# Velocity of the center of mass

1. Oct 24, 2008

### JJones_86

1. The problem statement, all variables and given/known data
If a particle of mass 5.6 kg is moving east at 10 m/s and a particle of mass 17 kg is moving west at 10 m/s, what is the speed of the center of mass of the pair?

2. Relevant equations

Not sure how it would relate, but to find the center of mass = (m1x1 + m2x2)/(m1+m2)

3. The attempt at a solution

I can't figure out where to start. Our homework does not come from our textbook, so our textbook doesn't have any relevant equations/solutions for this problem.

2. Oct 24, 2008

### LowlyPion

Actually your intuition is pretty good. Because if you were to treat the momentum of the particles as vectors and add them, then you have a vector for the combined momentum of the particle system. Since the momentum of this system can be expressed as the Velocity Vector times the scalar of the combined mass, then your result would be the Velocity Vector of the system. Just replace the x1 and x2 in your equation with the velocities and ... you have the equation for the Velocity of the Center of Mass.

3. Oct 24, 2008

### JJones_86

Ok, so let me see if I'm following you..
So I find the momentum of Particle 1 and Particle 2, and since they are moving towards eachother, i find the differnce, and this is the combined momentum of the particle system. I'm not sure what you mean by this momentum can be expressed as the velocity vector times the scalar of the combined mass...

4. Oct 24, 2008

### LowlyPion

$$m_1\vec V_1 + m_2\vec V_2 = M_{total} * \vec V_{CofM}$$

5. Oct 24, 2008

### JJones_86

Ok, but I'm getting that the velocity is 10 m/s, and it is the incorrect answer

I did this:

(5.6 kg(10 m/s) + 17 kg(10 m/s))/(5.6 kg + 17 kg) = 10 m/s....

6. Oct 24, 2008

### LowlyPion

You didn't treat them as vectors.

One is moving east, the other west. You want something more like (17 - 5.6)/(17 + 5.6)

7. Oct 24, 2008

### JJones_86

Ok, I figured it out. Once again I appreciate it.

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