first i want to thank the readers in advance for their helpful comments.
I suppose we will begin with the simple one:
Solving for T is simple enough, but for the life of me I can't come up with a useful expression to help me get any forces on the pulleys, at least as far as combining the resultant with trig functions of the angles going on. The back of the book says the force on pulleys A and D is 14.9 newtons and the Force on B and C is 40.8 newtons. This doesn't help me reverse-engineer the expression they used, however. I think the slightest hint on this problem would get me pointed in the right direction. it looks simple but i've never done a problem like this before (and there are no complete solutions in my book).
The second problem is a little trickier.
I'm sure I'll be setting up the equilibrium equations and solving them as a system, with the obvious AB = 2AD = 2AC substitution that they hand you, but expressing the equations as a function of d? Should that even be part of the strategy? Let me show you what I have for equilibrium:
The z angles are the angles between AC and AD vectors and the xy plane. These are also the angles used in the first trig factors in my x and y sums. The 71.57 and 108.435 are the angles AC and AD and the positive y axis, and the 198.435 and 161.565 are between the vectors and positive x axis.
But I have no strategy from here. I'm going to spend more time tomorrow on it but any thoughts of yours in the meantime would be very helpful. I think in the meantime I'm going to try to balance the equations without worrying about d, and if i can do that while satisfying AB = 2AD = 2AC, maybe it'll just work out.