If two particles have equal kinetic energies, are their momenta necessarily equal?
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No, the momenta of two particles with equal kinetic energies are not necessarily equal.
Kinetic energy is given by the formula:
KE = (1/2)mv^2
where m represents mass and v represents velocity. The kinetic energy depends on the square of the velocity, not the momentum.
Momentum, on the other hand, is given by the formula:
p = mv
where p represents momentum. Momentum is directly proportional to both mass and velocity.
Since kinetic energy depends only on the square of the velocity, particles with equal kinetic energies could have different velocities and therefore different momenta.
To summarize, while equal kinetic energies imply equal amounts of energy, they do not imply equal momenta.