{"id":2193,"date":"2014-08-23T21:25:35","date_gmt":"2014-08-23T19:25:35","guid":{"rendered":"http:\/\/www.zsvltava.cz\/fyzika\/?p=2193"},"modified":"2025-06-26T11:47:19","modified_gmt":"2025-06-26T09:47:19","slug":"zavisi-gravitacni-sila-na-hmotnosti-telesa","status":"publish","type":"post","link":"https:\/\/www.zsvltava.cz\/fyzika\/?p=2193","title":{"rendered":"Z\u00e1vis\u00ed gravita\u010dn\u00ed s\u00edla na hmotnosti t\u011blesa?"},"content":{"rendered":"<p>Odpov\u011b\u010f zn\u00ed ano. <a href=\"\/fyzika\/?p=1089\">Newton\u016fv z\u00e1kon<\/a> zn\u00ed jasn\u011b. 2 t\u011blesa na sebe p\u016fsob\u00ed v\u017edy stejn\u011b velkou silou, opa\u010dn\u00e9ho sm\u011bru. V p\u0159\u00edpad\u011b <a href=\"\/fyzika\/?p=1619\">zemsk\u00e9 gravitace<\/a> je jednou ze sil ta, kterou na n\u00e1s p\u016fsob\u00ed Zem\u011b. P\u0159esto, pokud budeme pozorovat p\u00e1d r\u016fzn\u011b t\u011b\u017ek\u00fdch p\u0159edm\u011bt\u016f, zjist\u00edme, \u017ee dopadaj\u00ed k zemi <strong>stejn\u011b rychle<\/strong>. P\u0159esv\u011bd\u010dit se je snadn\u00e9. Stoupn\u011bte si na most, vezm\u011bte velmi t\u011b\u017ek\u00fd a velmi lehk\u00fd k\u00e1men a spus\u0165te je ve stejn\u00fd okam\u017eik. <\/p>\n<p>P\u0159ita\u017eliv\u00e1 s\u00edla je \u00fam\u011brn\u00e1 hmotnosti t\u011bles. Jeliko\u017e je hmotnost Zem\u011b: <\/p>\n<p>5 972 000 000 000 000 000 000 000 kg (6 . 10<sup>24<\/sup> kg)<\/p>\n<p>jsou v\u0161echna b\u011b\u017en\u00e1 t\u011blesa ve srovn\u00e1n\u00ed prakticky zanedbateln\u011b lehk\u00e1. Proto nen\u00ed v b\u011b\u017en\u00fdch situac\u00edch mo\u017en\u00e9 pozorovat rozd\u00edl.<\/p>\n<p>N\u011bkte\u0159\u00ed ned\u016fv\u011b\u0159ivci ob\u010das oponuj\u00ed p\u0159\u00edkladem, kdy jedn\u00edm z p\u0159edm\u011bt\u016f je p\u00edrko. To dopadne v\u017edy pozd\u011bji. D\u016fvodem je v\u0161ak p\u016fsoben\u00ed proud\u011bn\u00ed a odporu vzduchu, kter\u00fd se projev\u00ed.<\/p>\n<p>Profesor Brian Cox provedl \u00fa\u017easn\u00fd experiment ve vakuov\u00e9 komo\u0159e. Tedy v m\u00edst\u011b, ze kter\u00e9ho byl ods\u00e1t\u00fd vzduch. P\u00e1du tud\u00ed\u017e nic nebr\u00e1nilo a nemohlo vznikat ani minim\u00e1ln\u00ed proud\u011bn\u00ed.<\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"\/\/www.youtube.com\/embed\/E43-CfukEgs?rel=0\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<h2>Vyj\u00e1d\u0159eno matematicky<\/h2>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 34px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-94e86c7e808baec66c4a91120e0fa569_l3.png\" height=\"34\" width=\"133\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91; &#70;&#32;&#61;&#32;&#71;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#95;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#109;&#95;&#50;&#125;&#123;&#114;&#94;&#50;&#125; &#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-f04dbe505acfab6c4685b5a6523d826a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"\/> \u2013 velikost gravita\u010dn\u00ed s\u00edly (v newtonech, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-4e6ffedce72675a0aae278c6e81ab7b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"\/>)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-531006075515a832ae3ece04e1700017_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\"\/> \u2013 gravita\u010dn\u00ed konstanta (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-3bf28f1ed02f09907368bd185ce787a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#44;&#125;&#54;&#55;&#52;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#45;&#49;&#49;&#125;&#32;&#92;&#44;&#32;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#78;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#109;&#94;&#50;&#32;&#47;&#32;&#107;&#103;&#94;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"202\" style=\"vertical-align: -5px;\"\/>)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-b7c82e1506cfcc4fbd26da482c555b33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"\/> \u2013 hmotnost prvn\u00edho t\u011blesa (v kilogramech, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-df3019a4d6fa6829bce83b0fac487a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#107;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"20\" style=\"vertical-align: -4px;\"\/>)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-10e48dd77188405a44fa2374b2cef88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"\/> \u2013 hmotnost druh\u00e9ho t\u011blesa (v kilogramech, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-df3019a4d6fa6829bce83b0fac487a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#107;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"20\" style=\"vertical-align: -4px;\"\/>)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-a05d21231b95a3cca8e9f374ca9465cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> \u2013 vzd\u00e1lenost mezi st\u0159edy obou t\u011bles (v metrech, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-c7a7d3d0d4f2ff7a16f1c5626231a2b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"16\" style=\"vertical-align: 0px;\"\/>)<\/p>\n<h2>Jin\u00fd pohled<\/h2>\n<p>Na situaci lze nahl\u00e9dnout i p\u0159es gravita\u010dn\u00ed konstantu. Ozna\u010dujeme g, jej\u00ed hodnota je 9,81 m\/s<sup>2<\/sup>. Jedn\u00e1 se o tzv. (t\u00edhov\u00e9) gravita\u010dn\u00ed zrychlen\u00ed. Jeliko\u017e je to konstanta, nem\u011bn\u00ed se. (Jedn\u00e1 se o dohodnut\u00fd pr\u016fm\u011br. Ve skute\u010dnosti se velmi m\u00edrn\u011b zvy\u0161uje sm\u011brem od rovn\u00edku k p\u00f3l\u016fm.)<\/p>\n<p>Vztah mezi (okam\u017eitou) rychlost\u00ed a zrychlen\u00edm je n\u00e1sleduj\u00edc\u00ed: <\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 63px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-1f82708930a0be7781a1689de719f13a_l3.png\" height=\"63\" width=\"87\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91; &#97;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#118;&#125;&#123;&#116;&#125; &#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p>Zrychlen\u00ed `a`  v tomto p\u0159\u00edpad\u011b odpov\u00edd\u00e1 gravita\u010dn\u00ed konstant\u011b `g`. Jak vidno, nevyskytuje se nikde ve vztahu hmotnost, pouze \u010das. Tud\u00ed\u017e z\u00e1le\u017e\u00ed pouze na tom, jak dlouho t\u011bleso pad\u00e1 a nikoliv na tom, kolik v\u00e1\u017e\u00ed. Tak\u017ee v\u00edme-li jak dlouho t\u011bleso pad\u00e1, dos\u00e1hne ur\u010dit\u00e9ho zrychlen\u00ed bez ohledu na to, kolik v\u00e1\u017e\u00ed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Odpov\u011b\u010f zn\u00ed ano. Newton\u016fv z\u00e1kon zn\u00ed jasn\u011b. 2 t\u011blesa na sebe p\u016fsob\u00ed v\u017edy stejn\u011b velkou silou, opa\u010dn\u00e9ho sm\u011bru. V p\u0159\u00edpad\u011b zemsk\u00e9 gravitace je jednou ze &#8230;. <\/p>\n","protected":false},"author":1,"featured_media":5237,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[35,13],"tags":[53,17],"class_list":["post-2193","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sila","category-zajimavosti","tag-gravitace","tag-video"],"_links":{"self":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/2193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2193"}],"version-history":[{"count":3,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/2193\/revisions"}],"predecessor-version":[{"id":6014,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/2193\/revisions\/6014"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/media\/5237"}],"wp:attachment":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}