{"id":40186,"date":"2025-06-27T14:20:27","date_gmt":"2025-06-27T14:20:27","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40186"},"modified":"2025-06-27T14:20:29","modified_gmt":"2025-06-27T14:20:29","slug":"a-4600-kg-helicopter-accelerates-upward-at-2-0-mls","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-4600-kg-helicopter-accelerates-upward-at-2-0-mls\/","title":{"rendered":"A 4600 kg helicopter accelerates upward at 2.0 mls&#8221;"},"content":{"rendered":"\n<p>A 4600 kg helicopter accelerates upward at 2.0 mls&#8221; _ Determine the lift force exerted on the propellers by the air: Make quantitative force diagram: Write net force equation for the axis along which forces are not balanced: The maximum force that grocery bag can withstand without ripping is 250 N. Suppose that the bag is filled with 20 kg of groceries and lifted with an acceleration of 5.0 m\/s? Do the groceries stay in the bag? Make # quantitative force diagram. Write net force equation for the axis along which forces are not balanced<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 1: Helicopter Lift Force Calculation<\/h3>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass of helicopter, <em>m<\/em> = 4600 kg<\/li>\n\n\n\n<li>Acceleration upward, <em>a<\/em> = 2.0 m\/s\u00b2<\/li>\n\n\n\n<li>Gravitational force, <em>Fg<\/em> = <em>m \u00d7 g<\/em> = 4600 kg \u00d7 9.8 m\/s\u00b2 = 45,080 N<\/li>\n<\/ul>\n\n\n\n<p><strong>Quantitative Force Diagram:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Upward Force:<\/strong> Lift Force (<em>FL<\/em>)<\/li>\n\n\n\n<li><strong>Downward Force:<\/strong> Gravitational Force (<em>Fg<\/em>)<\/li>\n<\/ul>\n\n\n\n<p><strong>Net Force Equation (Vertical Axis):<\/strong><br>\u2211F = FL &#8211; Fg = m \u00d7 a<\/p>\n\n\n\n<p><strong>Substitute known values:<\/strong><br>FL &#8211; 45,080 N = 4600 kg \u00d7 2.0 m\/s\u00b2<br>FL &#8211; 45,080 N = 9,200 N<br>FL = 9,200 N + 45,080 N = <strong>54,280 N<\/strong><\/p>\n\n\n\n<p><strong>Lift Force Exerted:<\/strong> <strong>54,280 N upward<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Part 2: Grocery Bag Problem<\/h3>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Maximum force bag can withstand = 250 N<\/li>\n\n\n\n<li>Mass of groceries, <em>m<\/em> = 20 kg<\/li>\n\n\n\n<li>Acceleration upward, <em>a<\/em> = 5.0 m\/s\u00b2<\/li>\n\n\n\n<li>Gravitational force, <em>Fg<\/em> = <em>m \u00d7 g<\/em> = 20 kg \u00d7 9.8 m\/s\u00b2 = 196 N<\/li>\n<\/ul>\n\n\n\n<p><strong>Quantitative Force Diagram:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Upward Force:<\/strong> Tension in the bag (<em>T<\/em>)<\/li>\n\n\n\n<li><strong>Downward Force:<\/strong> Gravitational Force (<em>Fg<\/em>)<\/li>\n<\/ul>\n\n\n\n<p><strong>Net Force Equation (Vertical Axis):<\/strong><br>\u2211F = T &#8211; Fg = m \u00d7 a<\/p>\n\n\n\n<p><strong>Substitute known values:<\/strong><br>T &#8211; 196 N = 20 kg \u00d7 5.0 m\/s\u00b2<br>T &#8211; 196 N = 100 N<br>T = 100 N + 196 N = <strong>296 N<\/strong><\/p>\n\n\n\n<p><strong>Analysis:<\/strong><br>The tension required to lift the groceries with the given acceleration is <strong>296 N<\/strong>, but the bag can only withstand <strong>250 N<\/strong>. Therefore, the groceries <strong>do not stay in the bag<\/strong>, the bag will rip.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>For the helicopter, the total lift force must overcome both the gravitational pull and provide additional force for upward acceleration. By using Newton&#8217;s Second Law (F = ma), we combine gravitational force with the force due to acceleration to find the total lift.<\/p>\n\n\n\n<p>Similarly, in the grocery bag scenario, the bag not only has to support the weight of the groceries but also provide extra force for the upward acceleration. The required tension exceeds the bag&#8217;s maximum limit, so the bag fails. Quantitative force diagrams help visualize these situations by clearly representing all acting forces, allowing for precise application of Newton&#8217;s laws to solve for unknown quantities.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1236.jpeg\" alt=\"\" class=\"wp-image-40187\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1236.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1236-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1236-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A 4600 kg helicopter accelerates upward at 2.0 mls&#8221; _ Determine the lift force exerted on the propellers by the air: Make quantitative force diagram: Write net force equation for the axis along which forces are not balanced: The maximum force that grocery bag can withstand without ripping is 250 N. Suppose that the bag [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-40186","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=40186"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40186\/revisions"}],"predecessor-version":[{"id":40188,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40186\/revisions\/40188"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}