Two particles collide, COM frame, relativistic velocities.

In summary, the problem involves a 2-body collision in the center of mass frame, where the total energy is conserved. We need to show that the derivative of the energy with respect to the momentum of the final state is equal to the sum of the velocities of the final particles. This holds true even in the relativistic case, though the equations may need to be modified.
  • #1
EdgyWaters
1
0

Homework Statement


2-body, COM frame collision
a+b ---> c+d
E = Ea+Eb = Ec+Ed
Show that
dE/dPf = Vc+Vd
Show that the answer is the same when the velocities are relativistic
I don''t know how to work out the relativistic aspect of the question.

Homework Equations

The Attempt at a Solution


E = Pc^2/2Mc - Pd^2/2Md
(Pf^2)/2(I/Mc + I/Md) = (Pf^2)/2(Md+Mc/McMd)
dE/dPf = Pf(1/Mc+I/Md) = Vc + Vd
 
Physics news on Phys.org
  • #2
What is Pf?
How can E depend on anything if it is fully determined by the initial (or final) state?

If you can solve it in the Newtonian case, replace all Newtonian equations with their relativistic versions, and see if it still works.
 

1. What is the COM frame in the context of two particles colliding?

The COM (center-of-mass) frame is a reference frame in which the total momentum of the two colliding particles is equal to zero. In other words, it is the frame of reference in which the two particles appear to have equal and opposite velocities.

2. How are relativistic velocities defined?

Relativistic velocities are velocities that take into account the effects of special relativity, which states that the laws of physics are the same in all inertial reference frames. These velocities cannot exceed the speed of light and are calculated using the Lorentz transformation equations.

3. Why is it important to consider relativistic velocities in the context of particle collisions?

In particle collisions, particles may reach very high velocities, approaching the speed of light. In these cases, classical (non-relativistic) equations and calculations are no longer accurate and must be replaced with relativistic equations to accurately describe the behavior and outcomes of the collision.

4. How does the mass of the particles affect the collision in the COM frame?

In the COM frame, the masses of the particles do not affect the outcome of the collision. This is because the COM frame is a reference frame in which the total momentum of the particles is zero, regardless of their individual masses. Therefore, the masses do not play a role in determining the velocities and outcomes of the collision.

5. Can particles with relativistic velocities ever reach a state of rest in the COM frame?

No, particles with relativistic velocities cannot reach a state of rest in the COM frame. This is because the speed of light is the maximum velocity that can be reached, and it is impossible for an object to have zero velocity in one frame of reference and then exceed the speed of light in another frame of reference.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Special and General Relativity
Replies
8
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
940
  • Special and General Relativity
Replies
10
Views
1K
Back
Top