# Relativistic collision and max energy

1. Oct 6, 2008

a relaticistic particle collide with another rest particle. what is the maximum energy transmitted to the particle after collision?

2. Oct 6, 2008

### Antenna Guy

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

3. Oct 6, 2008

### RandallB

100%
thats what happens when a photon is Absorbed

4. Oct 6, 2008

### Antenna Guy

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

Regards,

Bill

5. Oct 6, 2008

### granpa

what is the maximum amount converted to heat or the maximum amount transferred to the other particle?

6. Oct 6, 2008

### Antenna Guy

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

Regards,

Bill

7. Oct 6, 2008

### granpa

8. Oct 7, 2008

to the other particle.

9. Oct 7, 2008

### clem

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. Oct 12, 2008

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. Oct 13, 2008

### clem

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
$$E_L+M=\sqrt{p^2+m^2}+\sqrt{(p+p_L)^2+M^2}$$, where$$E_L$$ 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. Oct 14, 2008

### granpa

why cant 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. Oct 14, 2008

### clem

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.