{"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":"kesisen-kuvvetler-vs-kesismeyen-kuvvet-sistemleri","status":"publish","type":"post","link":"https:\/\/solveredu.com\/tr\/post\/zbiezny-vs-dowolny-rozbiezny-uklad-sil\/","title":{"rendered":"Yak\u0131nsak ve Iraksak (Divergent) kuvvetler sistemi - Farkl\u0131l\u0131klar ve hesaplama y\u00f6ntemleri"},"content":{"rendered":"<h2 class=\"wp-block-heading has-medium-font-size\">Mekanikle sava\u015fmay\u0131 nas\u0131l b\u0131rak\u0131rs\u0131n\u0131z? G\u00fc\u00e7 sistemlerinde bir kez ve herkes i\u00e7in ustala\u015f\u0131n!<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">M\u00fchendislik okumak vekt\u00f6rlerle s\u00fcrekli bir sava\u015f halidir ve mekanik kolokyumlar\u0131 bir kabus olabilir. En b\u00fcy\u00fck sorun nedir? Genellikle kuvvet sistemlerinin t\u00fcrlerini kar\u0131\u015ft\u0131r\u0131r\u0131z ve bu da en ba\u015f\u0131ndan yanl\u0131\u015f denklemlere yol a\u00e7ar. Bug\u00fcn, bunu \u00e7\u00f6zece\u011fiz ve i\u015fleri kendiniz i\u00e7in nas\u0131l kolayla\u015ft\u0131raca\u011f\u0131n\u0131z\u0131 g\u00f6sterece\u011fiz.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"#zbiezny\"><strong>Yak\u0131nsak m\u0131 yoksa keyfi mi? \u0130kisi aras\u0131nda ayr\u0131m yapmal\u0131s\u0131n\u0131z!<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#warunki\"><strong>Denge ko\u015fullar\u0131 - fark nerede?<\/strong><\/a><\/li>\n\n\n\n<li><a href=\"#przykladowe\"><strong>G\u00f6rev \u00f6rnekleri<\/strong><\/a><\/li>\n<\/ol>\n\n\n\n<h3 id=\"zbiezny\" class=\"wp-block-heading\">1. Yak\u0131nsak m\u0131 yoksa keyfi mi? \u0130kisi aras\u0131nda ayr\u0131m yapman\u0131z gerekir!<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Hesaplamalara ge\u00e7meden \u00f6nce sisteminizi do\u011fru bir \u015fekilde s\u0131n\u0131fland\u0131rman\u0131z gerekir. Bu, ka\u00e7 denklem yazman\u0131z gerekti\u011fini ve sayma anlar\u0131yla kar\u015f\u0131 kar\u015f\u0131ya kal\u0131p kalmayaca\u011f\u0131n\u0131z\u0131 belirleyecektir.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Yak\u0131nsayan g\u00fc\u00e7 sistemleri:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D\u00fcz yak\u0131nsak kuvvet sistemi<\/strong> - Mekanikte, d\u00fczlemsel bir yak\u0131nsak kuvvet sistemi, t\u00fcm kuvvet vekt\u00f6rlerinin ayn\u0131 y\u00f6nde hareket etti\u011fi bir sistemdir. <strong>bir u\u00e7ak<\/strong>, ve \u00e7izgileri (y\u00f6nleri) tam olarak \u015fu noktada kesi\u015fir <strong>bir nokta<\/strong>. Her bir kafes kiri\u015f d\u00fc\u011f\u00fcm\u00fc, tam olarak yak\u0131nsak kuvvetlerin d\u00fczlemsel bir sistemi olarak kabul edilir<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Birle\u015ftirici g\u00fc\u00e7lerin mekansal d\u00fczenlemesi<\/strong> - Rijit bir cisme uygulanan ve etki y\u00f6nleri a\u015fa\u011f\u0131daki noktalarda kesi\u015fen kuvvetler sistemi <strong>bir nokta<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Keyfi (\u0131raksak) kuvvetlerin d\u00fczenlemeleri:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>G\u00fc\u00e7lerin da\u011f\u0131n\u0131k oldu\u011fu bir durumdur. Hareket hatlar\u0131n\u0131n tek bir temas noktas\u0131 yoktur. B\u00f6yle bir sistem v\u00fccudu sadece yukar\u0131, a\u015fa\u011f\u0131 veya yanlara do\u011fru hareket ettirmekle kalmaz, her \u015feyden \u00f6nce - -. <strong>bir ciroya neden olabilir<\/strong>. B\u00f6yle bir sistem, t\u00fcm kuvvetlerin tek bir d\u00fczlemde yer ald\u0131\u011f\u0131 d\u00fczlemsel veya kuvvetlerin farkl\u0131 d\u00fczlemlerde yer ald\u0131\u011f\u0131 uzaysal olabilir.<\/li>\n<\/ul>\n\n\n\n<h3 id=\"warunki\" class=\"wp-block-heading\">2 Denge ko\u015fullar\u0131 - fark nerede?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Hangi sistemle u\u011fra\u015ft\u0131\u011f\u0131n\u0131za ba\u011fl\u0131 olarak, uygun say\u0131da denklem yazman\u0131z gerekir. Yak\u0131nsak bir kuvvet sistemi, e\u011fer kuvvet vekt\u00f6rleri bir <strong>kapal\u0131 \u00e7okgen<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><td><strong>\u00d6zellik<\/strong><\/td><td><strong>Birle\u015fik sistem<\/strong><\/td><td><strong>Herhangi Bir D\u00fczenleme<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>D\u00fcz<\/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>Mek\u00e2nsal<\/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\">D\u00fczlemsel keyfi bir sistemde, \u00fc\u00e7\u00fcnc\u00fc bir denklem devreye girer - se\u00e7ilen bir noktaya g\u00f6re momentlerin toplam\u0131. Momentin y\u00f6n\u00fcn\u00fc ya da kuvvetin kolunu unutarak en \u00e7ok hata yapt\u0131\u011f\u0131m\u0131z yer buras\u0131d\u0131r.<\/p>\n\n\n\n<h4 id=\"przykladowe\" class=\"wp-block-heading\">3 \u00d6rnek g\u00f6revler<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A\u015fa\u011f\u0131da, yak\u0131nsayan kuvvetler sistemine sahip bir g\u00f6rev \u00f6rne\u011fi bulacaks\u0131n\u0131z.<\/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\/tr\/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=\"Yak\u0131nsak g\u00fc\u00e7ler sistemi, \u00f6rnek g\u00f6rev, 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>Yak\u0131nsak <em>d\u00fcz <\/em>g\u00fc\u00e7 dengesi<\/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\/tr\/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=\"Herhangi bir kuvvet sistemi, \u00f6rnek g\u00f6rev, 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>Herhangi bir d\u00fcz kuvvet sistemi<\/em><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">D\u00fczlem kuvvet sistemlerinin g\u00f6revlerine y\u00f6nelik \u00e7\u00f6z\u00fcmleri \u00fccretsiz arac\u0131mda e\u011fitebilirsiniz <a href=\"https:\/\/solveredu.com\/tr\/duzlemsel-kuvvet-sistemi-hesaplayici\/\" data-type=\"page\" data-id=\"2945\"><strong>D\u00fcz Kuvvet Hesaplay\u0131c\u0131 <\/strong><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Yukar\u0131da g\u00f6sterilen \u00f6rnekler, bir kuvvet sisteminin bile\u015fke ve asal momentinin hesaplanabildi\u011fi d\u00fczlemsel kuvvet sistemlerinin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in bu programda olu\u015fturulmu\u015ftur.<\/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_post_was_ever_published":false,"_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},"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\/tr\/wp-json\/wp\/v2\/posts\/3192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/comments?post=3192"}],"version-history":[{"count":16,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/3192\/revisions"}],"predecessor-version":[{"id":3232,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/posts\/3192\/revisions\/3232"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media\/2953"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/media?parent=3192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/categories?post=3192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/tr\/wp-json\/wp\/v2\/tags?post=3192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}