CINXE.COM

<!DOCTYPE html> <html class="client-nojs" lang="fi" dir="ltr"> <head> <meta charset="UTF-8"> <title>Potentiaalienergia – Wikipedia</title> <script>(function(){var className="client-js";var cookie=document.cookie.match(/(?:^|; )fiwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t."," \t,"],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"fi normal","wgMonthNames":["","tammikuu","helmikuu","maaliskuu","huhtikuu","toukokuu","kesäkuu","heinäkuu","elokuu","syyskuu","lokakuu","marraskuu","joulukuu"],"wgRequestId":"b159a786-f3ff-49c1-9ab7-7258fdbdca2b","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Potentiaalienergia","wgTitle":"Potentiaalienergia","wgCurRevisionId":22804302,"wgRevisionId":22804302,"wgArticleId":14640,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null, "wgUserGroups":["*"],"wgCategories":["Seulonnan keskeiset artikkelit","Painovoima","Astrodynamiikka","Energia"],"wgPageViewLanguage":"fi","wgPageContentLanguage":"fi","wgPageContentModel":"wikitext","wgRelevantPageName":"Potentiaalienergia","wgRelevantArticleId":14640,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgFlaggedRevsParams":{"tags":{"accuracy":{"levels":3}}},"wgStableRevisionId":22804302,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"fi","pageLanguageDir":"ltr","pageVariantFallbacks":"fi"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":6000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition": "interlanguage","wgULSisCompactLinksEnabled":true,"wgVector2022LanguageInHeader":false,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q155640","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.hidePersonalSandboxEdits":"ready","ext.gadget.fiwiki_flaggedrevs_css_rcfix":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.styles.legacy":"ready","ext.flaggedRevs.basic":"ready","mediawiki.codex.messagebox.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","codex-search-styles":"ready","ext.uls.interlanguage": "ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","site","mediawiki.page.ready","mediawiki.toc","skins.vector.legacy.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.flaggedRevs.advanced","ext.gadget.publicarttablesort","ext.gadget.ViikonKilpailu","ext.gadget.WikiLovesMonunmets","ext.gadget.ProtectionIndicator","ext.gadget.frwiki_infobox_v3","ext.gadget.linkeddata","ext.gadget.perustiedotwikidatassa","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.compactlinks","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=fi&modules=codex-search-styles%7Cext.cite.styles%7Cext.flaggedRevs.basic%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cmediawiki.codex.messagebox.styles%7Cskins.vector.styles.legacy%7Cwikibase.client.init&only=styles&skin=vector"> <script async="" src="/w/load.php?lang=fi&modules=startup&only=scripts&raw=1&skin=vector"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=fi&modules=ext.gadget.fiwiki_flaggedrevs_css_rcfix%2ChidePersonalSandboxEdits&only=styles&skin=vector"> <link rel="stylesheet" href="/w/load.php?lang=fi&modules=site.styles&only=styles&skin=vector"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Potentiaalienergia – Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//fi.m.wikipedia.org/wiki/Potentiaalienergia"> <link rel="alternate" type="application/x-wiki" title="Muokkaa" href="/w/index.php?title=Potentiaalienergia&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (fi)"> <link rel="EditURI" type="application/rsd+xml" href="//fi.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://fi.wikipedia.org/wiki/Potentiaalienergia"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.fi"> <link rel="alternate" type="application/atom+xml" title="Wikipedia-Atom-syöte" href="/w/index.php?title=Toiminnot:Tuoreet_muutokset&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin-vector-legacy mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Potentiaalienergia rootpage-Potentiaalienergia skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Potentiaalienergia</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">Wikipediasta</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Siirry navigaatioon</a> <a class="mw-jump-link" href="#searchInput">Siirry hakuun</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fi" dir="ltr"><p><b>Potentiaalienergia</b> eli <b>asemaenergia</b> kuvaa kappaleen kykyä tehdä työtä asemansa ansiosta. Potentiaalienergiasta puhutaan, kun kappaleeseen vaikuttaa jokin <a href="/wiki/Konservatiivinen_voima" title="Konservatiivinen voima">konservatiivinen voima</a>. <a href="/wiki/Voima_(fysiikka)" title="Voima (fysiikka)">Voima</a> on konservatiivinen, jos se riippuu vain kappaleen paikasta ja sen tekemä <a href="/wiki/Ty%C3%B6_(fysiikka)" title="Työ (fysiikka)">työ</a> kappaleen siirtyessä tietystä paikasta toiseen on riippumaton kappaleen kulkemasta reitistä.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Tällöin se ei muuta <a href="/wiki/Mekaaninen_energia" title="Mekaaninen energia">energiaa</a> <a href="/wiki/L%C3%A4mp%C3%B6" title="Lämpö">lämmöksi</a>. Konservatiivisia voimia ovat muun muassa <a href="/wiki/Gravitaatiovoima" class="mw-redirect" title="Gravitaatiovoima">gravitaatiovoima</a> ja jousivoima. Myös voima, jolla staattinen <a href="/wiki/S%C3%A4hk%C3%B6kentt%C3%A4" title="Sähkökenttä">sähkökenttä</a> vaikuttaa sähkövarauksiin, on konservatiivinen. Sitä vastoin esimerkiksi <a href="/wiki/Kitka" title="Kitka">kitka</a> ei ole konservatiivinen voima, sillä se muuttaa liike-energiaa lämmöksi. </p><p>Esimerkiksi kun kappale nostetaan pöydälle, <a href="/wiki/Energian_s%C3%A4ilymislaki" title="Energian säilymislaki">energian säilymislain</a> mukaisesti kappaleelle annettu <a href="/wiki/Kineettinen_energia" class="mw-redirect" title="Kineettinen energia">kineettinen energia</a> muuttuu Maan konservatiivisessa gravitaatiokentässä kappaleen potentiaalienergiaksi, joka taas muuttuu takaisin kineettiseksi energiaksi kappaleen pudotessa pöydältä. </p><p>Kappaleen potentiaalienergia ei ole yksikäsitteisesti määritettävissä, vaan ainoastaan sen muutoksilla kappaleen siirtyessä paikasta toiseen on merkitystä. Tämän vuoksi on aina sovittava kohta, jossa potentiaalienergia määritellään nollaksi (esimerkiksi lattia). Potentiaalienergian tunnus on <b>E<sub>p</sub></b> tai <b>U</b>. </p><p>Yleisesti potentiaalienergia määritellään samoin kuin mekaaninen <a href="/wiki/Ty%C3%B6_(fysiikka)" title="Työ (fysiikka)">työ</a>, joka on tehtävä siirrettäessä kappale pisteestä A pisteeseen B: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{S}=\int _{S}^{}\mathbf {F} \cdot d\mathbf {s} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>⋅</mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{S}=\int _{S}^{}\mathbf {F} \cdot d\mathbf {s} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c71c04981a4f9d13e262b880539189d7dbcce09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.837ex; height:5.676ex;" alt="{\displaystyle W_{S}=\int _{S}^{}\mathbf {F} \cdot d\mathbf {s} .}"></span></dd></dl> <p>Yleisessä tapauksessa työn määrä riippuu käytetystä reitistä, joten voima olisi integroitava kyseistä reittiä pitkin. Jos kuitenkin kaikki vaikuttavat voimat ovat konservatiivisia, kappaleen siirtämiseksi tarvittava työ määräytyy yksikäsitteisesti alku- ja lopputilan perusteella. Siksi kirjoitetaan </p><p><br /> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}\mathbf {F} \cdot d\mathbf {r} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>⋅</mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}\mathbf {F} \cdot d\mathbf {r} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd482e3bec16175a1ebb15fb724e2462c9cbe4f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:17.96ex; height:6.176ex;" alt="{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}\mathbf {F} \cdot d\mathbf {r} ,}"></span></dd></dl> <p>missä </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74b041d193c6b8de0113f5a5e8d8e00d05afa339" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.774ex; height:2.843ex;" alt="{\displaystyle E_{p}}"></span> = potentiaalienergia</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da18bef8c979f3548bb0d8976f5844012d7b8256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.683ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} }"></span> = vastustava konservatiivinen voima</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbe39f0fedae3334af5c4ffaedf25c9778363400" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.156ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{0}}"></span> = reitin alkupiste</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.102ex; height:1.676ex;" alt="{\displaystyle \mathbf {r} }"></span> = reitin loppupiste</dd></dl> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="fi" dir="ltr"><h2 id="mw-toc-heading">Sisällys</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Potentiaalienergia_gravitaatiokentässä"><span class="tocnumber">1</span> <span class="toctext">Potentiaalienergia gravitaatiokentässä</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Jousen_potentiaalienergia"><span class="tocnumber">2</span> <span class="toctext">Jousen potentiaalienergia</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Lähteet"><span class="tocnumber">3</span> <span class="toctext">Lähteet</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Aiheesta_muualla"><span class="tocnumber">4</span> <span class="toctext">Aiheesta muualla</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Potentiaalienergia_gravitaatiokentässä"><span id="Potentiaalienergia_gravitaatiokent.C3.A4ss.C3.A4"></span>Potentiaalienergia gravitaatiokentässä</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiaalienergia&veaction=edit&section=1" title="Muokkaa osiota Potentiaalienergia gravitaatiokentässä" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Potentiaalienergia&action=edit&section=1" title="Muokkaa osion lähdekoodia: Potentiaalienergia gravitaatiokentässä"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Gravitaatio" class="mw-redirect" title="Gravitaatio">Gravitaatiokentässä</a> kappaleeseen vaikuttaa gravitaatiovoima, jonka suuruus lasketaan <a href="/wiki/Painovoima#Newtonin_painovoimalaki" title="Painovoima">Newtonin painovoimalain</a> avulla seuraavasti. Kaava on tarkasti voimassa vain massapisteille ja homogeenisille pallomaisille kappaleille. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=G\cdot {\frac {m_{1}m_{2}}{r^{2}}}=\left(G{\frac {m_{1}}{r^{2}}}\right)\cdot m_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>G</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=G\cdot {\frac {m_{1}m_{2}}{r^{2}}}=\left(G{\frac {m_{1}}{r^{2}}}\right)\cdot m_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7838389dc0ccac48376fcfa85a60802e5229b926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.421ex; height:6.176ex;" alt="{\displaystyle F=G\cdot {\frac {m_{1}m_{2}}{r^{2}}}=\left(G{\frac {m_{1}}{r^{2}}}\right)\cdot m_{2}}"></span>,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></dd></dl> <p>missä </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> = gravitaatiovoima kappaleiden 1 ja 2 välillä</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> = kappaleiden (keskipisteiden) välinen etäisyys</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> = kokeellisesti mitattu <a href="/wiki/Gravitaatiovakio" title="Gravitaatiovakio">gravitaatiovakio</a> ≈ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 6,67\cdot 10^{-11}{\frac {{\text{N}}\cdot {\text{m}}^{2}}{{\text{kg}}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>6</mn> <mo>,</mo> <mn>67</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>N</mtext> </mrow> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>kg</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 6,67\cdot 10^{-11}{\frac {{\text{N}}\cdot {\text{m}}^{2}}{{\text{kg}}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70b64e702d3d9cc069474acfc79576c3cd382a54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:18.929ex; height:6.676ex;" alt="{\displaystyle 6,67\cdot 10^{-11}{\frac {{\text{N}}\cdot {\text{m}}^{2}}{{\text{kg}}^{2}}}}"></span></dd></dl> <p>Kun kappale on lähellä Maan pintaa, siihen vaikuttava Maan vetovoima on yhtä suuri kuin sen massa kerrottuna <a href="/wiki/Putoamiskiihtyvyys" title="Putoamiskiihtyvyys">putoamiskiihtyvyydellä</a> <i>g</i>, eli </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=mg}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=mg}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7b20a4e286bff05ecae34cb5c3b87fc884e7af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.996ex; height:2.509ex;" alt="{\displaystyle F=mg}"></span>.</dd></dl> <p>Potentiaalienergian muutos esimerkiksi Maan gravitaatiokentässä on siten </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}F(r)\,dr=\int _{r_{0}}^{r}G\cdot {\frac {mM}{r^{2}}}\,dr=-G\cdot mM\cdot \left({\frac {1}{r}}-{\frac {1}{r_{0}}}\right)=m\int _{r_{0}}^{r}g(r)\,dr.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <mi>F</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>r</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <mi>G</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mi>M</mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>r</mi> <mo>=</mo> <mo>−</mo> <mi>G</mi> <mo>⋅</mo> <mi>m</mi> <mi>M</mi> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <mi>g</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>r</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}F(r)\,dr=\int _{r_{0}}^{r}G\cdot {\frac {mM}{r^{2}}}\,dr=-G\cdot mM\cdot \left({\frac {1}{r}}-{\frac {1}{r_{0}}}\right)=m\int _{r_{0}}^{r}g(r)\,dr.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/972fe61e3e77475a8a4b14f2710b3f3c73d7436c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:79.68ex; height:6.343ex;" alt="{\displaystyle \Delta E_{p}=\int _{r_{0}}^{r}F(r)\,dr=\int _{r_{0}}^{r}G\cdot {\frac {mM}{r^{2}}}\,dr=-G\cdot mM\cdot \left({\frac {1}{r}}-{\frac {1}{r_{0}}}\right)=m\int _{r_{0}}^{r}g(r)\,dr.}"></span></dd></dl> <p>missä <i>g(r)</i> on putoamiskiihtyvyys paikassa <i>r</i>. Riittävän pienillä matkoilla putoamiskiihtyvyys <i>g</i> on jokseenkin vakio, eli sen muutokset eivät ole merkittäviä. Jos siis oletetaan, että kohtuullisilla siirtymillä putoamiskiihtyvyys on likipitäen vakio, voidaan kappaleen potentiaalienergiassa tapahtuvaa muutosta arvioida seuraavasti: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{p}=m\int _{h_{0}}^{h}g(h)\,dh=mg\int _{h_{0}}^{h}\,dh=mgh-mgh_{0}=mg\Delta h,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <mi>g</mi> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>h</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>h</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi>h</mi> <mo>−</mo> <mi>m</mi> <mi>g</mi> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi mathvariant="normal">Δ</mi> <mi>h</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{p}=m\int _{h_{0}}^{h}g(h)\,dh=mg\int _{h_{0}}^{h}\,dh=mgh-mgh_{0}=mg\Delta h,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6adbd14bf82c0a460a37dbaabdc4ee19f8c19be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:61.247ex; height:6.676ex;" alt="{\displaystyle \Delta E_{p}=m\int _{h_{0}}^{h}g(h)\,dh=mg\int _{h_{0}}^{h}\,dh=mgh-mgh_{0}=mg\Delta h,}"></span></dd></dl> <p>missä </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> = siirrettävän kappaleen massa</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> = keskimääräinen putoamiskiihtyvyys sillä korkeudella, jolla kappaletta siirretään (Maan pinnan lähellä noin 9,81 m/s<sup>2</sup>)</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> = kappaleen korkeus eli etäisyys niin sanotun vertailutason, nollapotentiaalin, suhteen.</dd></dl> <p>Todella suurilla korkeuseroilla, kuten lennätettäessä rakettia avaruuteen, putoamiskiihtyvyyden arvon muutokset ovat jo niin merkittäviä, ettei potentiaalienergiaa voi enää äskeisellä tavalla arvioida. Yleensä tämän pelkistetyn kaavan soveltaminen laskuissa antaa kuitenkin riittävän tarkkoja tuloksia. </p> <div class="mw-heading mw-heading2"><h2 id="Jousen_potentiaalienergia">Jousen potentiaalienergia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiaalienergia&veaction=edit&section=2" title="Muokkaa osiota Jousen potentiaalienergia" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Potentiaalienergia&action=edit&section=2" title="Muokkaa osion lähdekoodia: Jousen potentiaalienergia"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jousivoima on esimerkki <a href="/wiki/Harmoninen_voima" title="Harmoninen voima">harmonisesta voimasta</a>, jonka suuruus on <a href="/wiki/Hooken_laki" title="Hooken laki">Hooken lain</a> mukaisesti </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =-k\mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =-k\mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fb7683e13476df7cc750da3549ba7b3d6ca05d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.212ex; height:2.343ex;" alt="{\displaystyle \mathbf {F} =-k\mathbf {x} }"></span>,</dd></dl> <p>missä </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da18bef8c979f3548bb0d8976f5844012d7b8256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.683ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} }"></span> = jousivoima</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> = jousen materiaalista ja rakenteesta riippuva <a href="/wiki/Jousivakio" title="Jousivakio">jousivakio</a></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32adf004df5eb0a8c7fd8c0b6b7405183c5a5ef2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {x} }"></span> = siirtymä tasapainoasemasta, jota kohti voima aina osoittaa</dd></dl> <p>Jousen potentiaalienergia voidaan laskea määritelmän mukaan </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{p}=\int _{0}^{x}F\,dx=\int _{0}^{x}kx\,dx={\frac {1}{2}}kx^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <mi>F</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <mi>k</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>k</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{p}=\int _{0}^{x}F\,dx=\int _{0}^{x}kx\,dx={\frac {1}{2}}kx^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dff95714350cbd6441c6c603c813ebca16ee7fb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.505ex; height:5.843ex;" alt="{\displaystyle E_{p}=\int _{0}^{x}F\,dx=\int _{0}^{x}kx\,dx={\frac {1}{2}}kx^{2}.}"></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Lähteet"><span id="L.C3.A4hteet"></span>Lähteet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiaalienergia&veaction=edit&section=3" title="Muokkaa osiota Lähteet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Potentiaalienergia&action=edit&section=3" title="Muokkaa osion lähdekoodia: Lähteet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="viitteet-malline" class="viitteet-malline" style="list-style-type:decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="kirjaviite" title="Kirjaviite">Kaarle ja Riitta Kurki-Suonio: <i>Vuorovaikuttavat kappaleet – mekaniikan perusteet</i>, s. 165–166.  Limes r.y., 1995.  <a href="/wiki/Toiminnot:Kirjal%C3%A4hteet/9517451679" title="Toiminnot:Kirjalähteet/9517451679">ISBN 9517451679</a> </span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Kurki-Suonio, s. 212</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Kurki-Suonio, s. 178</span> </li> </ol> </div> <div class="mw-heading mw-heading2"><h2 id="Aiheesta_muualla">Aiheesta muualla</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiaalienergia&veaction=edit&section=4" title="Muokkaa osiota Aiheesta muualla" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Potentiaalienergia&action=edit&section=4" title="Muokkaa osion lähdekoodia: Aiheesta muualla"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/10px-Commons-logo.svg.png" decoding="async" width="10" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Kuvia tai muita tiedostoja aiheesta <b><a href="https://commons.wikimedia.org/wiki/Category:Potential_energy" class="extiw" title="commons:Category:Potential energy">Potentiaalienergia</a></b> <a href="https://commons.wikimedia.org/wiki/Etusivu" class="extiw" title="commons:Etusivu">Wikimedia Commonsissa</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Noudettu kohteesta ”<a dir="ltr" href="https://fi.wikipedia.org/w/index.php?title=Potentiaalienergia&oldid=22804302">https://fi.wikipedia.org/w/index.php?title=Potentiaalienergia&oldid=22804302</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Toiminnot:Luokat" title="Toiminnot:Luokat">Luokat</a>: <ul><li><a href="/wiki/Luokka:Painovoima" title="Luokka:Painovoima">Painovoima</a></li><li><a href="/wiki/Luokka:Astrodynamiikka" title="Luokka:Astrodynamiikka">Astrodynamiikka</a></li><li><a href="/wiki/Luokka:Energia" title="Luokka:Energia">Energia</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Piilotettu luokka: <ul><li><a href="/wiki/Luokka:Seulonnan_keskeiset_artikkelit" title="Luokka:Seulonnan keskeiset artikkelit">Seulonnan keskeiset artikkelit</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigointivalikko</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Henkilökohtaiset työkalut</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="IP-osoitteesi käyttäjäsivu">Et ole kirjautunut</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Toiminnot:Oma_keskustelu" title="Keskustelu tämän IP-osoitteen muokkauksista [n]" accesskey="n"><span>Keskustelu</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Toiminnot:Omat_muokkaukset" title="Luettelo tästä IP-osoitteesta tehdyistä muokkauksista [y]" accesskey="y"><span>Muokkaukset</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:Luo_tunnus&returnto=Potentiaalienergia" title="On suositeltavaa luoda käyttäjätunnus ja kirjautua sisään. Se ei kuitenkaan ole pakollista."><span>Luo tunnus</span></a></li><li id="pt-login" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:Kirjaudu_sis%C3%A4%C3%A4n&returnto=Potentiaalienergia" title="On suositeltavaa kirjautua sisään. Se ei kuitenkaan ole pakollista. [o]" accesskey="o"><span>Kirjaudu sisään</span></a></li> </ul> </div> </nav> <div id="left-navigation"> <nav id="p-namespaces" class="mw-portlet mw-portlet-namespaces vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-namespaces-label" > <h3 id="p-namespaces-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Nimiavaruudet</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected mw-list-item"><a href="/wiki/Potentiaalienergia" title="Näytä sisältösivu [c]" accesskey="c"><span>Artikkeli</span></a></li><li id="ca-talk" class="mw-list-item"><a href="/wiki/Keskustelu:Potentiaalienergia" rel="discussion" title="Keskustele sisällöstä [t]" accesskey="t"><span>Keskustelu</span></a></li> </ul> </div> </nav> <nav id="p-variants" class="mw-portlet mw-portlet-variants emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-variants-label" > <input type="checkbox" id="p-variants-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-variants" class="vector-menu-checkbox" aria-labelledby="p-variants-label" > <label id="p-variants-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">suomi</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> </div> <div id="right-navigation"> <nav id="p-views" class="mw-portlet mw-portlet-views vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-views-label" > <h3 id="p-views-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Näkymät</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected mw-list-item"><a href="/wiki/Potentiaalienergia"><span>Lue</span></a></li><li id="ca-ve-edit" class="mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&veaction=edit" title="Muokkaa tätä sivua [v]" accesskey="v"><span>Muokkaa</span></a></li><li id="ca-edit" class="collapsible mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&action=edit" title="Muokkaa tämän sivun lähdekoodia [e]" accesskey="e"><span>Muokkaa wikitekstiä</span></a></li><li id="ca-history" class="mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&action=history" title="Sivun aikaisemmat versiot [h]" accesskey="h"><span>Näytä historia</span></a></li> </ul> </div> </nav> <nav id="p-cactions" class="mw-portlet mw-portlet-cactions emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-cactions-label" title="Lisää valintoja" > <input type="checkbox" id="p-cactions-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-cactions" class="vector-menu-checkbox" aria-labelledby="p-cactions-label" > <label id="p-cactions-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Muut</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <h3 >Haku</h3> <form action="/w/index.php" id="searchform" class="vector-search-box-form"> <div id="simpleSearch" class="vector-search-box-inner" data-search-loc="header-navigation"> <input class="vector-search-box-input" type="search" name="search" placeholder="Hae Wikipediasta" aria-label="Hae Wikipediasta" autocapitalize="sentences" title="Hae Wikipediasta [f]" accesskey="f" id="searchInput" > <input type="hidden" name="title" value="Toiminnot:Haku"> <input id="mw-searchButton" class="searchButton mw-fallbackSearchButton" type="submit" name="fulltext" title="Hae sivuilta tätä tekstiä" value="Hae"> <input id="searchButton" class="searchButton" type="submit" name="go" title="Siirry sivulle, joka on tarkalleen tällä nimellä" value="Siirry"> </div> </form> </div> </div> </div> <div id="mw-panel" class="vector-legacy-sidebar"> <div id="p-logo" role="banner"> <a class="mw-wiki-logo" href="/wiki/Wikipedia:Etusivu" title="Etusivu"></a> </div> <nav id="p-navigation" class="mw-portlet mw-portlet-navigation vector-menu-portal portal vector-menu" aria-labelledby="p-navigation-label" > <h3 id="p-navigation-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Valikko</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Wikipedia:Etusivu" title="Siirry etusivulle [z]" accesskey="z"><span>Etusivu</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:Tietoja"><span>Tietoja Wikipediasta</span></a></li><li id="n-allarticles" class="mw-list-item"><a href="/wiki/Wikipedia:Selaa_luokittain"><span>Kaikki sivut</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Toiminnot:Satunnainen_sivu" title="Avaa satunnainen sivu [x]" accesskey="x"><span>Satunnainen artikkeli</span></a></li> </ul> </div> </nav> <nav id="p-interaction" class="mw-portlet mw-portlet-interaction vector-menu-portal portal vector-menu" aria-labelledby="p-interaction-label" > <h3 id="p-interaction-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Osallistuminen</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Ohje:Sis%C3%A4llys" title="Ohjeita"><span>Ohje</span></a></li><li id="n-Kahvihuone" class="mw-list-item"><a href="/wiki/Wikipedia:Kahvihuone"><span>Kahvihuone</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Ajankohtaista" title="Taustatietoa tämänhetkisistä tapahtumista"><span>Ajankohtaista</span></a></li><li id="n-Tuoreet-odottavat-muutokset" class="mw-list-item"><a href="//fi.wikipedia.org/wiki/Toiminnot:Tuoreet_muutokset?damaging=&goodfaith=&hideliu=0&hideanons=0&userExpLevel=&hidemyself=0&hidebyothers=0&hidebots=1&hidehumans=0&hidepatrolled=1&hideunpatrolled=0&hideminor=0&hidemajor=0&hidepageedits=0&hidenewpages=0&hidecategorization=1&hideWikibase=1&hidelog=0&highlight=1&goodfaith__verylikelybad_color=c5&goodfaith__likelybad_color=c4&goodfaith__maybebad_color=c3&damaging__verylikelybad_color=c5&damaging__likelybad_color=c4&damaging__maybebad_color=c3"><span>Tuoreet odottavat muutokset</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Toiminnot:Tuoreet_muutokset" title="Luettelo tuoreista muutoksista [r]" accesskey="r"><span>Tuoreet muutokset</span></a></li><li id="n-sitesupport" class="mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_fi.wikipedia.org&uselang=fi" title="Tue meitä"><span>Lahjoitukset</span></a></li> </ul> </div> </nav> <nav id="p-tb" class="mw-portlet mw-portlet-tb vector-menu-portal portal vector-menu" aria-labelledby="p-tb-label" > <h3 id="p-tb-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Työkalut</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Toiminnot:T%C3%A4nne_viittaavat_sivut/Potentiaalienergia" title="Lista sivuista, jotka viittaavat tänne [j]" accesskey="j"><span>Tänne viittaavat sivut</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Toiminnot:Linkitetyt_muutokset/Potentiaalienergia" rel="nofollow" title="Viimeisimmät muokkaukset sivuissa, joille viitataan tältä sivulta [k]" accesskey="k"><span>Linkitettyjen sivujen muutokset</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Toiminnot:Toimintosivut" title="Näytä toimintosivut [q]" accesskey="q"><span>Toimintosivut</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&oldid=22804302" title="Ikilinkki tämän sivun tähän versioon"><span>Ikilinkki</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&action=info" title="Enemmän tietoa tästä sivusta"><span>Sivun tiedot</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:Viittaus&page=Potentiaalienergia&id=22804302&wpFormIdentifier=titleform" title="Tietoa tämän sivun lainaamisesta"><span>Viitetiedot</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:UrlShortener&url=https%3A%2F%2Ffi.wikipedia.org%2Fwiki%2FPotentiaalienergia"><span>Lyhennä URL-osoite</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:QrCode&url=https%3A%2F%2Ffi.wikipedia.org%2Fwiki%2FPotentiaalienergia"><span>Lataa QR-koodi</span></a></li> </ul> </div> </nav> <nav id="p-coll-print_export" class="mw-portlet mw-portlet-coll-print_export vector-menu-portal portal vector-menu" aria-labelledby="p-coll-print_export-label" > <h3 id="p-coll-print_export-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Tulosta/vie</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:DownloadAsPdf&page=Potentiaalienergia&action=show-download-screen"><span>Lataa PDF-tiedostona</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Potentiaalienergia&printable=yes" title="Tulostettava versio [p]" accesskey="p"><span>Tulostettava versio</span></a></li> </ul> </div> </nav> <nav id="p-wikibase-otherprojects" class="mw-portlet mw-portlet-wikibase-otherprojects vector-menu-portal portal vector-menu" aria-labelledby="p-wikibase-otherprojects-label" > <h3 id="p-wikibase-otherprojects-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Muissa hankkeissa</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Potential_energy" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q155640" title="Linkki yhdistettyyn keskustietovaraston kohteeseen [g]" accesskey="g"><span>Wikidata-kohde</span></a></li> </ul> </div> </nav> <nav id="p-lang" class="mw-portlet mw-portlet-lang vector-menu-portal portal vector-menu" aria-labelledby="p-lang-label" > <h3 id="p-lang-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Muilla kielillä</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%A7%D9%82%D8%A9_%D9%88%D8%B6%D8%B9" title="طاقة وضع — arabia" lang="ar" hreflang="ar" data-title="طاقة وضع" data-language-autonym="العربية" data-language-local-name="arabia" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BF%E0%A6%A4%E0%A6%BF_%E0%A6%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF" title="স্থিতি শক্তি — assami" lang="as" hreflang="as" data-title="স্থিতি শক্তি" data-language-autonym="অসমীয়া" data-language-local-name="assami" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Enerx%C3%ADa_potencial" title="Enerxía potencial — asturia" lang="ast" hreflang="ast" data-title="Enerxía potencial" data-language-autonym="Asturianu" data-language-local-name="asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Potensial_enerji" title="Potensial enerji — azeri" lang="az" hreflang="az" data-title="Potensial enerji" data-language-autonym="Azərbaycanca" data-language-local-name="azeri" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Energi_potensial" title="Energi potensial — indonesia" lang="id" hreflang="id" data-title="Energi potensial" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tenaga_keupayaan" title="Tenaga keupayaan — malaiji" lang="ms" hreflang="ms" data-title="Tenaga keupayaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malaiji" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%AC_%E0%A6%B6%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF" title="বিভব শক্তি — bengali" lang="bn" hreflang="bn" data-title="বিভব শক্তি" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D1%82%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F" title="Патэнцыяльная энергія — valkovenäjä" lang="be" hreflang="be" data-title="Патэнцыяльная энергія" data-language-autonym="Беларуская" data-language-local-name="valkovenäjä" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D0%B0%D1%82%D1%8D%D0%BD%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D1%8D%D1%80%D0%B3%D1%96%D1%8F" title="Патэнцыйная энэргія — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Патэнцыйная энэргія" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Enerhiyang_potensyal" title="Enerhiyang potensyal — Central Bikol" lang="bcl" hreflang="bcl" data-title="Enerhiyang potensyal" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Potencijalna_energija" title="Potencijalna energija — bosnia" lang="bs" hreflang="bs" data-title="Potencijalna energija" data-language-autonym="Bosanski" data-language-local-name="bosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Потенциална енергия — bulgaria" lang="bg" hreflang="bg" data-title="Потенциална енергия" data-language-autonym="Български" data-language-local-name="bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Energia_potencial" title="Energia potencial — katalaani" lang="ca" hreflang="ca" data-title="Energia potencial" data-language-autonym="Català" data-language-local-name="katalaani" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BB%D0%B0_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Потенциалла энерги — tšuvassi" lang="cv" hreflang="cv" data-title="Потенциалла энерги" data-language-autonym="Чӑвашла" data-language-local-name="tšuvassi" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Potenci%C3%A1ln%C3%AD_energie" title="Potenciální energie — tšekki" lang="cs" hreflang="cs" data-title="Potenciální energie" data-language-autonym="Čeština" data-language-local-name="tšekki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Simba_reChakunga" title="Simba reChakunga — šona" lang="sn" hreflang="sn" data-title="Simba reChakunga" data-language-autonym="ChiShona" data-language-local-name="šona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Egni_potensial" title="Egni potensial — kymri" lang="cy" hreflang="cy" data-title="Egni potensial" data-language-autonym="Cymraeg" data-language-local-name="kymri" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Potentiel_energi" title="Potentiel energi — tanska" lang="da" hreflang="da" data-title="Potentiel energi" data-language-autonym="Dansk" data-language-local-name="tanska" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Potentielle_Energie" title="Potentielle Energie — saksa" lang="de" hreflang="de" data-title="Potentielle Energie" data-language-autonym="Deutsch" data-language-local-name="saksa" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Potentsiaalne_energia" title="Potentsiaalne energia — viro" lang="et" hreflang="et" data-title="Potentsiaalne energia" data-language-autonym="Eesti" data-language-local-name="viro" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE_%CE%B5%CE%BD%CE%AD%CF%81%CE%B3%CE%B5%CE%B9%CE%B1" title="Δυναμική ενέργεια — kreikka" lang="el" hreflang="el" data-title="Δυναμική ενέργεια" data-language-autonym="Ελληνικά" data-language-local-name="kreikka" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Potential_energy" title="Potential energy — englanti" lang="en" hreflang="en" data-title="Potential energy" data-language-autonym="English" data-language-local-name="englanti" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Energ%C3%ADa_potencial" title="Energía potencial — espanja" lang="es" hreflang="es" data-title="Energía potencial" data-language-autonym="Español" data-language-local-name="espanja" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Potenciala_energio" title="Potenciala energio — esperanto" lang="eo" hreflang="eo" data-title="Potenciala energio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Energia_potentzial" title="Energia potentzial — baski" lang="eu" hreflang="eu" data-title="Energia potentzial" data-language-autonym="Euskara" data-language-local-name="baski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%B1%DA%98%DB%8C_%D9%BE%D8%AA%D8%A7%D9%86%D8%B3%DB%8C%D9%84" title="انرژی پتانسیل — persia" lang="fa" hreflang="fa" data-title="انرژی پتانسیل" data-language-autonym="فارسی" data-language-local-name="persia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89nergie_potentielle" title="Énergie potentielle — ranska" lang="fr" hreflang="fr" data-title="Énergie potentielle" data-language-autonym="Français" data-language-local-name="ranska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Fuinneamh_poit%C3%A9insi%C3%BAil" title="Fuinneamh poitéinsiúil — iiri" lang="ga" hreflang="ga" data-title="Fuinneamh poitéinsiúil" data-language-autonym="Gaeilge" data-language-local-name="iiri" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Enerx%C3%ADa_potencial" title="Enerxía potencial — galicia" lang="gl" hreflang="gl" data-title="Enerxía potencial" data-language-autonym="Galego" data-language-local-name="galicia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%84%EC%B9%98_%EC%97%90%EB%84%88%EC%A7%80" title="위치 에너지 — korea" lang="ko" hreflang="ko" data-title="위치 에너지" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%B8%D5%BF%D5%A5%D5%B6%D6%81%D5%AB%D5%A1%D5%AC_%D5%A7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1" title="Պոտենցիալ էներգիա — armenia" lang="hy" hreflang="hy" data-title="Պոտենցիալ էներգիա" data-language-autonym="Հայերեն" data-language-local-name="armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BF%E0%A4%A4%E0%A4%BF%E0%A4%9C_%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE" title="स्थितिज ऊर्जा — hindi" lang="hi" hreflang="hi" data-title="स्थितिज ऊर्जा" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Potencijalna_energija" title="Potencijalna energija — kroatia" lang="hr" hreflang="hr" data-title="Potencijalna energija" data-language-autonym="Hrvatski" data-language-local-name="kroatia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Isidlakathi" title="Isidlakathi — zulu" lang="zu" hreflang="zu" data-title="Isidlakathi" data-language-autonym="IsiZulu" data-language-local-name="zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/St%C3%B6%C3%B0uorka" title="Stöðuorka — islanti" lang="is" hreflang="is" data-title="Stöðuorka" data-language-autonym="Íslenska" data-language-local-name="islanti" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Energia_potenziale" title="Energia potenziale — italia" lang="it" hreflang="it" data-title="Energia potenziale" data-language-autonym="Italiano" data-language-local-name="italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A0%D7%A8%D7%92%D7%99%D7%94_%D7%A4%D7%95%D7%98%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA" title="אנרגיה פוטנציאלית — heprea" lang="he" hreflang="he" data-title="אנרגיה פוטנציאלית" data-language-autonym="עברית" data-language-local-name="heprea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Energi_Potensial" title="Energi Potensial — jaava" lang="jv" hreflang="jv" data-title="Energi Potensial" data-language-autonym="Jawa" data-language-local-name="jaava" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%82%E0%B2%A4%E0%B2%B8%E0%B3%8D%E0%B2%A5_%E0%B2%B6%E0%B2%95%E0%B3%8D%E0%B2%A4%E0%B2%BF" title="ಅಂತಸ್ಥ ಶಕ್ತಿ — kannada" lang="kn" hreflang="kn" data-title="ಅಂತಸ್ಥ ಶಕ್ತಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%9D%E1%83%A2%E1%83%94%E1%83%9C%E1%83%AA%E1%83%98%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%94%E1%83%9C%E1%83%94%E1%83%A0%E1%83%92%E1%83%98%E1%83%90" title="პოტენციური ენერგია — georgia" lang="ka" hreflang="ka" data-title="პოტენციური ენერგია" data-language-autonym="ქართული" data-language-local-name="georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Потенциалдық энергия — kazakki" lang="kk" hreflang="kk" data-title="Потенциалдық энергия" data-language-autonym="Қазақша" data-language-local-name="kazakki" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/En%C3%A8ji_potansy%C3%A8l_chimik" title="Enèji potansyèl chimik — haiti" lang="ht" hreflang="ht" data-title="Enèji potansyèl chimik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haiti" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/%C3%89nerji_potansy%C3%A8l" title="Énerji potansyèl — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Énerji potansyèl" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Energia_potentialis" title="Energia potentialis — latina" lang="la" hreflang="la" data-title="Energia potentialis" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Potenci%C4%81l%C4%81_ener%C4%A3ija" title="Potenciālā enerģija — latvia" lang="lv" hreflang="lv" data-title="Potenciālā enerģija" data-language-autonym="Latviešu" data-language-local-name="latvia" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Potencin%C4%97_energija" title="Potencinė energija — liettua" lang="lt" hreflang="lt" data-title="Potencinė energija" data-language-autonym="Lietuvių" data-language-local-name="liettua" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Potenci%C3%A1lis_energia" title="Potenciális energia — unkari" lang="hu" hreflang="hu" data-title="Potenciális energia" data-language-autonym="Magyar" data-language-local-name="unkari" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%98%D0%B0" title="Потенцијална енергија — makedonia" lang="mk" hreflang="mk" data-title="Потенцијална енергија" data-language-autonym="Македонски" data-language-local-name="makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BF%E0%B4%A4%E0%B4%BF%E0%B4%95%E0%B5%8B%E0%B5%BC%E0%B4%9C%E0%B5%8D%E0%B4%9C%E0%B4%82" title="സ്ഥിതികോർജ്ജം — malajalam" lang="ml" hreflang="ml" data-title="സ്ഥിതികോർജ്ജം" data-language-autonym="മലയാളം" data-language-local-name="malajalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%9C_%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE" title="स्थितीज ऊर्जा — marathi" lang="mr" hreflang="mr" data-title="स्थितीज ऊर्जा" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Потенциал энерги — mongoli" lang="mn" hreflang="mn" data-title="Потенциал энерги" data-language-autonym="Монгол" data-language-local-name="mongoli" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%90%E1%80%8A%E1%80%BA%E1%80%85%E1%80%BD%E1%80%99%E1%80%BA%E1%80%B8%E1%80%A1%E1%80%84%E1%80%BA" title="အတည်စွမ်းအင် — burma" lang="my" hreflang="my" data-title="အတည်စွမ်းအင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Potenti%C3%ABle_energie" title="Potentiële energie — hollanti" lang="nl" hreflang="nl" data-title="Potentiële energie" data-language-autonym="Nederlands" data-language-local-name="hollanti" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BD%8D%E7%BD%AE%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="位置エネルギー — japani" lang="ja" hreflang="ja" data-title="位置エネルギー" data-language-autonym="日本語" data-language-local-name="japani" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Potensiell_energi" title="Potensiell energi — norjan bokmål" lang="nb" hreflang="nb" data-title="Potensiell energi" data-language-autonym="Norsk bokmål" data-language-local-name="norjan bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Potensiell_energi" title="Potensiell energi — norjan nynorsk" lang="nn" hreflang="nn" data-title="Potensiell energi" data-language-autonym="Norsk nynorsk" data-language-local-name="norjan nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Energia_potenciala" title="Energia potenciala — oksitaani" lang="oc" hreflang="oc" data-title="Energia potenciala" data-language-autonym="Occitan" data-language-local-name="oksitaani" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Anniisaa_Kuufamaa" title="Anniisaa Kuufamaa — oromo" lang="om" hreflang="om" data-title="Anniisaa Kuufamaa" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Potensial_energiya" title="Potensial energiya — uzbekki" lang="uz" hreflang="uz" data-title="Potensial energiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%81%E0%A8%9F%E0%A9%88%E0%A8%82%E0%A8%B8%E0%A8%BC%E0%A8%B2_%E0%A8%8A%E0%A8%B0%E0%A8%9C%E0%A8%BE" title="ਪੁਟੈਂਸ਼ਲ ਊਰਜਾ — pandžabi" lang="pa" hreflang="pa" data-title="ਪੁਟੈਂਸ਼ਲ ਊਰਜਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Potenshal_enaji" title="Potenshal enaji — jamaikankreolienglanti" lang="jam" hreflang="jam" data-title="Potenshal enaji" data-language-autonym="Patois" data-language-local-name="jamaikankreolienglanti" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Energ%C3%ACa_potensial" title="Energìa potensial — piemonte" lang="pms" hreflang="pms" data-title="Energìa potensial" data-language-autonym="Piemontèis" data-language-local-name="piemonte" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Energia_potencjalna" title="Energia potencjalna — puola" lang="pl" hreflang="pl" data-title="Energia potencjalna" data-language-autonym="Polski" data-language-local-name="puola" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Energia_potencial" title="Energia potencial — portugali" lang="pt" hreflang="pt" data-title="Energia potencial" data-language-autonym="Português" data-language-local-name="portugali" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Energie_poten%C8%9Bial%C4%83" title="Energie potențială — romania" lang="ro" hreflang="ro" data-title="Energie potențială" data-language-autonym="Română" data-language-local-name="romania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Потенциальная энергия — venäjä" lang="ru" hreflang="ru" data-title="Потенциальная энергия" data-language-autonym="Русский" data-language-local-name="venäjä" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Energjia_potenciale" title="Energjia potenciale — albania" lang="sq" hreflang="sq" data-title="Energjia potenciale" data-language-autonym="Shqip" data-language-local-name="albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Potential_energy" title="Potential energy — Simple English" lang="en-simple" hreflang="en-simple" data-title="Potential energy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Potenci%C3%A1lna_energia" title="Potenciálna energia — slovakki" lang="sk" hreflang="sk" data-title="Potenciálna energia" data-language-autonym="Slovenčina" data-language-local-name="slovakki" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Potencialna_energija" title="Potencialna energija — sloveeni" lang="sl" hreflang="sl" data-title="Potencialna energija" data-language-autonym="Slovenščina" data-language-local-name="sloveeni" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Awood_Kaydsan" title="Awood Kaydsan — somali" lang="so" hreflang="so" data-title="Awood Kaydsan" data-language-autonym="Soomaaliga" data-language-local-name="somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%98%D0%B0" title="Потенцијална енергија — serbia" lang="sr" hreflang="sr" data-title="Потенцијална енергија" data-language-autonym="Српски / srpski" data-language-local-name="serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Potencijalna_energija" title="Potencijalna energija — serbokroaatti" lang="sh" hreflang="sh" data-title="Potencijalna energija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaatti" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Potentiell_energi" title="Potentiell energi — ruotsi" lang="sv" hreflang="sv" data-title="Potentiell energi" data-language-autonym="Svenska" data-language-local-name="ruotsi" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88%E0%AE%AF%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D" title="நிலையாற்றல் — tamili" lang="ta" hreflang="ta" data-title="நிலையாற்றல்" data-language-autonym="தமிழ்" data-language-local-name="tamili" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Potentsial%27_energi%C3%A4" title="Potentsial' energiä — tataari" lang="tt" hreflang="tt" data-title="Potentsial' energiä" data-language-autonym="Татарча / tatarça" data-language-local-name="tataari" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B1%8D%E0%B0%A5%E0%B0%BF%E0%B0%A4%E0%B0%BF_%E0%B0%B6%E0%B0%95%E0%B1%8D%E0%B0%A4%E0%B0%BF" title="స్థితి శక్తి — telugu" lang="te" hreflang="te" data-title="స్థితి శక్తి" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%87%E0%B8%B2%E0%B8%99%E0%B8%A8%E0%B8%B1%E0%B8%81%E0%B8%A2%E0%B9%8C" title="พลังงานศักย์ — thai" lang="th" hreflang="th" data-title="พลังงานศักย์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Th%E1%BA%BF_n%C4%83ng" title="Thế năng — vietnam" lang="vi" hreflang="vi" data-title="Thế năng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Potansiyel_enerji" title="Potansiyel enerji — turkki" lang="tr" hreflang="tr" data-title="Potansiyel enerji" data-language-autonym="Türkçe" data-language-local-name="turkki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F" title="Потенціальна енергія — ukraina" lang="uk" hreflang="uk" data-title="Потенціальна енергія" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AC%DB%81%D8%AF%DB%8C_%D8%AA%D9%88%D8%A7%D9%86%D8%A7%D8%A6%DB%8C" title="جہدی توانائی — urdu" lang="ur" hreflang="ur" data-title="جہدی توانائی" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%8B%A2%E8%83%BD" title="勢能 — klassinen kiina" lang="lzh" hreflang="lzh" data-title="勢能" data-language-autonym="文言" data-language-local-name="klassinen kiina" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Enerhiya_potensyal" title="Enerhiya potensyal — waray" lang="war" hreflang="war" data-title="Enerhiya potensyal" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8A%BF%E8%83%BD" title="势能 — wu-kiina" lang="wuu" hreflang="wuu" data-title="势能" data-language-autonym="吴语" data-language-local-name="wu-kiina" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BD%8D%E8%83%BD" title="位能 — kantoninkiina" lang="yue" hreflang="yue" data-title="位能" data-language-autonym="粵語" data-language-local-name="kantoninkiina" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8A%BF%E8%83%BD" title="势能 — kiina" lang="zh" hreflang="zh" data-title="势能" data-language-autonym="中文" data-language-local-name="kiina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q155640#sitelinks-wikipedia" title="Muokkaa kieltenvälisiä linkkejä" class="wbc-editpage">Muokkaa linkkejä</a></span></div> </div> </nav> </div> </div> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sivua on viimeksi muutettu 13. marraskuuta 2024 kello 04.52.</li> <li id="footer-info-copyright">Teksti on saatavilla <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.fi">Creative Commons Attribution/Share-Alike</a> -lisenssillä; lisäehtoja voi sisältyä. Katso <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/fi">käyttöehdot</a>.<br /> Wikipedia® on <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundationin</a> rekisteröimä tavaramerkki.<br /> <a href="/wiki/Wikipedia:Artikkelien_ongelmat" title="Wikipedia:Artikkelien ongelmat">Ongelma artikkelissa?</a></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Tietosuojakäytäntö</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Tietoja">Tietoja Wikipediasta</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Vastuuvapaus">Vastuuvapaus</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Käytössäännöstö</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Kehittäjät</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/fi.wikipedia.org">Tilastot</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Evästekäytäntö</a></li> <li id="footer-places-mobileview"><a href="//fi.m.wikipedia.org/w/index.php?title=Potentiaalienergia&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobiilinäkymä</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> <script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("This page is using the deprecated ResourceLoader module \"codex-search-styles\".\n[1.43] Use a CodexModule with codexComponents to set your specific components used: https://www.mediawiki.org/wiki/Codex#Using_a_limited_subset_of_components");mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-98vmp","wgBackendResponseTime":158,"wgPageParseReport":{"limitreport":{"cputime":"0.065","walltime":"0.161","ppvisitednodes":{"value":335,"limit":1000000},"postexpandincludesize":{"value":1421,"limit":2097152},"templateargumentsize":{"value":176,"limit":2097152},"expansiondepth":{"value":14,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":2033,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 52.289 1 -total"," 79.29% 41.458 4 Malline:Wikidata"," 51.55% 26.957 1 Malline:Commonscat-rivi"," 48.28% 25.247 1 Malline:Viitteet"," 45.85% 23.976 1 Malline:Commons-rivi"," 38.08% 19.913 1 Malline:Kirjaviite"]},"scribunto":{"limitreport-timeusage":{"value":"0.004","limit":"10.000"},"limitreport-memusage":{"value":631972,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-5dc468848-h67qk","timestamp":"20241123083528","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Potentiaalienergia","url":"https:\/\/fi.wikipedia.org\/wiki\/Potentiaalienergia","sameAs":"http:\/\/www.wikidata.org\/entity\/Q155640","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q155640","author":{"@type":"Organization","name":"Wikimedia-hankkeiden muokkaajat"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-08-03T14:55:48Z","headline":"kappaleen kyky tuntea tai aiheuttaa voimia paikkansa ansiosta"}</script> </body> </html>