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Two lifeguards pull on ropes attached to a raft. If they pull in the same direction, the raft experiences a net external force of 347 N to the right. If they pull in opposite directions, the raft experiences a net external force of 122 N to the left.
Draw a free body diagramfor each situation and find the magnitude of the larger of the two individual forces.

Answer :

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Answer:

F1 = 234.5

Explanation:

F1 = force applied by the first life guard

F2 = force applied by the second life guard

  • In the first scenario both lifeguards pull in the same direction and the raft experiences a net  force of 347 N

          F1 + F2 = 347  ...equation 1

  • In the second scenario both lifeguards pull in  different directions and the raft experiences a net  force of 122 N

             F1 - F2 = 122 ....equation 2

  • from equation 1 , F1 = 347 - F2 .....equation 3
  • substituting equation 3 into equation 2

        (347 - F2) - F2 = 122

         347 - 2F2 = 122

           2F2 =347 - 122

            F2 = 225 ÷ 2 = 112.5 N

  • substituting the value F2 = 112.5 N into equation 1

               F1 + F2 = 347

               F1 + 112.5 = 347

               F1 = 347 - 112.5 = 234.5 N

     

Therefore F1 = 234.5 and F2 = 112.5

     the larger of the two forces is F1 = 234.5

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