Imagine two high-voltage-masts/poles

[Galileo]

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?)

 

[chroot]

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

 

[K.J.Healey]

Is it about 55m apart?

 

[Rogerio]

Is it about 55m apart?

It cannt be - the cable is only 18m long.

 

[K.J.Healey]

ha, totally wasnt paying attention and made a dumb mistake. Hold on.

seperation ~ 4.256m?

even that's looking wrong to me now... myabe i did the arc length wrong.

 

[TenaliRaman]

djZblzrTdzbpZbpz`

 

[Adam]

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.

 

[Galileo]

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.

djZblzrTdzbpZbpz`

Whazzat mean?

 

[musky_ox]

Is this actually some type of brain teaser or an arc question?

 

[Gokul43201]

Ha ha...I've never seen this one before, but all it takes is a diagram - a good, complete diagram.

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]

 

[Gokul43201]

Whazzat mean?

Oh, that's the answer in a language known only to Tenali. He will translate it eventually.

 

[Learning Curve]

Im going to say 27 meters.

 

[chroot]

*bites tongue so hard it starts to bleed*

- Warren

 

[Adam]

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.

 

[Gokul43201]

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 ?

 

[Gokul43201]

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.

 

[K.J.Healey]

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.

 

[Adam]

Good grief. I drew it. Where is that window...?

 

[TenaliRaman]

Whazzat mean?

Oh, that's the answer in a language known only to Tenali. He will translate it eventually.

I think its time to translate
::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::

 

[Galileo]

Ok Tenali, so 'dj' equals '25', Z means 'minus', 'z'='0' etc.

Question: Why?

 

[Learning Curve]

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.

 

[TenaliRaman]

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

 

[vabamyyr]

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

 

[croxbearer]

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)

 

[Cybersteve]

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!

 

[Jimmy Snyder]

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..

 

[Cybersteve]

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!

 

[Jimmy Snyder]

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

 

[Cybersteve]

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!

 

[geniusprahar_21]

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.

 

[DaveC426913]

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.

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.

 

[Jimmy Snyder]

.Yeeeees, it *would* hang in a parabola

No it would not. Please read post #28 of this thread.

 

[Galileo]

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.

 

[DaveC426913]

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.

 

[DaveC426913]

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?

 

[Cybersteve]

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?

 

[Jimmy Snyder]

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.

 

[Cybersteve]

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.

 

[Jimmy Snyder]

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.

 

[croxbearer]

isn't it that if your draw it in a diagram, it would look like a straight line?

 

[Jimmy Snyder]

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.

 

[DaveC426913]

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.

 

[Integral]

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?"

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.

 

[beanybag]

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.

 

[Cybersteve]

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!

 

[Nathaniel]

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:

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

Please tell If I'm right...Thanks.