Center of Mass of a System Problem

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SUMMARY

The center of mass (CM) of a system consisting of two particles, m1 = 1kg and m2 = 2kg, is calculated using their position vectors at t = 1 second. The position vectors are r1(t) = (txhat - t^2yhat)m and r2(t) = (txhat + t^3yhat)m. The correct formula for the center of mass is given by (m1 * r1 + m2 * r2) / (m1 + m2). After substituting the values, the position of the center of mass is determined to be at (3x, 2y) in the x-y plane, with the velocity and acceleration needing to be derived from the respective derivatives of the position vectors.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with Newtonian mechanics
  • Knowledge of derivatives and their applications in physics
  • Basic concepts of center of mass in multi-particle systems
NEXT STEPS
  • Study the derivation of the center of mass for systems with multiple particles
  • Learn about vector differentiation to find velocity and acceleration
  • Explore the implications of center of mass in different inertial frames
  • Investigate the role of mass distribution in determining center of mass
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Students in physics, particularly those studying mechanics, as well as educators and anyone interested in understanding the dynamics of multi-particle systems.

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Homework Statement



From an inertial reference frame S, the vector position of a particle of mass
m1 = 1kg is given by r1(t)=(txhat - t^2yhat)m.
The vector position of a particle m2=2m1 is given by r2=(t)=(txhat +t^3yhat)m

Assume t=1second
Find the position, the velocity and the acceleration of the center of mass of the composite system: xCM vCM a CM


Homework Equations



m1 x1(1) + m2 x2(1) / m1 + m2


The Attempt at a Solution



3xkg/ 3kg = 3x-direction

velocity = x
acceleration = 0

I do not think this is right, could some one help?

 
Physics news on Phys.org
There is an x and y component to the position vector. You need to take both into consideration.
 

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