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Load weight on a horizontal wireframe ladder

Physics Asked by beastx on February 16, 2021

I’m wondering about the following scenario.
A wire cable ladder is mounted horizontally and a person uses the rungs to navigate from one end to the other (imagine monkey bars).

If the wire cable is ~15 metres in length and supported in the middle by another top down wire to prevent sagging and offer some tension (from a roof), how much strain/weight/load could a person possibly cause, if for example the person was 90kg, 100kg, 110kg

Alternative would be two ~7metre ladders joined and suspended in the middle.

wiring

2 Answers

I don't have any formulas for you, but I can mostly answer your question. If both the 15 meter and 2 7 meter ladders were both the same distance they would experience the same strain, weight and load as each other.(unless the connection between the 2 7 meter ladders was weaker than that of the middle of the 15 meter ladder) A person would cause the most strain on the ladders when they are in the middle of them, and the least the farther away from the center they are. I don't know how much load the ladders can take A, because I don't know how strong the ladders are and the supports keeping them up, and B, I don't even have an equation to calculate that. I hope this answers you general question even if I can't give you any formulas.

Answered by Daniel Turczynskyj on February 16, 2021

The problem is complex enough to need computer simulation for a reasonable answer.

As a first stab at it you can look at the wire ladder (black lines) spanning a distance $S$ between points A and B below:

pic

The middle support (blue line) connects to the ladder at C and to the ceiling at D. The load $W$ is at point G a distance $x$ from A.

If the angle $varphi$ is near zero, then the support forces $F_A$ and $F_B$ need to be really large to counteract the weight $W$. The angle increases as the ladder and/or the supports stretch. The higher the load the more stretch

The solution will be found when the elastic forces match the forces from the sketch above

pic2

Answered by John Alexiou on February 16, 2021

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