Two protons (mass = 1.67 x 10 -27 kg) withequal speeds in opposite directions co

Question

Two protons (mass = 1.67 x 10-27 kg) withequal speeds in opposite directions collide head-on, producing aparticle called a pi meson (0, mass = 2.40 x10-28 kg). These reactions are how the Large HadronCollider is producing new particles. (a) If all the particles are at rest after the collision, findthe initial kinetic energy and initial speed of each proton. (b) What is the initial momentum of one of the protons beforethe collision? (as measured from an observer in the lab frame atrest) (c) How is the rest energy of the pi meson related to thetotal initial kinetic energy of the protons? Two protons (mass = 1.67 x 10-27 kg) withequal speeds in opposite directions collide head-on, producing aparticle called a pi meson (0, mass = 2.40 x10-28 kg). These reactions are how the Large HadronCollider is producing new particles. (a) If all the particles are at rest after the collision, findthe initial kinetic energy and initial speed of each proton. (b) What is the initial momentum of one of the protons beforethe collision? (as measured from an observer in the lab frame atrest) (c) How is the rest energy of the pi meson related to thetotal initial kinetic energy of the protons?

Explanation / Answer

the energy loss during the collision is use to create the pimeson. the energy is transfomed into matter . you can obtain theinitial energy by E=mc^2
(b) E=p/c in the momentum=0 frame ... andp=mv...
Ok so... I would divide my energy in 2, because both protonshave the same amount of energy, then multiply by light speed ''c''to have the momentum of one proton. the question of the lab frameintrigues me, it looks too simplist . I would like to hear yourtoughts about it. I'll think about it tomorow during the day.
(c) E= mc^2 . (same idea as in (a) ) , the kinetic energy istransformed into matter. the kinetic energy is proportional to themass of the particule created. Since there`s no kinetic energy atthe end, all the energy has been transformed to create a newparticule. Understand that with the same amount of energy we couldhave create a lighter particule but there will be a final positiveamount of kinetic energy after the colision.
I hope it had helped you a bit . please contact me for yourtought about (b)

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