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$\degree$ 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$\degree$ 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

To solve for the tension in the cable, we need to first calculate the torque due to the weight of the beam and the person about the pivot point.

Torque = force x perpendicular distance from the pivot

For the beam, the force acting downwards is its weight (25g) and the perpendicular distance from the pivot is half its length, since it is a uniform beam pivoted at one end. So,

Torque due to beam = (25g)(10/2) = 125g

For the person, the force acting downwards is their weight (60g) and the perpendicular distance from the pivot is 3.0 m. So,

Torque due to person = (60g)(3.0) = 180g

Since the cable is the only other force acting on the beam and it is perpendicular to the beam, the torque due to the tension in the cable must balance out the torques due to the weight of the beam and the person.

Tension in cable x sin(51°) x 10 = 125g + 180g

Tension in cable = (125g + 180g) / (10 x sin(51°))

Tension in cable = 0.38 kN

Therefore, the correct choice is C, 0.38 kN.

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

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