Impuls sile — разлика између измена
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{{Short description|Integral sile u vremenskom intervalu}} |
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[[Датотека:Elastischer stoß 2D.gif|thumb|desno|250п|Elastični [[Судари|sudar]] u dve dimenzije. Ukupni iznos impulsa sile i [[energija|energije]] za savršeno [[Elastičnost (fizika)|elastičan]] sudar ostaje sačuvan.]] |
[[Датотека:Elastischer stoß 2D.gif|thumb|desno|250п|Elastični [[Судари|sudar]] u dve dimenzije. Ukupni iznos impulsa sile i [[energija|energije]] za savršeno [[Elastičnost (fizika)|elastičan]] sudar ostaje sačuvan.]] |
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[[Датотека:Moglfm19p13 pendulo balistico.jpg|thumb|desno|250п|[[Balističko klatno]] je uređaj za određivanje brzine [[balistika|balističkih]] [[projektil]]a, na primjer [[Puška|puščanoga]] zrna.]] |
[[Датотека:Moglfm19p13 pendulo balistico.jpg|thumb|desno|250п|[[Balističko klatno]] je uređaj za određivanje brzine [[balistika|balističkih]] [[projektil]]a, na primjer [[Puška|puščanoga]] zrna.]] |
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[[Датотека:Happy vs. Sad Ball.webm|thumbnail|250п|Impuls koji ''štap'' predaje<ref>{{cite web|url=http://materialseducation.org/educators/matedu-modules/docs/Property_Differences_in_Polymers.pdf |title= Property Differences in Polymers: Happy/Sad Balls |last=Stoebe|first=Thomas|publisher = University of Washington |location= Seattle, WA |date=2007 }}</ref> lopti je -{mv<sub>0</sub>}-, gde je -{v<sub>0</sub>}- brzina pri sudaru.]] |
[[Датотека:Happy vs. Sad Ball.webm|thumbnail|250п|Impuls koji ''štap'' predaje<ref>{{cite web|url=http://materialseducation.org/educators/matedu-modules/docs/Property_Differences_in_Polymers.pdf |title= Property Differences in Polymers: Happy/Sad Balls |last=Stoebe|first=Thomas|publisher = University of Washington |location= Seattle, WA |date=2007 }}</ref> lopti je -{mv<sub>0</sub>}-, gde je -{v<sub>0</sub>}- brzina pri sudaru.]] |
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'''Impuls sile''' ([[Latinski jezik|lat]]. ''impulsus'': udarac, podsticaj), u [[mehanika|mehanici]] (oznaka -{''I''}-),<ref>Beer, F.P., E.R. Johnston, Jr., D.F. Mazurek, P.J. Cornwell, and E.R. Eisenberg. (2010). ''Vector Mechanics for Engineers; Statics and Dynamics.'' 9th ed. Toronto: McGraw-Hill.</ref> [[vektor]]ska je [[fizička veličina]] određena (definisana) kao [[Množenje|umnožak]] [[sila|sile]] i [[Vreme (fizika)|vremena]] tokom kojeg je ta sila delovala.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html Impulse of Force], Hyperphysics</ref> [[Matematika|Matematički]] se računa kao: |
'''Impuls sile''' ([[Latinski jezik|lat]]. ''impulsus'': udarac, podsticaj), u [[mehanika|mehanici]]<ref>{{cite encyclopedia |title=mechanics |encyclopedia=Oxford English Dictionary |year=1933 |url=https://archive.org/details/in.ernet.dli.2015.271836/page/n817 }}</ref><ref>{{cite encyclopedia |title=mechanics |author = Liddell Scott |encyclopedia=A Greek-English Lexicon |year=1940 |url=http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dmhxaniko%2Fs }}</ref><ref>{{Cite book|last=Young, Hugh D. (Hugh David), 1930-|url=https://www.worldcat.org/oclc/1104689918|title=Sears and Zemansky's university physics : with modern physics|publisher=|others=Freedman, Roger A., Ford, A. Lewis (Albert Lewis), Estrugo, Katarzyna Zulteta|date=2 September 2019|isbn=978-1-292-31473-0|edition=Fifteenth edition in SI units|location=Harlow|pages=62|oclc=1104689918}}</ref>(oznaka -{''I''}-),<ref>Beer, F.P., E.R. Johnston, Jr., D.F. Mazurek, P.J. Cornwell, and E.R. Eisenberg. (2010). ''Vector Mechanics for Engineers; Statics and Dynamics.'' 9th ed. Toronto: McGraw-Hill.</ref> [[vektor]]ska je [[fizička veličina]] određena (definisana) kao [[Množenje|umnožak]] [[sila|sile]] i [[Vreme (fizika)|vremena]] tokom kojeg je ta sila delovala.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html Impulse of Force], Hyperphysics</ref> [[Matematika|Matematički]] se računa kao: |
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:<math>\vec{I}=\vec{F}t</math> |
:<math>\vec{I}=\vec{F}t</math> |
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Ovakav matematički zapis je posve korektan samo ako je sila delovala na telo u mirovanju. Opštiji zapis ima sledeći oblik: |
Ovakav matematički zapis je posve korektan samo ako je sila delovala na telo u mirovanju. Opštiji zapis ima sledeći oblik: |
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:<math>\vec{I}=m \cdot \vec{v}_2-m \cdot \vec{v}_1</math> |
:<math>\vec{I}=m \cdot \vec{v}_2-m \cdot \vec{v}_1</math> |
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iz čega je očito da je impuls sile jednak promeni [[Količina kretanja|količine kretanja]]. Drugim rečima, impuls sile uzrokuje promenu stanja [[Kretanje|kretanja]] baš kao što to može utvrditi i za silu konstantnog intenziteta. |
iz čega je očito da je impuls sile jednak promeni [[Količina kretanja|količine kretanja]].<ref name="BookRags">{{cite book |url = http://www.bookrags.com/research/eulers-laws-of-motion-wom/ |title = Euler's Laws of Motion |access-date = 2009-03-30 |url-status=live |archive-url = https://web.archive.org/web/20090710162552/http://www.bookrags.com/research/eulers-laws-of-motion-wom/ |archive-date = 2009-07-10}}</ref><ref name="McGillKing">{{cite book |title=Engineering Mechanics: An Introduction to Dynamics |edition=3rd |last1=McGill |first1=David J. |last2=King |first2=Wilton W. |publisher=PWS |date=1995 |isbn=978-0-534-93399-9}}</ref> Drugim rečima, impuls sile uzrokuje promenu stanja [[Kretanje|kretanja]] baš kao što to može utvrditi i za silu konstantnog intenziteta. |
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Takođe, matematički je lako pokazati da je promena [[Kinetička energija|kinetičke energije]] jednaka [[skalarni proizvod|skalarnom umnošku]] impulsa sile i vektora srednje [[brzina|brzine]]. |
Takođe, matematički je lako pokazati da je promena [[Kinetička energija|kinetičke energije]] jednaka [[skalarni proizvod|skalarnom umnošku]] impulsa sile i vektora srednje [[brzina|brzine]]. |
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:<math> m \cdot v_2 = m \cdot v_1 + m \cdot a \cdot t </math> |
:<math> m \cdot v_2 = m \cdot v_1 + m \cdot a \cdot t </math> |
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Kako je prema [[Њутнови закони|drugom Njutnovom zakonu kretanja]]:<ref>{{cite book|last1=Greiner|first1=Walter|title=Classical mechanics: point particles and relativity|url=https://archive.org/details/springer_10.1007-b97649|date=2003|publisher=Springer|location=New York|isbn=978-0-387-21851-9}}</ref><ref>{{cite book |last1=Zeidler|first1=E. |title=Nonlinear Functional Analysis and its Applications IV: Applications to Mathematical Physics|date=1988|publisher=Springer|location=New York|isbn=978-1-4612-4566-7}}</ref><ref>{{cite book|last1=Wachter|first1=Armin |last2=Hoeber|first2=Henning|title=Compendium of theoretical physics|date=2006|publisher=Springer|location=New York|isbn=978-0-387-25799-0}}</ref> |
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Kako je prema [[Њутнови закони|drugom Njutnovom zakonu kretanja]]: |
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:<math> F = m \cdot a </math> |
:<math> F = m \cdot a </math> |
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== Reference == |
== Reference == |
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== Literatura == |
== Literatura == |
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* {{cite book|ref=harv|last=Bergmann|first=Ludwig|last2=Schaefer|first2=Clemens|title= Mechanik – Akustik – Wärme. In: ''Lehrbuch der Experimentalphysik.'' Bd. 1, 12. |publisher= Walter de Gruyter |location= Berlin |year=2008|isbn=978-3-11-019311-4|pages=}} |
* {{cite book|ref=harv|last=Bergmann|first=Ludwig|last2=Schaefer|first2=Clemens|title= Mechanik – Akustik – Wärme. In: ''Lehrbuch der Experimentalphysik.'' Bd. 1, 12. |publisher= Walter de Gruyter |location= Berlin |year=2008|isbn=978-3-11-019311-4|pages=}} |
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* {{cite book|ref=harv|last=Verma|first=H.C. |title=Concepts of Physics Vol 1. |edition=2004 Reprint |publisher=Bharti Bhavan |year=2004|isbn=978-81-7709-187-8|pages=}} |
* {{cite book|ref=harv|last=Verma|first=H.C. |title=Concepts of Physics Vol 1. |edition=2004 Reprint |publisher=Bharti Bhavan |year=2004|isbn=978-81-7709-187-8|pages=}} |
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* [[Robert Stawell Ball]] (1871) [https://books.google.com/books?id=CPo4AAAAMAAJ Experimental Mechanics] from [[Google books]]. |
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* {{cite book |author1= Lev Landau |author2= Evgeny Lifshitz | title=Mechanics and Electrodynamics, Vol. 1 | publisher=Franklin Book Company, Inc | year=1972 | isbn=978-0-08-016739-8}} |
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* {{cite book|last1=Truesdell|first1=C.|title=Essays in the History of Mechanics|date=1968|publisher=[[Springer Berlin Heidelberg]]|location=Berlin, Heidelberg|isbn=9783642866470}} |
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* {{cite book|last1=Maddox|first1=René Dugas ; foreword by Louis de Broglie ; translated into English by J.R.|title=A history of mechanics|date=1988|publisher=[[Dover Publications]]|location=New York|isbn=0-486-65632-2|edition=Dover}} |
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* {{cite book|editor-last1=Buchwald|editor-first1=Jed Z.|editor-last2=Fox|editor-first2=Robert|last3=Caparrini|first3=Sandro|last4=Fraser|first4=Craig|title=The Oxford handbook of the history of physics|date=2013|publisher=[[Oxford University Press]]|location=Oxford|isbn=9780199696253|pages=358–405|edition=First}} |
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* {{cite journal |last1=Rovelli |first1=Carlo |title=Aristotle's Physics: A Physicist's Look |journal=Journal of the American Philosophical Association |volume=1 |issue=1 |year=2015 |pages=23–40 |doi=10.1017/apa.2014.11|arxiv=1312.4057 |s2cid=44193681 }} |
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* {{cite journal |doi=10.1086/384242 |title=Wrestling with Proteus: Francis Bacon and the "Torture" of Nature |author=Peter Pesic |journal=Isis |volume=90 |number=1 |date=March 1999 |pages=81–94 |publisher=The University of Chicago Press on behalf of The History of Science Society |jstor=237475|s2cid=159818014 }} |
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* {{cite journal | last1 = Espinoza | first1 = Fernando | date = 2005 | title = An analysis of the historical development of ideas about motion and its implications for teaching | journal = Physics Education | volume = 40 | issue = 2| page = 141 | doi=10.1088/0031-9120/40/2/002|bibcode = 2005PhyEd..40..139E }} |
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* {{Cite book |title=The Islamic intellectual tradition in Persia |author= Seyyed Hossein Nasr |author2= Mehdi Amin Razavi |publisher=[[Routledge]] |date=1996 |isbn=978-0-7007-0314-2 |page=72}} |
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* {{cite journal|doi=10.1111/j.1749-6632.1987.tb37219.x|author= Aydin Sayili |date=1987|title=Ibn Sīnā and Buridan on the Motion of the Projectile|journal=Annals of the New York Academy of Sciences|volume=500|issue=1|pages=477–482|bibcode=1987NYASA.500..477S|s2cid=84784804}} |
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* {{Cite book|title=Pseudo-Avicenna, Liber Celi Et Mundi: A Critical Edition|first=Oliver|last=Gutman|publisher=[[Brill Publishers]]|year=2003|isbn=90-04-13228-7|page=193}} |
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* {{Cite journal|last=Palmieri|first=Paolo|date=2003-06-01|title=Mental models in Galileo's early mathematization of nature|url=https://www.sciencedirect.com/science/article/pii/S0039368103000256|journal=Studies in History and Philosophy of Science Part A|language=en|volume=34|issue=2|pages=229–264|doi=10.1016/S0039-3681(03)00025-6|bibcode=2003SHPSA..34..229P |issn=0039-3681}} |
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* {{cite arXiv|last=Blåsjö|first=Viktor|date=2021-02-12|title=Galileo, Ignoramus: Mathematics versus Philosophy in the Scientific Revolution|class=math.HO|eprint=2102.06595}} |
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* {{Cite journal|last=Cohen|first=H. Floris|date=1991|editor-last=Yoder|editor-first=Joella G.|title=How Christiaan Huygens Mathematized Nature|jstor=4027017|journal=The British Journal for the History of Science|volume=24|issue=1|pages=79–84|doi=10.1017/S0007087400028466|s2cid=122825173 |issn=0007-0874|url=https://research.utwente.nl/en/publications/how-christiaan-huygens-mathematized-nature(b5f84142-a700-4797-9768-271f55f52c84).html}} |
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* {{Cite web|title=Christiaan Huygens - Biography|url=https://mathshistory.st-andrews.ac.uk/Biographies/Huygens/|access-date=2021-04-06|website=Maths History|language=en}} |
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* {{Cite book|last=Dijksterhuis|first=Fokko Jan|url=https://www.springer.com/gp/book/9781402026973|title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century|date=2004|publisher=Springer Netherlands|isbn=978-1-4020-2697-3|series=Archimedes|language=en}} |
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Верзија на датум 25. јун 2023. у 03:36
Impuls sile (lat. impulsus: udarac, podsticaj), u mehanici[2][3][4](oznaka I),[5] vektorska je fizička veličina određena (definisana) kao umnožak sile i vremena tokom kojeg je ta sila delovala.[6] Matematički se računa kao:
ili, u integralnom obliku, ako sila nije konstantna, već je funkcija vremena (tokom vremena od trenutka t1 do t2):[7]
Uz pojam impulsa sile usko je vezana količina kretanja čestice, koja je umnožak njene mase i vektora brzine m ∙ v. Bez delovanja impulsa nema promene brzine čestice, jer je (zakon količine kretanja):
gde je:
- F - sila koja deluje na telo,
- t1 i t2 - vreme ili trenutak kada sila počinje da deluje, odnosno kada sila prestaje da deluje,
- m - masa tela,
- v2 - konačna brzina tela,
- v1 - početna brzina tela,
- Δp - promena količine kretanja.
Ta se veza impulsa sa količinom kretanja izvodi za česticu integrisanjem drugog Njutnovog zakona po vremenu, a u sličnom obliku postoji i kod kretanja krutog tela. Merna jedinica impulsa je njutn sekunda (N s).[8]
Očito je da je derivacija impulsa po vremenu jednaka sili, te stoga iz definicije drugog Njutnovog zakona proizlazi da je impuls ekvivalentan količini kretanja. Može se stoga pisati:
Ovakav matematički zapis je posve korektan samo ako je sila delovala na telo u mirovanju. Opštiji zapis ima sledeći oblik:
iz čega je očito da je impuls sile jednak promeni količine kretanja.[9][10] Drugim rečima, impuls sile uzrokuje promenu stanja kretanja baš kao što to može utvrditi i za silu konstantnog intenziteta.
Takođe, matematički je lako pokazati da je promena kinetičke energije jednaka skalarnom umnošku impulsa sile i vektora srednje brzine.
gde je . Ovde je važno uočiti da se radi o vektorskom, a ne skalarnom zbiru.
Impuls sile i količina kretanja
Neka se kugla mase m kreće uniformnom brzinom v1. Ako se na tu kuglu deluju silom F, ona će dobiti ubrzanje ili akceleraciju a, pa će njena brzina v2 biti (uniformno ubrzano pravolinijsko kretanje):
Kad se pomnoži leva i desna strana ove jednačine sa m, dobija se:
Kako je prema drugom Njutnovom zakonu kretanja:[11][12][13]
to je:
pa se dobija:
Umnožak sile F i vremena t, u kojem je sila delovala na telo, zove se impuls sile, a umnožak mase i brzine zove se količina kretanja.
Kako je m v2 = količina kretanja na kraju intervala t, a m v1 = količina kretanja pre delovanja sile F, to je m v2 - m v1 = prirast količine kretanja. Prema tome, navedeni izraz u matematičkom obliku pokazuje da je: „Impuls sile za neko vreme t jednak prirastu količine kretanja za to vreme”.
Ako kugla miruje pre delovanja sile, to jest v1 = 0, onda je:
što znači da je impuls sile za neko vreme t jednak količini kretanja.[14]
Reference
- ^ Stoebe, Thomas (2007). „Property Differences in Polymers: Happy/Sad Balls” (PDF). Seattle, WA: University of Washington.
- ^ „mechanics”. Oxford English Dictionary. 1933.
- ^ Liddell Scott (1940). „mechanics”. A Greek-English Lexicon.
- ^ Young, Hugh D. (Hugh David), 1930- (2. 9. 2019). Sears and Zemansky's university physics : with modern physics. Freedman, Roger A., Ford, A. Lewis (Albert Lewis), Estrugo, Katarzyna Zulteta (Fifteenth edition in SI units изд.). Harlow. стр. 62. ISBN 978-1-292-31473-0. OCLC 1104689918.
- ^ Beer, F.P., E.R. Johnston, Jr., D.F. Mazurek, P.J. Cornwell, and E.R. Eisenberg. (2010). Vector Mechanics for Engineers; Statics and Dynamics. 9th ed. Toronto: McGraw-Hill.
- ^ Impulse of Force, Hyperphysics
- ^ Hibbeler, Russell C. (2010). Engineering Mechanics (12th изд.). Pearson Prentice Hall. стр. 222. ISBN 978-0-13-607791-6.
- ^ Impuls, [1] "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.
- ^ Euler's Laws of Motion. Архивирано из оригинала 2009-07-10. г. Приступљено 2009-03-30.
- ^ McGill, David J.; King, Wilton W. (1995). Engineering Mechanics: An Introduction to Dynamics (3rd изд.). PWS. ISBN 978-0-534-93399-9.
- ^ Greiner, Walter (2003). Classical mechanics: point particles and relativity. New York: Springer. ISBN 978-0-387-21851-9.
- ^ Zeidler, E. (1988). Nonlinear Functional Analysis and its Applications IV: Applications to Mathematical Physics. New York: Springer. ISBN 978-1-4612-4566-7.
- ^ Wachter, Armin; Hoeber, Henning (2006). Compendium of theoretical physics. New York: Springer. ISBN 978-0-387-25799-0.
- ^ Velimir Kruz: "Tehnička fizika za tehničke škole", "Školska knjiga" Zagreb, 1969.
Literatura
- Hibbeler, Russell C. (2010). Engineering Mechanics (12th изд.). Pearson Prentice Hall. стр. 222. ISBN 978-0-13-607791-6.
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- Sears, F.; Zemansky, M.; Young, H. (1982). University Physics. Reading, Massachusetts: Addison-Wesley. ISBN 978-0-201-07199-3.
- Tipler, Paul A. (2000). Physik. 3. korrigierter Nachdruck der 1. Heidelberg / Berlin: Spektrum Akademischer Verlag. ISBN 978-3-86025-122-5.
- Bergmann, Ludwig; Schaefer, Clemens (2008). Mechanik – Akustik – Wärme. In: Lehrbuch der Experimentalphysik. Bd. 1, 12. Berlin: Walter de Gruyter. ISBN 978-3-11-019311-4.
- Verma, H.C. (2004). Concepts of Physics Vol 1. (2004 Reprint изд.). Bharti Bhavan. ISBN 978-81-7709-187-8.
- Robert Stawell Ball (1871) Experimental Mechanics from Google books.
- Lev Landau; Evgeny Lifshitz (1972). Mechanics and Electrodynamics, Vol. 1. Franklin Book Company, Inc. ISBN 978-0-08-016739-8.
- Truesdell, C. (1968). Essays in the History of Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 9783642866470.
- Maddox, René Dugas ; foreword by Louis de Broglie ; translated into English by J.R. (1988). A history of mechanics (Dover изд.). New York: Dover Publications. ISBN 0-486-65632-2.
- Buchwald, Jed Z.; Fox, Robert, ур. (2013). The Oxford handbook of the history of physics (First изд.). Oxford: Oxford University Press. стр. 358–405. ISBN 9780199696253.
- Rovelli, Carlo (2015). „Aristotle's Physics: A Physicist's Look”. Journal of the American Philosophical Association. 1 (1): 23—40. S2CID 44193681. arXiv:1312.4057 . doi:10.1017/apa.2014.11.
- Peter Pesic (март 1999). „Wrestling with Proteus: Francis Bacon and the "Torture" of Nature”. Isis. The University of Chicago Press on behalf of The History of Science Society. 90 (1): 81—94. JSTOR 237475. S2CID 159818014. doi:10.1086/384242.
- Espinoza, Fernando (2005). „An analysis of the historical development of ideas about motion and its implications for teaching”. Physics Education. 40 (2): 141. Bibcode:2005PhyEd..40..139E. doi:10.1088/0031-9120/40/2/002.
- Seyyed Hossein Nasr; Mehdi Amin Razavi (1996). The Islamic intellectual tradition in Persia. Routledge. стр. 72. ISBN 978-0-7007-0314-2.
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