What is the speed, as a fraction of c, of a particle whose momentum is mc?
Speed of particle is 0.707c.
We have given that, particle has momentum mc.
The formula of relativistic momentum is :
here, m = mass of particle
v = velocity of particle
c = speed of light
= relativistic momentum
We have given that the relativistic momentum is mc.
Substituting the values in formula :
The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply . The mass of a proton, to four significant figures, is , and the mass of a helium nucleus is known to be .
a. How much energy is released in each fusion?
b. What fraction of the initial rest mass energy is this energy?
One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed directly—is immediately transformed into two photons emitted back to back. Two photons, with momenta , were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass.
A ball of mass m traveling at a speed of has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass departs the collision with a speed of . Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.
a. What is, written as a fraction like a/b?
b. What is the initial total momentum? Give your answer as a fraction times .
c. What is the initial total energy? Give your answer as a fraction times . Don’t forget that there are two balls.
d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is. Instead, let the final state of the system be an unknown mass traveling at an unknown speed . You have two conservation laws. Find and .
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