- #1
Eirik
- 12
- 2
Hi! Hope I'm posting this in the right place! I'm practicing for exams and came over this question:
A proton with mass ##m_p## is accelerated to a relativistic velocity, with kinetic energy ##K##. It collides completely inelastic with another proton, which has the same kinetic energy, ##K##, and velocity in the opposite direction. How big does K have to be, in order for the composite particle to have energy equal to 150 GeV?
Intuitively I would use conservation of energy to solve this, which gives me:
##E=2(K+mc^2)##
This gives me K=75GeV.
However, I found a formula for essentially the exact same problem in my physics book, which states that:
##E=2mc^2(1+\frac{K}{mc^2})##
Which gives me about K=74.1 GeV.
The last formula should be the right one, but I don't really see how, as both protons have kinetic energy, ##K##.. Any input?
A proton with mass ##m_p## is accelerated to a relativistic velocity, with kinetic energy ##K##. It collides completely inelastic with another proton, which has the same kinetic energy, ##K##, and velocity in the opposite direction. How big does K have to be, in order for the composite particle to have energy equal to 150 GeV?
Intuitively I would use conservation of energy to solve this, which gives me:
##E=2(K+mc^2)##
This gives me K=75GeV.
However, I found a formula for essentially the exact same problem in my physics book, which states that:
##E=2mc^2(1+\frac{K}{mc^2})##
Which gives me about K=74.1 GeV.
The last formula should be the right one, but I don't really see how, as both protons have kinetic energy, ##K##.. Any input?