A spring compresses in length by 0.14 in for every 1 lbf of applied force. Determine the mass of an object, in pounds mass, that causes a spring deflection of 1.8 in. The local acceleration of gravity 5 31 ft\/s2.<\/p>\n\n\n\n
At a certain elevation, the pilot of a balloon has a mass of 120 lb and a weight of 119 lbf. What is the local acceleration of gravity, in ft\/s2, at that elevation? If the balloon drifts to another elevation where g 5 32.05 ft\/s2, what is her weight, in lbf, and mass, in lb?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n A spring compresses 0.14 inches<\/strong> for every 1 lbf<\/strong> applied. To find the force required for a 1.8-inch<\/strong> deflection, we use:<\/p>\n\n\n\n [ Since weight (( W )) is related to mass (( m )) by gravity:<\/p>\n\n\n\n [ where ( g_{\\text{standard}} = 32.174 ) ft\/s\u00b2, and ( g_{\\text{local}} = 31 ) ft\/s\u00b2.<\/p>\n\n\n\n [ We know the pilot\u2019s mass is constant<\/strong> at 120 lbm<\/strong>. The weight equation:<\/p>\n\n\n\n [ Initially, the weight is 119 lbf<\/strong>, so we calculate the local gravity:<\/p>\n\n\n\n [ At the new elevation where ( g = 32.05 ) ft\/s\u00b2, the new weight is:<\/p>\n\n\n\n [ Thus, her weight increases slightly at the new elevation<\/strong>, but her mass remains the same<\/strong>.<\/p>\n\n\n\n These calculations demonstrate how weight varies with gravity, while mass remains constant.<\/p>\n","protected":false},"excerpt":{"rendered":" A spring compresses in length by 0.14 in for every 1 lbf of applied force. Determine the mass of an object, in pounds mass, that causes a spring deflection of 1.8 in. The local acceleration of gravity 5 31 ft\/s2. At a certain elevation, the pilot of a balloon has a mass of 120 lb […]<\/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-190939","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190939","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=190939"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190939\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Answers:<\/h3>\n\n\n\n
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\n\n\n\nExplanation:<\/h3>\n\n\n\n
Spring Problem<\/strong><\/h4>\n\n\n\n
F = \\frac{\\text{spring deflection}}{\\text{deflection per lbf}} = \\frac{1.8}{0.14} = 12.86 \\text{ lbf}
]<\/p>\n\n\n\n
W = m \\cdot \\frac{g_{\\text{local}}}{g_{\\text{standard}}}
]<\/p>\n\n\n\n
m = W \\times \\frac{g_{\\text{standard}}}{g_{\\text{local}}} = 12.86 \\times \\frac{32.174}{31} = 13.34 \\text{ lbm}
]<\/p>\n\n\n\n
\n\n\n\nBalloon Problem<\/strong><\/h4>\n\n\n\n
W = m \\cdot \\frac{g}{g_{\\text{standard}}}
]<\/p>\n\n\n\n
g_{\\text{initial}} = \\frac{W \\cdot g_{\\text{standard}}}{m} = \\frac{119 \\times 32.174}{120} = 31.91 \\text{ ft\/s\u00b2}
]<\/p>\n\n\n\n
W_{\\text{new}} = m \\cdot \\frac{g_{\\text{new}}}{g_{\\text{standard}}} = 120 \\times \\frac{32.05}{32.174} = 119.54 \\text{ lbf}
]<\/p>\n\n\n\n