{"id":3192,"date":"2026-03-10T22:12:49","date_gmt":"2026-03-10T21:12:49","guid":{"rendered":"https:\/\/solveredu.com\/?p=3192"},"modified":"2026-03-10T22:12:55","modified_gmt":"2026-03-10T21:12:55","slug":"sbizna-vs-obecna-soustava-sil","status":"publish","type":"post","link":"https:\/\/solveredu.com\/cs\/post\/zbiezny-vs-dowolny-rozbiezny-uklad-sil\/","title":{"rendered":"Konvergentn\u00ed vs. divergentn\u00ed (rozb\u00edhav\u00fd) syst\u00e9m sil - rozd\u00edly a metody v\u00fdpo\u010dtu"},"content":{"rendered":"<h2 class=\"wp-block-heading has-medium-font-size\">Jak p\u0159estat bojovat s mechanikou? Ovl\u00e1dn\u011bte energetick\u00e9 syst\u00e9my jednou prov\u017edy!<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Studium in\u017een\u00fdrstv\u00ed je neust\u00e1l\u00fd boj s vektory a kolokvia z mechaniky mohou b\u00fdt no\u010dn\u00ed m\u016frou. Nejv\u011bt\u0161\u00ed probl\u00e9m? \u010casto si pleteme typy silov\u00fdch soustav, co\u017e vede k chybn\u00fdm rovnic\u00edm hned na za\u010d\u00e1tku. Dnes to rozebereme a uk\u00e1\u017eeme v\u00e1m, jak si v\u0161e usnadnit.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"#zbiezny\"><strong>Konvergentn\u00ed nebo arbitr\u00e1rn\u00ed? Je t\u0159eba mezi nimi rozli\u0161ovat!<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#warunki\"><strong>Podm\u00ednky rovnov\u00e1hy - kde je rozd\u00edl?<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#przykladowe\"><strong>P\u0159\u00edklady \u00fakol\u016f<\/strong><\/a><\/li>\n<\/ol>\n\n\n\n<h3 id=\"zbiezny\" class=\"wp-block-heading\">1. konvergentn\u00ed nebo arbitr\u00e1rn\u00ed? Je t\u0159eba mezi nimi rozli\u0161ovat!<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ne\u017e se pust\u00edte do v\u00fdpo\u010dt\u016f, mus\u00edte sv\u016fj syst\u00e9m spr\u00e1vn\u011b klasifikovat. To ur\u010d\u00ed, kolik rovnic budete muset zapsat a zda se budete pot\u00fdkat s po\u010d\u00edtac\u00edmi momenty.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Konverguj\u00edc\u00ed silov\u00e9 syst\u00e9my:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ploch\u00fd syst\u00e9m sb\u00edhav\u00fdch sil<\/strong> - V mechanice je rovinn\u00e1 konvergentn\u00ed soustava sil takov\u00e1, v n\u00ed\u017e v\u0161echny vektory sil p\u016fsob\u00ed v jedn\u00e9 rovin\u011b. <strong>jedno letadlo<\/strong>, a jejich p\u0159\u00edmky (sm\u011bry) se prot\u00ednaj\u00ed p\u0159esn\u011b v bod\u011b <strong>jeden bod<\/strong>. Ka\u017ed\u00fd jednotliv\u00fd uzel p\u0159\u00edhradov\u00e9 konstrukce je uva\u017eov\u00e1n pr\u00e1v\u011b jako rovinn\u00e1 soustava sb\u00edhav\u00fdch sil.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Prostorov\u00e9 uspo\u0159\u00e1d\u00e1n\u00ed sbli\u017euj\u00edc\u00edch se sil<\/strong> - Soustava sil p\u016fsob\u00edc\u00edch na tuh\u00e9 t\u011bleso, jejich\u017e sm\u011bry p\u016fsoben\u00ed se prot\u00ednaj\u00ed v bod\u011b. <strong>jeden bod<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Uspo\u0159\u00e1d\u00e1n\u00ed libovoln\u00fdch (divergentn\u00edch) sil:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Jedn\u00e1 se o situaci, kdy jsou s\u00edly rozpt\u00fdleny. Jejich ak\u010dn\u00ed linie nemaj\u00ed jeden sty\u010dn\u00fd bod. Takov\u00fd syst\u00e9m je schopen nejen pohybovat t\u011blem nahoru, dol\u016f nebo do stran, ale p\u0159edev\u0161\u00edm - -. <strong>m\u016f\u017ee zp\u016fsobit obrat<\/strong>. Takov\u00e1 soustava m\u016f\u017ee b\u00fdt rovinn\u00e1, pokud v\u0161echny s\u00edly le\u017e\u00ed v jedn\u00e9 rovin\u011b, nebo prostorov\u00e1, pokud s\u00edly le\u017e\u00ed v r\u016fzn\u00fdch rovin\u00e1ch.<\/li>\n<\/ul>\n\n\n\n<h3 id=\"warunki\" class=\"wp-block-heading\">2 Rovnov\u00e1\u017en\u00e9 podm\u00ednky - kde je rozd\u00edl?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">V z\u00e1vislosti na tom, o jakou soustavu se jedn\u00e1, je t\u0159eba zapsat p\u0159\u00edslu\u0161n\u00fd po\u010det rovnic. Sb\u00edhav\u00e1 soustava sil je v rovnov\u00e1ze, jestli\u017ee vektory sil tvo\u0159\u00ed rovinu. <strong>uzav\u0159en\u00fd polygon<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><td><strong>Funkce<\/strong><\/td><td><strong>Konvergovan\u00fd syst\u00e9m<\/strong><\/td><td><strong>Uspo\u0159\u00e1d\u00e1n\u00ed Jak\u00e9koli<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>Ploch\u00e9<\/strong><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math>   <br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math>   <math data-latex=\"\\sum M_o = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>o<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_o = 0<\/annotation><\/semantics><\/math> <\/td><\/tr><tr><td><strong>Prostorov\u00e9<\/strong><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math> <br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_z = 0<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"\\sum F_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_x = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_x = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_x = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_y = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_y = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_y = 0<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sum F_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>F<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\F_z = 0<\/annotation><\/semantics><\/math>     <math data-latex=\"\\sum M_z = 0\"><semantics><mrow><mo movablelimits=\"false\">\u2211<\/mo><msub><mi>M<\/mi><mi>z<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\M_z = 0<\/annotation><\/semantics><\/math><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">V rovinn\u00e9 libovoln\u00e9 soustav\u011b vstupuje do hry t\u0159et\u00ed rovnice - sou\u010det moment\u016f vzhledem ke zvolen\u00e9mu bodu. Zde se dopou\u0161t\u00edme nejv\u00edce chyb, kdy\u017e zapom\u00edn\u00e1me na sm\u011br momentu nebo rameno s\u00edly.<\/p>\n\n\n\n<h4 id=\"przykladowe\" class=\"wp-block-heading\">3 P\u0159\u00edklady \u00fakol\u016f<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">N\u00ed\u017ee najdete p\u0159\u00edklad \u00falohy se sb\u00edhaj\u00edc\u00ed se soustavou sil.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1215\" height=\"903\" data-attachment-id=\"2953\" data-permalink=\"https:\/\/solveredu.com\/cs\/zad2_en\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1215%2C903&amp;ssl=1\" data-orig-size=\"1215,903\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"zad2_en\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1024%2C761&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=1215%2C903&#038;ssl=1\" alt=\"Konverguj\u00edc\u00ed soustava sil, vzorov\u00e1 \u00faloha, Solveredu\" class=\"wp-image-2953\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?w=1215&amp;ssl=1 1215w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=300%2C223&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=1024%2C761&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=768%2C571&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><figcaption class=\"wp-element-caption\"><em>Konvergentn\u00ed <em>flat <\/em>rovnov\u00e1ha sil<\/em><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1217\" height=\"890\" data-attachment-id=\"2952\" data-permalink=\"https:\/\/solveredu.com\/cs\/zad1_en\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?fit=1217%2C890&amp;ssl=1\" data-orig-size=\"1217,890\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"zad1_en\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?fit=1024%2C749&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=1217%2C890&#038;ssl=1\" alt=\"Jak\u00fdkoli syst\u00e9m sil, uk\u00e1zkov\u00e1 \u00faloha, Solveredu\" class=\"wp-image-2952\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?w=1217&amp;ssl=1 1217w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=300%2C219&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=1024%2C749&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=768%2C562&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad1_en.jpg?resize=16%2C12&amp;ssl=1 16w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><figcaption class=\"wp-element-caption\"><em>Jak\u00e1koli plo\u0161n\u00e1 soustava sil<\/em><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0158e\u0161en\u00ed \u00faloh rovinn\u00fdch silov\u00fdch soustav m\u016f\u017eete tr\u00e9novat v m\u00e9m bezplatn\u00e9m n\u00e1stroji <a href=\"https:\/\/solveredu.com\/cs\/kalkulator-plaskiego-ukladu-sil\/\" data-type=\"page\" data-id=\"2945\"><strong>Kalkula\u010dka plo\u0161n\u00e9 s\u00edly <\/strong><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00fd\u0161e uveden\u00e9 p\u0159\u00edklady jsou vytvo\u0159eny v tomto programu pro \u0159e\u0161en\u00ed rovinn\u00fdch silov\u00fdch soustav, kde lze vypo\u010d\u00edtat v\u00fdslednici a hlavn\u00ed moment silov\u00e9 soustavy.<\/p>","protected":false},"excerpt":{"rendered":"<p>Jak przesta\u0107 walczy\u0107 z mechanik\u0105? Opanuj uk\u0142ady si\u0142 raz a dobrze! Studia techniczne to nieustanna walka z wektorami, a kolokwia z mechaniki potrafi\u0105 \u015bni\u0107 si\u0119 po nocach. Najwi\u0119kszy problem? Cz\u0119sto mylimy typy uk\u0142ad\u00f3w si\u0142, co prowadzi do b\u0142\u0119dnych r\u00f3wna\u0144 ju\u017c na starcie. Dzi\u015b rozbijemy to na czynniki pierwsze i poka\u017cemy Ci, jak u\u0142atwi\u0107 sobie \u017cycie. [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":2953,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[14815,14816],"tags":[14846,14820,14845,14847],"class_list":["post-3192","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","category-wytrzymalosc-materialow","tag-belka-swobodnie-podparta","tag-rownania-rownowagi","tag-reakcje-podporowe","tag-stateczna-wyznaczalnosc"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2025\/11\/zad2_en.jpg?fit=1215%2C903&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-Pu","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/3192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/comments?post=3192"}],"version-history":[{"count":16,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/3192\/revisions"}],"predecessor-version":[{"id":3232,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/posts\/3192\/revisions\/3232"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media\/2953"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/media?parent=3192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/categories?post=3192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/cs\/wp-json\/wp\/v2\/tags?post=3192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}