Tension in Cable: Solving Using Trig

[ChaosCon343]

Homework Statement

A 36.0 kg uniform beam is attached to a wall with a hinge while its far end is supported by a cable such that the beam is horizontal.

http://a1.educog.com/res/msu/physicslib/msuphysicslib/24_Statics_Equilibrium/graphics/prob20_beamhinge2.gif

If the angle between the beam and the cable is θ = 69.0° what is the tension in the cable?

Homework Equations

Unknown other than basic trigonometry

The Attempt at a Solution

I tried using simple trigonometry; Cos(69)=(36*g)/h, but to no avail. I believe the reason it didn't work to be because the cable is not attached to the bar's center of mass, but I've no idea how to correct this. A point in the right direction would be greatly appreciated!

 

[azatkgz]

Use torque about hinge.

 

[ogb p]

Dear student,

Thank you for sharing your attempt at solving this problem. It seems like you have the right idea, but as you mentioned, the cable is not attached to the beam's center of mass, which means the center of mass is not directly below the point where the cable is attached. This creates a moment arm, which must be taken into account in your calculations.

To solve this problem, you can use the concept of static equilibrium, which means that the sum of all forces and torques acting on the beam must equal zero. In this case, the only external force acting on the beam is the tension in the cable, and the only torque is the one created by the weight of the beam. This torque can be calculated by multiplying the weight of the beam (36.0 kg * 9.8 m/s^2) by the distance from the hinge to the center of mass of the beam.

Once you have this information, you can set up an equation that takes into account the horizontal and vertical components of the tension in the cable, as well as the torque created by the weight of the beam. From there, you can solve for the unknown tension in the cable.

I hope this helps guide you in the right direction. Keep in mind that understanding and applying concepts of static equilibrium is crucial in solving problems like this. Best of luck with your studies!