Understanding the Total Energy After Particle Collision

[charged-ant]

Homework Statement

In a particle accelerator a proton and an antiproton, traveling at the same speed, undergo a head on collision and produce subatomic particles. The total kinetic energy of the two particles just before the collision is 3.2 x 10$^{}-10$ J.

State why the total energy after the collision is more than 3.2 x 10$^{}-10$ J.

Homework Equations

e=mc$^{}2$
hf$_{}min$ = E$_{}0$ where E0 is rest energy of electron

The Attempt at a Solution

I thought energy, mass and charged were conserved...

 

[member 553083]

so why would the total energy after the collision be more than 3.2 x 10^{}-10 J? The total energy of the two particles just before the collision is 3.2 x 10^{}-10 J. Because of the conservation of energy, the total energy after the collision must also be 3.2 x 10^{}-10 J. However, during the collision, some of the kinetic energy of the two particles is converted into the rest energy of subatomic particles. This means that the total energy of the system after the collision will be greater than 3.2 x 10^{}-10 J. This is because the rest energy of the subatomic particles is given by E_{}0 = mc^{}2, where m is the mass of the particle and c is the speed of light. The rest energy is greater than the kinetic energy of the two particles before the collision, so when this energy is added to the 3.2 x 10^{}-10 J, the total energy after the collision will be greater than 3.2 x 10^{}-10 J.