To learn the basic physics of collisions between high-energy particles. Particle accelerators are used to create well-controlled beams of high-energy particles. Such beams have many uses, both in research and industry. One promising line of research has been in exploring the collisions between the accelerated particles. In such collisions, new particles can be formed. The kinetic energy of the colliding particles helps trigger transformations that rarely--if ever--occur in nature: For instance, new particles can be formed. It is, therefore, essential for a researcher to determine the amount of energy available to initiate such transformations. Let us recall some basic mechanics to explain why the available energy is usually less than the total kinetic energy of the colliding particles. Consider a particle of mass m moving at a speed v. It collides head-on with a particle of mass M. A proton of mass m and energy Em collides with a stationary alpha particle that has a mass of approximately 4m. Find the available energy Ea. Express your answer in terms of m, Em, and appropriate constants.
A proton of mass m and energy Em collides with a stationary proton. Find the available energy Ea. Express your answer in terms of m, Em, and appropriate constants.
A proton and an antiproton have equal energies of 450GeV. The particles collide head-on. Find the available energy Ea. The rest energy of the proton is 938MeV. Express your answer in billions of electron volts to two significant figures