Finding Center of Mass and Velocity of Three Moving Balls

[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.

 

[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.

 

[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?

 

[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.

 

[Gisellebarr]

Oh! That makes sense! Thanks :)