The kinetic energy of motion, 7, of a particle is the relativistic total energy minus the rest energy, i.e.. T=ymoc²-moe², where is the speed of light. (a) A particle has rest mass me and speed v. Ifc, then show that the kinetic energy due to motion is approximated by the well-known classical expression for the kinetic energy, i.e.. (b) What is the particle's speed if its kinetic energy 7 is equal to its rest energy? (c) Express the momentum p of the particle as a function of the rest mass mo and the kinetic energy of the motion, 7, Your expression should contain mo and T, not or 1 [Hint: Use the relation between E and p that does not involveu ory.]

The kinetic energy of motion, 7, of a particle is the relativistic total energy minus the rest energy, i.e.. T=ymoc²-moe², where is the speed of light. (a) A particle has rest mass me and speed v. Ifc, then show that the kinetic energy due to motion is approximated by the well-known classical expression for the kinetic energy, i.e.. (b) What is the particle's speed if its kinetic energy 7 is equal to its rest energy? (c) Express the momentum p of the particle as a function of the rest mass mo and the kinetic energy of the motion, 7, Your expression should contain mo and T, not or 1 [Hint: Use the relation between E and p that does not involveu ory.]

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter14: Special Theory Of Relativity

Section: Chapter Questions

Problem 14.39P

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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

The kinetic energy of motion, 7, of a particle is the relativistic total energy minus the rest
energy, i.e..
T=ymor²- moe²,
where is the speed of light.
(a) A particle has rest mass mo and speed v. Ifc, then show that the kinetic energy
due to motion is approximated by the well-known classical expression for the kinetic
energy, i.e..
(b) What is the particle's speed if its kinetic energy 7 is equal to its rest energy?
(c) Express the momentum p of the particle as a function of the rest mass mo and the
kinetic energy of the motion, 7, Your expression should contain mo and T, not or
[Hint: Use the relation between E and p that does not involveu ory.]

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Step 1: Introduce the relativistic kinetic energy and momentum

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Step 2: Derive non relativistic kinetic energy

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Step 3: Calculate the velocity when kinetic energy is equal to rest mass energy

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Step 4: Derive the expression of momentum

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