Center of mass, Newton's third law, and rocket thrust

[PhysicsKid0123]

Can someone clarify this for me-- how is the motion of the center of mass unaffected by internal forces, as is stated towards the end of the paragraph in the picture I've provided. It seems to me that motion of the center of mass directly affected by these internal forces. Specifically, the center of mass moves or undergoes motion because of the force of thrust that emerges from the rocket, which by Newton's third law, there is an equal and opposite force that causes the rocket (and the center of mass) to move forward. Can someone clarify this point for me?

 

[scottdave]

It would be nice to see the context of this equations. Consider this. A 200 kg astronaut throws a 1 kg hammer. Does the astronaut's center of mass move? What about the hammer? Ok. What about the combined system of astronaut and hammer as they are flying away from each other?

 

[PhysicsKid0123]

It would be nice to see the context of this equations. Consider this. A 200 kg astronaut throws a 1 kg hammer. Does the astronaut's center of mass move? What about the hammer? Ok. What about the combined system of astronaut and hammer as they are flying away from each other?

Center of mass would actually move for the combined system of astronaut and hammer. These are slides which briefly paraphrase Goldstein's classical mechanics-- these equations is Newtons 2nd law for a system of particles.

 

[jbriggs444]

how is the motion of the center of mass unaffected by internal forces

If you are considering the center of mass of the rocket alone, the reaction force between the rocket and its exhaust stream is an external force.

 

[PhysicsKid0123]

If you are considering the center of mass of the rocket alone, the reaction force between the rocket and its exhaust stream is an external force.

So Goldstein says: "In order that the motion of the center of mass (didn't make reference to just the rocket alone, it is kind ambiguous) be unaffected, the ejection of the exhaust gases at high velocity must be counterbalanced by the forward motion of the vehicle." Can you elaborate what is being said? Is this what you are saying?

 

[jbriggs444]

So Goldstein says: "In order that the motion of the center of mass (didn't make reference to just the rocket alone, it is kind ambiguous) be unaffected, the ejection of the exhaust gases at high velocity must be counterbalanced by the forward motion of the vehicle." Can you elaborate what is being said? Is this what you are saying?

Goldstein is considering the center of mass of the rocket plus exhaust stream. Accordingly, the force is internal and the center of mass is unaffected.

 

[PhysicsKid0123]

Goldstein is considering the center of mass of the rocket plus exhaust stream. Accordingly, the force is internal and the center of mass is unaffected.

I'm having a hard time wrapping my head around this. If the thrust force is internal, and by Newton's third law, there is the reaction force that moves the rocket, how does this not induce or affect motion of the center of mass? And by the way, thanks for helping me understand this!

 

[Nugatory]

I'm having a hard time wrapping my head around this. If the thrust force is internal, and by Newton's third law, there is the reaction force that moves the rocket, how does this not induce or affect motion of the center of mass?

The exhaust moves to the left, the rocket moves to the right, and the center of mass of the rocket+exhaust system stays in the same place.

 

[scottdave]

Center of mass would actually move for the combined system of astronaut and hammer.

I recommend working through my example to see how the center of mass postion changes. Say for 10 sec after the astronaut throws it and 100 seconds. Let's say velocity of the hammer is 20 m/s. What is the velocity of the astronaut?