# Homework Help: Center of mass with one object moving

1. Apr 2, 2012

### DrummingAtom

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

Two objects are on a stick where one is stuck in place and the other one can slide. Both objects have the same mass and the stick has negligible mass.

2. Relevant equations

$$COM = \frac{m_1 x_1 + m_2x_2}{m_1+m_2}$$
$$v_1 = t$$

3. The attempt at a solution

$$COM = \frac{m_1 \int v_1 + m_2x_2}{m_1+m_2}$$

Would this be correct assuming that the starting point for measuring x1 and x2 would be the left side? Thanks

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2. Apr 2, 2012

### RoshanBBQ

I would be a little careful here. You need to know the initial position of the moving mass:
$$\frac{m_1\left (\int v_1(t) \,dt +x_1(0) \right ) + m_2x_2}{m_1+m_2}$$
where x_1(t) is a function of time and x_1(0) is the constant of integration.

Last edited: Apr 2, 2012
3. Apr 2, 2012

### DrummingAtom

Thanks for responding. Ahh yes good point. Adding your part, would that be correct? I just made up the problem which is why I'm a little unsure of the conceptual part.

4. Apr 2, 2012

### RoshanBBQ

I believe it is all right. The equation gives the center of mass as a function of time.

5. Apr 3, 2012

### DrummingAtom

Ok cool. Thanks for your help. By the way.. Roshan from DotA?

6. Apr 3, 2012

### RoshanBBQ

Yes. DotA 2 now.