Question on Newton's first law of motion

[ranger]

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.

 

[Doc Al]

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.

 

[ranger]

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?

 

[Doc Al]

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" .

 

[neutrino]

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.

 

[ranger]

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?

 

[Doc Al]

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.

 

[neutrino]

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. :)

 

[masudr]

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).