Imagine two high-voltage-masts/poles

  • Context: High School 
  • Thread starter Thread starter Galileo
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Discussion Overview

The discussion revolves around a problem involving two high-voltage poles and a suspended cable, focusing on determining the distance between the poles based on the given dimensions and the cable's lowest point above the ground. The nature of the problem is conceptual and mathematical, with participants exploring various approaches and reasoning.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants suggest that the distance between the poles could be around 55 meters, but this is challenged due to the cable's length being only 18 meters.
  • One participant proposes a separation of approximately 4.256 meters but later questions their own calculation.
  • Another participant mentions that the tension in the cable and environmental factors could affect the distance, indicating a level of uncertainty in the problem's parameters.
  • Several participants assert that the distance between the poles is zero, reasoning that the cable's length and the height of the poles lead to this conclusion.
  • There is a discussion about whether the cable hangs in a parabolic shape or a catenary, with conflicting views on the correct model to apply.
  • One participant emphasizes the importance of drawing a diagram to visualize the problem, suggesting that it could clarify the situation.
  • Another participant humorously notes the complexity of the problem and the frustration it can cause if not solved quickly.
  • Some participants express confusion over the mathematical representations and reasoning used in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the distance between the poles, with multiple competing views and calculations presented throughout the discussion. The nature of the cable's shape and the influence of external factors also remain points of contention.

Contextual Notes

Participants highlight various assumptions and factors that could influence the problem, such as the tension in the cable, temperature, and the condition of the poles, which are not explicitly defined in the original problem statement.

  • #31
geniusprahar_21 said:
the cable will be hanging down in the shape of a parabola...right??
geniusprahar_21 said:
if yes, then you get a really bad equation in natural logs and roots and stuff. but...it can be solved to get the the distance.

This reminds me of a story about mathematicians who used to use slide rules for EVERYTHING. When asked for the square root of 100, they would race through their calculations to get an answer of 9.9999.. "Sorry, how many decimal places did you want?"

geniusprahar_21: that's a huge hint. Yeeeees, it *would* hang in a parabola, and yeeees, that *would* be hard to calculate...

But before you give up, try drawing the diagram. Accurately.
 
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  • #32
DaveC426913 said:
.Yeeeees, it *would* hang in a parabola
No it would not. Please read post #28 of this thread.
 
  • #33
It's unbelievable how long this thread lingers and is still receiving clueless answers. The answer has appeared in the thread almost a dozen times for those who took the effort to read.
 
  • #34
jimmysnyder said:
DaveC426913 said:
Yeeeees, it *would* hang in a parabola
No it would not. Please read post #28 of this thread.
You misunderstand my post. (And you are, at least technically, incorrect, though you are correct in spirit).

The poster is correct in principle that it forms a parabola (which, technically, it does). It's just a parabola with some very unique values (Google "degenerate parabola") and I expect that if he did the calculations the hard way, he would still arrive at the correct answer - and then slap himself on the forehead.

I'm trying to hint to him that *knowing* it is a parabola is not going to get him to the *easy* answer.
 
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  • #35
Galileo said:
It's unbelievable how long this thread lingers and is still receiving clueless answers. The answer has appeared in the thread almost a dozen times for those who took the effort to read.
Some people are still trying to solve it without peeking. Surely you don't object?
 
  • #36
DaveC426913 said:
You misunderstand my post. (And you are, at least technically, incorrect, though you are correct in spirit).
The poster is correct in principle that it forms a parabola (which, technically, it does). It's just a parabola with some very unique values (Google "degenerate parabola") and I expect that if he did the calculations the hard way, he would still arrive at the correct answer - and then slap himself on the forehead.
I'm trying to hint to him that *knowing* it is a parabola is not going to get him to the *easy* answer.
I'm slightly confused - nothing new there!
I think I am the "poster" you're referring to, I did get the answer almost straight away -at least as soon as I tried to draw the situation.
But the link you posted says:
"In 1669, Jungius disproved Galileo's claim that the curve of a chain hanging under gravity would be a parabola"
Now you say it is a parabola, or at least a special kind of parabola.
So who's right? You, me, Galileo or Jungius (whoever he might be)
Lastly don't you think it's about time somebody "put some ink in their pen" and writes the answer in a readable form?
 
  • #37
Cybersteve said:
Lastly don't you think it's about time somebody "put some ink in their pen" and writes the answer in a readable form?
To read the unreadable answers, drag your mouse across them. They will become readable.

The facts are these. The solution to the immediate problem involves a certain unusual kind of parabola. However, some have opined that in general (not limited to this problem) a hanging cable takes the shape of a parabola. While it is true in this particular case (in a funny way) it is not true in general. In the general case the cable takes the shape of a catenary.
 
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  • #38
Hi jimmysnyder,
I'm not sure who's addressing who(m) anymore.

I knew how to highlight the answers given. I was just surprised that after it had been posted so many times there were still people who haven't seem to have got it yet.

As a newbie here I didn't think it was my place to put them out of their misery and wondered why someone hadn't done so.
 
  • #39
Cybersteve said:
Hi jimmysnyder,
I'm not sure who's addressing who(m) anymore.
Oops. I'm not making thing clearer am I? That part of my post is in error and I am going over there to edit it right now.
 
  • #40
isn't it that if your draw it in a diagram, it would look like a straight line?
 
  • #41
croxbearer said:
isn't it that if your draw it in a diagram, it would look like a straight line?
Response in white Yes, look like one and even more in the mathematical world of puzzles, be one. And as DaveC426913 pointed out, a straight line is a degenerate parabola.
 
  • #42
jimmysnyder said:
a hanging cable takes the shape of a parabola. While it is true in this particular case (in a funny way) it is not true in general. In the general case the cable takes the shape of a catenary.
I stand corrected.
 
  • #43
This reminds me of a story about mathematicians who used to use slide rules for EVERYTHING. When asked for the square root of 100, they would race through their calculations to get an answer of 9.9999.. "Sorry, how many decimal places did you want?"
:rolleyes:

Trouble is, in the section of the slide rule that you would be looking at for 9.99 or .999 all you can get is 3 sig digits. It was not till calculators came along that you saw anybody writing down .9999999 and pretending like the last 4 9s had any meaning. Slide rules FORCED you to use only significant digits.

Any way any decent slide rule would give \sqrt 100 = 10 without any round off error, again that is an artifact of calculators.

Yes, I learned to run a slide rule in high school, long before anyone had ever heard of a hand held calculator.
 
  • #44
im going to clarify for soem ppl who are waaaaay overdoing this. the poles are 25m high. the cable is 18 m long. when its hanging, it goes 9m down from one pole, then 9m up to connect to the top of the other, so that its hanging at its lowest part 16m off the ground. therefore the poles are no disntance apart. or you could say their distance apart is equal to the widdth of t he cable about. jeez.
 
  • #45
beanybag said:
im going to clarify for soem ppl who are waaaaay overdoing this. the poles are 25m high. the cable is 18 m long. when its hanging, it goes 9m down from one pole, then 9m up to connect to the top of the other, so that its hanging at its lowest part 16m off the ground. therefore the poles are no disntance apart. or you could say their distance apart is equal to the widdth of t he cable about. jeez.
I think you should have stopped before this part -"or you could say their distance apart is equal to the width of the cable about."
You may just have opened up a whole new can of worms!:wink:
 
  • #46
I just got decipher the problem with the help of my pop.

Actually the problem was quite tricky... I have been to a lot of equations using my little knowledge in trigonometry and Geometry...dut it resulted nothing unlike i realized that i needs no trigonometry or Geometry. Here is my answer::rolleyes:

Actually the two poles were not apart they were close together. The distance between poles is 0 meters.:rolleyes:

Please tell If I'm right...Thanks.
 

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