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I'm trying to understand how force interacts with a system of multiple particles. If a force is applied to a system with one particle, it produces acceleration based on F=ma. However, when the same force is applied to a system with multiple particles (e.g., two particles of equal mass), the acceleration is reduced because the total mass increases.

Does this mean the force gets distributed among the particles, with each particle experiencing a portion of the total force?

nani chan
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1 Answers1

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In your example, the system as a whole will experience half the acceleration. But this applies to the center of gravity of the system (being just in the middle of the two particles) and tells you nothing about the individual motions of the two particles.

The individual motion depends upon the inner coupling of the system, meaning which inner forces between the particles arise if one particle starts moving relative to the others.

  • If the particles are not coupled at all, just one particle gets the full acceleration, and the other one stays in place. Their center (being in the middle) experiences half the acceleration.
  • If the particles are tightly coupled (as in a rigid body), they will compensate any movement of a single particle "out of its place" with a force that pushes it back into place. And because of "actio = reactio", this also pushes the other particles forward. Effectively, they will all move as one body with lower (half the) acceleration. This results in the force being distributed evenly over the particles (by means of inner forces).
Ralf Kleberhoff
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