Buttered toasts and cats

From: "Ady"

When buttered toast is dropped it usually lands
buttered side down and when a cat falls it usually lands on it's
feet. So if you strap a piece of buttered toast to a cat's back what
happens when the cat falls off of something? Will the cat land on
it's feet defeating the buttered toast theory or will the toast land
buttered side down defeating the cat landing theory??

**After posting this I have come to wonder what
kind of people are really out there that are seriously putting
toasts on kitty's feet! There has got to be some kind of animal
rights law against that! Well heres what we have come up with:**

**Catt:** What would happens is the cat
would fall onto its side due to paranormal quanta thingy reasons

**Casey:** All I have to say is......there's only
one way to find out. <evil laugh>

**Todd:** The cat will land on its feet. A cat
quickly turns itself while it is falling. Gravity pulls the buttered
side on the toast because it is heavier then the side without
butter. Now to actually prove this would be most likely be
impossible because it is hard to strap anything to a cats back.

**rebel:** the cat weighs more so the cat
will land on it's feet

**Edwin:** Here is a joke "scientific
analysis" that I came up with for the cat-and-buttered-toast
problem:

To understand how to analyze this dilemma, we must first understand
what it is that makes cats land on their feet and what makes
buttered toast always land toast-side down.

For the cat problem:

To start, we will take a diagram of a falling cat. The basic forces
acting on the cat are gravity and air resistance, given by mg and

b(v^2) respectively, where m is the mass of the cat, g is the
gravitational acceleration constant, b is the wind resistance
constant, and v^2 is the velocity at any one point in time, squared.
We know that average the mass, m, of a cat is about 3 kilograms, and
we know g, so we know gravity's force mg, but what about b(v^2)?
Well, the b for an animal or person can be calculated from Sir
Frodenheim's air resistance equation (or "ye winde resistance" as it
was called at his time). Sir Frodenheim was compelled to study the
dilemma of falling people and animals because of his love for
defenestrating his coworkers and their pets. Sir Frodenheim's
equation is given by:

b = (A * rho * e^2 * delta) / (theta * kappa * flappa * shmelta *
IHateTheseStupidGreekLetters)

where A is the flux (perpendicular surface area), rho is air's
density (or the density of whatever fluid the creature is falling
through), delta is a value determined by the manner in which the cat
is released, and is usually higher if the object is thrown
forcefully, for example if the cat is punted out the window like a
football, and e^2 is of course the constant e squared. The remaining
variables represent different weather and humidity conditions and
are generally very close to one, so they may be ignored.

Another condition we need to mention, however, is that the weight of
the cat is distributed unevenly throughout its body, for it is not a
completely symmetric object. The body of the cat of course has more
mass than the legs, and so a torque that acts on the body is created
by gravity.

Looking at gravity alone, one would conclude that the cat would land
on its back because of the torque. But, when we plug in the air
resistance equation, we get greater upwards forces acting on the
body, because it has more surface area, to which b is proportional
(see Frodenheim's equation above). These upwards forces generate an
upwards torque on the body (because they do not act on the cat's
center of gravity) that invariably aligns the cat straight-up on its
feet.

For the buttered toast problem:

The buttered toast problem is almost identical to the cat problem.
In the buttered toast problem, the air resistance constant, b, is
enormous on the un-buttered side of the toast because the toast's
bumpy, porous structure give it a huge A value, while the liquid
molten butter on the other side covers these bumps and holes,
drastically reducing b. Again, we get a torque caused by air
resistance, but this time it acts upwards on the un-buttered side,
and so this side invariably flips upward, leaving the buttered side
facing the ground until the toast lands.

Now for the joining of the two:

Now we must analyze what happens when a piece of buttered toast is
strapped onto a cat's back, buttered-side up, of course. In this
situation, we must consider the added element of the rope - we need
to know how ropes behave in terms of air resistance. It turns out
that this problem was solved during the Spanish Inquisition in 1478
by Don Alejandro, who was hired by Torquemada to make a more
efficient gallows for hanging people during the Inquisition. Don
Alejandro theorized that the air resistance, I, could be found with
b(v^3) where v is the velocity at any one time cubed, and b is the
air-resistance constant. He further theorized that b could be found
with:

b = (Q * rho * ((T * pi / 2) * (sin(theta) / L)) )

where rho is the density of the air (or the density of whatever
fluid the rope is falling through), ((T * pi / 2) * (sin(theta) /
L)) represents the flux (perpendicular surface area) of the rope
since T is the rope's thickness, L is the rope's length, and theta
is the rope's angle from the vertical as it falls. Finally, Q is a
constant that is determined by the rope's material and construction.

In his studies, Don Alejandro found that the value of Q was zero
when the angle, theta, was zero, but rose to enormous values when
theta strayed even the slightest from zero. After further research,
Don Allejandro found that this occurred because of billions of
micro-grooves that occur in any rope because of the splintering,
wooden nature of rope material. These grooves form pockets and cause
wind resistance, and their sheer numbers causes the rope to "grab"
the air at any angle and twist with great force until the rope is
falling oriented horizontally with the ground.

So, when something with a rope tied to it is falling, such as a
"heretic" with a noose on his neck, as in Don Allejandro's case, or
in our case a cat and a piece of buttered toast, the object will
land in whatever orientation keeps any exposed rope horizontal to
the ground. In our case, the rope will be exposed at the juncture
between the bread and the cat, where the rope goes up, across a tiny
gap between the cat and the toast, and up to the toast. Since the
rope is exposed at this juncture, this is where the cat-toast
combination will land.

In other words, the cat will land on its side with the toast tied to
its back, and so the toast will have also landed, and both are
touching the ground.

Of course, this analysis is only an idealization. Many different
conditions can occur that would throw off this calculation. For
example, you might be only be using the buttered toast as flavoring
as you use the cat to feed your pet bear, in which case the cat
doesn't even land on the ground but in the bear's mouth. Or, you
could be a bastard and try to prove my analysis wrong by using
smooth nylon fishing wire so that Allejandro's equation doesn't
apply. And, in many cases, the cat will simply use magical powers to
fly away.

**Pector:** I have actually tested the
combined theories of cats and buttered toast on a neighbor's cat.
The result of 20 tests brings me to the conclusion that two things
will actually happen. 1) the cat will land on its feet and 2) it
will immediately roll over due in part to the buttered toast effect
and in part a (usually) vain attempt to remove the toast from it's
back. After 20 attempts from various (cat-safe) heights, the
neighbor's cat has decided to stay away from me at all costs. I am
currently seeking more cat volunteers and a research grant for
further exploration of this phenomenon.

**i know all:** well at first thought you
would think on the side but WRONG!!!!!!!! bcuz if it did then
neither the toast or the cat myth would be true. for them both to
stay true the toast would have to fall off the cat and then land
butter side down and then the cat lands feet first OR what you could
do is just when you strap the toast onto the cat have it butter side
down