How can I solve for W in this tricky statics problem without exceeding 1050N?

[paul11273]

I am having trouble with a HW question that has been driving me crazy for a few days now. I have to solve for W ( a hanging weight) that will not cause either T1 or T2 to exceed 1050N. So far I have drawn the free body diagram that is attached as a word doc, and the angles I found based on the dimensions given. The problem gives T3 as 680N and shows the slope to be 8/5. This causes (I think) T3 and T2 to be directly in line with each other. I feel like I am letting this fact throw me off. Also, when I start trying to break up each one into component vectors, it seems that I have too many unknowns. I have tried several different approaches but each leads me to an incorrect answer. The book gives a range for W of 0 < W < 609N.
Can you help me figure this one out? Atleast lead me in the right direction? Thanks.

 

[Moose352]

These are the two equations:

1. cos(28)T2 - cos(53)T1 = cos(28)680
2. sin(53)T1 + sin(28)T2 - sin(28)680 = W

You are trying to find W where T1 or T2 is equal to 1050. So substitute 1050 in for T1 or T2, and solve for the other T. Then solve for the weight.

 

[paul11273]

Thanks!
I can't believe that I killed myself over this question. I had those two equations, but failed to see that I need to sub in 1050 for either T1 or T2, then solve for the other.
I have completed it, and found that T2 will be 1050N when the W is 609N, and T1 will 544N.
I let T3 confuse me, and it had me thinking the problem would be more complicated.
Thanks again. You have sold me on this forum. I will check here regularly, and hopefully I can contribute as well.

 

[turin]

You have 3 unknowns: T₁, T₂, and W
You have 2 equations, as Moose pointed out.
You also have 2 inequalities, one of which you must "max out", and the other of which you must ensure holds. Pick one of the inequalities, arbitrarily, and max it out (turn it into an equality). This fixes one of your unknowns (T₁ or T₂, whichever you chose). Then, solve the equations, and afterwards make sure the other inequality holds. If it does not, then just go back and max out the other inequality and solve.