High-voltage!

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

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

TenaliRaman

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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

Nope.
Oh, and the cable is extremely flexible.

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.

Gokul43201

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 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.