Question

An 73.9 kg construction worker sits down 2.16 m from the end of a 1415.9 kg steel beam to eat his lunch. The cable supporting the beam is rated at 16576 N. Should the worker be worried? (To answer that question calculate the tension in the cable. Use θ=32°, L=6.8 m.)

Answer 1

Suppose the tension in cable is T, Now applying torque balance about the away end of beam from worker

Vertical component of tension in cable = T*sin 32 deg

Weight of beam = M*g = 1415.9*9.81

Weight of worker = m*g = 73.9*9.81

Now apply torque balance

Net torque = 0, So

T*sin 32 deg*L - M*g*(L/2) - m*g*(6.8 - 2.16) = 0

L = length of beam = 6.8 m

T*6.8*sin 32 deg = M*g*3.4 + m*g*4.64

T = (1415.9*9.81*3.4 + 73.9*9.81*4.64)/(6.8*sin 32 deg)

T = 14039.2 N

14039.2 < 16576, So

Since tension in beam is lower than rate of beam 16576 N, So Worker should not be worried.

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