# Tension of a high wire problem

1. Oct 10, 2012

### vysero

A circus performer of weight W is walking along a "high wire" as shown. Then tension in the wire is: A) approximately W, B) approximately w/2 C) mush less than W, D) much more than W, E) depends on weather he stands on one or two feet

Description of picture: Their are two polls in the ground. A wire has been staked to the ground left of the first pull. It is then laid over the top of the first poll and runs across to the second poll and over the top of it. It is then staked down to the right of the second poll. A man is standing on top of the rope in the middle of the two polls which causes some slack in the rope. This obviously causes the two ends of the rope on either side of the poll to tense up. Maybe there are some grooves on top of the poll's or something keeping the rope from slipping; the picture is not that descriptive.

This question confuses me. My answer was A and I was wrong, the correct answer was D. Can someone please explain to me why this is the correct answer?

2. Oct 10, 2012

### PhanthomJay

Small deflections in the rope at mid span from the man's weight result in a very large rope tension, much greater than W. Draw a free body diagram of the point in the rope where the man is standing. Let's say for talking purposes the span between poles is 20 m, the rope is initially taut, and the vertical deflection of the rope under his weight at midspan is 0.5 m. And the guy weighs 800 N. Then the vertical component of the tension in each part of the rope on either side of the man is 400 N, and using basic geometry, the horizontal component of the tension is 20 times that, or about 8000 N. So the rope tension is over 8000 N, some ten times his weight. The poles must be anchored to prevent them from tipping over or breaking under that load.

Last edited: Oct 10, 2012