{"id":23980,"date":"2025-06-18T08:58:40","date_gmt":"2025-06-18T08:58:40","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=23980"},"modified":"2025-06-18T08:58:41","modified_gmt":"2025-06-18T08:58:41","slug":"consider-a-wheeled-537-kg-cannon-firing-a-2-kg-cannonball","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/consider-a-wheeled-537-kg-cannon-firing-a-2-kg-cannonball\/","title":{"rendered":"Consider a wheeled, 537 kg cannon firing a 2 kg cannonball"},"content":{"rendered":"\n

Consider a wheeled, 537 kg cannon firing a 2 kg cannonball<\/p>\n\n\n\n

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

To analyze this scenario, we can apply conservation of momentum<\/strong>.<\/p>\n\n\n\n

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

When the 2 kg cannonball is fired from a 537 kg wheeled cannon (initially at rest), the cannon will recoil<\/strong> in the opposite direction due to the law of conservation of momentum<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation (300 words):<\/strong><\/h3>\n\n\n\n

The law of conservation of momentum states that the total momentum of a closed system remains constant<\/strong> if no external forces act on it. Initially, both the cannon and the cannonball are at rest, so the total momentum of the system is zero.<\/p>\n\n\n\n

Let\u2019s define:<\/p>\n\n\n\n

    \n
  • Mass of cannon: M=537\u2009kgM = 537 \\, \\text{kg}<\/li>\n\n\n\n
  • Mass of cannonball: m=2\u2009kgm = 2 \\, \\text{kg}<\/li>\n\n\n\n
  • Velocity of cannonball after firing: vv<\/li>\n\n\n\n
  • Recoil velocity of cannon: VV<\/li>\n<\/ul>\n\n\n\n

    After the cannon fires the cannonball, the system\u2019s total momentum must still be zero: Total initial momentum=0\\text{Total initial momentum} = 0 Total final momentum=mv+MV\\text{Total final momentum} = mv + MV<\/p>\n\n\n\n

    Since momentum is conserved: mv+MV=0\u21d2MV=\u2212mv\u21d2V=\u2212mvMmv + MV = 0 \\Rightarrow MV = -mv \\Rightarrow V = -\\frac{mv}{M}<\/p>\n\n\n\n

    This equation shows that the cannon moves in the opposite direction<\/strong> of the cannonball’s motion, and with a much smaller velocity<\/strong>, due to its much greater mass.<\/p>\n\n\n\n

    \n\n\n\n

    Key Concepts:<\/strong><\/h3>\n\n\n\n
      \n
    • Recoil:<\/strong> When the cannon fires, the explosion pushes the cannonball forward and pushes the cannon backward (Newton\u2019s Third Law).<\/li>\n\n\n\n
    • Velocity relationship:<\/strong> Because m\u226aMm \\ll M, the cannon\u2019s recoil speed is much less than the cannonball\u2019s speed.<\/li>\n\n\n\n
    • Practical implication:<\/strong> Cannons are mounted on wheels or platforms to absorb or allow controlled recoil motion.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Example Calculation:<\/strong><\/h3>\n\n\n\n

      If the cannonball leaves the cannon at 300 m\/s: V=\u22122\u00d7300537\u2248\u22121.12\u2009m\/sV = -\\frac{2 \\times 300}{537} \\approx -1.12 \\, \\text{m\/s}<\/p>\n\n\n\n

      So the cannon recoils at approximately 1.12 m\/s in the opposite direction<\/strong>.<\/p>\n\n\n\n

      This situation illustrates Newton\u2019s third law and conservation of momentum in real-world mechanics.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Consider a wheeled, 537 kg cannon firing a 2 kg cannonball The correct answer and explanation is: To analyze this scenario, we can apply conservation of momentum. Correct Answer: When the 2 kg cannonball is fired from a 537 kg wheeled cannon (initially at rest), the cannon will recoil in the opposite direction due to […]<\/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-23980","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23980","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=23980"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23980\/revisions"}],"predecessor-version":[{"id":23981,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23980\/revisions\/23981"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23980"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23980"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}