What Is the Internal Energy of an Electron Moving at 0.750c0?

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SUMMARY

The internal energy of an electron moving at 0.750c in the Earth reference frame can be calculated using the principles of relativistic energy. The correct equations to use are the rest energy formula E=mc², the total energy formula E_T = mc² / √(1 - v²/c²), and the kinetic energy formula KE = E_T - E. The term "internal energy" in this context refers to the rest energy of the electron, which is simply its mass-energy at rest, represented by mc². The confusion arises from the terminology used in the question, which incorrectly implies a need to consider the particle's speed.

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  • Understanding of Einstein's mass-energy equivalence (E=mc²)
  • Familiarity with relativistic physics concepts, particularly total energy and kinetic energy
  • Knowledge of the speed of light (c) and its significance in physics
  • Basic algebra for manipulating equations involving square roots and fractions
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  • Study the derivation of the total energy formula in special relativity
  • Learn about the implications of relativistic speeds on mass and energy
  • Explore examples of kinetic energy calculations for particles moving at relativistic speeds
  • Review the terminology used in physics to avoid confusion in energy concepts
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Students studying physics, particularly those focusing on relativity, educators teaching energy concepts, and anyone interested in the behavior of particles at high velocities.

Barry Melby
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Homework Statement


What is the internal energy of an electron moving at 0.750c0 in the Earth reference frame?

Homework Equations

The Attempt at a Solution


E = mc^2
E = (9.11 * 10^-31)(.750)(3*10^8)

However, this appears incorrect. What have I done wrong or what am i missing?
 
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What do you mean "internal" energy? It's just one particle, so the options are "rest energy", "kinetic energy" and "total energy".
If m is the mass of an electron, c is light speed, and v is the speed of the electron, then:

Rest energy is E=mc^2
Total energy is E_T = \frac{mc^2}{ \sqrt{1 - \frac{v^2}{c^2}}}
Kinetic energy is KE = E_T - E
 
I ran into this post trying to solve a question from Pearson's Principles and Practices of Physics (by Mazur). The question is looking for the "intrinsic" energy: the energy of the particle when it appears at rest; i.e. ##mc ^ 2##. I don't know why they use the wrong term or why they mention the speed of the particle.
 

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