New value of the particle's total energy?

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SUMMARY

The total energy of a charged particle moving at 0.700c is 0.642 MeV. When the particle's speed increases to 0.980c, its total energy can be calculated using the relativistic energy equations: E0=mc² for rest mass energy and K=(γ-1)mc² for kinetic energy. The correct approach involves determining the rest mass energy first and then applying the Lorentz factor (γ) to find the new total energy at the increased speed. The solution requires careful application of these equations to achieve accurate results.

PREREQUISITES
  • Understanding of relativistic energy equations, specifically E0=mc² and K=(γ-1)mc².
  • Familiarity with the concept of Lorentz factor (γ) in special relativity.
  • Basic knowledge of charged particle dynamics and motion at relativistic speeds.
  • Ability to manipulate algebraic equations and ratios effectively.
NEXT STEPS
  • Study the derivation and application of the Lorentz factor (γ) in relativistic physics.
  • Learn how to calculate kinetic energy for particles moving at relativistic speeds.
  • Explore the relationship between total energy, rest mass energy, and kinetic energy in special relativity.
  • Investigate the implications of relativistic speeds on particle behavior in linear accelerators.
USEFUL FOR

Students studying physics, particularly those focusing on special relativity, as well as educators and anyone involved in particle physics or accelerator technology.

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Homework Statement



A charged particle is observed to have a total energy of 0.642 MeV when it is moving at 0.700c. If this particle enters a linear accelerator and its speed is increased to 0.980c, what is the new value of the particle's total energy?

Homework Equations


Rest mass energy:
E0=mc2

Kinetic energy:
K=(\gamma-1)mc2

Total energy:
E=E0+K


The Attempt at a Solution


I tried to solve for the rest mass energy using the original speed and total energy, but got stuck. I also tried to set up a ratio of old total E on top of new total E, but that didn't give me the correct answer.

Can anyone help? Thanks!
 
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