{"id":1805,"date":"2022-11-24T17:00:00","date_gmt":"2022-11-24T16:00:00","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=1805"},"modified":"2022-11-24T15:42:13","modified_gmt":"2022-11-24T14:42:13","slug":"stoss-projektil-trifft-auf-scheibe","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/en\/2022\/11\/24\/stoss-projektil-trifft-auf-scheibe\/","title":{"rendered":"Sto\u00df: Projektil trifft auf Scheibe"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wir widmen uns wieder einem Sto\u00dfbeispiel. Dieses Mal geht es um ein Projektil das auf eine aufgeh\u00e4ngte Scheibe auftrifft und in diese eindringt. <\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Ein Projektil der Masse m<sub>P<\/sub> dringt mit der Geschwindigkeit v<sub>P<\/sub> in die Mantelfl\u00e4che einer Scheibe der Masse m<sub>S<\/sub> unter dem Winkel \u03b1 zur Horizontalen ein. Unmittelbar vor dem Sto\u00df befindet sich die Scheibe in Ruhe. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Geg.: m<sub>P<\/sub> = 7g, m<sub>S<\/sub> = 5kg, v<sub>P<\/sub> = 800m\/s, r = 0.2m, \u03b1 = 30\u00b0 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ges.: <br>*die Winkelgeschwindigkeit \u03c9\u2032<sub>S<\/sub> der Scheibe unmittelbar nach dem Eindringen des Projektils. <br>*der Winkel \u03b8 um den die Scheibe schwingt bis sie ihren Umkehrpunkt erreicht hat.<\/p>\n<cite>Quelle: Aufgabe x.x (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 is-style-default\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"623\" height=\"414\" data-attachment-id=\"1806\" data-permalink=\"https:\/\/technischemechanik.com\/en\/2022\/11\/24\/stoss-projektil-trifft-auf-scheibe\/stoss_2015_06_11\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss_2015_06_11.jpg?fit=623%2C414&amp;ssl=1\" data-orig-size=\"623,414\" 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=\"Stoss_2015_06_11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss_2015_06_11.jpg?fit=623%2C414&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss_2015_06_11.jpg?resize=623%2C414&#038;ssl=1\" alt=\"\" class=\"wp-image-1806\" srcset=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss_2015_06_11.jpg?w=623&amp;ssl=1 623w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss_2015_06_11.jpg?resize=300%2C199&amp;ssl=1 300w\" sizes=\"auto, (max-width: 623px) 100vw, 623px\" \/><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Die Angabe gibt es wie gewohnt auch 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\/11\/Stoss-S22.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stoss-S22.\"><\/object><a id=\"wp-block-file--media-4e5714be-99df-4f5e-81ca-014eebd2dbbe\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss-S22.pdf\">Stoss-S22<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss-S22.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4e5714be-99df-4f5e-81ca-014eebd2dbbe\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In diesem Fall bevorzuge ich die Zerlegung des Systems in Projektil und Scheibe und die Einf\u00fchrung eines inneren Sto\u00dfantriebs. So k\u00f6nnen wir einen Impulssatz f\u00fcr das Projektil anschreiben, das wir als Punktmasse betrachten d\u00fcrfen. Andererseits l\u00e4sst sich f\u00fcr die Scheibe ein Drehimpulssatz um das Lager aufstellen. Zus\u00e4tzlich ben\u00f6tigen wir nat\u00fcrlich noch eine kinematische Bedingungen. Diese ist hier jene des rauen Sto\u00dfes, also gleiche Geschwindigkeitsvektoren von Projektil und Eindringpunkt unmittelbar nach dem Sto\u00dfvorgang. Damit l\u00e4sst sich dann die Winkelgeschwindigkeit der Scheibe bestimmen. Schlie\u00dflich k\u00f6nnen wir \u00fcber eine einfach Energiebetrachtung noch den Umkehrpunkt der Schwingung bestimmen. Wie das geht besprechen wir im verlinkten Video im Detail. Viel Spa\u00df damit!<\/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\/-h_EJMvV224?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\">Wie auch schon die letzten Male stelle ich zus\u00e4tzlich wieder ein pdf mit dem vollst\u00e4ndigen L\u00f6sungsweg zur Verf\u00fcgung. <\/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\/11\/S22.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of S22.\"><\/object><a id=\"wp-block-file--media-4e5714be-99df-4f5e-81ca-014eebd2dbbe\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/S22.pdf\">S22<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/S22.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4e5714be-99df-4f5e-81ca-014eebd2dbbe\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Bei Fragen k\u00f6nnt ihr jederzeit gerne entweder hier oder auf YouTube einen Kommentar hinterlassen. Ich werde alle Kommentare wie immer schnellstm\u00f6glich beantworten. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hat euch das Beispiel und die Erkl\u00e4rung dazu gefallen? Dann lasst bitte auch ein Like auf YouTube da und abonniert diesen Blog. Abonniert auch unbedingt den YouTube Kanal um kein Video mehr zu verpassen und empfehlt mich gerne weiter. Vielen herzlichen Dank!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bis bald mit dem n\u00e4chsten Beispiel,<br>Markus <\/p>\n\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\"><div class=\"crowdsignal-vote-wrapper\" data-crowdsignal-vote=\"{&quot;pollId&quot;:&quot;455b5e0c-f331-43d3-a592-cc8d4f4d6034&quot;,&quot;title&quot;:&quot;Unbenannte Abstimmung&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;:11248173,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannte Abstimmung&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;:51387767,&quot;client_id&quot;:&quot;d5667f32-027e-4631-be77-a98f311ddd25&quot;},{&quot;answer_text&quot;:&quot;down&quot;,&quot;id&quot;:51387768,&quot;client_id&quot;:&quot;65db896a-3d1c-4cf4-90e9-efbc5b828961&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;455b5e0c-f331-43d3-a592-cc8d4f4d6034&quot;}}\">\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;d5667f32-027e-4631-be77-a98f311ddd25&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;65db896a-3d1c-4cf4-90e9-efbc5b828961&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\"><div class=\"crowdsignal-applause-wrapper\" data-crowdsignal-applause=\"{&quot;pollId&quot;:&quot;c0b767e1-47b5-4dc0-a3d5-76f3bacda917&quot;,&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;answerId&quot;:&quot;e8a232bc-57f1-4fa4-8c99-4926af8f11b8&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;:11248174,&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;:51387769,&quot;client_id&quot;:&quot;e8a232bc-57f1-4fa4-8c99-4926af8f11b8&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;c0b767e1-47b5-4dc0-a3d5-76f3bacda917&quot;}}\"><\/div><\/div>\n<\/div>\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;:2707661,&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;emailResponses&quot;:true,&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>","protected":false},"excerpt":{"rendered":"<p>Herzlich Willkommen! Wir widmen uns wieder einem Sto\u00dfbeispiel. Dieses Mal geht es um ein Projektil das auf eine aufgeh\u00e4ngte Scheibe auftrifft und in diese eindringt. Ein Projektil der Masse mP dringt mit der Geschwindigkeit vP in die Mantelfl\u00e4che einer Scheibe der Masse mS unter dem Winkel \u03b1 zur Horizontalen ein. Unmittelbar vor dem Sto\u00df befindet &hellip; <a href=\"https:\/\/technischemechanik.com\/en\/2022\/11\/24\/stoss-projektil-trifft-auf-scheibe\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Sto\u00df: Projektil trifft auf Scheibe<\/span><\/a><\/p>","protected":false},"author":110396568,"featured_media":1815,"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":[2602546,1145536,2552358],"tags":[129538,25466,2245662,750913297,14741952,35890,350894,166867,47541,22094049,911145,569973948,4288685,122966141,1488390,947685,5685069,775366,662707,720191,1213491,9160793,10126,67765249,73726871,27746161,161115,301853,750913300,172005,2411,122145655,1121513,727213064,82782145,2326513,2121286,2722,462567],"class_list":["post-1805","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ubungsaufgaben","category-dynamik","category-stos","tag-aufgabe","tag-beispiel","tag-beschleunigung","tag-dynamik","tag-einfach-erklart","tag-featured","tag-grundlagen","tag-hochschule","tag-impact","tag-kinetische-energie","tag-klausur","tag-klausuraufgabe","tag-klausurvorbereitung","tag-koordinatentransformation","tag-kugel","tag-losung","tag-lernhilfe","tag-maschine","tag-maschinenbau","tag-mechanik","tag-nachhilfe","tag-onlinekurs","tag-physik","tag-physik-grundlagen","tag-physik-nachhilfe","tag-potentielle-energie","tag-screencast","tag-stab","tag-stos","tag-studieren","tag-studium","tag-studyhelp","tag-technische-mechanik","tag-technische-mechanik-1","tag-technische-mechanik-3","tag-tm-1","tag-tutorium","tag-uni","tag-wiederholung"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2022\/11\/Stoss-S22.png?fit=1280%2C720&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-t7","jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1805","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=1805"}],"version-history":[{"count":7,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1805\/revisions"}],"predecessor-version":[{"id":1816,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1805\/revisions\/1816"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media\/1815"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media?parent=1805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/categories?post=1805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/tags?post=1805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}