{"id":13480,"date":"2021-01-29T10:06:20","date_gmt":"2021-01-29T09:06:20","guid":{"rendered":"https:\/\/botland.com.pl\/blog\/?p=13480"},"modified":"2025-01-15T09:37:38","modified_gmt":"2025-01-15T08:37:38","slug":"masa-a-ciezar-dlaczego-nie-mozesz-mylic-tych-pojec","status":"publish","type":"post","link":"https:\/\/botland.com.pl\/blog\/masa-a-ciezar-dlaczego-nie-mozesz-mylic-tych-pojec\/","title":{"rendered":"Masa a ci\u0119\u017car &#8211; dlaczego nie mo\u017cesz myli\u0107 tych poj\u0119\u0107?"},"content":{"rendered":"<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">Czas czytania:<\/span> <span class=\"rt-time\"> 5<\/span> <span class=\"rt-label rt-postfix\">min.<\/span><\/span>\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"13480\" class=\"elementor elementor-13480\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-52ad9f1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"52ad9f1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6e09006\" data-id=\"6e09006\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-074e14a elementor-widget elementor-widget-text-editor\" data-id=\"074e14a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Terminy &#8220;masa&#8221; i &#8220;ci\u0119\u017car&#8221; w potocznej mowie i rozmowie s\u0105 cz\u0119sto u\u017cywane zamiennie. Te dwa s\u0142owa nie oznaczaj\u0105 jednak tego samego. A ju\u017c na pewno nie dla fizyka, zatem dla elektronika i robotyka to rozr\u00f3\u017cnienie te\u017c si\u0119 przyda.<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cf38cfe elementor-widget elementor-widget-text-editor\" data-id=\"cf38cfe\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"blog-special\"><strong>Symbol masy<\/strong> &#8211; w uk\u0142adzie SI podstawow\u0105 jednostk\u0105 masy jest kilogram (kg), masa oznaczana jest liter\u0105 &#8220;m&#8221;.<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8b6e87f elementor-widget elementor-widget-image\" data-id=\"8b6e87f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"485\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ciezar.jpg\" class=\"attachment-large size-large wp-image-13482\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ciezar.jpg 768w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ciezar-300x189.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ciezar-640x404.jpg 640w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-56cd103 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"56cd103\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-86cb75a\" data-id=\"86cb75a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7691bbf elementor-widget elementor-widget-heading\" data-id=\"7691bbf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Zanim zaczniemy, czyli masa a waga<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-91f2f68 elementor-widget elementor-widget-text-editor\" data-id=\"91f2f68\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Opr\u00f3cz tematu artyku\u0142u, czyli masy i ci\u0119\u017caru, dyskusja mo\u017ce rozbrzmie\u0107 r\u00f3wnie\u017c w temacie s\u0142\u00f3w <b>waga <\/b>i <b>masa<\/b>.\u00a0 Fachowcy, czyli w tym przypadku g\u0142\u00f3wnie fizycy i technicy, r\u00f3\u017cnice mi\u0119dzy mas\u0105 i wag\u0105 znajduj\u0105. J\u0119zyk og\u00f3lny jednak zaciera t\u0119 r\u00f3\u017cnic\u0119. Jak podaje prof. Miros\u0142aw Ba\u0144ko w internetowej poradni j\u0119zykowej na portalu PWN:\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fbd371c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fbd371c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b1d9c48\" data-id=\"b1d9c48\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8add158 elementor-widget elementor-widget-text-editor\" data-id=\"8add158\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><i>W podr\u0119czniku fizyki spodziewamy si\u0119 wi\u0119c sformu\u0142owa\u0144 typu przedmiot o masie 10 kg, ale w innych publikacjach za poprawne nale\u017cy uwa\u017ca\u0107 konstrukcje typu przedmiot o wadze stu ton, na przyk\u0142ad: \u201eNa wie\u017cyczce mo\u017ce wisie\u0107 dzwon o wadze co najmniej 300 kg (\u2026)\u201d (Tygodnik Podhala\u0144ski), albo: \u201eW szpitalu im. Jana Bo\u017cego urodzi\u0142 si\u0119 ch\u0142opczyk o wadze 7200 gram\u00f3w\u201d (Metropol), albo: \u201eZak\u0142adali nam kajdany o wadze trzech kilogram\u00f3w nie tylko w nocy, ale i w dzie\u0144\u201d (Micha\u0142 Komar, O obrotach los\u00f3w i cia\u0142), \u201ealbo: Dwa kamienie podtrzymuj\u0105 olbrzymi meteoryt o wadze pi\u0119tnastu ton\u201d (Anna Cechnica, Znak Anny).<\/i><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fcf7083 elementor-widget elementor-widget-text-editor\" data-id=\"fcf7083\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>I jak \u017cy\u0107? W fizyce Newtonowskiej jedno i drugie, masa i waga, to w\u0142a\u015bciwie to samo. W<span style=\"font-size: 1rem;\">\u00a0reklamach o odchudzaniu lub t\u0142umaczeniach technicznych zawieraj\u0105cych mas\u0119 przedmiotu wkrada si\u0119 b\u0142\u0105d, bo zamiennie u\u017cywane s\u0105 dwa s\u0142owa: masa i waga. Nie jest wielce ra\u017c\u0105cy dla przeci\u0119tnego u\u017cytkownika&#8230; j\u0119zyka u\u017cytkowego, ale b\u0142\u0105d jest b\u0142\u0119dem.\u00a0<\/span><span style=\"font-size: 1rem;\">Warto zwraca\u0107 uwag\u0119 na terminy i pami\u0119ta\u0107, \u017ce waga oznacza urz\u0105dzenie &#8211; o, na przyk\u0142ad <b><a href=\"https:\/\/botland.com.pl\/289-wagi\" data-wpel-link=\"internal\">jedno z takich<\/a><\/b> &#8211; kt\u00f3re s\u0142u\u017cy do pomiaru masy danego przedmiotu.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9658f4d elementor-widget elementor-widget-heading\" data-id=\"9658f4d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Masa a ci\u0119\u017car<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7388426 elementor-widget elementor-widget-text-editor\" data-id=\"7388426\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Masa jest warto\u015bci\u0105 skalarn\u0105 wyra\u017can\u0105 w gramach, kt\u00f3ra jest niezale\u017cn\u0105 od warto\u015bci si\u0142y grawitacji.\u00a0<span style=\"font-size: 1rem;\">Oznacza to, \u017ce masa cia\u0142a o wadze 50 kg b\u0119dzie taka sama na Ziemi, jak i na Ksi\u0119\u017cycu, bo jej warto\u015b\u0107\u00a0<\/span><span style=\"font-size: 1rem;\">wyliczana jest jako iloczyn g\u0119sto\u015bci do obj\u0119to\u015bci:<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8ee92d elementor-widget elementor-widget-text-editor\" data-id=\"d8ee92d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>&nbsp;m=(ro)*V<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-334ce61 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"334ce61\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-92f8f02\" data-id=\"92f8f02\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ef6a84 elementor-widget elementor-widget-image\" data-id=\"1ef6a84\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"199\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/weight-2541651_960_720-300x199.png\" class=\"attachment-medium size-medium wp-image-13524\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/weight-2541651_960_720-300x199.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/weight-2541651_960_720-768x510.png 768w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/weight-2541651_960_720-640x425.png 640w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/weight-2541651_960_720.png 960w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0665c9f elementor-widget elementor-widget-heading\" data-id=\"0665c9f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Masa jest miar\u0105 ilo\u015bci materii. Masa jest oznaczana za pomoc\u0105 m lub M.\n<div><br><\/div><\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-caa600c elementor-widget elementor-widget-image\" data-id=\"caa600c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"223\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/loads-2495144_960_720-300x223.png\" class=\"attachment-medium size-medium wp-image-13528\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/loads-2495144_960_720-300x223.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/loads-2495144_960_720-768x570.png 768w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/loads-2495144_960_720-640x475.png 640w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/loads-2495144_960_720.png 960w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ade1f84 elementor-widget elementor-widget-heading\" data-id=\"ade1f84\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Ci\u0119\u017car jest miar\u0105 wielko\u015bci si\u0142y dzia\u0142aj\u0105cej na mas\u0119 w wyniku przyspieszenia spowodowanego <br>si\u0142\u0105 grawitacji. Ci\u0119\u017car jest oznaczany za pomoc\u0105 W.<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bf459c6 elementor-widget elementor-widget-spacer\" data-id=\"bf459c6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e873c9d elementor-widget elementor-widget-text-editor\" data-id=\"e873c9d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Ci\u0119\u017car, czyli si\u0142a ci\u0119\u017cko\u015bci, jest wielko\u015bci\u0105 fizyczn\u0105 charakteryzuj\u0105c\u0105 zale\u017cno\u015b\u0107 mi\u0119dzy mas\u0105 a warto\u015bci\u0105 przyspieszenia grawitacyjnego. Jednostk\u0105 ci\u0119\u017caru jest Newton [N]. Jeden Newton to si\u0142a, z jaka dzia\u0142a na obiekt o masie 1 kg powoduj\u0105ca, \u017ce b\u0119dzie mia\u0142 przyspieszenie 1m\/s<sup style=\"color: #202124; font-family: arial, sans-serif;\">2.<\/sup><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11507c3 elementor-widget elementor-widget-spacer\" data-id=\"11507c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-6d93024e elementor-section-content-middle elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6d93024e\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-14b345dd\" data-id=\"14b345dd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-531fd950 elementor-widget elementor-widget-image\" data-id=\"531fd950\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"626\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/08\/okladkafizyka.jpg\" class=\"attachment-large size-large wp-image-9047\" alt=\"automatyka i robotyka studia nauka\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/08\/okladkafizyka.jpg 626w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/08\/okladkafizyka-300x300.jpg 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/08\/okladkafizyka-150x150.jpg 150w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-53859614\" data-id=\"53859614\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5cb8d34f elementor-widget elementor-widget-text-editor\" data-id=\"5cb8d34f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Wielko\u015b\u0107 skalarna w fizyce &#8211; co to jest?<\/b><\/p><p>Wielko\u015b\u0107 skalarna to poj\u0119cie u\u017cywane w fizyce. Oznacza wielko\u015b\u0107, do kt\u00f3rej okre\u015blenia wystarczy liczba rzeczywista z wymiarem wielko\u015bci fizycznej, bez uk\u0142adu wsp\u00f3\u0142rz\u0119dnych. Zaliczaj\u0105 si\u0119 do nich np. d\u0142ugo\u015b\u0107, temperatura, czas czy praca. Na skalarach mo\u017cna wykonywa\u0107 podstawowe dzia\u0142ania matematyczne, pot\u0119gowa\u0107 i u\u017cywa\u0107 funkcji trygonometrycznych czy logarytmicznych, ale trzeba pami\u0119ta\u0107 o wyra\u017ceniu wielko\u015bci w tych samych jednostkach i niemieszanie wielko\u015bci, np. masy i temperatury. Pr\u0119dko\u015bci wektorowe to natomiast np. si\u0142a, pr\u0119dko\u015b\u0107 czy przy\u015bpieszenie.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7c39164 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7c39164\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6557f12\" data-id=\"6557f12\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6954cee elementor-widget elementor-widget-heading\" data-id=\"6954cee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">K\u0142opotliwe pary. Por\u00f3wnanie masy i ci\u0119\u017caru<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9e2ac12 elementor-widget elementor-widget-text-editor\" data-id=\"9e2ac12\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><strong>Masa<\/strong> to w\u0142a\u015bciwo\u015b\u0107 materii. Masa przedmiotu jest wsz\u0119dzie taka sama.<\/li><li><strong>Ci\u0119\u017car<\/strong> zale\u017cy od wp\u0142ywu grawitacji. Zwi\u0119ksza si\u0119 z wi\u0119ksz\u0105 i zmniejsza si\u0119 z zmniejsz\u0105 grawitacj\u0105.<\/li><\/ul><ul><li><div><b>Masa <\/b>nie mo\u017ce wynosi\u0107 zero.<\/div><\/li><li><div><b>Ci\u0119\u017car <\/b>mo\u017ce wynosi\u0107 zero, gdy nie ma grawitacji &#8211; tak jak w pr\u00f3\u017cni absolutnej. \u015aci\u015blej m\u00f3wi\u0105c to sytuacja hipotetyczna &#8211; oddzia\u0142ywanie grawitacyjne jest wsz\u0119dzie. Mo\u017cemy zamieni\u0107 &#8220;mo\u017ce wynosi\u0107&#8221; na &#8220;m\u00f3g\u0142by\u00a0<span style=\"font-size: 1rem;\">wynosi\u0107&#8221;.<\/span><\/div><\/li><\/ul><ul><li><div><b>Masa <\/b>to wielko\u015b\u0107 skalarna. Ma wielko\u015b\u0107.\u00a0<\/div><\/li><li><div><b>Ci\u0119\u017car <\/b>to wielko\u015b\u0107 wektorowa. Posiada wielko\u015b\u0107 i jest zwr\u00f3cony wobec \u015brodka Ziemi.<\/div><\/li><\/ul><div><ul><li><b>Masa <\/b>mo\u017ce by\u0107 mierzona za pomoc\u0105 zwyk\u0142ej wagi.\u00a0<\/li><li>Do pomiaru <b>ci\u0119\u017caru <\/b>potrzeba wagi spr\u0119\u017cynowej.<\/li><\/ul><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-a15da8c elementor-section-content-middle elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a15da8c\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-8605962\" data-id=\"8605962\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a6f3650 elementor-widget elementor-widget-image\" data-id=\"a6f3650\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"155\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/silomierz.jpg\" class=\"attachment-large size-large wp-image-13504\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-cc1439d\" data-id=\"cc1439d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1d13dae elementor-widget elementor-widget-text-editor\" data-id=\"1d13dae\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Waga spr\u0119\u017cynowa &#8211; co to jest?<\/b><\/p><p>Waga spr\u0119\u017cynowa, inaczej si\u0142omierz albo dynamometr, to przyrz\u0105d do pomiaru si\u0142y. Sk\u0142ada si\u0119 ze sr\u0119\u017cyny wyd\u0142u\u017caj\u0105cej si\u0119 pod wp\u0142ywem dzia\u0142aj\u0105cych na ni\u0105 si\u0142 i podzia\u0142ki z warto\u015bciami w niutonach (N). \u0141atwo pomyli\u0107 go z popularn\u0105 w\u015br\u00f3d w\u0119dkarzy wag\u0105 hakow\u0105! Znane z deptak\u00f3w albo centr\u00f3w handlowych automaty si\u0142owe z workiem do boksowania zast\u0105pi\u0142y w\u0142a\u015bnie popularne dawniej si\u0142omierze.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2a93462 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a93462\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-03ee9b1\" data-id=\"03ee9b1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d16ad3f elementor-widget elementor-widget-text-editor\" data-id=\"d16ad3f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><b>Masa\u00a0<\/b>jest zwykle wyra\u017cana w gramach albo kilogramach.<\/li><li><b>Ci\u0119\u017car\u00a0<\/b>jest mierzony w niutonach &#8211; jednostce si\u0142y.\u00a0<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-eaebc7b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"eaebc7b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-698780e\" data-id=\"698780e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-be5fdc7 elementor-widget elementor-widget-image\" data-id=\"be5fdc7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"79\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat1-300x79.png\" class=\"attachment-medium size-medium wp-image-13509\" alt=\"Schemat fizyczny - grawitacja\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat1-300x79.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat1.png 488w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc57b57 elementor-widget elementor-widget-text-editor\" data-id=\"fc57b57\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Si\u0142a grawitacji dzia\u0142a pomi\u0119dzy wszystkimi obiektami.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e4c562 elementor-widget elementor-widget-image\" data-id=\"8e4c562\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"87\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat2-300x87.png\" class=\"attachment-medium size-medium wp-image-13510\" alt=\"schemat fizyczny - grawitacja\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat2-300x87.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat2.png 488w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d872a9e elementor-widget elementor-widget-text-editor\" data-id=\"d872a9e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Je\u017celi ro\u015bnie masa, ro\u015bnie r\u00f3wnie\u017c si\u0142a grawitacji.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0e922af elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0e922af\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-848beea\" data-id=\"848beea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-21684be elementor-widget elementor-widget-image\" data-id=\"21684be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"69\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat3-300x69.png\" class=\"attachment-medium size-medium wp-image-13511\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat3-300x69.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/schemat3.png 488w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57d91db elementor-widget elementor-widget-text-editor\" data-id=\"57d91db\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Je\u017celi ro\u015bnie odleg\u0142o\u015b\u0107, maleje si\u0142a grawitacji.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ea1e69 elementor-widget elementor-widget-heading\" data-id=\"2ea1e69\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\u015arodek ci\u0119\u017cko\u015bci a \u015brodek masy<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fa9697c elementor-widget elementor-widget-text-editor\" data-id=\"fa9697c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u015arodek ci\u0119\u017cko\u015bci i \u015brodek masy pokrywaj\u0105 si\u0119 niemal zawsze.\u00a0W przypadku cia\u0142 symetrycznych &#8211; np. prostego, jednorodnego pr\u0119ta, kuli,\u00a0<span style=\"font-size: 1rem;\">ko\u0142a\u00a0<\/span><span style=\"font-size: 1rem;\">czy sze\u015bcianu \u015brodek masy znajduje si\u0119 w \u015brodku geometrycznym cia\u0142a.\u00a0<\/span>Trudniej wyznaczy\u0107 \u015brodek masy, je\u015bli ta jest roz\u0142o\u017cona nier\u00f3wnomiernie &#8211; dzieje si\u0119 tak czasem\u00a0 z powodu skomplikowanych rozmiar\u00f3w albo niejednorodno\u015bci materia\u0142u.\u00a0<span style=\"font-size: 1rem;\">Cia\u0142o zawsze posiada \u015brodek masy, nawet je\u017celi nie dzia\u0142a na nie si\u0142a grawitacji. W ca\u0142kowitej pr\u00f3\u017cni kosmicznej cia\u0142o mia\u0142oby mas\u0119, ale nie mia\u0142oby ci\u0119\u017caru &#8211; bo nie by\u0142oby grawitacji. Skoro \u015brodek masy &#8220;zachodzi&#8221; wsz\u0119dzie, to ci\u0105gni\u0119cie za sob\u0105 g\u0142azu w takim kosmosie ruchem przy\u015bpieszonym, to nie przekr\u0119ci\u0142by si\u0119 on ani troch\u0119. Wi\u0105\u017c\u0105 si\u0119 z tym <\/span><b style=\"font-size: 1rem;\">ruch post\u0119powy<\/b><span style=\"font-size: 1rem;\"> (powi\u0105zany z ruchem \u015brodka masy) i <\/span><b style=\"font-size: 1rem;\">ruch obrotowy<\/b><span style=\"font-size: 1rem;\"> (dokonuj\u0105cy wok\u00f3\u0142 \u015brodka masy).<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ff1cfa elementor-widget elementor-widget-heading\" data-id=\"4ff1cfa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Obliczanie po\u0142o\u017cenia \u015brodka masy dw\u00f3ch punkt\u00f3w<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01b190b elementor-widget elementor-widget-text-editor\" data-id=\"01b190b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Zobaczmy to na przyk\u0142adzie zadania z portalu <a href=\"http:\/\/www.fizykon.org\/statyka_osr_ciagle\/masa_a_ciezar_ciala.htm\" data-wpel-link=\"external\" target=\"_blank\" rel=\"nofollow external noopener noreferrer\"><b>fizykon.org<\/b><\/a>.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f79208e elementor-widget elementor-widget-text-editor\" data-id=\"f79208e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>W jakiej odleg\u0142o\u015bci od \u015brodka Ziemi znajduje si\u0119 \u015brodek masy uk\u0142adu Ziemia \u2013 Ksi\u0119\u017cyc?<\/p><p>Czy jest on w \u015brodku, czy na zewn\u0105trz planety?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16c5507 elementor-widget elementor-widget-image\" data-id=\"16c5507\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"488\" height=\"128\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/zadanie1.png\" class=\"attachment-large size-large wp-image-13515\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/zadanie1.png 488w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/zadanie1-300x79.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-66be39a elementor-widget elementor-widget-text-editor\" data-id=\"66be39a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Po lewej Ziemia, po prawej Ksi\u0119\u017cyc.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a08106 elementor-widget elementor-widget-text-editor\" data-id=\"6a08106\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Masa Ziemi: M<sub>z<\/sub>\u00a0\u2248 6 \u2219 10<sup>24<\/sup>\u00a0kg<br \/>Masa Ksi\u0119\u017cyca: M<sub>k<\/sub>\u00a0\u2248 7.3 \u2219 10<sup>22<\/sup>\u00a0kg<br \/>\u015arednia odleg\u0142o\u015b\u0107 od Ksi\u0119\u017cyca do Ziemi: d \u2248 3.84\u2219 10<sup>8<\/sup>\u00a0m<br \/>\u015aredni promie\u0144 Ziemi: R<sub>Kuli_ziemskiej<\/sub>\u00a0\u2248 6.37\u2219 10<sup>6<\/sup>\u00a0m<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c4ebab9 elementor-widget elementor-widget-text-editor\" data-id=\"c4ebab9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Szukamy:<br \/>x \u2013 odleg\u0142o\u015bci \u015brodka masy uk\u0142adu od \u015brodka Ziemi.<\/p><p>Rozwi\u0105zanie:<br \/>Z rysunku wida\u0107, \u017ce odleg\u0142o\u015b\u0107 Ksi\u0119\u017cyca od \u015brodka masy uk\u0142adu wynosi:<\/p><p>xk = d \u2013 x<\/p><p>Wielko\u015bci te b\u0119dziemy podstawiali do wzoru:<\/p><p>MKRK = MZRZ<\/p><p>Przy czym:<\/p><p>Rz = x<\/p><p>Rk = xk = d \u2013 x<\/p><p>Dlatego:<\/p><p>MK \u2219 (d &#8211; x) = MZ \u2219 x<\/p><p>Wymna\u017camy nawias:<\/p><p>MK \u2219 d &#8211; MK \u2219 x = MZ \u2219 x<\/p><p>Przenosimy MK \u2219 x na lew\u0105 stron\u0105 (z przeciwnym znakiem):<\/p><p>MK \u2219 d = MZ \u2219 x + MK \u2219 x<\/p><p>Wyci\u0105gamy x przed nawias:<\/p><p>MK \u2219 d = (MZ + MK) \u2219 x<\/p><p>Wreszcie dzielimy obie strony r\u00f3wnania przez ca\u0142y nawias zamieniaj\u0105c przy tym strony r\u00f3wnania, aby z lewej strony mie\u0107 wielko\u015b\u0107 niewiadom\u0105 x:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4abd9b3 elementor-widget elementor-widget-image\" data-id=\"4abd9b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"93\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ulamek1.png\" class=\"attachment-large size-large wp-image-13517\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5326aad elementor-widget elementor-widget-text-editor\" data-id=\"5326aad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Podstawiamy jeszcze wielko\u015bci liczbowe:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-876ff0c elementor-widget elementor-widget-image\" data-id=\"876ff0c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"729\" height=\"93\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ulamek2.png\" class=\"attachment-large size-large wp-image-13516\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ulamek2.png 729w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ulamek2-300x38.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/ulamek2-640x82.png 640w\" sizes=\"(max-width: 729px) 100vw, 729px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e1f532 elementor-widget elementor-widget-text-editor\" data-id=\"8e1f532\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>St\u0105d:<\/p><p>x \u2248 4,6 \u2219 106 m<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7bd826c elementor-widget elementor-widget-text-editor\" data-id=\"7bd826c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Poniewa\u017c \u015bredni promie\u0144 Ziemi: R<sub>Kuli_ziemskiej<\/sub>\u00a0\u2248 6,37\u2219 10<sup>6<\/sup>\u00a0m, wi\u0119c wida\u0107, \u017ce \u015brodek masy uk\u0142adu Ziemia \u2013 Ksi\u0119\u017cyc znajduje si\u0119 we wn\u0119trzu Ziemi (bo\u00a0<i>x<\/i>\u00a0&lt; R<sub>Kuli_ziemskiej<\/sub>).\u00a0Wniosek jest taki, \u017ce Ziemia wykonuje dwa ruchy obrotowe. Jeden to zwyk\u0142y wok\u00f3\u0142 swojego \u015brodka geometrycznego (te\u017c \u015brodka masy, ale samej kuli ziemskiej), natomiast drugi to ruch obrotowy, nak\u0142adaj\u0105cy si\u0119 na pierwszy, to wirowanie wok\u00f3\u0142 \u015brodka masy wok\u00f3\u0142 uk\u0142adu Ziemia &#8211; Ksi\u0119\u017cyc.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c1e922b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c1e922b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d9d9ed3\" data-id=\"d9d9ed3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0787ce4 elementor-widget elementor-widget-heading\" data-id=\"0787ce4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Bonus, czyli grawitacja w kosmosie<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f4f8ef3 elementor-widget elementor-widget-image\" data-id=\"f4f8ef3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"168\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/planeta-300x168.png\" class=\"attachment-medium size-medium wp-image-13520\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/planeta-300x168.png 300w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/planeta.png 500w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ddb1a58 elementor-widget elementor-widget-text-editor\" data-id=\"ddb1a58\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Podczas gdy masa nie zmienia si\u0119 nigdzie indziej w Uk\u0142adzie S\u0142onecznym, to przyspieszenie spowodowane grawitacj\u0105 zmienia si\u0119 ju\u017c gwa\u0142townie. Obliczanie grawitacji na powierzchni innych planet, podobnie jak na Ziemi, zale\u017cy nie tylko od masy, ale tak\u017ce od tego, jak daleko &#8220;powierzchnia&#8221; znajduje si\u0119 od \u015brodka ci\u0119\u017cko\u015bci. Na Ziemi, na przyk\u0142ad, Tw\u00f3j ci\u0119\u017car jest nieco ni\u017cszy na szczycie g\u00f3ry ni\u017c na \u0142odzi p\u0142yn\u0105cej po morzu. Efekt staje si\u0119 jeszcze bardziej zauwa\u017calny w przypadku du\u017cych cia\u0142 &#8211; na przyk\u0142ad takich jak Jowisz. Podczas gdy grawitacja wywierana przez gazowego giganta ze wzgl\u0119du na jego mas\u0119 jest 316 razy wi\u0119ksza od ziemskiej, nie wa\u017cy\u0142by\u015b wcale 316 razy wi\u0119cej, poniewa\u017c jego &#8220;powierzchnia&#8221; (lub poziom chmury, kt\u00f3ry nazywamy powierzchni\u0105) jest daleko od \u015brodka ci\u0119\u017cko\u015bci.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ce61c3 elementor-widget elementor-widget-image\" data-id=\"6ce61c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"610\" height=\"337\" src=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/tabela1.png\" class=\"attachment-large size-large wp-image-13518\" alt=\"\" srcset=\"https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/tabela1.png 610w, https:\/\/botland.com.pl\/blog\/wp-content\/uploads\/2020\/12\/tabela1-300x166.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-570c81c elementor-widget elementor-widget-text-editor\" data-id=\"570c81c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Ci\u0119\u017car na innych planetach naprawd\u0119 zaskakuje. Akurat fakt, \u017ce cz\u0142owiek wa\u017cy\u0142by mniej wi\u0119cej tyle samo na Wenus, co na Ziemi, poniewa\u017c planeta ta jest mniej wi\u0119cej tej samej wielko\u015bci i masy co Ziemia, tak\u0105 niespodziank\u0105 nie jest. Jednak mo\u017ce si\u0119 wydawa\u0107 dziwne, \u017ce w rzeczywisto\u015bci wa\u017cyliby\u015bmy mniej na gazowym gigancie Uranie. Nasz ci\u0119\u017car by\u0142by tylko nieznacznie wi\u0119kszy na Saturnie czy na Neptunie. Chocia\u017c Merkury jest znacznie mniejszy od Marsa, Wasz ci\u0119\u017car by\u0142by mniej wi\u0119cej taki sam na obu planetach. Wreszcie nasza gwiazda zwana S\u0142o\u0144cem jest znacznie masywniejsza ni\u017c jakiekolwiek inne cia\u0142o w Uk\u0142adzie S\u0142onecznym, ale wa\u017cyliby\u015bmy tam &#8220;tylko&#8221; oko\u0142o 28 razy wi\u0119cej. Gro\u017ane nie by\u0142yby tylko temperatura i promieniowanie &#8211; nawet gdyby by\u0142o tam zimno, to intensywna grawitacja na planecie czy innym ciele niebieskim tej wielko\u015bci by\u0142aby zab\u00f3jcza.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bdd7949 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bdd7949\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d59b4ff\" data-id=\"d59b4ff\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-953dd2e elementor-widget elementor-widget-text-editor\" data-id=\"953dd2e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div id=\"k-faq-accord\">\n<h2>Masa a ci\u0119\u017car &#8211; FAQ<\/h2>\n\n<div class=\"tabs\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/FAQPage\">\n<div class=\"tab\" itemprop=\"mainEntity\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Question\"><input id=\"chck1\" type=\"checkbox\" \/>\n<h3><label class=\"tab-label\" itemprop=\"name\" for=\"chck1\">Czym r\u00f3\u017cni si\u0119 masa i ci\u0119\u017car?<label><\/h3>\n<div class=\"tab-content\" itemprop=\"acceptedAnswer\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Answer\">\n\n<div itemprop=\"text\">Masa jest oznaczona jako m lub M. To miara, kt\u00f3r\u0105 okre\u015bla si\u0119 konkretn\u0105 ilo\u015b\u0107 danej materii. Z kolei ci\u0119\u017car oznaczany jako W (jednostka to N) okre\u015bla si\u0142\u0119, a w zasadzie wielko\u015b\u0107 si\u0142y, kt\u00f3ra dzia\u0142a na mas\u0119 na skutek przyspieszenia, kt\u00f3re jest wynikiem si\u0142y grawitacji. Wi\u0119cej informacji na temat masy i ci\u0119\u017caru mo\u017cna znale\u017a\u0107 w tym <a href=\"https:\/\/botland.com.pl\/blog\/masa-a-ciezar-dlaczego-nie-mozesz-mylic-tych-pojec\/\" data-wpel-link=\"internal\">artykule<\/a>.\n<\/div>\n\n<\/div>\n<\/div>\n\n<div class=\"tab\" itemprop=\"mainEntity\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Question\"><input id=\"chck2\" type=\"checkbox\" \/>\n<h3><label class=\"tab-label\" itemprop=\"name\" for=\"chck2\">Jak zamieni\u0107 mas\u0119 na ci\u0119\u017car?<\/label><\/h3>\n<div class=\"tab-content\" itemprop=\"acceptedAnswer\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Answer\">\n\n<div itemprop=\"text\">Aby obliczy\u0107 mas\u0119 na ci\u0119\u017car nale\u017cy wykorzysta\u0107 wz\u00f3r P= m*g, gdzie m to masa np. w kilogramach, a g to przyspieszenie ziemskie r\u00f3wne 9,81 m\/s2 . Niekiedy dla uproszczenia przyjmuje si\u0119 10 m\/s2.\n<\/div>\n\n<\/div>\n<\/div>\n\n<div class=\"tab\" itemprop=\"mainEntity\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Question\"><input id=\"chck3\" type=\"checkbox\" \/>\n<h3><label class=\"tab-label\" itemprop=\"name\" for=\"chck3\">Co wskazuje waga mas\u0119 czy ci\u0119\u017car?<\/label><\/h3>\n<div class=\"tab-content\" itemprop=\"acceptedAnswer\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Answer\">\n\n<div itemprop=\"text\">Waga np. domowa lub kuchenna wskazuje mas\u0119 wyra\u017con\u0105 w kilogramach lub gramach. Z kolei wagi przemys\u0142owe wykazuj\u0105 mas\u0119 w tonach.\n<\/div>\n\n<\/div>\n<\/div>\n\n<div class=\"tab\" itemprop=\"mainEntity\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Question\"><input id=\"chck4\" type=\"checkbox\" \/>\n<h3><label class=\"tab-label\" itemprop=\"name\" for=\"chck4\">Co to ci\u0119\u017car?<\/label><\/h3>\n<div class=\"tab-content\" itemprop=\"acceptedAnswer\" itemscope=\"\" itemtype=\"https:\/\/schema.org\/Answer\">\n\n<div itemprop=\"text\">Ci\u0119\u017car jest r\u00f3wnie\u017c nazywany si\u0142\u0105 ci\u0119\u017cko\u015bci. Okre\u015bla zale\u017cno\u015b\u0107 mi\u0119dzy przyspieszeniem grawitacyjnym a mas\u0105. Jeden Newton (N) jest r\u00f3wnoznaczny z si\u0142\u0105 jaka oddzia\u0142ywuje na element, kt\u00f3rego masa 1 kg sprawia, \u017ce jego przyspieszenie wynosi 1m\/s\u00b2. Ci\u0119\u017car wskazuje si\u0142\u0119 ci\u0119\u017cko\u015bci obiektu wyra\u017con\u0105 w m\/s\u00b2. Ci\u0119\u017car obiektu jest uzale\u017cniony od si\u0142y grawitacyjnej. Innymi s\u0142owy ten sam obiekt na ksi\u0119\u017cycu i ziemi b\u0119dzie charakteryzowa\u0142 si\u0119 innym ci\u0119\u017carem. Z kolei masa to ilo\u015b\u0107 materii. Wyra\u017camy j\u0105 w kilogramach. Masa jest zawsze taka sama, poniewa\u017c jej warto\u015b\u0107 jest iloczynem obj\u0119to\u015bci i g\u0119sto\u015bci.\n<\/div>\n\n<\/div>\n<\/div>\n\n\n<\/div>\n<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Terminy &#8220;masa&#8221; i &#8220;ci\u0119\u017car&#8221; w potocznej mowie i rozmowie s\u0105 cz\u0119sto u\u017cywane zamiennie. Te dwa s\u0142owa nie oznaczaj\u0105 jednak tego samego. A ju\u017c na pewno nie dla fizyka, zatem dla elektronika i robotyka to rozr\u00f3\u017cnienie te\u017c si\u0119 przyda.<\/p>\n","protected":false},"author":10,"featured_media":61356,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[179],"tags":[211,201],"class_list":["post-13480","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kompendium","tag-fizyka","tag-porady"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Masa a ci\u0119\u017car - dlaczego nie mo\u017cesz myli\u0107 tych poj\u0119\u0107? - Botland<\/title>\n<meta name=\"description\" content=\"Terminy &quot;masa&quot; i &quot;ci\u0119\u017car&quot; w potocznej mowie i rozmowie s\u0105 cz\u0119sto u\u017cywane zamiennie. 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