How Do You Calculate Tension in Angled Cables?

[jonyamikun]

[SOLVED] Tension in two cables

Homework Statement
21.0 kg loudspeaker is suspended 2.40 m below the ceiling by two 3.90 m long cables that angle outward at equal angles.

The attempt at a solution
So my homework comes from the MasteryingPhysics online homework.

What I first start out with is my free body diagram. I have 3 arrows, one pointing down for weight of the speakers by the Earth (Wse) and two arrows pointing up diagonally (Ts1 and Ts2). Since the speaker is static you have Ts1 + Ts2 + Wse = 0.

That was about as far as I could go. I then looked up information in my book but couldn't find much and so I resorted to the internet. I came across this page: http://science.palomar.edu/physics/Physics230/Tutor/4-31.html
I used the equation they give T = mg/2sin(theta)

I set a x-y axis starting with the speaker as the origin. I find the triangle that one string forms with the y-axis and the ceiling.

I find the angle that corresponds with the picture on the page I found and plug in the information I have into the equation: T = (21*9.81)/(2sin(37.98))

Putting this data into the answer box, I get the feedback: "Remember to use radians, not degrees, in arguments to trigonometric functions."

I don't lose any attempts with the answer so I think I'm on the right track but I don't know what to do at this point.

 

[chrsr34]

It sounds to me like the angle is a 3-4-5 triangle. Don't use 2sin(37.98) in the denominator, it is at best an approximation.
Use 2(3/5). When you are given those little reference triangles (dont know actual names), just remember your trig SOH CAH TOA. Since you are looking for the sin, which is S=O/H, that should give you 3/5. Thats all you need. Multiply it bye the magnitude 2.

For your answer I am getting 171.675.

Mastering physics is a good HW site, but just be aware that they are occasional mistakes too.
Good luck and I hope this helped.

Chris

 

[Moetasim]

I would first like to commend you for approaching the problem with a free body diagram and using the appropriate equations to solve for the tension in the cables. Your approach is correct and you have identified the key forces acting on the speaker.

The feedback you received about using radians instead of degrees is important to note. In scientific calculations, angles are usually measured in radians rather than degrees. This is because radians are a more natural unit for measuring angles in mathematical equations.

To convert from degrees to radians, you can use the following formula:
radians = (π/180) * degrees

In your case, the angle of 37.98 degrees would convert to 0.663 radians. Plugging this value into your equation would give you the correct answer for the tension in the cables.

In summary, your approach to the problem was correct and the only thing that needed to be adjusted was the unit for the angle. Keep up the good work!