The cow and the silo. - Page 3

Wacky · 2003-09-02, 23:44

Quote:

Originally Posted by rpresser

... the length of the cow's neck. Or more precisely, the distance between where the chain attaches to the cow and the spot where grass enters the cow's face. It seems to me that if you are giving answers with so many decimal places you should consider how this affects the solution.

A point well taken. That is one of the difficulties in presenting "problems" as "puzzles". IMHO, the true "puzzles" hinge on a concept that is not subject to "reasonable interpretation" (eg: where is the cow's mouth in relation to the end of the chain), but rather on a concept whereby the solution is not the "obvious" one, but rather something viewed differently.

Quote:

Originally Posted by rpresser

Not to mention the fact that the chain, having nonzero weight, is going to drag on the ground, so a few inches of chain will be unavailable to the cow....

I fail to accept the mass/weight of the chain as causing any effect on the solution. In order to reach the maximum extent, the cow would have to cause the attachment point to be on (or very close to) the ground. The weight of the chain might affect the rate at which the cow could forage, but not the area, given enough time to stretch the chain. (OK, I acknowledge that incremental adjustments in link tension would interact with the ground friction in a non-linear manner. But otherwise time cures all problems of mass.)

Fusion_power · 2003-09-03, 04:32

Maybe I missed something but I thought the original statement of the puzzle from above was:

Quote:

the cow's mouth is at the tip of the chain

Fusion

asdf · 2003-09-03, 07:02

What if the cow turned around?

graeme · 2003-09-03, 09:16

Just to show that I am full of useless knowlege, the shape of the curve of the chain is called a catenary. (as long as it hangs freely between the cow's neck and its hook).

xilman · 2003-09-03, 09:36

Quote:

Originally Posted by graeme

Just to show that I am full of useless knowlege, the shape of the curve of the chain is called a catenary. (as long as it hangs freely between the cow's neck and its hook).

Only if the chain is infinitely flexible. It it consists of rigid links which can move only where links join it will only be an approximation to a catenary.

Yes, I enjoy pedantry too.

Paul

nomadicus · 2003-09-03, 18:07

Quote:

Originally Posted by xilman

Quote:

Originally Posted by graeme

Just to show that I am full of useless knowlege, the shape of the curve of the chain is called a catenary. (as long as it hangs freely between the cow's neck and its hook).

Only if the chain is infinitely flexible. It it consists of rigid links which can move only where links join it will only be an approximation to a catenary.

Approximations aside . . .
Power cables between telephone poles form the shape of an eliptical curve (that's what I've been told). A chain hanging from the cow's neck and a hook both at equal heights is catenary, not eliptical?

Wacky · 2003-09-03, 18:17

Quote:

Originally Posted by nomadicus

Approximations aside . . .
Power cables between telephone poles form the shape of an eliptical curve (that's what I've been told). A chain hanging from the cow's neck and a hook both at equal heights is catenary, not eliptical?

Perhaps the person who "told" you is confused. Or, perhaps, they used the term "eliptical" in a generic sense to avoid confusing their audience with the more exact "catenary" shape.

eepiccolo · 2003-09-03, 18:18

Quote:

Originally Posted by nomadicus

Quote:

Originally Posted by xilman

Quote:

Originally Posted by graeme

Just to show that I am full of useless knowlege, the shape of the curve of the chain is called a catenary. (as long as it hangs freely between the cow's neck and its hook).

Only if the chain is infinitely flexible. It it consists of rigid links which can move only where links join it will only be an approximation to a catenary.

Approximations aside . . .
Power cables between telephone poles form the shape of an eliptical curve (that's what I've been told). A chain hanging from the cow's neck and a hook both at equal heights is catenary, not eliptical?

And just to throw in further confusion, I was told by my Calc I professor that a hanging chain followed a sinc function. Hmmm....

roy1942 · 2003-09-03, 18:41

Quote:

Originally Posted by Wackerbarth

Quote:

Originally Posted by nomadicus

Approximations aside . . .
Power cables between telephone poles form the shape of an eliptical curve (that's what I've been told). A chain hanging from the cow's neck and a hook both at equal heights is catenary, not eliptical?

Perhaps the person who "told" you is confused. Or, perhaps, they used the term "eliptical" in a generic sense to avoid confusing their audience with the more exact "catenary" shape.

I agree that it would be a catenary. Now, for extra credit, what's the shape of the cable supporting a suspension bridge?

nomadicus · 2003-09-03, 18:44

Quote:

Originally Posted by Wackerbarth

Quote:

Originally Posted by nomadicus

Approximations aside . . .
Power cables between telephone poles form the shape of an eliptical curve (that's what I've been told). A chain hanging from the cow's neck and a hook both at equal heights is catenary, not eliptical?

Perhaps the person who "told" you is confused. Or, perhaps, they used the term "eliptical" in a generic sense to avoid confusing their audience with the more exact "catenary" shape.

If you look here, the graph of a catenary appears to be asymtotic.
Bad graph eh?

eepiccolo · 2003-09-03, 18:47

Oh, when I said sinc, I meant cosh. I get the two confused. And a catenary is a cosh function! It all makes sense now.

And the professor who told us that a chain follows a cosh also said a cable on a suspension bridge follows a parabola.

2003-09-03, 09:16	#26
graeme Jul 2003 29₁₆ Posts	pedants unite Just to show that I am full of useless knowlege, the shape of the curve of the chain is called a catenary. (as long as it hangs freely between the cow's neck and its hook).

2003-09-03, 07:02	#25
asdf Sep 2002 2²·3·5 Posts	What if the cow turned around?

2003-09-03, 18:47	#33
eepiccolo Dec 2002 Frederick County, MD 370₁₀ Posts	Oh, when I said sinc, I meant cosh. I get the two confused. And a catenary is a cosh function! It all makes sense now. And the professor who told us that a chain follows a cosh also said a cable on a suspension bridge follows a parabola.