I've been wracking my brains over this and haven't gotten much closer to an answer so I was hoping someone could help.
Assume I take a rope and tie it to an attachment point using a mid-line knot (essentially making two independent ropes) and I hang a weight (x) from the two ropes with even distribution. Let's call this scenario A.
Now, I take the same weight and hang it from the same rope except this time, the rope has not been doubled up. Let's call this scenario B.
My question is this: Does the force placed on the attachment point differ between the two scenarios (T2 and T4 in the image)? If so, why (with mathematical proof)?
I've found heaps of stuff about two ropes on different angles, but nothing when the ropes are in parallel.
The force applied on the ceiling will be exactly the same ($T_2=T_4$). This is because essentially, the same mass is pulling both the points. In the scenario A, the tension is split between the wires but then merges at the ceiling. The final result will be $2T_1=T_2=T_3=T_4$
Now this is assuming that the two ropes in scenario A are perfectly parallel to each other and normal to the ceiling. If the ropes were at an angle $\theta$ with each other at the ceiling, the force on the ceiling will be less ($T_2{\lt}T_4$). More precisely, $T_4=mg$ and $T_2=mg\;{\cos {{\theta}\over 2}}$. What you are asking is simply the condition at ${\theta}=0$