Center of Mass of system of particles

In summary, the problem involves four particles with different masses, positions, and velocities in a 2-D plane. The question asks for the x and y positions of the center of mass, which are calculated to be 1.07m and -1.22m respectively. The next question asks for the speed of the center of mass, which is not simply the magnitude of the distance from the origin, but rather the actual speed, calculated to be 1.622 m/s.
  • #1
BEEFCOPTER
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Homework Statement



Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below:

M X Y Vx Vy

1 8.9kg -2.6m -4.8m 3.2m/s -3.9m/s

2 7.9kg -3.4m 3.6m -5m/s -5.2m/s

3 9kg 4.7m -5.4m -6.3m/s 2m/s

4 8kg 5.5m 2.7m 4.1m/s - 3.3m/s
OK, so it first asks:
What is the x position of the center of mass
and
What is the y position of the center of massI have answered these correctly as:
CMx =1.07
CMy =-1.22The next question asks:
What is the speed of the center of mass:?

I THOUGHT this would simply be sqrt[(CMx^2) + (CMy^2)] <-(the magnitude of CMy) which would be 1.622 m/s
but this is INCORRECT. I have stared and re-read this question for an hour and simply cannot think of any other way to calculate.

any thoughts would be greatly appreciated?
 
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  • #2
after typing out the question, I may ahve already seen my error, I just calculated the magnitude of the distance from the origin, not its actual speed.. funny how asking the question makes you see things
 

Related to Center of Mass of system of particles

What is the center of mass?

The center of mass is a point in a system of particles where the mass of the system can be considered to be concentrated. It is the average position of all the particles in the system.

How is the center of mass calculated?

The center of mass is calculated by taking the weighted average of the positions of all the particles in the system. The weight for each position is determined by the mass of the particle.

Why is the center of mass important?

The center of mass is important because it helps us understand the overall motion and dynamics of a system. It also allows us to simplify complex systems and make predictions about their behavior.

Can the center of mass be outside of the physical system?

Yes, the center of mass can be outside of the physical system if there are external forces acting on the system. In these cases, the center of mass will still follow the laws of motion and behave as if it were a single particle.

How does the distribution of mass affect the center of mass?

The distribution of mass in a system can affect the position of the center of mass. If there is more mass located on one side of the system, the center of mass will be closer to that side. Additionally, the center of mass will move in the direction of the greater mass when external forces are applied to the system.

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