{"id":1251,"date":"2021-06-29T20:12:20","date_gmt":"2021-06-29T20:12:20","guid":{"rendered":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/?p=1251"},"modified":"2021-12-30T19:07:32","modified_gmt":"2021-12-30T19:07:32","slug":"sections-9-4-v2","status":"publish","type":"post","link":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2021\/06\/29\/sections-9-4-v2\/","title":{"rendered":"Chapter 9: Force"},"content":{"rendered":"\n

9.4: Problem solving steps<\/h2>\n\n\n\n

We\u2019ll follow the same problem-solving steps as with problems dealing with conservation laws, but this time we\u2019ll add an intermediate step between the drawing and the math:<\/p>\n\n\n\n

  1. Draw a picture.
    • Using your picture, draw a free body diagram<\/em> that represents the forces acting on one particular object.<\/li><\/ul><\/li>
    • Using your free body diagram, apply Newton\u2019s second law.<\/li>
    • Solve. <\/li><\/ol>\n\n\n\n

      A free body diagram (FBD) is a problem-solving tool that we\u2019ll use to bridge the gap between the very visual and intuitive picture, and the more abstract mathematical representation. To draw a free body diagram, represent your object as a single point, then draw arrows coming from that point that represent the different forces acting on that particular object. You also need to include coordinate axes for reference.<\/p>\n\n\n\n

      Example 9.3<\/h4>\n\n\n\n

      You are designing an elevator and need to determine the tension in the cable. Your elevator will have a mass of 1200 kg (including passengers) at it’s maximum load, and it needs to be able to accelerate at 1.5 m\/s2<\/sup>. Under these conditions, what is the tension in the cable?<\/p>\n\n\n\n

      The drawing should be pretty simple (it’s just a person standing in an elevator), so I’ll start with a free body diagram for the elevator. The elevator, and everything inside of it, is represented by a single point, and all the force acting on it are represented by arrows. In this case, there are only two forces: the tension in the cable, and the weight of the elevator.<\/p>\n\n\n\n

      FBD\u2014Elevator<\/h5>\n\n\n\n
      \"A
      Free body diagram for the elevator<\/figcaption><\/figure><\/div>\n\n\n\n

      Note that the acceleration of the elevator does not<\/em> appear on the free body diagram. Remember that acceleration is a description of an object’s motion\u2014not a force\u2014and a free body diagram only shows the forces which are acting.<\/p>\n\n\n\n

      Now, apply Newton’s second law and solve:<\/p>\n\n\n

      \\[
      \n \\begin{align*}
      \n F_\\textit{net,y} &= ma_y \\\\
      \n F^T – F^G &= ma_y \\\\
      \n F^T – mg &= ma_y \\\\
      \n F^T &= ma_y + mg \\\\
      \n &= m(a_y + g) \\\\
      \n &= (1200\\ \\textrm{kg})(1.5 + 9.81)\\ \\textrm{m\/s}^2 \\\\
      \n &= 13.6\\ \\textrm{kN}
      \n \\end{align*}
      \n\\]<\/p>\n\n\n\n

      The cable you choose for your elevator must be able to withstand a tension of at least 13.6 kN without breaking.<\/p>\n\n\n\n

      Practice 9.3<\/h4>\n\n\n\n\n