{"id":40179,"date":"2025-06-27T14:14:58","date_gmt":"2025-06-27T14:14:58","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40179"},"modified":"2025-06-27T14:15:02","modified_gmt":"2025-06-27T14:15:02","slug":"a-7000-kg-helicopter-accelerates-upward-at-3-m-s2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-7000-kg-helicopter-accelerates-upward-at-3-m-s2\/","title":{"rendered":"A 7000 kg helicopter accelerates upward at 3 m\/s^2"},"content":{"rendered":"\n

A 7000 kg helicopter accelerates upward at 3 m\/s^2. What lift force is exerted by the air on the helicopter’s propellers?<\/p>\n\n\n\n

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

Correct Answer:<\/h3>\n\n\n\n

The lift force exerted by the air on the helicopter’s propellers is 77,900 N<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Detailed Explanation:<\/h3>\n\n\n\n

To calculate the lift force acting on the helicopter, we need to consider both the gravitational force (weight) and the additional force required to accelerate the helicopter upward.<\/p>\n\n\n\n

The forces acting on the helicopter are:<\/p>\n\n\n\n

    \n
  1. Weight of the helicopter (W)<\/strong>
    W=m\u00d7gW = m \\times gW=m\u00d7g
    Where:
    m=7000\u2009kgm = 7000 \\, \\text{kg}m=7000kg (mass of the helicopter)
    g=9.8\u2009m\/s2g = 9.8 \\, \\text{m\/s}^2g=9.8m\/s2 (acceleration due to gravity) So:
    W=7000\u00d79.8=68,600\u2009NW = 7000 \\times 9.8 = 68,600 \\, \\text{N}W=7000\u00d79.8=68,600N<\/li>\n\n\n\n
  2. Net Force Required for Upward Acceleration (F_net)<\/strong>
    Fnet=m\u00d7aF_{\\text{net}} = m \\times aFnet\u200b=m\u00d7a
    Where:
    a=3\u2009m\/s2a = 3 \\, \\text{m\/s}^2a=3m\/s2 (upward acceleration) So:
    Fnet=7000\u00d73=21,000\u2009NF_{\\text{net}} = 7000 \\times 3 = 21,000 \\, \\text{N}Fnet\u200b=7000\u00d73=21,000N<\/li>\n\n\n\n
  3. Total Lift Force (F_lift)<\/strong>
    The lift force must overcome both the weight of the helicopter and provide the additional upward force for acceleration. Using Newton’s Second Law:
    Flift\u2212W=FnetF_{\\text{lift}} – W = F_{\\text{net}}Flift\u200b\u2212W=Fnet\u200b Rearranging the equation:
    Flift=Fnet+WF_{\\text{lift}} = F_{\\text{net}} + WFlift\u200b=Fnet\u200b+W Substituting the known values:
    Flift=21,000+68,600=89,600\u2009NF_{\\text{lift}} = 21,000 + 68,600 = 89,600 \\, \\text{N}Flift\u200b=21,000+68,600=89,600N Correction: There was a slight mistake above, let me correct it properly:<\/li>\n<\/ol>\n\n\n\n

    Step-by-step correction:<\/strong><\/p>\n\n\n\n

      \n
    1. Weight:
      W=7000\u00d79.8=68,600\u2009NW = 7000 \\times 9.8 = 68,600 \\, \\text{N}W=7000\u00d79.8=68,600N<\/li>\n\n\n\n
    2. Net Force required for upward acceleration:
      Fnet=7000\u00d73=21,000\u2009NF_{\\text{net}} = 7000 \\times 3 = 21,000 \\, \\text{N}Fnet\u200b=7000\u00d73=21,000N<\/li>\n\n\n\n
    3. Lift force:
      Flift=W+Fnet=68,600+21,000=89,600\u2009NF_{\\text{lift}} = W + F_{\\text{net}} = 68,600 + 21,000 = 89,600 \\, \\text{N}Flift\u200b=W+Fnet\u200b=68,600+21,000=89,600N<\/li>\n<\/ol>\n\n\n\n

      Final Lift Force:<\/h3>\n\n\n\n

      The correct lift force exerted by the air is 89,600 N<\/strong>.<\/p>\n\n\n\n

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

      The helicopter experiences two forces: its weight pulling it downward and the lift from the air pushing it upward. For it to accelerate upward at 3\u2009m\/s23 \\, \\text{m\/s}^23m\/s2, the lift force must be greater than the gravitational force. This requires the propellers to exert a lift of 89,600 N<\/strong>, combining the force needed to counteract gravity and the extra force needed for acceleration.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      A 7000 kg helicopter accelerates upward at 3 m\/s^2. What lift force is exerted by the air on the helicopter’s propellers? The Correct Answer and Explanation is: Correct Answer: The lift force exerted by the air on the helicopter’s propellers is 77,900 N. Detailed Explanation: To calculate the lift force acting on the helicopter, we […]<\/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-40179","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40179","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=40179"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40179\/revisions"}],"predecessor-version":[{"id":40181,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40179\/revisions\/40181"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}