{"id":195529,"date":"2025-02-28T12:03:50","date_gmt":"2025-02-28T12:03:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195529"},"modified":"2025-02-28T12:03:52","modified_gmt":"2025-02-28T12:03:52","slug":"a-war-wolf-or-trebuchet-is-a-device-used-during-the-middle-ages-to-throw-rocks-at-castles-and-now-sometimes-used-to-fling-large-vegetables-and-pianos-as-a-sport","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/a-war-wolf-or-trebuchet-is-a-device-used-during-the-middle-ages-to-throw-rocks-at-castles-and-now-sometimes-used-to-fling-large-vegetables-and-pianos-as-a-sport\/","title":{"rendered":"A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport"},"content":{"rendered":"\n<p>A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d 2.75 m long o ning particles of mass m1 0.115 kg and m2 58.5 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 12.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation. nI (a) Find the maximum speed that the small-mass object attains when it leaves the trebuchet horizontally. 33.8 Your response differs from the correct answer by more than 10%. Double check your calculations.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve for the maximum speed of the small mass ( m_1 ) when the trebuchet is released from the horizontal position, we use energy conservation principles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given Data:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( d = 2.75 ) m (total length of the trebuchet arm)<\/li>\n\n\n\n<li>( m_1 = 0.115 ) kg (small mass)<\/li>\n\n\n\n<li>( m_2 = 58.5 ) kg (large mass)<\/li>\n\n\n\n<li>Pivot is located ( d_p = 12.0 ) cm = 0.12 m from ( m_2 )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine Distances from the Pivot<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Distance of ( m_1 ) from pivot:<br>[<br>r_1 = d &#8211; d_p = 2.75 &#8211; 0.12 = 2.63 \\text{ m}<br>]<\/li>\n\n\n\n<li>Distance of ( m_2 ) from pivot:<br>[<br>r_2 = d_p = 0.12 \\text{ m}<br>]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Compute Initial Potential Energy<\/h3>\n\n\n\n<p>Potential energy is taken relative to the lowest point of rotation. In the initial horizontal position:<\/p>\n\n\n\n<p>[<br>PE_{\\text{initial}} = m_1 g r_1 + m_2 g r_2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Compute Final Potential Energy<\/h3>\n\n\n\n<p>At the lowest point:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( m_1 ) moves to ( r_1 ) below the pivot.<\/li>\n\n\n\n<li>( m_2 ) moves to ( r_2 ) above the pivot.<\/li>\n<\/ul>\n\n\n\n<p>[<br>PE_{\\text{final}} = &#8211; m_1 g r_1 + m_2 g r_2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Apply Energy Conservation<\/h3>\n\n\n\n<p>Total mechanical energy is conserved:<\/p>\n\n\n\n<p>[<br>KE_{\\text{final}} + PE_{\\text{final}} = PE_{\\text{initial}}<br>]<\/p>\n\n\n\n<p>The kinetic energy of the system is rotational:<\/p>\n\n\n\n<p>[<br>KE = \\frac{1}{2} I \\omega^2<br>]<\/p>\n\n\n\n<p>where ( I ) is the moment of inertia:<\/p>\n\n\n\n<p>[<br>I = m_1 r_1^2 + m_2 r_2^2<br>]<\/p>\n\n\n\n<p>[<br>I = (0.115)(2.63)^2 + (58.5)(0.12)^2<br>]<\/p>\n\n\n\n<p>[<br>I = 0.791 + 0.843 = 1.634 \\text{ kg} \\cdot \\text{m}^2<br>]<\/p>\n\n\n\n<p>Solving for ( \\omega ):<\/p>\n\n\n\n<p>[<br>m_1 g r_1 + m_2 g r_2 = \\frac{1}{2} I \\omega^2 + (- m_1 g r_1 + m_2 g r_2)<br>]<\/p>\n\n\n\n<p>[<br>2 m_1 g r_1 = \\frac{1}{2} I \\omega^2<br>]<\/p>\n\n\n\n<p>[<br>\\omega = \\sqrt{\\frac{4 m_1 g r_1}{I}}<br>]<\/p>\n\n\n\n<p>[<br>\\omega = \\sqrt{\\frac{4 (0.115)(9.81)(2.63)}{1.634}}<br>]<\/p>\n\n\n\n<p>[<br>\\omega = \\sqrt{7.723} = 2.78 \\text{ rad\/s}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Find the Maximum Speed<\/h3>\n\n\n\n<p>Velocity of ( m_1 ):<\/p>\n\n\n\n<p>[<br>v_1 = r_1 \\omega<br>]<\/p>\n\n\n\n<p>[<br>v_1 = (2.63)(2.78)<br>]<\/p>\n\n\n\n<p>[<br>v_1 = 7.31 \\text{ m\/s}<br>]<\/p>\n\n\n\n<p>Thus, the <strong>correct answer<\/strong> is:<\/p>\n\n\n\n<p>[<br>\\mathbf{7.31 \\text{ m\/s}}<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Now, let&#8217;s generate the image of the trebuchet.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1666.png\" alt=\"\" class=\"wp-image-195530\"\/><\/figure>\n\n\n\n<p>Here is the generated image of the trebuchet, illustrating the dimensions, pivot point, counterweight, and projectile. Let me know if you need any modifications or further explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d 2.75 m long o ning particles [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-195529","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195529","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=195529"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195529\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}