determined from the graph) and then adding the two momentums together.

3. During the collision, the two objects will stick together and move with a common velocity (since it was an inelastic collision). This common velocity is the velocity of the centre of mass after the collision.

4. To find this common velocity, you can use the conservation of momentum principle. This states that the total momentum of a system before a collision is equal to the total momentum after the collision. So, you can set the total momentum calculated in step 2 equal to the product of the total mass (calculated in step 1) and the common velocity.

5. Solve for the common velocity, which will give you the speed of the centre of mass after the collision.

6. To find the momentum of the centre of mass, you can simply multiply the mass of the system (calculated in step 1) by the common velocity (calculated in step 5).

In summary, to find the speed of the centre of mass after a 2D collision, you will need to use the conservation of momentum principle and consider the total mass of the