Question

A 12.0m uniform beam is hinged to a vertical wall and held horizontally by a 5.00m cable attached to the wall 4.00m above the hinge, as shown in the figure below (Figure 1) . The metal of this cable has a test strength of 1.00kN , which means that it will break if the tension in it exceeds that amount.

What is the heaviest beam that the cable can support with the given configuration?

Find the horizontal component of the force the hinge exerts on the beam.

Find the vertical component of the force the hinge exerts on the beam.

Answer 1

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A 11.0m uniform beam is hinged to a vertical wall and held horizontally by a 5.00m cable attached to the wall 4.00m above the hinge. The metal of this cable has a test strength of .800kN, which means that it will break if the tension in it exceeds that amount. What is the heaviest beam that the cable can support with the given configuration? Find the horizontal component of the force the hinge exerts on the beam. Find the vertical component of the force the hinge exerts on the beam.

Answer

The tention in the string is T = 800  N

          The length of the beam is L = 11.0m

           The length of the cable is x = 5.0m

            Theheight is h = 4.00m    

        

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   From the figure the angle sin? =4.00m/5.00m

                                                ? = sin^-1(4.00m/5.00m)

                                                    = 53.13⁰

      Apply moment of torque at pointA then

               Mg*AB  - Tsin?*AC = 0

               

           from the given data AB = 3.2 m

                                          AC = 6.4 m

           substitude these values in above equation then we get

                                 M=Tsin?*AC /AB*g

                                    = 130.6 Kg

  

      The horizontal component of the force that the string exert on the beam,

                 Tx = T cos? = 800 * cos53.13 = 480 N

       The vertical component of the force that the string exert on the beam,

                 Ty = T sin? = 800 * sin53.13 = 640 N