# Help! Center of Mass Velocity

1. Nov 17, 2009

### Gisellebarr

Three Balls are moving along a straight line having the instantaneous positions shown in figure 8.15. At that instant, find the location and velocity of the center of mass of this system.

Figure 8.15

Mass A---------------------Mass B-----------------------------------Mass C

Mass A is moving at 8 m/s to the left with mass 2.00 kg

Mass B is moving at 6.00 m/s to the right with mass 3.00 kg

Mass C is moving at 2.00 m/s to the right with mass 4.00 kg

Mass A is 5.00 m from Mass B

Mass B is 7.00 m from Mass C

As simple as this problem is I don't even know where to start! The only thing I understand from the problem is conservation of momentum but I don't know how to apply it to this situation.

2. Nov 17, 2009

### kuruman

This is not a conservation of momentum situation. What is the equation that gives the position of the center of mass of any number of masses? Look it up in your textbook.

3. Nov 17, 2009

### Gisellebarr

Okay I rechecked the book and tried to work out a similar problem

I set the location of each mass on the x axis with Mass A at 0, Mass B at 5 in the +x direction and Mass C at 12 in the + x direction

I applied that Xcm= mAxA+mBxB+mCxC/ mA+mB+mC= 7 m

To find the location of the center of Mass

Then

Vcm= mAvA+mBvB+mCvC/ mA+mB+mC= 4.67 m/s

To find the velocity of the center of mass.

Is this correct?

4. Nov 17, 2009

### kuruman

The position of the center of mass is correct, but the its velocity is not. Your equation is correct, but you plugged in the wrong numbers. Remember: If something moving to the right has positive velocity, something moving to the left has negative velocity.

5. Nov 17, 2009

### Gisellebarr

Oh! That makes sense! Thanks :)