Again, I have the answer and can follow for about half way through. Tension prob
ID: 1978862 • Letter: A
Question
Again, I have the answer and can follow for about half way through. Tension problems seem to be giving me the most trouble.A 150 N bird feeder is supported by three cables. Find the tension in each cable. Their force diagram has T1 to the right (+x) at 30 degrees and T2 to the left (-x) at 60 degrees. T3 is unlabeled but is the 150N force in the -y direction.
Sum fx=0, T1 cos 30- T2 cos 60 =0
T1 = .577T2 (which they came up with by T1= .5/.866 T2-they didn't explain but the book states we are doing this to solve for T1).
From sum fy=0, T1sin30 + T2sin60 _ 150N = 0
Using the above it is found that T1 = 75N and T2+ 130N
So I tried substituting T1 in to the fy formula
T2 .577 (.5) + T2 .866 -150N =0
T2 .2885 + T2 .866 - 150 N
2T2 1.1545 = 150N
2T2 = 129.9
T2 =64.96
However that isn't the answer that they arrived at above. What am I doing wrong?
Explanation / Answer
Sum fx=0
T 1 cos 30 - T 2 cos 60 =0
T 1 = T 2 cos 60 / cos 30
T1 = 0.577T2 ------------( 1)
From sum fy=0
T1sin30 + T2sin60 - 150N = 0
Using the above it is found that T1 = 75N and T2+ 130N
So I tried substituting T1 in to the fy formula
0.577 T2 (0.5) + T2 (0.866) -150N =0
T2 (0.2885 )+ T2 (0.866) = 150 N
T2(1.1545) = 150N
T 2 = 129.9 N
From eq( 1) , T1 = 74.95 N