A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/236635 |
Resumo: | Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations. |
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Duarte, Sérgio Eduardo SilvaLima, Nathan Willig2022-04-06T04:45:57Z20210031-9120http://hdl.handle.net/10183/236635001127672Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations.application/pdfengPhysics education. Vol. 56, no. 3 (May 2021), 035028, 9p.Teoria da relatividadeRelatividadeMassaEnergiaSpecial theory of relativityRelativityEquivalence relationMassEnergyA simple thought experiment to discuss the mass–energy equivalence in the special theory of relativityEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001127672.pdf.txt001127672.pdf.txtExtracted Texttext/plain19833http://www.lume.ufrgs.br/bitstream/10183/236635/2/001127672.pdf.txt9523762bedd9170bc07ae5e698f9a9c0MD52ORIGINAL001127672.pdfTexto completo (inglês)application/pdf627266http://www.lume.ufrgs.br/bitstream/10183/236635/1/001127672.pdf90df75fd7ad5e1edd13a7e9b9f8e01bdMD5110183/2366352023-07-20 03:36:43.718117oai:www.lume.ufrgs.br:10183/236635Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-07-20T06:36:43Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
title |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
spellingShingle |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity Duarte, Sérgio Eduardo Silva Teoria da relatividade Relatividade Massa Energia Special theory of relativity Relativity Equivalence relation Mass Energy |
title_short |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
title_full |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
title_fullStr |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
title_full_unstemmed |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
title_sort |
A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity |
author |
Duarte, Sérgio Eduardo Silva |
author_facet |
Duarte, Sérgio Eduardo Silva Lima, Nathan Willig |
author_role |
author |
author2 |
Lima, Nathan Willig |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Duarte, Sérgio Eduardo Silva Lima, Nathan Willig |
dc.subject.por.fl_str_mv |
Teoria da relatividade Relatividade Massa Energia |
topic |
Teoria da relatividade Relatividade Massa Energia Special theory of relativity Relativity Equivalence relation Mass Energy |
dc.subject.eng.fl_str_mv |
Special theory of relativity Relativity Equivalence relation Mass Energy |
description |
Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations. |
publishDate |
2021 |
dc.date.issued.fl_str_mv |
2021 |
dc.date.accessioned.fl_str_mv |
2022-04-06T04:45:57Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
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publishedVersion |
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http://hdl.handle.net/10183/236635 |
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0031-9120 |
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001127672 |
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http://hdl.handle.net/10183/236635 |
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eng |
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eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physics education. Vol. 56, no. 3 (May 2021), 035028, 9p. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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