Изворни код странице Impuls sile

[[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:Moglfm19p13 pendulo balistico.jpg|thumb|desno|250п|[[Balističko klatno]] je uređaj za određivanje brzine [[balistika|balističkih]] [[projektil]]a, na primjer [[Puška|puščanoga]] zrna.]]
[[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.]]

'''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: 

:<math>\vec{I}=\vec{F}t</math>

ili, u [[integral]]nom obliku, ako sila nije konstantna, već je funkcija vremena (tokom vremena od trenutka -{''t<sub>1</sub>'' do ''t<sub>2</sub>'')}-:<ref>{{Cite book|title=Engineering Mechanics |url=https://archive.org/details/engineeringmecha00hibb_792 |edition=12th |first=Russell C.|last=Hibbeler|publisher=Pearson Prentice Hall|year=2010 |isbn=978-0-13-607791-6 |page=[https://archive.org/details/engineeringmecha00hibb_792/page/n238 222]}}</ref>

:<math>\mathbf{I} = \int_{t_1}^{t_2} \mathbf{F}\, dt</math>

Uz pojam impulsa sile usko je vezana [[količina kretanja]] čestice, koja je umnožak njene [[masa|mase]] i [[vektor]]a [[brzina|brzine]] -{''m ∙ v''}-. Bez delovanja impulsa nema promene brzine čestice, jer je (zakon količine kretanja):
:<math>\mathbf{I} = \int_{t_1}^{t_2} \mathbf{F}\, dt = \Delta\mathbf{p} = m \mathbf{v_2} - m \mathbf{v_1}</math>
gde je:
: -{''F''}- - [[sila]] koja deluje na [[Telo (fizika)|telo]],
: -{''t''}-<sub>1</sub> i ''t''<sub>2</sub> - vreme ili trenutak kada sila počinje da deluje, odnosno kada sila prestaje da deluje,
: -{''m''}- - [[masa]] tela,
: -{''v''}-<sub>2</sub> - konačna [[brzina]] tela,
: -{''v''}-<sub>1</sub> - početna brzina tela,
: -{''Δp''}- - promena [[količina kretanja|količine kretanja]].

Ta se veza impulsa sa količinom kretanja izvodi za česticu [[integral|integrisanjem]] [[Њутнови закони|drugog Njutnovog zakona po vremenu]], a u sličnom obliku postoji i kod [[kretanje|kretanja]] krutog tela. [[Merna jedinica]] impulsa je [[njutn]] [[sekunda]] (-{N s}-).<ref>''Impuls'', [http://www.enciklopedija.hr/Natuknica.aspx?ID=27229] "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.</ref>

Očito je da je [[derivacija]] impulsa po vremenu jednaka sili, te stoga iz definicije drugog Njutnovog zakona proizlazi da je impuls ekvivalentan [[Količina kretanja|količini kretanja]]. Može se stoga pisati:
:<math>\vec{I}=\vec{p}</math>
:<math>\vec{F} \cdot t=m \cdot \vec{v}</math>

Ovakav matematički zapis je posve korektan samo ako je sila delovala na telo u mirovanju. Opštiji zapis ima sledeći oblik:
:<math>\vec{I}=m \cdot \vec{v}_2-m \cdot \vec{v}_1</math>
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 |url=https://archive.org/details/engineeringmecha0000mcgi_t7i4 |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.

Takođe, matematički je lako pokazati da je promena [[Kinetička energija|kinetičke energije]] jednaka [[skalarni proizvod|skalarnom umnošku]] impulsa sile i vektora srednje [[brzina|brzine]].
:<math>E_{K2}-E_{K1}=\vec{I}\cdot\vec{v}_{sr}</math>
gde je <math>\vec{v}_{sr}={{\vec{v}_2+\vec{v}_1} \over 2}</math>. Ovde je važno uočiti da se radi o [[vektor]]skom, a ne [[skalar]]nom [[zbir]]u.

== Impuls sile i količina kretanja ==
{{Glavni|Količina kretanja}}
[[Датотека:Armedforces jeffery tee shot.jpg|thumb|desno|250п|U [[golf]]u, impuls sile palice se prenosi na [[količina kretanja|količinu kretanja]] loptice.]]

Neka se [[kugla]] mase -{''m''}- kreće uniformnom brzinom -{''v<sub>1</sub>''}-. Ako se na tu kuglu deluju silom -{''F''}-, ona će dobiti [[ubrzanje]] ili akceleraciju -{''a''}-, pa će njena [[brzina]] -{''v<sub>2</sub>''}- biti ([[Linear motion|uniformno ubrzano pravolinijsko kretanje]]):

:<math> v_2 = v_1 + a \cdot t </math>

Kad se [[Množenje|pomnoži]] leva i desna strana ove jednačine sa -{''m''}-, dobija se:

:<math> m \cdot v_2 = m \cdot v_1 + m \cdot a \cdot t </math>

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|url=https://archive.org/details/compendiumoftheo0000wach|date=2006|publisher=Springer|location=New York|isbn=978-0-387-25799-0}}</ref>

:<math> F = m \cdot a </math>

to je:

:<math> m \cdot v_2 = m \cdot v_1 + F \cdot t </math>

pa se dobija:

:<math> F \cdot t = m \cdot v_2 -  m \cdot v_1 </math>

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 v<sub>2</sub>''}- = količina kretanja na kraju intervala -{''t''}-, a -{''m v<sub>1</sub>''}- = količina kretanja pre delovanja sile -{''F''}-, to je -{''m v<sub>2</sub> - m v<sub>1</sub>''}- = 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 -{''v<sub>1</sub>''}- = 0, onda je:

:<math> F \cdot t = m \cdot v </math>

što znači da je impuls sile za neko vreme -{''t''}- jednak količini kretanja.<ref> Velimir Kruz: "Tehnička fizika za tehničke škole", "Školska knjiga" Zagreb, 1969.</ref>

== Reference ==
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{{Литература крај}}

== Spoljašnje veze ==
{{Commonscat-lat|Impulse (physics)}}
* -{[http://www.rwc.uc.edu/koehler/biophys/2c.html Dynamics]}-

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