{"id":188450,"date":"2025-02-07T04:00:56","date_gmt":"2025-02-07T04:00:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188450"},"modified":"2025-02-07T04:00:58","modified_gmt":"2025-02-07T04:00:58","slug":"on-a-certain-mill-the-rolling-load-for-a-30-percent-reduction-is-7-6-kn-mm-of-width","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/07\/on-a-certain-mill-the-rolling-load-for-a-30-percent-reduction-is-7-6-kn-mm-of-width\/","title":{"rendered":"On a certain mill the rolling load for a 30 percent reduction is 7.6 kN\/mm of width"},"content":{"rendered":"\n<p>On a certain mill the rolling load for a 30 percent reduction is 7.6 kN\/mm of width. What is the rolling load when a back tension of 150 MPa and a front tension of 120 MPa are applied? Assume that S 500 MPa.<\/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 this problem, we can use the relationship between rolling load, tension, and reduction in width. The formula for the rolling load is:<\/p>\n\n\n\n<p>[<br>P = \\sigma \\cdot A<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( P ) is the rolling load<\/li>\n\n\n\n<li>( \\sigma ) is the average flow stress, which is the average of the back and front tension in this case<\/li>\n\n\n\n<li>( A ) is the contact area (width of the mill and reduction in thickness)<\/li>\n<\/ul>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rolling load for 30% reduction is ( 7.6 \\, \\text{kN\/mm of width} )<\/li>\n\n\n\n<li>Back tension = 150 MPa<\/li>\n\n\n\n<li>Front tension = 120 MPa<\/li>\n\n\n\n<li>Material yield stress ( S ) = 500 MPa<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine the average flow stress<\/h3>\n\n\n\n<p>The flow stress is the average of the back and front tension:<\/p>\n\n\n\n<p>[<br>\\sigma = \\frac{\\text{Back Tension} + \\text{Front Tension}}{2} = \\frac{150 \\, \\text{MPa} + 120 \\, \\text{MPa}}{2} = 135 \\, \\text{MPa}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the relationship between rolling load and tension<\/h3>\n\n\n\n<p>The rolling load is proportional to the tension and width of the mill. Since we know the rolling load for a 30% reduction is 7.6 kN\/mm of width, we can calculate the rolling load for the given tension values by scaling accordingly. The stress ( \\sigma ) affects the rolling load in proportion to its value relative to the yield stress ( S ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the new rolling load<\/h3>\n\n\n\n<p>Since the back and front tension are now 135 MPa on average, which is less than the material&#8217;s yield stress (500 MPa), the rolling load will adjust proportionally. The proportional factor is the ratio of the average flow stress to the material&#8217;s yield stress:<\/p>\n\n\n\n<p>[<br>\\text{Proportional Factor} = \\frac{\\sigma}{S} = \\frac{135}{500} = 0.27<br>]<\/p>\n\n\n\n<p>Now, we calculate the new rolling load by multiplying the given rolling load by this proportional factor:<\/p>\n\n\n\n<p>[<br>P_{\\text{new}} = 7.6 \\, \\text{kN\/mm} \\times 0.27 = 2.05 \\, \\text{kN\/mm of width}<br>]<\/p>\n\n\n\n<p>Thus, the rolling load when a back tension of 150 MPa and a front tension of 120 MPa are applied is approximately <strong>2.05 kN\/mm of width<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>On a certain mill the rolling load for a 30 percent reduction is 7.6 kN\/mm of width. What is the rolling load when a back tension of 150 MPa and a front tension of 120 MPa are applied? Assume that S 500 MPa. The Correct Answer and Explanation is : To solve this problem, we [&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-188450","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188450","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=188450"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188450\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}