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Unformatted text preview: Systems of More than Two Particles We have derived a method of making mechanical calculations for a system of particles. For simplicity's sake, however, we only derived this for a two- particle system. A derivation for an n particle system would be quite complex. A simple extension of our two particle equations to an n particle system will suffice. Center of Mass of Many Particles Previously, M was defined as M = m 1 + m 2 . However, to continue the study of center of mass we must make this definition more general. If there are n particles in a system, M = m 1 + m 2 + m 3 + ... + m n . In other words, M gives the total mass of the system. Equipped with this definition, we can simply state the equations for the position, velocity, and acceleration of the center of mass of a many particle system, similar to the two-particle case. Thus for a system of n particles: x cm = m n x n v cm = m n v n a cm = m n a n F ext = Ma cm These equations require little explanation, as they are identical in form to our two particle...
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This note was uploaded on 02/09/2012 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.
- Fall '10