Question on Newton's first law of motion

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Discussion Overview

The discussion revolves around Newton's first law of motion, particularly in the context of internal forces and the behavior of a body in motion when it undergoes fragmentation. Participants explore the implications of internal forces on the motion of the center of mass and the individual fragments of an object.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how a rock that explodes internally can change its trajectory without external forces acting on it.
  • Another participant asserts that the motion of the center of mass remains uniform due to the absence of external forces, while individual fragments experience external forces.
  • A participant expresses difficulty in understanding how the center of mass can exist or maintain uniform motion after fragmentation.
  • It is clarified that the center of mass is an abstract point and its definition applies regardless of whether the object is whole or fragmented.
  • Further discussion highlights that after fragmentation, the forces between the pieces are equal and opposite, resulting in a net force of zero on the center of mass.
  • A participant notes that Newton's laws apply to particles, and the center of mass can be derived from the displacements and masses of individual particles in a collection.

Areas of Agreement / Disagreement

Participants generally agree on the concept that the center of mass remains in uniform motion in the absence of external forces, but there is some confusion and debate regarding the implications of fragmentation and the nature of internal versus external forces.

Contextual Notes

Some participants express uncertainty about the abstract nature of the center of mass and its relationship to physical objects, indicating a need for clarification on definitions and concepts related to motion and forces.

ranger
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Okay, so its stated that a body in motion stays uniformly in motion unless influenced by an external force. But what happens if that force is internal? For example, a rock moving in space that explodes from the inside. This causes the rock to fragment and move in different directions. This has changed its trajectory without any external forces. How would you explain this?

--thanks.
 
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The motion of the center of mass will remain in uniform motion, since there is no external force on the object (ignore gravity for the moment). But each individual piece does experience external forces, so they do get accelerated.
 
The motion of the center of mass will remain in uniform motion, since there is no external force on the object
I find it hard to grasp that concept. How can the center of mass stay in uniform motion or even exist after the entire object has been fragmented?
 
The center of mass of an object or collection of objects is an abstract point, not a physical part of an object. It's definition is the same whether it involves a single object or multiple pieces. See this: http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html" .
 
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ranger said:
I find it hard to grasp that concept. How can the center of mass stay in uniform motion or even exist after the entire object has been fragmented?

The cm's acceleration depends upon the net force on the whole object (or its constituents, whichever the case may be). Initially, there is no net external force, but after the fragmentation both objects experience equal and opposite forces (to conserve momentum of the system). Therefore, the net force is zero.
 
Thanks a lot, it makes more sense now.

btw, neutrino, when you say "both objects experience equal and opposite forces". Are the two objects you are referring to the cm and the actual object itself?
 
ranger said:
Are the two objects you are referring to the cm and the actual object itself?
The cm is not an object! So it can't exert a force. neutrino is using an example where the original object breaks into two pieces--both pieces exert equal and opposite forces on each other. The cm of the system remains the same.
 
Doc Al said:
The cm is not an object! So it can't exert a force. neutrino is using an example where the original object breaks into two pieces--both pieces exert equal and opposite forces on each other. The cm of the system remains the same.

Thanks for clearing that up. For some reason I had the two-fragment scenario in mind. Makes it simpler to understand, though. :)
 
To add a bit to the previous posts:

Newton's laws as they are usually given apply to particles only. When you are considering a piece of rock, you are actually considering a (continuous) collection of particles.

It can then be formally derived that there is a particular function of the displacements of each particle and their masses that stays in uniform motion with the absence of external forces. This function becomes useful, so we give it a name: the center of mass.

The fact that the C.M. of a collection of particles remains in uniform motion in the absence of external forces is kind of the 1st law for collections of particles (but note that the proper 1st law still holds for all the individual particles that make up our collection).
 

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