Question about energy in C-O-M frame and Lab frame.

In summary: This is really confusing me. :(In summary, this textbook says that if you have a particle in a center of momentum frame (C-O-M), there is more energy there than in any other frame. However, I'm not sure if this is correct or not because the text is very famous.
  • #1
sukho
5
0
Hi, I just register to this site.
I'm reading a famous classical mechanics textbook. and it state that
'Since the spatial momentum in the C-O-m frame is zero, there is clearly more energy, p0, in this frame than in the laboratory frame.'

I think the energy in the center of momentum(C-O-M) frame should be less than in all other frame.
However, I've still not sure that it's right or wrong because this textbook is very famous.

Thanks.
PS. Should I states the name of the text?
 
Physics news on Phys.org
  • #2
welcome to pf!

hi sukho! welcome to pf! :smile:

that certainly looks wrong, but i wonder what the context is

can you provide a link?​
 
  • #3
sukho, you are correct, it should be less. It's a well-known theorem in mechanics that the kinetic energy of a system of particles can be written as a sum of two terms: T = ½ MV2 + ∑ ½ mivi2, where M is the total mass, V is the velocity of the center of mass, and vi are the velocities of the individual particles with respect to the center of mass. Clearly this is a minimum when V = 0.
 
  • #4
Oops, just noticed this is the relativity group. Ok, even easier. The total 4-momentum of the system of particles is P = (E/c, p). This has norm P·P = (E/c)2 - p.p. Since the norm must be the same in all reference frames, E will be minimum in the center of mass frame where p = 0.
 
  • #5
It would help, if you can give the exact reference, to see the context of that quote.
The book could be talking about available COM energy, which is larger in a colliding beam accelerator.
 
  • #6
It would help, if you can give the exact reference, to see the context of that quote.
The book could be talking about available COM energy, which is larger in a colliding beam accelerator.
 
  • #7
Hi, everyone.
The book I read is 'Classical Mechanics' 3ed by 'Goldstein Poole & Safko' on page 302 line 16
and if u see the footnote on this page, it's kind of support the context. I also confuse about the footnote too.
Thanks.
 
  • #8
hi sukho! :wink:

i don't think that's available online …

can you post a picture? :smile:​
 
  • #9
Hi. I attached pdf file of the context.
The attached file is a page 302, Goldstein. and the context is on line 16.
Thanks.
 

Attachments

  • 302 goldstein.pdf
    292.6 KB · Views: 235
  • #10
hmm … it refers to equations (7.79) and (7.80) which are on the previous page :redface:
 
  • #11
sukho said:
Hi. I attached pdf file of the context.
The attached file is a page 302, Goldstein. and the context is on line 16.
Thanks.
Reading it in context, it does not make too much sense. I am not sure what their p^0 refers to.
Maybe just ignore that sentence.
 
Last edited by a moderator:
  • #12
clem said:
Reading it in context, I see (as I thought) that G is referring to the sum of the energies of the two particles. Since E^2-p^2 is invariant, this is largest when p-0.


Why it's not minimum energy when p=0, as Bill_K said? it's minus sign before p^2.
and the I've attached the previous pages.
Thanks.
 

Attachments

  • 300-301 goldstein.pdf
    766.4 KB · Views: 269
  • #13
I think I'll just ignore that context.
Thank you guys.
 

FAQ: Question about energy in C-O-M frame and Lab frame.

What is the difference between the C-O-M frame and the Lab frame?

The C-O-M (center-of-mass) frame is a reference frame in which the total momentum of a system is zero. The Lab frame, on the other hand, is a reference frame in which an observer is stationary. The main difference between these frames is that the C-O-M frame is used to analyze the motion of a system as a whole, while the Lab frame is used to analyze the motion of individual particles within the system.

How is energy conserved in the C-O-M frame and the Lab frame?

In both the C-O-M frame and the Lab frame, energy is conserved. This means that the total amount of energy in a system remains constant. In the C-O-M frame, the total energy is conserved because the total momentum is zero, so the kinetic energy and potential energy of the system must balance out. In the Lab frame, energy is conserved due to the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

3. Can energy be transferred between the C-O-M frame and the Lab frame?

Yes, energy can be transferred between these frames. In the C-O-M frame, energy can be transferred between particles within the system. In the Lab frame, energy can be transferred between the system and its surroundings. However, the total amount of energy in the system remains constant in both frames.

4. How does the C-O-M frame affect the energy calculations of a system?

The C-O-M frame is a useful reference frame for energy calculations because it simplifies the motion of a system by eliminating the effects of external forces. In this frame, the total momentum is zero, so the kinetic energy and potential energy of the system can be easily calculated without having to consider the individual forces acting on each particle.

5. Is the C-O-M frame the only frame in which energy can be conserved?

No, energy can be conserved in any inertial reference frame. The C-O-M frame is just one specific frame that is useful for analyzing the motion and energy of a system. Other frames, such as the Lab frame or a frame moving at a constant velocity, can also be used to analyze energy conservation in a system.

Similar threads

Question about "Rest frame of a photon" FAQ
Replies
19
Views
2K
I Lab energy available in threshold (endothermic) reactions
Replies
5
Views
1K
A Exact meaning of the mass M in the Kerr metric event horizon formula?
Replies
4
Views
609
Proving the Uniqueness of Center of Momentum Frame
Replies
2
Views
2K
I Cross-Section from Lab Frame to C-O-M Frame
Replies
2
Views
2K
How Do You Calculate Proton Beam Energy in a Lab Frame?
Replies
7
Views
2K
How Does the Relativistic Rocket Equation Describe Velocity?
Replies
2
Views
1K
Lorentz ether frame, Relativistic Mass, and Inertia
Replies
5
Views
4K
Relativistic Time & Mass-Energy Phasors
Replies
1
Views
1K
Planck constant is Lorentz invariant?
5
Replies
170
Views
29K

Hot Threads

Recent Insights

Back
Top