The force applied is directly proportional to the stretch of a coil. If a force of 132 Newtons stretches a coil 0.07 meters, what force would be needed to stretch a coil 0.1 meter? Round your answer to the nearest tenth.<\/p>\n\n\n\n
A.
92.4 Newtons<\/p>\n\n\n\n
B.
1885.7 Newtons<\/p>\n\n\n\n
C.
188.6 Newtons<\/p>\n\n\n\n
D.
136.0 Newtons<\/p>\n\n\n\n
The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the problem, we first need to understand the relationship between the force applied to a coil and its stretch, which is expressed mathematically as F=k\u22c5xF = k \\cdot xF=k\u22c5x, where FFF is the force, kkk is the spring constant (a measure of stiffness), and xxx is the stretch of the coil.<\/p>\n\n\n\n We are given that a force of 132 Newtons stretches the coil by 0.07 meters. We can use this information to find the spring constant kkk:k=Fx=132\u2009N0.07\u2009m\u22481885.71\u2009N\/mk = \\frac{F}{x} = \\frac{132 \\, \\text{N}}{0.07 \\, \\text{m}} \\approx 1885.71 \\, \\text{N\/m}k=xF\u200b=0.07m132N\u200b\u22481885.71N\/m<\/p>\n\n\n\n Now that we have the spring constant kkk, we can find the force required to stretch the coil 0.1 meters. Using the formula F=k\u22c5xF = k \\cdot xF=k\u22c5x, we can substitute xxx with 0.1 meters:F=1885.71\u2009N\/m\u22c50.1\u2009m\u2248188.57\u2009NF = 1885.71 \\, \\text{N\/m} \\cdot 0.1 \\, \\text{m} \\approx 188.57 \\, \\text{N}F=1885.71N\/m\u22c50.1m\u2248188.57N<\/p>\n\n\n\n Rounding this to the nearest tenth gives us:F\u2248188.6\u2009NF \\approx 188.6 \\, \\text{N}F\u2248188.6N<\/p>\n\n\n\n Now we can match our answer to the provided options. The correct answer is C. 188.6 Newtons<\/strong>.<\/p>\n\n\n\n This problem demonstrates the principle of Hooke’s Law, which states that the force required to extend or compress a spring is directly proportional to the distance it is stretched or compressed. The constant of proportionality, known as the spring constant, varies for different springs based on their material and construction.<\/p>\n\n\n\n In this situation, we first calculated the spring constant based on the initial force and stretch. After determining kkk, we could easily compute the force needed for a different stretch. This illustrates how physical systems can often be analyzed mathematically to predict behavior under different conditions, reinforcing the connection between theory and practical application in physics and engineering.<\/p>\n\n\n\n Understanding this relationship is essential in various fields, including mechanical engineering, physics, and materials science, where the properties of materials under stress are critical to design and functionality.<\/p>\n","protected":false},"excerpt":{"rendered":" The force applied is directly proportional to the stretch of a coil. If a force of 132 Newtons stretches a coil 0.07 meters, what force would be needed to stretch a coil 0.1 meter? Round your answer to the nearest tenth. A.92.4 Newtons B.1885.7 Newtons C.188.6 Newtons D.136.0 Newtons The Correct answer and Explanation is: […]<\/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-143130","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143130","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=143130"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143130\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=143130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=143130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=143130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n