Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 5kg. The ropes, fastened at different heights make angles of 52 degrees and 40 degrees with the horizontal. Find the tension in each wire and the magnitude of each tension.
I started with an example in the book and then realized that the lengths of the rope where the same. This is what I did:
T1 = -T1cos(52) + T1sin(52)
T2 = T2cos(40) + T2sin(40)
T1 + T2 = 5
(-T1cos(52) + T2cos(40))i +( T1sin(52)+ T2sin(40))j = 5
-T1cos(52) + T2cos(40) = 0
T1sin(52)+ T2sin(40) = 5
T2 = (T1cos52)/cos40
T1sin(52)+ ((T1cos52)/cos40)sin(40) = 5
T1 = 3.83kg
T2 = ((3.83)cos52)/cos40
T2 = 3.1kg
and this is where I realized I forgot about the different lengths of the ropes. Can anyone help? I don't have any idea how to go about this problem.