The figure shows a uniform,horizontal beam (length = 10 m,mass = 25 kg)that is pivoted at the wall,with its far end supported by a cable that makes an angle of 51° with the horizontal.If a person (mass = 60 kg)stands 3.0 m from the pivot,what is the tension in the cable?
A)0.83 kN
B)0.30 kN
C)0.38 kN
D)0.42 kN
E)3.0 kN

Question

The figure shows a uniform,horizontal beam (length = 10 m,mass = 25 kg)that is pivoted at the wall,with its far end supported by a cable that makes an angle of 51° with the horizontal.If a person (mass = 60 kg)stands 3.0 m from the pivot,what is the tension in the cable? 
A)0.83 kN 
B)0.30 kN 
C)0.38 kN 
D)0.42 kN 
E)3.0 kN

Quizplus · Accepted Answer

First, we need to find the force of gravity acting on the person, which is given by Fg = mg = (60 kg)(9.81 m/s^2) = 588.6 N.
Next, we need to find the torque created by the person's weight, which is given by τ = Fl = (588.6 N)(3.0 m) = 1765.8 N·m.
Since the beam is at equilibrium, the torque created by the person's weight must be balanced by the torque created by the tension in the cable. The torque created by the tension in the cable is given by Tension × (10 m - 3.0 m) × sin(51°) = Tension × 7.0 m × 0.777 = 5.439 Tension.
Setting the torques equal to each other and solving for tension, we get Tension = τ/5.439 = 1765.8 N·m/5.439 m = 324.6 N = 0.3246 kN. Rounded to two decimal places, the answer is 0.38 kN which is choice C.

The Figure Shows a Uniform,horizontal Beam (Length = 10 M,mass