Here's an old one

[Meatman]

This is one of the first threads I read on snowest a long time ago. Here goes nothing rocket scientists (i think it went something like this)

If a cow was tied around the nexk to a silo that was 10ft in diameter with a rope that was 100ft long...what is the square area of grass that cow could eat?

(I believe this was the question or close to it.) Anyone remember this one?

 

[SAWYER]

It wouldn't be a square area, it would be a circle

 

[EastcapeAngler]

..Just like the airplane thing. not enough info.. How big is the cows neck? How thick is the rope? How big is the knot & what type of knots are used?
does the cow eat it all in one standing? Is the cow hungry? Is the cow a sierra club member,, cuz if he/she is, then it will refuse to eat the grass for fear of the greenhouse effects. Does the farmer kill the cow to take to market before it eats it's fill?

 

[Barnes]

I remember this one, depends if the rope is able to slide around the silo as the cow walks around or if its held in place and gets shorter as the cow walks around. Not enough information to give a "correct" answer.

 

[Meatman]

I know there are a lot of variables but hey....fill in the blanks lol

 

[Ex-Member]

It does depend on several things... but you can make assumptions and go from there....

1) Rope will not slide around silo. (That'd make it real easy, area of circle with radius being the length of rope minus circ. of silo plus the radius of the silo, then subtract area of silo)
2) Length of rope used around cow's neck is negligible, using end of rope as a point for equation.
3) Cow cannot eat beyond point made by end of rope.
4) Ignore length of rope used by knots in the rope.
5) Rope cannot go over or under silo, must go around the outer circumference.

And since I feel like "geeking out" a bit.... here goes.

Establish constants.


mmmboy... i just realized this is going to involve arc length and not knowing the distance to the top of the ellipse (Blue area) from the top of the circle.

Going to post this, and continue later...

 

[Ex-Member]

Okay, so we know the length of the rope the cow has from the point on the silo. What we don't know is the length of the arc that the rope is in contact with the silo with when the cow is 180° from the point at which the rope is tied to the silo.

We do, however, know the radius of the silo, and that the rope will be linear between the tangent point on the silo and the point 180° from the knot.

A few more things I should point out:
6) The rope does not stretch.
7) Sections 2 and 3 are symmetrical, solving for area of one of those sections.
8) In case you haven't figured this out, my drawings are NOT to scale.

Now, TRIANGLES!



Okay... I can't brain today, I have the dumb... I'm still going to need one more angle or side of this triangle to finger it out... Angle A+B has to equal 90, and c^2/b^2 has to be 25.

Someone else gets to take over from here... i'm going to bed... spent way too much time on this thread.... 00:35 already?

 

[cowkiller]

Whoa!

what's the cow's name?
who gives a sh**! the cow will be hamburger in a week anyway!

 

[Ex-Member]

It wouldn't be a square area, it would be a circle

no, it's not going to be a circle... going to be the area of a semicircle (see above) plus integration of the length of the rope to linear distance of the rope as the cow changes angle in reference to the position at which the rope is anchored to the silo.

Also, I hate calculus. Don't mind geometry so much, but I really dislike calculus.

 

[REV414]

After looking at it for a couple minutes my guess with animule's facts is somewhere between 22-24k sf

 

[Ex-Member]

After looking at it for a couple minutes my guess with animule's facts is somewhere between 22-24k sf

sounds way huge... like, twice what I'd bet. Look at the area of a circle with the radius of the remaining rope, that's 14.7k feet^2. The actual area will be less than that because of the shortening of the rope due to the arc length around the silo, and the fact that the area the silo sits on cannot be used. I'm guessing 14-14.5k ft^2. Maybe even in the upper 13k's.

 

[cowkiller]

kill the cow!

the cow is tied around the neck TO the silo. it does not matter how long the rope is. Or what kind of sled the farmer rides.
therefore the cow can't eat and will be dead in a week. Let's eat!

 

[REV414]

Yeah I wasn't thinking when I posted that I should have said 11-12k I forgot to divide it by two.