(25 points) 3. A 9.00 m-long uniform beam is hinged to a vertical wall and held

Question

(25 points) 3. A 9.00 m-long uniform beam is hinged to a vertical wall and held horiaontally by a 5.00-m-long cable attached to the wal 4.00 m above the hinge. The metal of this cable has a test strength of 1.00 kN, which means that it will break if the tension in it exceeds that amount a. Draw a free-body diagram of the beam s 0 1m cable 4 0 1 What is the heaviest beam that the cable can support in this configuration? Find the horizontal and vertical components of the force the hinge exerts on the beam. b. e.

Explanation / Answer

B) We must have a 3-4-5 triangle; the cable attaches to the beam 3 m from the wall. At the threshold of failing,
M = 0 = 1000N * 3m * (4/5) - M * 9.81 m/s² * 4.5m
M = 54.366 kg
(533.33 N)

C) the force is to the right, and it has magnitude
Fx = T*cos = 1000N * (3/5) = 600 N

For vertical equilibrium,
F = 0 = T*sin - W + Fy
0 = 1000N * (4/5) - 533.33 N + Fy
Fy = -266.67 N

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