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Writer's picturekeshprad

PhysicsBowl 2019 Q49


49) This question requires relativistic energy and momentum to solve for the combined mass. We know that the two objects move at the same speed but in opposite directions. We can set up a series of equations to help us solve this problem.

Where m is rest mass, v is velocity, and γ is the Lorentz factor

Since the two objects have the same mass and same speed in opposite directions, this tells us the momentum of the system is 0. This implies that after colliding the speed of the combined mass will be 0.

Where m is rest mass, c is speed of light, γ is the Lorentz factor, and M is the combined mass

Remember that because the combined mass is at rest, we don't need the Lorentz factor, and we can instead use the mass-energy equivalence. Since energy is a scalar, although the objects move in opposite directions, we still sum the energy of the objects.


Finally, by expanding the Lorentz factor we can solve for M, the combined mass.

Where M is combined mass, m is rest mass, v is velocity, and c is the speed of light

Answer: D

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