{"id":1865,"date":"2022-12-22T17:00:00","date_gmt":"2022-12-22T16:00:00","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=1865"},"modified":"2022-12-21T16:45:51","modified_gmt":"2022-12-21T15:45:51","slug":"relativkinematik-eisenbahnkran","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/en\/2022\/12\/22\/relativkinematik-eisenbahnkran\/","title":{"rendered":"Relativkinematik: Eisenbahnkran"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wir hatten erst vor kurzem das fahrende Feuerwehrauto als Beispiel der Relativkinematik. Ein sehr \u00e4hnliches Beispiel wollen wir uns hier ansehen, n\u00e4mlich einen Eisenbahnkran mit folgender Angabe:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Der Eisenbahnkran lt. Skizze f\u00e4hrt mit der Geschwindigkeit v und der Beschleunigung a in Richtung der positiven y\u2212Achse, w\u00e4hrend der Ausleger sich mit der Winkelgeschwindigkeit \u03c9<sub>1<\/sub> und der Winkelbeschleunigung \u03c9\u02d9<sub>1<\/sub> um die z\u2212Achse dreht. Im gezeichneten Augenblick (Winkellage \u03b8) richtet sich der Ausleger mit konstanter Winkelgeschwindigkeit \u03b8\u02d9 auf. <br>Geg.: d = 3m, l = 20m, v = 2m\/s, a = 1.5m\/s\u00b2, \u03b8 = 30\u00b0, \u03c91 = 0.5 1\/s, \u03c9\u02d91 = 3 1\/s\u00b2, \u03b8\u02d9 = 3 1\/s <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bestimme Geschwindigkeit und Beschleunigung der Spitze B des Auslegers zum gezeichneten Zeitpunkt.<\/p>\n<cite>Quelle: Aufgabe 9.38 (S. xxx) aus Russell C. Hibbeler, Technische Mechanik 3 Dynamik, 12. Auflage, 2012 Pearson GmbH, M\u00fcnchen<\/cite><\/blockquote>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"566\" data-attachment-id=\"1867\" data-permalink=\"https:\/\/technischemechanik.com\/en\/2022\/12\/22\/relativkinematik-eisenbahnkran\/r13-neu\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?fit=968%2C770&amp;ssl=1\" data-orig-size=\"968,770\" 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=\"R13-neu\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?fit=712%2C566&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?resize=712%2C566&#038;ssl=1\" alt=\"\" class=\"wp-image-1867\" srcset=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?w=968&amp;ssl=1 968w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?resize=300%2C239&amp;ssl=1 300w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13-neu.jpg?resize=768%2C611&amp;ssl=1 768w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Hier wie gewohnt zuerst einmal die Angabe zum Download:<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/Relativkinetik_R13.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Relativkinetik_R13.\"><\/object><a id=\"wp-block-file--media-48c4727c-8c47-4f76-bf95-4e0c62853d74\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/Relativkinetik_R13.pdf\">Relativkinetik_R13<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/Relativkinetik_R13.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-48c4727c-8c47-4f76-bf95-4e0c62853d74\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Wir stellen bei diesem Beispiel einen Ortsvektor auf, der sich am analytischen Prinzip orientiert, d.h. vom Koordinatenursprung 0 bis zum Punkt B reicht. Nat\u00fcrlich l\u00e4sst sich die Rechnung auch aufsplitten in einen Teil 0-A sowie einen zweiten Teil A-B, aber aus meiner Sicht bietet der direkte Vektor den einfacheren Zugang. Danach m\u00fcssen wir nur noch Geschwindigkeit und Beschleunigung mittels der bekannten Formeln aus der Relativkinematik bestimmen und sind mit dem Beispiel auch schon fertig. Die genaue Erkl\u00e4rung dazu und auch eine kurze Diskussion \u00fcber die Praxisrelevanz solcher Berechnungen finden sich wie gewohnt im verlinkten Video! <\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-handler-einbetten wp-block-embed-handler-einbetten wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"712\" height=\"401\" src=\"https:\/\/www.youtube.com\/embed\/VBFMEaOnEO8?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-GB&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Den L\u00f6sungsweg in Form eines herunterladbaren pdf-Files findet ihr hier. <\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of R13.\"><\/object><a id=\"wp-block-file--media-48c4727c-8c47-4f76-bf95-4e0c62853d74\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13.pdf\">R13<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/R13.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-48c4727c-8c47-4f76-bf95-4e0c62853d74\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Bei Fragen oder Anmerkungen zu Beispiel oder Rechenweg bitte einfach hier oder auf YouTube einen Kommentar hinterlassen. Ich freue mich auf eure R\u00fcckmeldungen und beantworte gerne alle Fragen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hat euch das Video gefallen? Dann lasst bitte ein Like hier auf dem Blog und auf YouTube da. Abonniert auch unbedingt den Kanal um kein Video mehr zu verpassen. Vielen Dank!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bis bald,<br>Markus <\/p>\n\n\n<div class=\"crowdsignal-feedback-wrapper\" data-crowdsignal-feedback=\"{&quot;feedbackPlaceholder&quot;:&quot;Sag mir bitte was dir besonders gefallen hat und was ich verbessern soll! Vielen Dank!&quot;,&quot;submitText&quot;:&quot;Danke f\\u00fcr dein Feedback!&quot;,&quot;surveyId&quot;:2705235,&quot;title&quot;:&quot;Feedback&quot;,&quot;emailResponses&quot;:false,&quot;emailPlaceholder&quot;:&quot;Your Email&quot;,&quot;emailRequired&quot;:false,&quot;header&quot;:&quot;\\ud83d\\udc4b Hey there!&quot;,&quot;hideBranding&quot;:false,&quot;hideTriggerShadow&quot;:false,&quot;submitButtonLabel&quot;:&quot;Submit&quot;,&quot;toggleOn&quot;:&quot;click&quot;,&quot;triggerLabel&quot;:&quot;Feedback&quot;,&quot;x&quot;:&quot;left&quot;,&quot;y&quot;:&quot;bottom&quot;,&quot;status&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;nonce&quot;:&quot;77006c9619&quot;}\"><\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-vote-wrapper\" data-crowdsignal-vote=\"{&quot;pollId&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;,&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;hideBranding&quot;:false,&quot;pollStatus&quot;:&quot;open&quot;,&quot;size&quot;:&quot;medium&quot;,&quot;borderWidth&quot;:1,&quot;borderRadius&quot;:5,&quot;hideResults&quot;:false,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11269788,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;up&quot;,&quot;id&quot;:51460628,&quot;client_id&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;},{&quot;answer_text&quot;:&quot;down&quot;,&quot;id&quot;:51460629,&quot;client_id&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;}}\">\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;,&quot;type&quot;:&quot;up&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;,&quot;type&quot;:&quot;down&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-applause-wrapper\" data-crowdsignal-applause=\"{&quot;pollId&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;,&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;answerId&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;,&quot;hideBranding&quot;:false,&quot;size&quot;:&quot;medium&quot;,&quot;pollStatus&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11269789,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;clap&quot;,&quot;id&quot;:51460630,&quot;client_id&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;}}\"><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Herzlich Willkommen! Wir hatten erst vor kurzem das fahrende Feuerwehrauto als Beispiel der Relativkinematik. Ein sehr \u00e4hnliches Beispiel wollen wir uns hier ansehen, n\u00e4mlich einen Eisenbahnkran mit folgender Angabe: Der Eisenbahnkran lt. Skizze f\u00e4hrt mit der Geschwindigkeit v und der Beschleunigung a in Richtung der positiven y\u2212Achse, w\u00e4hrend der Ausleger sich mit der Winkelgeschwindigkeit \u03c91 &hellip; <a href=\"https:\/\/technischemechanik.com\/en\/2022\/12\/22\/relativkinematik-eisenbahnkran\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Relativkinematik: Eisenbahnkran<\/span><\/a><\/p>","protected":false},"author":110396568,"featured_media":1872,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":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},"jetpack_post_was_ever_published":false},"categories":[2602546,1145536,727213054],"tags":[25466,2245662,7978,750913297,14741952,100678,35890,750913306,350894,166867,5481156,911145,113216,19668,8207,5685069,662707,21322,720191,1213491,143003,10126,67765249,73726871,727213065,727213063,750913305,161115,750913295,2411,1121513,727213064,82782145,4159057,13416281,1097356,2722,33601,202894,1268153],"class_list":["post-1865","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ubungsaufgaben","category-dynamik","category-relativkinetik","tag-beispiel","tag-beschleunigung","tag-bildung","tag-dynamik","tag-einfach-erklart","tag-einfuhrung","tag-featured","tag-freikorperbild","tag-grundlagen","tag-hochschule","tag-kinetik","tag-klausur","tag-kraft","tag-lehrer","tag-lernen","tag-lernhilfe","tag-maschinenbau","tag-mathematik","tag-mechanik","tag-nachhilfe","tag-newton","tag-physik","tag-physik-grundlagen","tag-physik-nachhilfe","tag-relative-kinetics","tag-relativkinematik","tag-relativkinetik","tag-screencast","tag-statik","tag-studium","tag-technische-mechanik","tag-technische-mechanik-1","tag-technische-mechanik-3","tag-the-mechanik","tag-tm-3","tag-tm1","tag-uni","tag-universitat","tag-vektoren","tag-verstehen"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/12\/Relativkinetik-R13.png?fit=1280%2C720&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-u5","jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1865","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/users\/110396568"}],"replies":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/comments?post=1865"}],"version-history":[{"count":3,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1865\/revisions"}],"predecessor-version":[{"id":1871,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1865\/revisions\/1871"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media\/1872"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media?parent=1865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/categories?post=1865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/tags?post=1865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}