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

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SUMMARY

The discussion centers on the concept of the center of mass and its relationship with internal forces, specifically in the context of rocket thrust and Newton's third law. Participants clarify that the motion of the center of mass of a system, such as a rocket and its exhaust, remains unaffected by internal forces, as these forces are counterbalanced. Goldstein's classical mechanics principles are referenced, emphasizing that the ejection of exhaust gases must be counterbalanced by the rocket's forward motion to maintain the center of mass's position. The example of an astronaut throwing a hammer illustrates how the center of mass of the combined system does move, while the center of mass of the rocket-exhaust system does not.

PREREQUISITES
  • Understanding of Newton's third law of motion
  • Familiarity with the concept of center of mass
  • Basic knowledge of classical mechanics as outlined in Goldstein's textbook
  • Ability to analyze motion in a closed system
NEXT STEPS
  • Study the principles of classical mechanics in Goldstein's "Classical Mechanics" textbook
  • Learn about the mathematical formulation of center of mass in multi-body systems
  • Explore the implications of internal vs. external forces in dynamic systems
  • Investigate practical applications of rocket thrust and motion in aerospace engineering
USEFUL FOR

Students of physics, aerospace engineers, and anyone interested in understanding the dynamics of motion in systems involving internal forces and thrust mechanics.

PhysicsKid0123
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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?
 

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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?
 
scottdave said:
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.
 
PhysicsKid0123 said:
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.
 
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jbriggs444 said:
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?
 
PhysicsKid0123 said:
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.
 
jbriggs444 said:
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!
 
PhysicsKid0123 said:
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.
 
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PhysicsKid0123 said:
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?
 

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