Statics problem:
Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut.

Here is the picture: http://imgur.com/FAyAUGD

Question

Statics problem:
Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut.

Here is the picture: http://imgur.com/FAyAUGD

anonymous · Answer

I set up the equations for equilibrium for $$\sum_{}^{}F_x $$ and $$\sum_{}^{}F_y $$ but I'm getting 3 unknowns :(

$$\sum_{}^{}F_x = (4/5)*P-(600/650)*T_{AC}=0$$
$$\sum_{}^{}F_y = (250/200)*T_{AC}+T_{BC}+(3/5)*P-480=0$$

where do I go from here?

anonymous · Answer

I believe you need a third equation! Of which states that The net torque is also zero

anonymous · Answer

You may be right but I'm not sure, because the chapter doesn't cover torque.
What would that equation look like?

anonymous · Answer

Honestly, I don't fully know this stuff. What conditions are necessary for a cable to be taut? And what is P?

anonymous · Answer

I believe it means that it needs to be in equilibrium, so that none of the cables break.
P is the force shown in the diagram.

anonymous · Answer

Oh, so P is just some outside force that we're here to figure out? Alright! Haha, sorry for asking you when I'm supposed to be helping! Just needed a little bit of context, so Q is the load then I'm assuming?

anonymous · Answer

And the little triangle thing by P is describing the angle at which P is going to be?

anonymous · Answer

Haha that's alright. Yes, Q is the load. Not sure what you mean by your second question; the numbers on the triangle indicate that it is a "3 4 5 triangle" meaning that it must keep that ratio, if that makes any sense.

anonymous · Answer

Hmmm... I can kind of get that, but what is it in ratio with?

anonymous · Answer

Well for example, lets say that the magnitude of P is 35N (just made it up, that's not in the problem). Then to keep the triangle ratio the x component of P would be (4/5)*35=28, and the y component would be (3/5)*35=21.
Does that make sense?

anonymous · Answer

Right, we were actually saying the same thing....this means that P is directed at a specific angle if its components are in that ratio, but now that we're on the same page give me a minute and I'll be ready to help

anonymous · Answer

I think the trick here is eliminating the variable T(ac)

anonymous · Answer

I think the problem is with T(bc). If I could eliminate it then I would have 2 equations and 2 unknowns. But how do I do that?