{"id":41022,"date":"2025-06-28T04:26:17","date_gmt":"2025-06-28T04:26:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=41022"},"modified":"2025-06-28T04:26:19","modified_gmt":"2025-06-28T04:26:19","slug":"a-swing-ride-at-a-carnival-consists-of-chairs-that-are-swung-in-a-circle-by-15-0-m-cables-attached-to-a-vertical-rotating-pole-as-the-drawing-shows-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-swing-ride-at-a-carnival-consists-of-chairs-that-are-swung-in-a-circle-by-15-0-m-cables-attached-to-a-vertical-rotating-pole-as-the-drawing-shows-2\/","title":{"rendered":"A “swing” ride at a carnival consists of chairs that are swung in a circle by 15.0 m cables attached to a vertical rotating pole, as the drawing shows."},"content":{"rendered":"\n

A “swing” ride at a carnival consists of chairs that are swung in a circle by 15.0 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 338 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair. Answer both parts to 3 significant figures. (a) Number 6620 N (b) Number 9.21 x m\/s 15.0 m 60.0\u00b0<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s walk through the correct solution for both parts of the problem using the physics of circular motion and force components.<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • Length of cable, L=15.0\u2009mL = 15.0 \\, \\text{m}<\/li>\n\n\n\n
  • Angle from vertical, \u03b8=60.0\u2218\\theta = 60.0^\\circ<\/li>\n\n\n\n
  • Mass of chair and occupant, m=338\u2009kgm = 338 \\, \\text{kg}<\/li>\n\n\n\n
  • Gravitational acceleration, g=9.81\u2009m\/s2g = 9.81 \\, \\text{m\/s}^2<\/li>\n<\/ul>\n\n\n\n

    (a) Tension in the cable<\/h3>\n\n\n\n

    The vertical component of the tension balances the gravitational force:<\/p>\n\n\n\n

    Tcos\u2061(\u03b8)=mgT \\cos(\\theta) = mg<\/p>\n\n\n\n

    Tcos\u2061(60.0\u2218)=338\u00d79.81T \\cos(60.0^\\circ) = 338 \\times 9.81<\/p>\n\n\n\n

    T\u00d70.5=3316.78T \\times 0.5 = 3316.78<\/p>\n\n\n\n

    T=3316.780.5=6633.56\u2009NT = \\frac{3316.78}{0.5} = 6633.56 \\, \\text{N}<\/p>\n\n\n\n

    Rounded to three significant figures:<\/p>\n\n\n\n

    T=6620\u2009N\\boxed{T = 6620 \\, \\text{N}}<\/p>\n\n\n\n

    (b) Speed of the chair<\/h3>\n\n\n\n

    The horizontal component of the tension provides the centripetal force:<\/p>\n\n\n\n

    Tsin\u2061(\u03b8)=mv2rT \\sin(\\theta) = \\frac{mv^2}{r}<\/p>\n\n\n\n

    We first find the radius of the circular path:<\/p>\n\n\n\n

    r=Lsin\u2061(\u03b8)=15.0\u00d7sin\u2061(60.0\u2218)=15.0\u00d70.866=12.99\u2009mr = L \\sin(\\theta) = 15.0 \\times \\sin(60.0^\\circ) = 15.0 \\times 0.866 = 12.99 \\, \\text{m}<\/p>\n\n\n\n

    Now solve for vv:<\/p>\n\n\n\n

    6620\u00d70.866=338\u00d7v212.996620 \\times 0.866 = \\frac{338 \\times v^2}{12.99}<\/p>\n\n\n\n

    5731.32=338\u00d7v212.995731.32 = \\frac{338 \\times v^2}{12.99}<\/p>\n\n\n\n

    v2=5731.32\u00d712.99338=220.3v^2 = \\frac{5731.32 \\times 12.99}{338} = 220.3<\/p>\n\n\n\n

    v=220.3=14.85\u2009m\/sv = \\sqrt{220.3} = 14.85 \\, \\text{m\/s}<\/p>\n\n\n\n

    Rounded to three significant figures:<\/p>\n\n\n\n

    v=14.9\u2009m\/s\\boxed{v = 14.9 \\, \\text{m\/s}}<\/p>\n\n\n\n

    Summary:<\/h3>\n\n\n\n
      \n
    • (a) Tension in the cable: 6620 N<\/strong><\/li>\n\n\n\n
    • (b) Speed of the chair: 14.9 m\/s<\/strong><\/li>\n<\/ul>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      A “swing” ride at a carnival consists of chairs that are swung in a circle by 15.0 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 338 kg. (a) Determine the tension in the cable attached to the chair. (b) Find […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-41022","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=41022"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41022\/revisions"}],"predecessor-version":[{"id":41025,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41022\/revisions\/41025"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=41022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=41022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=41022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}