{"id":469,"date":"2025-02-13T19:45:16","date_gmt":"2025-02-13T19:45:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/physical-applications-apply-it\/"},"modified":"2025-02-13T19:45:16","modified_gmt":"2025-02-13T19:45:16","slug":"physical-applications-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/physical-applications-apply-it\/","title":{"raw":"Physical Applications: Apply It","rendered":"Physical Applications: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Calculate the mass of linear and circular objects using their density distributions<\/li>\n\t<li>Compute the work required in various situations, such as pumping fluids or moving objects along a path<\/li>\n\t<li>Determine the force exerted by water on a vertical surface underwater<\/li>\n<\/ul>\n<\/section>\n<h2>Applying Integration to Real-World Problems: Mass, Density, and Work<\/h2>\n<p>In this activity, we will explore the practical applications of integration in various real-world contexts. From calculating the total mass of objects with variable density to determining the work done by variable forces, integration provides a powerful tool for solving complex problems. These exercises will enhance your understanding of how integration is used in physics and engineering to solve practical problems.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288350[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288351[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288352[\/ohm_question]<\/p>\n<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the mass of linear and circular objects using their density distributions<\/li>\n<li>Compute the work required in various situations, such as pumping fluids or moving objects along a path<\/li>\n<li>Determine the force exerted by water on a vertical surface underwater<\/li>\n<\/ul>\n<\/section>\n<h2>Applying Integration to Real-World Problems: Mass, Density, and Work<\/h2>\n<p>In this activity, we will explore the practical applications of integration in various real-world contexts. From calculating the total mass of objects with variable density to determining the work done by variable forces, integration provides a powerful tool for solving complex problems. These exercises will enhance your understanding of how integration is used in physics and engineering to solve practical problems.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288350\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288350&theme=lumen&iframe_resize_id=ohm288350&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288351\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288351&theme=lumen&iframe_resize_id=ohm288351&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288352\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288352&theme=lumen&iframe_resize_id=ohm288352&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":6,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":450,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/469"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/469\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/450"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/469\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=469"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=469"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=469"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}