Center of Mass of system of particles

AI Thread Summary
The discussion revolves around calculating the center of mass (CM) for a system of four particles in a 2-D plane, with specific masses, positions, and velocities provided. The correct x and y positions of the center of mass were determined to be CMx = 1.07 and CMy = -1.22. The user initially miscalculated the speed of the center of mass by using the distance formula instead of the appropriate method for speed. Upon reflection, the user recognized the mistake in their approach. The conversation highlights the importance of understanding the difference between position magnitude and actual speed in physics calculations.
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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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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
 
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