Center of Mass of system of particles

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SUMMARY

The discussion centers on calculating the center of mass (CM) and its speed for a system of four particles in a 2-D plane. The participants provided the masses, positions, and velocities of the particles, leading to the correct x and y positions of the center of mass as CMx = 1.07 and CMy = -1.22. However, the initial attempt to calculate the speed of the center of mass using the formula for magnitude was incorrect. The correct approach involves using the velocities of the particles to find the speed of the center of mass, which requires a different calculation than simply determining the distance from the origin.

PREREQUISITES
  • Understanding of center of mass calculations
  • Familiarity with 2-D kinematics
  • Knowledge of vector magnitude calculations
  • Basic principles of mass and velocity in physics
NEXT STEPS
  • Learn how to calculate the speed of the center of mass using the formula: Vcm = (Σ(m_i * v_i)) / Σm_i
  • Explore the concept of momentum and its relation to center of mass
  • Study the effects of multiple particles on the center of mass in different coordinate systems
  • Investigate the application of center of mass in real-world physics problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators looking for examples of center of mass calculations in multi-particle systems.

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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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