# Imagine two high-voltage-masts/poles

1. Sep 10, 2004

### Galileo

Imagine two high-voltage-masts/poles. (I don't know the proper english word for it). You know what Im 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: Sep 10, 2004
2. Sep 10, 2004

### chroot

Staff Emeritus
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

3. Sep 10, 2004

### K.J.Healey

Is it about 55m apart?

4. Sep 10, 2004

### Rogerio

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

5. Sep 10, 2004

### K.J.Healey

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

seperation ~ 4.256m?

even thats looking wrong to me now... myabe i did the arc length wrong.

Last edited: Sep 10, 2004
6. Sep 11, 2004

### TenaliRaman

djZblzrTdzbpZbpz

7. Sep 11, 2004

### 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.

8. Sep 11, 2004

### Galileo

Nope.
Oh, and the cable is extremely flexible.

Whazzat mean?

9. Sep 11, 2004

### musky_ox

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

10. Sep 11, 2004

### Gokul43201

Staff Emeritus
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.

11. Sep 11, 2004

### Gokul43201

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

12. Sep 12, 2004

### Learning Curve

Im going to say 27 meters.

13. Sep 12, 2004

### chroot

Staff Emeritus
*bites tongue so hard it starts to bleed*

- Warren

14. Sep 12, 2004

### 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.

15. Sep 13, 2004

### Gokul43201

Staff Emeritus
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. Sep 13, 2004

### Gokul43201

Staff Emeritus
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. Sep 13, 2004

### K.J.Healey

ahhh, i got it finally. damn arc length took up all my time.

right next to eachother, 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. Sep 13, 2004

### Adam

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

19. Sep 14, 2004

### TenaliRaman

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::

20. Sep 16, 2004

### Galileo

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

Question: Why?

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