49) This question asks us to find the mass of a particle with a given momentum and energy. First, we can set up the relativistic energy and momentum for this problem.
After this, we want to simplify this equation. Some people might try to expand the Lorentz factor; this would leave them with two equations and two unknowns: velocity and mass. Although this could work, it will make the problem unnecessarily hard, and there is a much simpler solution.
We can divide the equations, therefore eliminating m and γ and alowing us to solve for velocity. After solving for velocity, we would then plug this back into the original equation to solve for mass.
Now that we have a plan to solve this problem, let's start by trying to divide the two equations.
Finally, we can use velocity to solve for the Lorentz factor, then use either of our initial equations to solve for mass.
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