teel strut, having mass 500 kg and length 6.0 m is hinged at a vertical wall and

Question

teel strut, having mass 500 kg and length 6.0 m is hinged at a vertical wall and supported at a horizontal distance of 5.0 m from the wall hinge by 1. A s a cable that makes an angle of 30° with the horizontal. A 70-kg construction worker sits on the strut at a distance of 2.5 m from the wall hinge while his daring Cable 85-kg assistant stands at a position 5.5 m from the wal hinge, as shown. 30° (a) Calculate the vertical and horizontal components o (o) Calculate the vertical and horizontal components of 2.5m 5 m the force exerted on the strut at the hinge at their current positions. 6 m (b) If this cable has a recommended maximum load of 8000 N, is it safe for these workers to be on the strut at these positions, as shown? Justify your answer by comparing the tension in the cable at their current positions with the load limit.

Explanation / Answer

1] For equilibrium, the net vertical and horizontal forces will be zero

so,

Tsin30 - 500g - 85g - 70g + Ry = 0

=> Ry = (500+70+85)g - Tsin30

for horizontal,

Tcos30 - Rx = 0

=> Rx = Tcos30

also, the net torque on the system should be zero for stability

therefore, taking moments from the wall hinge gives:

70g(2.5) + 500g(3) - Tsin30(5) + 85g(5.5) = 0

=> T = 8398.60 N

this is the tension in the cable.

therefore, the horizontal component of the force exerted on the strut at the hinge is:

Rx = Tcos30 = 7273.40 N

and Ry = (500+70+85)g - Tsin30 = 2219.70 N.

b] The obtained value of the tension: T = 8398.60 N is greater than the maximum tension and so it is not safe for the workers.

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