Physics Question help! (Particle Physics)

iLikePiano99

I need some help with this question from the 2009 paper:

Cockcroft and Walton’s apparatus is now displayed at CERN in Switzerland, where very high energy protons are used in the Large Hadron Collider.
In the Large Hadron Collider, two beams of protons are accelerated to high energies in a circular accelerator. The two beams of protons then collide producing new particles.
Each proton in the beams has a kinetic energy of 2.0 GeV.
(i) Explain why new particles are formed.
(ii) What is the maximum net mass of the new particles created per collision?

The last part is what I am having trouble with. In order for me to be happy, I need to understand the logics of the answer to the very end so bear with me here!

Basically the marking scheme uses m=E/c^2, using E as 4 GeV to find the mass...but I don't understand why because is 4GeV not what the energy was before the collision? There must be less energy after the collision with the addition of the new particles since energy has been converted to mass...according to the book the E in e=mc^2 means change in energy, so why don't you need to use the change of energy in this equation in order to find the mass? As far as I can see, the 4 GeV isn't the change in energy, it is just the energy of the protons before the collision.

Can someone please help me with this? It's been annoying me all day trying to figure it out!

whoopssinead

Its asking for the maximum mass of the new particles. Two protons hit each other at a combined kinetic energy of 4 GeV, so before hand the energy/mass is 4 GeV + the two protons. they collide and if they come to complete rest (Lose all kinetic energy) then after the collision they are still there, as are the particles formed from so by the conservation of energy, since the 2 protons are still there, all the 4 GeV will be used in the mc^2 eqn. Hope this helps, if not what part is confusing you

iLikePiano99

whoopssinead wrote: »

Its asking for the maximum mass of the new particles. Two protons hit each other at a combined kinetic energy of 4 GeV, so before hand the energy/mass is 4 GeV + the two protons. they collide and if they come to complete rest (Lose all kinetic energy) then after the collision they are still there, as are the particles formed from so by the conservation of energy, since the 2 protons are still there, all the 4 GeV will be used in the mc^2 eqn. Hope this helps, if not what part is confusing you

Thank you for the help! but I'm still a little confused. Should the 4GeV not have reduced after the collision since new particles have been produced? Hence more mass??? Whats the logic behind this? Sorry for the questions!

whoopssinead

Your dead right, the 4 GeV would be reduced. realistically after the collision of this energy would go towards forming the new particles, some would go towards the kinetic energy of the 2 protons and the newbies, and some would be lost as heat. This is a simplified situation were no energy is lost, and the particles have no kinetic energy at all after the collision, (i.e there at rest, no velocities) so all the energy 4GeV is used up in creating the new particles. if you look at the energy before and after you have this

Before = After (because of the conservation of energy)
4 GeV + 2(mass of proton*c^2) = (mass of new particle)*c^2 + 2(mass of proton*c^2)

There is no kinetic energy after the collision in this case because they asked for the maximum possible mass of the new particles.
Is this ok?

iLikePiano99

whoopssinead wrote: »

Your dead right, the 4 GeV would be reduced. realistically after the collision of this energy would go towards forming the new particles, some would go towards the kinetic energy of the 2 protons and the newbies, and some would be lost as heat. This is a simplified situation were no energy is lost, and the particles have no kinetic energy at all after the collision, (i.e there at rest, no velocities) so all the energy 4GeV is used up in creating the new particles. if you look at the energy before and after you have this

Before = After (because of the conservation of energy)
4 GeV + 2(mass of proton*c^2) = (mass of new particle)*c^2 + 2(mass of proton*c^2)

There is no kinetic energy after the collision in this case because they asked for the maximum possible mass of the new particles.
Is this ok?

Ah okay! I think I have it now. So because they are looking for the max mass, all of the energy 4GeV must have been used on creating the new particles. Therefore, there is no "left over" energy after the collision as it has all been converted to mass. E after collision is zero, therefore change in energy is the same as what we started out with - 4 GeV? Have I got it? Thank you so much for the help - really appreciate it!

whoopssinead

Exactly and no worries