WHat is better in a particle beam collider.

[ehabmozart]

When two particle beams meet head on, more energy is available than when the particle beam is directed at a fixed target. Why is this??

 

[M Quack]

Because of the conservation of momentum.

If you collide a fast particle with one at rest, then the center of mass has a large momentum. This is conserved in the collision. Therefore the center of mass of all the particles created in the collision also has to move with the same momentum. I.e. they have to have quite a lot of kinetic energy.

If you collide particle head-on, then the center of mass is at rest. Hence no energy is "wasted" on the kinetic energy of the resulting particles to keep the center of mass moving after the

 

[ZapperZ]

When two particle beams meet head on, more energy is available than when the particle beam is directed at a fixed target. Why is this??

Forget about particle beams. Can you do the reasoning when it is two cars colliding head on versus one hitting a wall?

Zz.

 

[the_emi_guy]

The car analogy may not a good one. A car hitting a immovable wall experiences the same trauma as a car hit head on by an identical car (in both cases the car is stopped dead in its tracks).
In the particle accelerator case, the "target" is either a similar particle in motion in a head on collision, in which case it may be stopped dead in its tracks, or a particle (atom?) at rest in the target material, in which case both will carry momentum in the direction of the original particle.

 

[daveb]

I think the car example is a good one, because the assumption is that you either have a car hitting a wall at 60mph, or two cars head on, each at 60mph so their impact is as if each hits a brick wall at 120mph. Of course, with the energy of particle beams, you have to take relativity into account and the speeds aren't additive.

 

[LURCH]

Because of the conservation of momentum.

If you collide a fast particle with one at rest, then the center of mass has a large momentum. This is conserved in the collision. Therefore the center of mass of all the particles created in the collision also has to move with the same momentum. I.e. they have to have quite a lot of kinetic energy.

If you collide particle head-on, then the center of mass is at rest. Hence no energy is "wasted" on the kinetic energy of the resulting particles to keep the center of mass moving after the

Forget about particle beams. Can you do the reasoning when it is two cars colliding head on versus one hitting a wall?

Zz.

Ok, change that to "versus hitting a parked car", and these two are saying the same thing. The real energy gain is in the fact that no target can remain fixed in a particle collsion (as the_EMI_guy was saying).

 

[the_emi_guy]

.. or two cars head on, each at 60mph so their impact is as if each hits a brick wall at 120mph.

No, two cars hitting head on at 60mph is the same impact as one hitting a brick wall at 60mph. The brick wall does the same thing as the head on car, it stops the first car dead in its tracks (final momentum = 0, final kinetic energy = 0).

 

[ZapperZ]

No, two cars hitting head on at 60mph is the same impact as one hitting a brick wall at 60mph. The brick wall does the same thing as the head on car, it stops the first car dead in its tracks (final momentum = 0, final kinetic energy = 0).

You are missing the point that I was asking the OP. I wanted to know if he/she understands the difference in the INITIAL conditions of the two scenarios. This is basic classical mechanics. Does he/she understand the total energy BEFORE each of the collisions.

When someone asks a question like this, it is IMPERATIVE that one first investigates what the person asking the question knows and doesn't know!

Zz.

 

[mfb]

While the car model can show that there is some difference (hit a parking cair vs. hit a moving car), the cars have an energy factor of just 2. This would not be a reason to build particle colliders. It is way easier to hit a solid target instead of another beam.

However, relativistic effects severly limit the energy of fixed-target experiments: There, the available energy just scales with the square root of the beam energy. In colliders, it is proportional to the beam energy.