Relativistic collision and max energy

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Discussion Overview

The discussion revolves around the maximum energy transmitted during a relativistic collision between a moving particle and a stationary particle. Participants explore theoretical aspects, mathematical formulations, and implications of energy transfer in such collisions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant queries the maximum energy transmitted to a rest particle during a relativistic collision.
  • Another participant suggests that momentum times the speed of light could be relevant, indicating a need to redefine particles if rest mass is transferred.
  • There is a mention of photon absorption and its relation to energy transfer, prompting questions about how this applies to relativistic particles that are not photons.
  • Several participants express confusion about the maximum energy converted to heat versus the maximum energy transferred to the other particle.
  • A participant notes that solving the problem involves significant algebra, mentioning the center of mass (cm) system and the importance of momentum and energy conservation.
  • Another participant proposes a conceptual model involving a massless spring between the particles, questioning its relevance and suggesting a frame where both particles move at the same speed.
  • One participant emphasizes the complexity of the algebra involved and the necessity of careful calculations to arrive at a logical result.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of certain models and the complexity of the algebra involved in solving the problem. There is no consensus on the best approach or the maximum energy transmitted, indicating ongoing debate and exploration.

Contextual Notes

Participants highlight the need for careful consideration of momentum and energy conservation laws, but the discussion does not resolve the mathematical complexities or assumptions involved in the calculations.

ghadir-jafari
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a relaticistic particle collide with another rest particle. what is the maximum energy transmitted to the particle after collision?
 
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I guess that would be momentum times the speed of light - since you would have to re-define your particles if rest mass were transferred.

Regards,

Bill
 
100%
thats what happens when a photon is Absorbed
 
RandallB said:
100%
thats what happens when a photon is Absorbed

How does that relate to relativistic particles that are not photons?

Regards,

Bill
 
what is the maximum amount converted to heat or the maximum amount transferred to the other particle?
 
granpa said:
what is the maximum amount converted to heat or the maximum amount transferred to the other particle?

I think the OP was fairly clear with respect to that.

Regards,

Bill
 
well we just had a thread about the other so i thought i would ask. it seems rather trivial if he is asking how much is transferred.
 
granpa said:
what is the maximum amount converted to heat or the maximum amount transferred to the other particle?

to the other particle.
 
There is a lot of algebra in solving this.
The max energy to the target is when the projectile goes straight back in the cm system.
First you have to find the cm momentum P and energy E of the target particle.
Then change its momentum direction to go forward and LT P and E back to the lab system.
 
  • #10
yes.but I can't solve this problem by very much algebra. I don't reach any logic result.
please give me a mathematic result.
 
  • #11
Conservation of energy and momentum for the incident particle m rebounding backwards with momentum p, which transmits the most energy (assuming the target mass M>m), gives the equation
E_L+M=\sqrt{p^2+m^2}+\sqrt{(p+p_L)^2+M^2}, whereE_L and
p_L are the incident energy and momentum.
It is not easy to solve for p, but that is what one of us must do.
 
  • #12
why can't we just imagine that there is a massless spring between the 2 particles then go to a frame where the particles are both moving at the same speed? I would think that the answer would be obvious. unless I am missing something.
 
  • #13
You are missing all the work involved.
The spring is irrelevant.
You seem to be describing my first suggestion to go to the cm system where the momenta (not the velocities) are equal in magnitude. Either method I proposed has some complicated algebra. But we all learned algebra in high school.
 

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