Can the Law of Sines Determine Chandelier Tension Accurately?

CandyApples
Messages
28
Reaction score
0

Homework Statement


A large chandelier is supported by two ropes. Rope 1 makes a 40 degree angle with the ceiling and has a tension of 150N. Rope two forms a 50 degree angle with the ceiling. What is the tension in rope 2 and what is the mass of the chandelier given the chandelier.


Homework Equations


F = ma
T-mg = ma
Law of sines?

The Attempt at a Solution


So i solved it through the law of sines and got an answer significantly different than what my professor said it should be. I would be interested in knowing why.
Here is the work:
150/sin(50) = T2/sin40
T2 = 150*sin(40)/sin(50)
T2 = 125.86N whereas the correct answer is 179N.

Then for the mass:
150*sin(40)+125.86*sin(50) = mg
m = 19.66kg whereas the correct answer is 23.8kg.

I was wondering why the law of sines did not provide a correct answer in this case, and what different steps I should take to get at the right answer. Thanks in advance!
 
Physics news on Phys.org
Is there any particular reason you are using the law of sines? Draw a picture, how can you divide the triangle into two right triangles? Once you do this it is simple right angle trigonometry .
 
My apologies, I overcomplicated this problem. Upon drawing a diagram it is obvious Fx = T2cos(50) - 150cos(40). Fy = T2sin50 + 150sin40. Apply second law to Fx and force comes out nicely to 178.8N, plug that into Fy and it is in fact 23.8kg. Thanks for the help :).
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
Back
Top