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3. (10 pts) High energy particle accelerators convert part of the energy of colliding particles into the masses of particles produced in the collisions. Consider a collision of two protons that produces two charged kaons. The mass of the proton is mp- 938.3 MeV/c2, and the mass of each kaon is mK 493.7 MeV/c2. The reaction is a) The total energy (kinetic energy and rest energy) and total momentum is conserved. Suppose one of the protons is at rest in the laboratory frame. Calculate the minimum kinetic energy that the other proton must have (in the laboratory frame) just before the collision if the reaction is to occur. You may find the center-of-momentum frame convenient: Use a Lorentz transformation to relate the velocities in the laboratory frame to the reference frame in which the total momentum of the two protons is zero b) Find the ratio of the minimum kinetic energy of part (a) to the rest energy of the two kaons. c) Suppose the two protons move in the laboratory frame at the same speed just before the collision. How much (kinetic) energy must be imparted to the protons for the reaction to proceed? Repeat part (b) for this scenario. d) Energy frontier particle accelerators are designed to collide two beams of par- ticles moving in opposite directions, not one beam of particles with a fixed target. Why?

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