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How Does the Total Energy of a Particle Depend on Speed

# How Does the Total Energy of a Particle Depend on Speed -...

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How Does the Total Energy of a Particle Depend on Speed? We have a formula for the total energy E = K.E. + rest energy, so we can see how total energy varies with speed. The momentum varies with speed as . How Does the Total Energy of a Particle Depend on Momentum? It turns out to be useful to have a formula for E in terms of p . Now so hence using p = mv we find . If p is very small, this gives

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, the usual classical formula. If p is very large, so c 2 p 2 >> m 0 2 c 4 , the approximate formula is E = cp . The High Kinetic Energy Limit: Rest Mass Becomes Unimportant! Notice that this high energy limit is just the energy-momentum relationship Maxwell found to be true for light, for all p . This could only be true for
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Unformatted text preview: all p if m 2 c 4 = 0, that is, m = 0. Light is in fact composed of “photons”—particles having zero “rest mass”, as we shall discuss later. The “rest mass” of a photon is meaningless, since they’re never at rest—the energy of a photon is of the form 0/0, since m = 0 and v = c , so “ m ” can still be nonzero. That is to say, the mass of a photon is really all K.E. mass. For very fast electrons, such as those produced in high energy accelerators, the additional K.E. mass can be thousands of times the rest mass. For these particles, we can neglect the rest mass and take E = cp ....
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How Does the Total Energy of a Particle Depend on Speed -...

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