{"id":241087,"date":"2025-07-03T14:51:45","date_gmt":"2025-07-03T14:51:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241087"},"modified":"2025-07-03T14:51:47","modified_gmt":"2025-07-03T14:51:47","slug":"the-distance-between-two-telephone-poles-is-50-0-m","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/the-distance-between-two-telephone-poles-is-50-0-m\/","title":{"rendered":"The distance between two telephone poles is 50.0 m"},"content":{"rendered":"\n

The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire.<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To draw a free-body diagram of the bird, we should focus on the forces acting on the bird.<\/p>\n\n\n\n

Free-Body Diagram of the Bird<\/h3>\n\n\n\n

In the free-body diagram, the bird experiences two forces:<\/p>\n\n\n\n

    \n
  1. Weight (W)<\/strong>: This is the force due to gravity acting downward on the bird. It is equal to the bird’s mass (1.00 kg) multiplied by the acceleration due to gravity (9.8 m\/s\u00b2). So, the weight of the bird is: W=mg=1.00\u2009kg\u00d79.8\u2009m\/s2=9.8\u2009NW = mg = 1.00 \\, \\text{kg} \\times 9.8 \\, \\text{m\/s}^2 = 9.8 \\, \\text{N}<\/li>\n\n\n\n
  2. Tension (T)<\/strong>: The wire exerts an upward tension force on the bird. Since the wire sags, the tension force in the wire has two components. There is a vertical component that balances the weight of the bird and a horizontal component that balances out the forces along the wire. The tension in the wire at both ends can be considered equal due to symmetry.<\/li>\n<\/ol>\n\n\n\n

    Calculation of Tension in the Wire<\/h3>\n\n\n\n

    Given that the wire sags 0.200 m and the distance between the poles is 50.0 m, the bird is placed 25.0 m away from each pole (half of the total distance). The sag creates a triangle, with the vertical distance being 0.200 m, the horizontal distance being 25.0 m, and the wire forming the hypotenuse.<\/p>\n\n\n\n

    We can use the geometry of the situation to determine the tension in the wire.<\/p>\n\n\n\n

    Step 1: Find the angle of the wire<\/h4>\n\n\n\n

    The angle \u03b8\\theta of the wire with respect to the horizontal can be found using the tangent of the angle: tan\u2061(\u03b8)=vertical displacementhorizontal distance=0.200\u2009m25.0\u2009m=0.008\\tan(\\theta) = \\frac{\\text{vertical displacement}}{\\text{horizontal distance}} = \\frac{0.200 \\, \\text{m}}{25.0 \\, \\text{m}} = 0.008<\/p>\n\n\n\n

    So, \u03b8=tan\u2061\u22121(0.008)\u22480.46\u2218\\theta = \\tan^{-1}(0.008) \\approx 0.46^\\circ<\/p>\n\n\n\n

    Step 2: Resolve the Tension<\/h4>\n\n\n\n

    Since the tension in the wire has both vertical and horizontal components, we can resolve the tension TT into its components:<\/p>\n\n\n\n

      \n
    • The vertical component of the tension TvT_v must balance the bird’s weight: Tv=Tsin\u2061(\u03b8)T_v = T \\sin(\\theta) Since the weight of the bird is 9.8 N, we can set up the equation: Tv=9.8\u2009NT_v = 9.8 \\, \\text{N} Therefore, using Tv=Tsin\u2061(\u03b8)T_v = T \\sin(\\theta): Tsin\u2061(0.46\u2218)=9.8\u2009NT \\sin(0.46^\\circ) = 9.8 \\, \\text{N} Solving for TT: T=9.8\u2009Nsin\u2061(0.46\u2218)\u22489.80.008=1225\u2009NT = \\frac{9.8 \\, \\text{N}}{\\sin(0.46^\\circ)} \\approx \\frac{9.8}{0.008} = 1225 \\, \\text{N}<\/li>\n<\/ul>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n

      The tension in the wire, due to the bird’s weight, is approximately 1225 N<\/strong>. This force is distributed between the two sides of the wire, and the wire forms a slight angle due to the sag caused by the bird’s weight.<\/p>\n","protected":false},"excerpt":{"rendered":"

      The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire. The correct answer and explanation […]<\/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-241087","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241087","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=241087"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241087\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241087"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241087"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241087"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}