A 9.00 m uniform beam is hinged to a vertical wall and held horizontally by a 5.

Question

A 9.00 m uniform beam is hinged to a vertical wall and held horizontally by a 5.00 m cable attached to the wall 4.00 m above the hinge, as shown in the figure below (Figure 1) . The metal of this cable has a test strength of 1.20 kN , which means that it will break if the tension in it exceeds that amount. Part A What is the heaviest beam that the cable can support with the given configuration? m = kg SubmitMy AnswersGive Up Part B Find the horizontal component of the force the hinge exerts on the beam. Enter positive value if the force is rightward and negative value if the force is leftward. Fh = N SubmitMy AnswersGive Up Part C Find the vertical component of the force the hinge exerts on the beam. Enter positive value if the force is upward and negative value if the force is downward.

Explanation / Answer

Given,

Length of beam, L = 9 m

Length of cable, l = 5 m

Considering diagram, total torque about the hinge, i.e. ?? = 0;

T x ?(52 - 42) x (4/5) -W x 4.5

Since, maximum tension that metal cable can carry is 1200 N

Therefore, W = 1200 x ?(25-16) x (4/5) / 4.5 = 640 N

B) The horizontal component of the hinge, ?Fx = 0;

Fx -T x ?(52-42) / 5

So, horizontal component, Fx = 720 N

C) The vertical component of the hinge, ?Fy = 0;

Fy + T x (4/5)- W

So, vertical component, Fy = -320 N

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