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class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Povijest" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povijest"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Povijest</span> </div> </a> <ul id="toc-Povijest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primjeri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primjeri"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Primjeri</span> </div> </a> <ul id="toc-Primjeri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Newtonova_mehanika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Newtonova_mehanika"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Newtonova mehanika</span> </div> </a> <button aria-controls="toc-Newtonova_mehanika-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Sadržaj cjeline Newtonova mehanika</span> </button> <ul id="toc-Newtonova_mehanika-sublist" class="vector-toc-list"> <li id="toc-Slobodni_pad_s_ujednačenom_silom_teže_bez_otpora_zraka" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Slobodni_pad_s_ujednačenom_silom_teže_bez_otpora_zraka"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Slobodni pad s ujednačenom silom teže bez otpora zraka</span> </div> </a> <ul id="toc-Slobodni_pad_s_ujednačenom_silom_teže_bez_otpora_zraka-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Slobodni_pad_s_ujednačenom_silom_teže_i_otporom_zraka" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Slobodni_pad_s_ujednačenom_silom_teže_i_otporom_zraka"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Slobodni pad s ujednačenom silom teže i otporom zraka</span> </div> </a> <ul id="toc-Slobodni_pad_s_ujednačenom_silom_teže_i_otporom_zraka-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Slobodni_pad_i_konačna_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Slobodni_pad_i_konačna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Slobodni pad i konačna brzina</span> </div> </a> <ul id="toc-Slobodni_pad_i_konačna_brzina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sila_teže" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sila_teže"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Sila teže</span> </div> </a> <ul id="toc-Sila_teže-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Povezani_članci" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povezani_članci"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Povezani članci</span> </div> </a> <ul id="toc-Povezani_članci-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaz sadržaja stranice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prikaz sadržaja stranice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Slobodni pad</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Idi na druge jezične varijante članka. Dostupan je na 60 jezika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-60" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">60 jezika</span> </label> <div class="vector-dropdown-content"> <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%B3%D9%82%D9%88%D8%B7_%D8%AD%D8%B1" title="سقوط حر – arapski" lang="ar" hreflang="ar" data-title="سقوط حر" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cayida_llibre" title="Cayida llibre – asturijski" lang="ast" hreflang="ast" data-title="Cayida llibre" data-language-autonym="Asturianu" data-language-local-name="asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%B2%D0%B0%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0%D0%B5_%D0%BF%D0%B0%D0%B4%D0%B7%D0%B5%D0%BD%D0%BD%D0%B5" title="Свабоднае падзенне – bjeloruski" lang="be" hreflang="be" data-title="Свабоднае падзенне" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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%92%D0%BE%D0%BB%D1%8C%D0%BD%D0%B0%D0%B5_%D0%BF%D0%B0%D0%B4%D0%B7%D0%B5%D0%BD%D1%8C%D0%BD%D0%B5" title="Вольнае падзеньне – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Вольнае падзеньне" 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-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%BE_%D0%BF%D0%B0%D0%B4%D0%B0%D0%BD%D0%B5" title="Свободно падане – bugarski" lang="bg" hreflang="bg" data-title="Свободно падане" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Slobodni_pad" title="Slobodni pad – bosanski" lang="bs" hreflang="bs" data-title="Slobodni pad" data-language-autonym="Bosanski" data-language-local-name="bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Caiguda_lliure" title="Caiguda lliure – katalonski" lang="ca" hreflang="ca" data-title="Caiguda lliure" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AF%D8%A7%DA%A9%DB%95%D9%88%D8%AA%D9%86%DB%8C_%D8%A6%D8%A7%D8%B2%D8%A7%D8%AF" title="داکەوتنی ئازاد – soranski kurdski" lang="ckb" hreflang="ckb" data-title="داکەوتنی ئازاد" data-language-autonym="کوردی" data-language-local-name="soranski kurdski" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Voln%C3%BD_p%C3%A1d" title="Volný pád – češki" lang="cs" hreflang="cs" data-title="Volný pád" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D1%80%C4%95%D0%BA%D0%BB%C4%95%D0%BD_%D3%B3%D0%BA%D0%BD%D0%B8" title="Ирĕклĕн ӳкни – čuvaški" lang="cv" hreflang="cv" data-title="Ирĕклĕн ӳкни" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Det_frie_fald" title="Det frie fald – danski" lang="da" hreflang="da" data-title="Det frie fald" data-language-autonym="Dansk" data-language-local-name="danski" 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/Freier_Fall" title="Freier Fall – njemački" lang="de" hreflang="de" data-title="Freier Fall" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%B5%CF%8D%CE%B8%CE%B5%CF%81%CE%B7_%CF%80%CF%84%CF%8E%CF%83%CE%B7" title="Ελεύθερη πτώση – grčki" lang="el" hreflang="el" data-title="Ελεύθερη πτώση" data-language-autonym="Ελληνικά" data-language-local-name="grčki" 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/Free_fall" title="Free fall – engleski" lang="en" hreflang="en" data-title="Free fall" data-language-autonym="English" data-language-local-name="engleski" 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/Ca%C3%ADda_libre" title="Caída libre – španjolski" lang="es" hreflang="es" data-title="Caída libre" data-language-autonym="Español" data-language-local-name="španjolski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Vaba_langemine" title="Vaba langemine – estonski" lang="et" hreflang="et" data-title="Vaba langemine" data-language-autonym="Eesti" data-language-local-name="estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erorketa_aske" title="Erorketa aske – baskijski" lang="eu" hreflang="eu" data-title="Erorketa aske" data-language-autonym="Euskara" data-language-local-name="baskijski" 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%B3%D9%82%D9%88%D8%B7_%D8%A2%D8%B2%D8%A7%D8%AF" title="سقوط آزاد – perzijski" lang="fa" hreflang="fa" data-title="سقوط آزاد" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Putoamisliike" title="Putoamisliike – finski" lang="fi" hreflang="fi" data-title="Putoamisliike" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Lutu_galala" title="Lutu galala – fidžijski" lang="fj" hreflang="fj" data-title="Lutu galala" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidžijski" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Chute_libre_(physique)" title="Chute libre (physique) – francuski" lang="fr" hreflang="fr" data-title="Chute libre (physique)" data-language-autonym="Français" data-language-local-name="francuski" 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/Saorthitim" title="Saorthitim – irski" lang="ga" hreflang="ga" data-title="Saorthitim" data-language-autonym="Gaeilge" data-language-local-name="irski" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%A4%D7%99%D7%9C%D7%94_%D7%97%D7%95%D7%A4%D7%A9%D7%99%D7%AA" title="נפילה חופשית – hebrejski" lang="he" hreflang="he" data-title="נפילה חופשית" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%A4_%E0%A4%AA%E0%A4%A4%E0%A4%A8" title="मुक्त पतन – hindski" lang="hi" hreflang="hi" data-title="मुक्त पतन" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szabades%C3%A9s" title="Szabadesés – mađarski" lang="hu" hreflang="hu" data-title="Szabadesés" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%A6%D5%A1%D5%BF_%D5%A1%D5%B6%D5%AF%D5%B8%D6%82%D5%B4" title="Ազատ անկում – armenski" lang="hy" hreflang="hy" data-title="Ազատ անկում" data-language-autonym="Հայերեն" data-language-local-name="armenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gerak_jatuh_bebas" title="Gerak jatuh bebas – indonezijski" lang="id" hreflang="id" data-title="Gerak jatuh bebas" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Caduta_libera" title="Caduta libera – talijanski" lang="it" hreflang="it" data-title="Caduta libera" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%87%AA%E7%94%B1%E8%90%BD%E4%B8%8B" title="自由落下 – japanski" lang="ja" hreflang="ja" data-title="自由落下" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B5%D0%BD%D0%B5%D0%BD%D1%96%D2%A3_%D0%B5%D1%80%D0%BA%D1%96%D0%BD_%D1%82%D2%AF%D1%81%D1%83%D1%96" title="Дененің еркін түсуі – kazaški" lang="kk" hreflang="kk" data-title="Дененің еркін түсуі" data-language-autonym="Қазақша" data-language-local-name="kazaški" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9E%90%EC%9C%A0_%EB%82%99%ED%95%98" title="자유 낙하 – korejski" lang="ko" hreflang="ko" data-title="자유 낙하" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Laisvasis_kritimas" title="Laisvasis kritimas – litavski" lang="lt" hreflang="lt" data-title="Laisvasis kritimas" data-language-autonym="Lietuvių" data-language-local-name="litavski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Br%C4%ABvais_kritiens" title="Brīvais kritiens – latvijski" lang="lv" hreflang="lv" data-title="Brīvais kritiens" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B1%D0%BE%D0%B4%D0%B5%D0%BD_%D0%BF%D0%B0%D0%B4" title="Слободен пад – makedonski" lang="mk" hreflang="mk" data-title="Слободен пад" data-language-autonym="Македонски" data-language-local-name="makedonski" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Jatuh_bebas" title="Jatuh bebas – malajski" lang="ms" hreflang="ms" data-title="Jatuh bebas" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vrije_val_(natuurkunde)" title="Vrije val (natuurkunde) – nizozemski" lang="nl" hreflang="nl" data-title="Vrije val (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Fritt_fall" title="Fritt fall – norveški nynorsk" lang="nn" hreflang="nn" data-title="Fritt fall" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fritt_fall" title="Fritt fall – norveški bokmål" lang="nb" hreflang="nb" data-title="Fritt fall" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Spadek_swobodny" title="Spadek swobodny – poljski" lang="pl" hreflang="pl" data-title="Spadek swobodny" data-language-autonym="Polski" data-language-local-name="poljski" 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/Queda_livre" title="Queda livre – portugalski" lang="pt" hreflang="pt" data-title="Queda livre" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Qispilla_urmay" title="Qispilla urmay – kečuanski" lang="qu" hreflang="qu" data-title="Qispilla urmay" data-language-autonym="Runa Simi" data-language-local-name="kečuanski" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/C%C4%83dere_liber%C4%83" title="Cădere liberă – rumunjski" lang="ro" hreflang="ro" data-title="Cădere liberă" data-language-autonym="Română" data-language-local-name="rumunjski" 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%A1%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%BE%D0%B5_%D0%BF%D0%B0%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" title="Свободное падение – ruski" lang="ru" hreflang="ru" data-title="Свободное падение" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Slobodni_pad" title="Slobodni pad – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Slobodni pad" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Free_fall" title="Free fall – Simple English" lang="en-simple" hreflang="en-simple" data-title="Free fall" 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/Vo%C4%BEn%C3%BD_p%C3%A1d" title="Voľný pád – slovački" lang="sk" hreflang="sk" data-title="Voľný pád" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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/Prosti_pad" title="Prosti pad – slovenski" lang="sl" hreflang="sl" data-title="Prosti pad" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/R%C3%ABnia_e_lir%C3%AB" title="Rënia e lirë – albanski" lang="sq" hreflang="sq" data-title="Rënia e lirë" data-language-autonym="Shqip" data-language-local-name="albanski" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B1%D0%BE%D0%B4%D0%B0%D0%BD_%D0%BF%D0%B0%D0%B4" title="Слободан пад – srpski" lang="sr" hreflang="sr" data-title="Слободан пад" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Fritt_fall" title="Fritt fall – švedski" lang="sv" hreflang="sv" data-title="Fritt fall" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</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%B5%E0%B1%87%E0%B0%9A%E0%B1%8D%E0%B0%9B%E0%B0%BE_%E0%B0%AA%E0%B0%A4%E0%B0%A8%E0%B0%82" title="స్వేచ్ఛా పతనం – teluški" lang="te" hreflang="te" data-title="స్వేచ్ఛా పతనం" data-language-autonym="తెలుగు" data-language-local-name="teluški" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D1%84%D1%82%D0%B8%D1%88%D0%B8_%D2%B7%D0%B8%D1%81%D0%BC" title="Афтиши ҷисм – tadžički" lang="tg" hreflang="tg" data-title="Афтиши ҷисм" data-language-autonym="Тоҷикӣ" data-language-local-name="tadžički" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Erkin_ga%C3%A7ma_tizlenmesi" title="Erkin gaçma tizlenmesi – turkmenski" lang="tk" hreflang="tk" data-title="Erkin gaçma tizlenmesi" data-language-autonym="Türkmençe" data-language-local-name="turkmenski" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Serbest_d%C3%BC%C5%9Fme" title="Serbest düşme – turski" lang="tr" hreflang="tr" data-title="Serbest düşme" data-language-autonym="Türkçe" data-language-local-name="turski" 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%92%D1%96%D0%BB%D1%8C%D0%BD%D0%B5_%D0%BF%D0%B0%D0%B4%D1%96%D0%BD%D0%BD%D1%8F" title="Вільне падіння – ukrajinski" lang="uk" hreflang="uk" data-title="Вільне падіння" data-language-autonym="Українська" data-language-local-name="ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Erkin_tushish" title="Erkin tushish – uzbečki" lang="uz" hreflang="uz" data-title="Erkin tushish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/R%C6%A1i_t%E1%BB%B1_do" title="Rơi tự do – vijetnamski" lang="vi" hreflang="vi" data-title="Rơi tự do" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%87%AA%E7%94%B1%E8%90%BD%E4%BD%93" title="自由落体 – wu kineski" lang="wuu" hreflang="wuu" data-title="自由落体" data-language-autonym="吴语" data-language-local-name="wu kineski" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E7%94%B1%E8%90%BD%E9%AB%94" title="自由落體 – kineski" lang="zh" hreflang="zh" data-title="自由落體" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%87%AA%E7%94%B1%E4%B8%8B%E5%A2%9C" title="自由下墜 – kantonski" lang="yue" hreflang="yue" data-title="自由下墜" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</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/Q140028#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Slobodni_pad" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Slobodni_pad&action=edit&redlink=1" rel="discussion" class="new" title="Razgovorna stranica (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">hrvatski</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Slobodni_pad"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Slobodni_pad&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Slobodni_pad&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Slobodni_pad&action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Pomagala" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Pomagala</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Pomagala</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sakrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Više mogućnosti" > <div class="vector-menu-heading"> Radnje </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Slobodni_pad"><span>Čitaj</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Slobodni_pad&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Slobodni_pad&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Slobodni_pad&action=history"><span>Vidi povijest</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Razno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovamo/Slobodni_pad" title="Popis svih stranica koje sadrže poveznice na ovu stranicu [j]" accesskey="j"><span>Što vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_promjene/Slobodni_pad" rel="nofollow" title="Nedavne promjene na stranicama koje su povezane s navedenom stranicom [k]" accesskey="k"><span>Povezane promjene</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedija:Upload" title="Postavi datoteke [u]" accesskey="u"><span>Postavi datoteku</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Popis svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Slobodni_pad&oldid=6896336" title="Trajna poveznica na ovu verziju 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Gravity_gravita_grave.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7d/Gravity_gravita_grave.gif" decoding="async" width="289" height="400" class="mw-file-element" data-file-width="289" data-file-height="400" /></a><figcaption>Uobičajeno je da se slobodni pad uzima kao primjer <a href="/wiki/Jednoliko_ubrzano_gibanje_po_pravcu" title="Jednoliko ubrzano gibanje po pravcu">jednolikog ubrzanog gibanja</a> (gibanja sa stalnim ubrzanjem). Pritom se pretpostavlja da nema otpora <a href="/wiki/Zrak" title="Zrak">zraka</a> ili <a href="/wiki/Trenje" title="Trenje">trenja</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Leaning_tower_of_pisa_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Leaning_tower_of_pisa_2.jpg/300px-Leaning_tower_of_pisa_2.jpg" decoding="async" width="300" height="400" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Leaning_tower_of_pisa_2.jpg/450px-Leaning_tower_of_pisa_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e4/Leaning_tower_of_pisa_2.jpg 2x" data-file-width="555" data-file-height="740" /></a><figcaption><a href="/wiki/Kosi_toranj_u_Pisi" title="Kosi toranj u Pisi">Kosi toranj u Pisi</a> gdje je <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a> utvrdio da je <a href="/wiki/Ubrzanje_zemljine_sile_te%C5%BEe" class="mw-redirect" title="Ubrzanje zemljine sile teže">ubrzanje</a> bilo kojega padajućeg tijela na površini Zemlje konstantno i da je jednako za sva tijela.</figcaption></figure> <p><b>Slobodni pad</b> je <a href="/wiki/Gibanje" title="Gibanje">gibanje</a> <a href="/wiki/Tijelo_(fizika)" title="Tijelo (fizika)">tijela</a> isključivo pod utjecajem <a href="/wiki/Gravitacija" title="Gravitacija">sile teže</a>. Zakonitosti slobodnoga pada prvi je proučavao <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a>, te ustanovio da je <a href="/wiki/Prije%C4%91eni_put" class="mw-redirect" title="Prijeđeni put">prijeđeni put</a> <i>s</i> proporcionalan kvadratu protekloga vremena <i>t</i>, a <a href="/wiki/Brzina" title="Brzina">brzina</a> <i>v</i> jednoliko raste s proteklim <a href="/wiki/Vrijeme_(fizika)" title="Vrijeme (fizika)">vremenom</a>, te da <a href="/wiki/Gibanje" title="Gibanje">gibanje</a> ne ovisi o <a href="/wiki/Masa" title="Masa">masi</a> tijela koje pada. Na temelju <a href="/wiki/Newtonovi_zakoni_gibanja" title="Newtonovi zakoni gibanja">Newtonovih jednadžbi gibanja</a> i <a href="/wiki/Newtonov_zakon_gravitacije" title="Newtonov zakon gravitacije">teorije gravitacije</a> te se proporcionalnosti izražavaju jednadžbama: </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 s={\frac {g}{2}}\cdot t^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>g</mi> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s={\frac {g}{2}}\cdot t^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58cf8f4bbd9b506325ffe5b08aa7afb625d3400b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.76ex; height:4.843ex;" alt="{\displaystyle s={\frac {g}{2}}\cdot t^{2}}"></span></dd></dl> <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 v=g\cdot t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>g</mi> <mo>⋅</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=g\cdot t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef887df09d0a7835b710e5ca4c62f4d8ff843b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.861ex; height:2.343ex;" alt="{\displaystyle v=g\cdot t}"></span></dd></dl> <p>gdje je: <i>g</i> - <a href="/wiki/Ubrzanje_zemljine_sile_te%C5%BEe" class="mw-redirect" title="Ubrzanje zemljine sile teže">ubrzanje sile teže</a> koje na <a href="/wiki/Zemlja" title="Zemlja">Zemlji</a> iznosi prosječno 9,8066 <a href="/wiki/Metar_u_sekundi_na_kvadrat" title="Metar u sekundi na kvadrat">m/s²</a> i mijenja se ovisno o položaju na površini Zemlje zbog njezina oblika (<a href="/wiki/Geoid" title="Geoid">geoid</a>), <a href="/wiki/Vrtnja" title="Vrtnja">vrtnje</a> (<a href="/wiki/Centrifugalna_sila" title="Centrifugalna sila">centrifugalna sila</a>) i rasporeda mase (kopno–more). Na <a href="/wiki/Mjesec" title="Mjesec">Mjesecu</a> je površinsko <a href="/wiki/Gravitacija" title="Gravitacija">gravitacijsko</a> <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanje</a> oko šest puta manje, a na <a href="/wiki/Mars" title="Mars">Marsu</a> tri puta. Te jednadžbe ne uzimaju u obzir otpor zraka pa striktno vrijede samo za slobodni pad u <a href="/wiki/Vakuum" title="Vakuum">vakuumu</a>, na primjer u vakumiranoj cijevi ili na <a href="/wiki/Svemirske_letjelice" title="Svemirske letjelice">svemirskim letjelicama</a> bez <a href="/wiki/Atmosfera" title="Atmosfera">atmosfere</a>. Iz navedenih jednadžbi moguće je uklanjanjem veličine <i>t</i> dobiti treću jednadžbu za slobodni pad: </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 v={\sqrt {2\cdot g\cdot s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mo>⋅</mo> <mi>g</mi> <mo>⋅</mo> <mi>s</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\sqrt {2\cdot g\cdot s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6aadfda04f3a780240bb32dc5834656a1f8796c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.277ex; height:3.509ex;" alt="{\displaystyle v={\sqrt {2\cdot g\cdot s}}}"></span></dd></dl> <p>koja daje vrijednost brzine u pojedinim točkama prijeđenoga puta.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Povijest">Povijest</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=1" title="Uredi odlomak: Povijest" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=1" title="Uredi kôd odjeljka Povijest"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Aristotel" title="Aristotel">Aristotel</a> je prva zabilježena osoba koji je opisao slobodni pad. Prije 16. stoljeća na Zapadu, postojalo je uopćeno mišljenje da brzina tijela u slobodnom padu je proporcionala masi tijela, tj. teže tijelo padat će brže od lakšeg tijela. Galileo Galilej proširio je aristotelova razmatranja o slobodnom padu kroz niz pokusa valjajući tijela niz kosine i rabeći vodene satove te promatranja otkucaja svog srca uspio je povezati slobodni pad sa silom teže. Ove eksperimente Galilej je ponovio nekoliko stotina puta i ovim je uspio nakupiti dovoljno podataka tako da je točnost bila između dva pokusa bila u oko jedne desetinke otkucaja. </p> <div class="mw-heading mw-heading2"><h2 id="Primjeri">Primjeri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=2" title="Uredi odlomak: Primjeri" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=2" title="Uredi kôd odjeljka Primjeri"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sljedeći su primjeri tijela u slobodnom padu: </p> <ul><li>svemirski brod s isključenim pogonom u putanji oko Zemlje ili nekog drugog nebeskog tijela</li> <li>tijelo bačeno prema gore s malom brzinom, gdje je otpor zraka zanemariv</li></ul> <p>Tijela koja nisu u slobodnom padu </p> <ul><li>svemirski brod s uključenim pogonom ili zrakoplov u letu - zbog pogona i uzgona dijelova zrakopolova, letjelica rabi aerodinamiku odnosno silu uzgona preko tijela i/ili krila letjelice</li> <li>spuštanje nekog tijela na neko nebesko tijelo koje posjeduje atmosferu s padobranom ili sličnom napravom - prilikom padanja kroz atmosferu tijelo rabi padobran ili sličnu napravu, da bi usporili svoj pad kroz silu otpora zraka i rad koje vrši padobran.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Newtonova_mehanika">Newtonova mehanika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=3" title="Uredi odlomak: Newtonova mehanika" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=3" title="Uredi kôd odjeljka Newtonova mehanika"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Falling_ball.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Falling_ball.jpg/220px-Falling_ball.jpg" decoding="async" width="220" height="739" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Falling_ball.jpg/330px-Falling_ball.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Falling_ball.jpg/440px-Falling_ball.jpg 2x" data-file-width="819" data-file-height="2751" /></a><figcaption>Prikaz promjene brzine lopte u slobodnom padu, pod konstantnom silom gravitacije</figcaption></figure> <p>Kao iznos <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanja</a> uzima se ubrzanje gravitacijske sile i iznosi ~9,81 m/s<sup>2</sup>. Pri tome se za izračunavanje ostalih <a href="/wiki/Fizika" title="Fizika">fizikalnih</a> veličina koriste formule za jednoliko ubrzano gibanje. </p> <div class="mw-heading mw-heading3"><h3 id="Slobodni_pad_s_ujednačenom_silom_teže_bez_otpora_zraka"><span id="Slobodni_pad_s_ujedna.C4.8Denom_silom_te.C5.BEe_bez_otpora_zraka"></span>Slobodni pad s ujednačenom silom teže bez otpora zraka</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=4" title="Uredi odlomak: Slobodni pad s ujednačenom silom teže bez otpora zraka" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=4" title="Uredi kôd odjeljka Slobodni pad s ujednačenom silom teže bez otpora zraka"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>U slobodnom padu prevaljeni put tijela koje slobodno pada (inače se označava sa <i>s</i>) je u ovom slučaju visina s koje tijelo pada te se označava s <i>h</i>, akceleracija ili ubrzanje (inače se označava s <i>a</i>) je u ovom slučaju gravitacija te se označava s <i>g</i>, vrijeme s <i>t</i>, a brzina s <i>v</i>. </p><p>Jednadžba jednolikog ubrzanog gibanja po pravcu </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 v=a\cdot t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=a\cdot t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/275f21f1bdc7af8a87f745c1b6f5bcdd3fa52c3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.975ex; height:2.009ex;" alt="{\displaystyle v=a\cdot t}"></span></dd></dl> <p>postaje jednadžba slobodnog pada </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 v=g\cdot t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>g</mi> <mo>⋅</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=g\cdot t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef887df09d0a7835b710e5ca4c62f4d8ff843b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.861ex; height:2.343ex;" alt="{\displaystyle v=g\cdot t}"></span></dd></dl> <p>Jednadžba koja opisuje zavisnost vremena o visini s koje tijelo pada i gravitaciji, glasi: </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 {t^{2}}={\frac {2\cdot h}{g}}=>t={\sqrt {\frac {2\cdot h}{g}}}=>h={\frac {g\cdot t^{2}}{2}}={\frac {v\cdot t}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>h</mi> </mrow> <mi>g</mi> </mfrac> </mrow> <mo>=></mo> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>h</mi> </mrow> <mi>g</mi> </mfrac> </msqrt> </mrow> <mo>=></mo> <mi>h</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mo>⋅</mo> <mi>t</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {t^{2}}={\frac {2\cdot h}{g}}=>t={\sqrt {\frac {2\cdot h}{g}}}=>h={\frac {g\cdot t^{2}}{2}}={\frac {v\cdot t}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/093d879a6841187d0ab985676280f14fd9d1ea0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:48.644ex; height:7.509ex;" alt="{\displaystyle {t^{2}}={\frac {2\cdot h}{g}}=>t={\sqrt {\frac {2\cdot h}{g}}}=>h={\frac {g\cdot t^{2}}{2}}={\frac {v\cdot t}{2}}}"></span></dd></dl> <p>Jednadžba koja opisuje zavisnost brzine o visini s koje tijelo pada i gravitaciji, glasi: </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 {v^{2}}={2\cdot h\cdot g}=>v={\sqrt {2\cdot h\cdot g}}=>h={\frac {v^{2}}{2\cdot g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>⋅</mo> <mi>h</mi> <mo>⋅</mo> <mi>g</mi> </mrow> <mo>=></mo> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mo>⋅</mo> <mi>h</mi> <mo>⋅</mo> <mi>g</mi> </msqrt> </mrow> <mo>=></mo> <mi>h</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>g</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {v^{2}}={2\cdot h\cdot g}=>v={\sqrt {2\cdot h\cdot g}}=>h={\frac {v^{2}}{2\cdot g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/560b8b850777b9049249e333a788ab71542bfc44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.826ex; height:6.176ex;" alt="{\displaystyle {v^{2}}={2\cdot h\cdot g}=>v={\sqrt {2\cdot h\cdot g}}=>h={\frac {v^{2}}{2\cdot g}}}"></span></dd></dl><p> Ono što je vidljivo jest da bez otpora zraka (vakum) da slobodni pad nije ovisan o težini nekog tijela koji je u slobodnom padu, već je isključivo ovisan o sili teže. Poznatu demonstraciju puštanja dva tijela različite težine izvršila je posada letjelice <a href="/w/index.php?title=Apollo_15&action=edit&redlink=1" class="new" title="Apollo 15 (stranica ne postoji)">Apollo 15</a>, kada je komandant David Scott ispustio u isto vrijeme čekić i sokolovo pero. Zbog vakuma, oba tijela spustila su se na tlo mjeseca u isto vrijeme.<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> </p><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Apollo_15_feather_and_hammer_drop.ogv/220px--Apollo_15_feather_and_hammer_drop.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="161" data-durationhint="48" data-mwtitle="Apollo_15_feather_and_hammer_drop.ogv" data-mwprovider="wikimediacommons" resource="/wiki/Datoteka:Apollo_15_feather_and_hammer_drop.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="654" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e8/Apollo_15_feather_and_hammer_drop.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="654" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="196" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="328" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="490" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="490" data-height="360" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=fr&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="fr" label="français ‪(fr)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=pt-br&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="pt-BR" label="português do Brasil ‪(pt-br)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=pt&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="pt" label="português ‪(pt)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=tok&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="tok" label="toki pona ‪(tok)‬" data-dir="ltr" /></video></span><figcaption>Videozapis izvedbe pokusa koji dočarava slobodni padu u bezzračnom prostoru koji je izveo komandat <a href="/w/index.php?title=David_Scott&action=edit&redlink=1" class="new" title="David Scott (stranica ne postoji)">David Scott</a> prilikom slijetanja letjelice <a href="/w/index.php?title=Apollo_15&action=edit&redlink=1" class="new" title="Apollo 15 (stranica ne postoji)">Apollo 15</a> na površinu mjeseca.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Slobodni_pad_s_ujednačenom_silom_teže_i_otporom_zraka"><span id="Slobodni_pad_s_ujedna.C4.8Denom_silom_te.C5.BEe_i_otporom_zraka"></span>Slobodni pad s ujednačenom silom teže i otporom zraka</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=5" title="Uredi odlomak: Slobodni pad s ujednačenom silom teže i otporom zraka" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=5" title="Uredi kôd odjeljka Slobodni pad s ujednačenom silom teže i otporom zraka"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Skydiving_4_way.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Skydiving_4_way.jpg/220px-Skydiving_4_way.jpg" decoding="async" width="220" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Skydiving_4_way.jpg/330px-Skydiving_4_way.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Skydiving_4_way.jpg/440px-Skydiving_4_way.jpg 2x" data-file-width="573" data-file-height="523" /></a><figcaption>Padobranci u slobodnom padu (</figcaption></figure> <p>Slobodni pad u vakumu je klasični pogled a model slobodnog pada, no ono je sasvim drugačiji od slobodnog pada koji mnogi ljudi susreću iz dana u dan. Recimo na Zemlji, tijelo koje slobodno pada kroz atmosferu susrest će čestice (molekule) raznih plinova i tekućina koje se susreću prilikom pada kroz atmosferu a tijelo s obzirom na svoj oblik i površinu bit će usporen u svom padu zbog otpora i trenja zraka dok se to tijelo kreće kroz plin/tekućinu. Na primjer padobranac/padobranka, ili bilo koje tijelo neke mase <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>, i popriječnog površinskog presjeka, <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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, s <a href="/wiki/Reynoldsov_broj" title="Reynoldsov broj">reynoldsovim brojem</a> iznad kritičnog reynoldsovog broja, stvara otpor u zraku koji je jednak kvadratu brzine pada <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 v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>, i može se izraziti sa sljedećom formulom: </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{\frac {dv}{dt}}={\frac {1}{2}}\rho C_{\mathrm {D} }Av^{2}-mg\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>v</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> </mrow> </msub> <mi>A</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>m</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m{\frac {dv}{dt}}={\frac {1}{2}}\rho C_{\mathrm {D} }Av^{2}-mg\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a492508015bdbfeb6f30ab69947bdde77e53ec29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.624ex; height:5.509ex;" alt="{\displaystyle m{\frac {dv}{dt}}={\frac {1}{2}}\rho C_{\mathrm {D} }Av^{2}-mg\,,}"></span></dd></dl> <p>gdje je <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> gustoća zraka dok je <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 C_{\mathrm {D} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {D} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97eb2f053635e128b44a71558c8b50b270413ae7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.15ex; height:2.509ex;" alt="{\displaystyle C_{\mathrm {D} }}"></span> koeficient otopra zraka koji se smatra konstatnim i ovisi reynoldsovom broju. </p><p>Uz predpostavku da tijelo pada iz počinka i da je gustoća zraka ne mijenja s visinom<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>: </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 v(t)=-v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mi>tanh</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mi>t</mi> </mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=-v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07c129824ef1b8b8cf2d27250c3930db8b7e18a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.633ex; height:6.176ex;" alt="{\displaystyle v(t)=-v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right),}"></span></dd></dl> <p>konačna brzina je </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 v_{\infty }={\sqrt {\frac {2mg}{\rho C_{D}A}}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mi>m</mi> <mi>g</mi> </mrow> <mrow> <mi>ρ</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mi>A</mi> </mrow> </mfrac> </msqrt> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\infty }={\sqrt {\frac {2mg}{\rho C_{D}A}}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a8f51836db07e5b80ee98ee737b096707602a5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:16.495ex; height:7.676ex;" alt="{\displaystyle v_{\infty }={\sqrt {\frac {2mg}{\rho C_{D}A}}}\,.}"></span></dd></dl> <p>Brzina tijela može se integrirati preko vremena i s tim se može izraziti položaj tijela na okomici: </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 y=y_{0}-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>g</mi> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mi>cosh</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mi>t</mi> </mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=y_{0}-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63ba760149ec33766fda828eb9b2177690469a71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.151ex; height:6.176ex;" alt="{\displaystyle y=y_{0}-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right).}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Slobodni_pad_i_konačna_brzina"><span id="Slobodni_pad_i_kona.C4.8Dna_brzina"></span>Slobodni pad i konačna brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=6" title="Uredi odlomak: Slobodni pad i konačna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=6" title="Uredi kôd odjeljka Slobodni pad i konačna brzina"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Sila_teže"><span id="Sila_te.C5.BEe"></span>Sila teže</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=7" title="Uredi odlomak: Sila teže" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=7" title="Uredi kôd odjeljka Sila teže"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sila teže nije jednaka na svim dijelovima Zemlje, i ovisna je o udaljenosti od središta Zemlje. Zbog rotacije oblik Zemlje nije kugla već spljoštena sfera oko polova, i zbog toga je sila teže veća na polovima nego na ekvatoru. Na planinama i brdima sile teže manje (zanemarivo manje) nego u dolinama. U sljedećoj tablici prikazane precizne vrijednosti akceleracije sile teže (gravitacijske sile) na nekim lokacijama u nekim gradovima Europe i Afrike. </p> <dl><dd><table class="wikitable"> <tbody><tr> <th>GRAD </th> <th><i>g</i> / (m/s<sup>2</sup>) </th></tr> <tr> <td>Reykjavik </td> <td>9, 822 80 </td></tr> <tr> <td>Helsinki </td> <td>9, 819 15 </td></tr> <tr> <td>Berlin </td> <td>9, 812 82 </td></tr> <tr> <td>Pariz </td> <td>9, 809 41 </td></tr> <tr> <td>München </td> <td>9, 807 44 </td></tr> <tr> <td>Zagreb/katedrala </td> <td>9, 806 7621 </td></tr> <tr> <td>Zagreb/tvornica OKI </td> <td>9, 806 8099 </td></tr> <tr> <td>Zagreb/Sveta Nedjelja </td> <td>9, 806 7327 </td></tr> <tr> <td>Rim </td> <td>9, 803 63 </td></tr> <tr> <td>Kinšasa </td> <td>9, 779 18 </td></tr> <tr> <td>Johannesburg </td> <td>9, 785 50 </td></tr> </tbody></table></dd></dl> <p><br /> Vrlo točne vrijednosti konstante <i>g</i> mogu pružiti informacije o geološkoj građi podzemlja, pa se rabe, na primjer, kao jedna od metoda pri traganju za ležištima nafte i plina. </p> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=8" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=8" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <b>slobodni pad</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=56667">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, enciklopedija.hr, 2015.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html">http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html</a> Demostracija ispuštanja dva tijela različite težine na Mjesecu (NASA, engleski)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">"High altitude free fall" by Mohazzabi, P. and Shea, J. in American Journal of Physics, v64, 1242 (1996).</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Povezani_članci"><span id="Povezani_.C4.8Dlanci"></span>Povezani članci</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slobodni_pad&veaction=edit&section=9" title="Uredi odlomak: Povezani članci" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Slobodni_pad&action=edit&section=9" title="Uredi kôd odjeljka Povezani članci"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Padobran" title="Padobran">Padobran</a></li> <li><a href="/wiki/Gravitacija" title="Gravitacija">Gravitacija</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; 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