Captain Hook is ghting Peter Pan, and they are about to step onto a tightrope strung horizontally between two maststhat are 16 m apart. When Pan and Hook are standing exactly halfway between the masts, the rope makes a 3 anglewith the horizontal. The rope has a diameter of 0.02 m and a Youngs modulus of 35 GPa. What is the combined mass, in kilograms, of Peter Pan and Captain Hook?

Complete Question

Captain Hook is fighting  Peter Pan, and they are about to step onto a tightrope strung horizontally between two masts that are 16 m apart. When Pan and Hook are standing exactly halfway between the masts, the rope makes a 3 anglewith the horizontal. The rope has a diameter of 0.02 m and a Youngs modulus of 35 GPa.

What is the combined mass,in kilograms, of Peter Pan and Captain Hook?

Their combined mass is

Explanation:

A sketch that describes the question is shown on the first uploaded image  

  From the question we are told that

          The distance apart is

          The angle the rope makes is

          The diameter of the rope is

          The Young modulus is  

From the diagram we see that the elongation of the rope can be  mathematically evaluated as

         

And applying  SOHCATOH rule    

   Substituting values

                             

                               

      And  

                     

The Tension on the rope can be mathematically represented as

               

Where A is the area and is mathematically represented as

             

 Substituting values

           

Now Substituting values into the formula for the tension on the rope

         

             

From the diagram we can mathematically evaluate the the weight of peter and hook as

             

Where

Now substituting this into the equation and making m the subject

                   

Substituting values

               

                   

Note  SOHCATOH is

                               

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