Imagine two high-voltage-masts/poles

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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.

Galileo
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Imagine two high-voltage-masts/poles. (I don't know the proper english word for it). You know what I`m talking about; the ones with cables to transport electricity. (Birds would sit on them and stuff.)

The two poles are both 25 meters in height and a cable of length 18 meters is suspended between the tops of the two poles.
When the cable is hanging, the lowest part of the cable is 16 meters above the ground.

Find the distance between the two poles. (i.e. How far are the two poles apart?)
 
Last edited:
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Well, perhaps I should not spoil it. This "brain teaser" has been around for a very long time, though, and has been posted here already numerous times.

- Warren
 
Is it about 55m apart?
 
Healey01 said:
Is it about 55m apart?

It cannt be - the cable is only 18m long. :smile:
 
ha, totally wasnt paying attention and made a dumb mistake. Hold on.

separation ~ 4.256m?

even that's looking wrong to me now... myabe i did the arc length wrong.
 
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djZblzrTdzbpZbpz`
:rolleyes:
 
Doesn't it sort of depend on the tension in the cable, the time of year and temperature, the age of the posts...? A bit difficult to say.
 
Adam said:
Doesn't it sort of depend on the tension in the cable, the time of year and temperature, the age of the posts...?
Nope.
Oh, and the cable is extremely flexible. :rolleyes:

Tenaliraman said:
djZblzrTdzbpZbpz`
Whazzat mean? :confused:
 
Is this actually some type of brain teaser or an arc question? :confused:
 
  • #10
Ha ha...I've never seen this one before, but all it takes is a diagram - a good, complete diagram. :wink:

I was all prepared to find the arc length of a catenary...before I drew the picture. Should have known better, since this is posted as a brain teaser.

<answer below>
The two poles are no distance apart. [/color]
 
  • #11
Galileo said:
Whazzat mean? :confused:

Oh, that's the answer in a language known only to Tenali. :wink: He will translate it eventually. :biggrin:
 
  • #12
Im going to say 27 meters.
 
  • #13
*bites tongue so hard it starts to bleed*

- Warren
 
  • #14
I must be doing this very wrong, since I can't see how to ignore temperature, tension, and other factors.

The only factors given are:
- 2 poles, each 25m high.
- 1 cable, 18 long.
- Cable is attached at the tops of the poles.
- Distance from cable to ground is 16m at lowest.

What you leave out is:
- Ground angle.
- Ground flatness.
- Pole age, condition, lean.
- Temperature.
- Tension on cable.

Eg: on a hot day, poles further apart will mean the cable hangs down to a height of 16m; on a cold day, poles closer together will mean the cable hangs down to a height of 16m.

No doubt I'm missing something though.
 
  • #15
Adam, the problem can be solved in the general case, under the single assumption that the cable has a uniform mass per unit length.

In this particular case though, it's much simpler than that.

Did you actually try and draw a figure...roughly to scale ? Get all the numbers right.

Learning Curve, the cable itself is only 18 meters long. How can the poles be 27 meters apart ?
 
  • #16
This is one of those problems where if you don't solve it in 2 minutes and either you get it much later, or someone tells you, you will want to jump out the nearest window, or into the nearest wall.
 
  • #17
ahhh, i got it finally. damn arc length took up all my time.

right next to each other, since its 9 meters from the top of the poles in the middle, and its a 18m cable then the only possible way is adjacent. Spending too much time in the homework section.
 
  • #18
Good grief. I drew it. Where is that window...?
 
  • #19
Galileo said:
Whazzat mean?
Gokul43201 said:
Oh, that's the answer in a language known only to Tenali.:wink: He will translate it eventually. :biggrin:

I think its time to translate :biggrin:
::djZblzrTdzbpZbpz` >>1 = 25-16=9*2=18-18=0::

Disclaimer : its not a mathematical formula, i have only put the answer in numbers rather than words. The equation means,
::25-16=9*2=18-18=0 ... 25m long poles ... lowest point 16m above which gives the longest height of the catenary as 9 but 9*2=18 which is nothing but the length of the cable and hence the distance between the poles is 0::
 
  • #20
Ok Tenali, so 'dj' equals '25', Z means 'minus', 'z'='0' etc.

Question: Why?
 
  • #21
because they just can...ummm...yea... I accutally did it and i got that given it's 16 meters above ground, they are 0 distance apart.
 
  • #22
Galileo said:
Ok Tenali, so 'dj' equals '25', Z means 'minus', 'z'='0' etc.

Question: Why?

if u meant "Why does dj equal 25 and so on?"
then the answer :- i denoted that in my post as ">>1".This is the right shift operator speaking in programming language terms.

If u meant "why do u need to put ur answer in that way?"
then the answer :- just thought i don't give the answer away so soon


-- AI
 
  • #23


correct me if I am wrong but i got that the 2 posts are away from each other 15.470 m

i got the equation 18/16 = sh(x/16) where x is the distance from 2 poles
 
  • #24
the distance between the two poles is zero.

25 m - 16 m = 9 m (length of half the cable at distance zero)

9 m x 2 = 18 m (length of cable)
 
  • #25
Galileo said:
Imagine two high-voltage-masts/poles. (I don't know the proper english word for it). You know what I`m talking about; the ones with cables to transport electricity. (Birds would sit on them and stuff.)

The two poles are both 25 meters in height and a cable of length 18 meters is suspended between the tops of the two poles.
When the cable is hanging, the lowest part of the cable is 16 meters above the ground.

Find the distance between the two poles. (i.e. How far are the two poles apart?)

They're called pylons!
 
  • #26
Actually it's pretty easy if you convert meters to furlongs and use a coordinate system centered on Saturn's moon Titan rotating at half the rotational speed of Mercury. Once you correct for special relativistic effects, general relativistic effects, quantum effects, special effects, and personal effects, you get:
0, rounded of course..
 
  • #27
Parabola?

I think everybody has the answer now. But would I be right in saying that the cable would ordinarily always hang in a parabola?
It's something I seem to remember learning at school 30 years ago!
Never had to use it until now!
 
  • #28
Cybersteve said:
would I be right in saying that the cable would ordinarily always hang in a parabola?
Warning, there is a spoiler in the sentence below. Do not highlight it if you don't want a hint to the problem.

If there were any slack in the cable, it would take a shape known as a catenary. Here is a site with more information.
http://mathworld.wolfram.com/Catenary.html
 
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  • #29
Disproved in 1669

It wasn't that long ago that I was at school!

Either my memory is playing tricks or I've got a case against my old maths teacher!
 
  • #30
the cable will be hanging down in the shape of a parabola...right??
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.
 

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