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Assume a hemispherical cow.
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You will need an adjustable speed treadmill and a basketball. Elevate the aft end of the treadmill. The height (angle) will need to be adjustable. Turn on the treadmill, and place the basketball on the middle of the rotating mat. Adjust the angle and speed of the treadmill until the basketball remains
in place. Voila! A cool looking display of a basketball rolling down an incline but never gets to the bottom.
Okay - Here we go again
[normzone, Aug 21 2008]
||Oops. I think I just voted for my own
invention. Please bear with me, first post.
Greetings to all.
||pssst, I think it's allowed.
||Now I know what to use as my centerpiece for the bar mitzvah.
||Suppose we put some different size/mass balls on the treadmill. Couldn't we have some balls slowly rising, some slowly descending, and some rolling in place at the same time?
||Does not work unless there is
considerable friction arresting the
acceleration of the ball such as it having
some sand in it or a very rough surface
to cause air resistance. To help you
understand why imagine placing a ball
bearing on a pencil then touching the
bearing to the face of an inverted belt
sander. A bearing in good condition will
immediately accelerate to the speed of
the belt with very little pressure against
the pencil. The tendency of the pencil to
move forward could be described as the
"drag" of the bearing. Once the system
is in equilibrium the drag is very
uniform and the angle of the sander
could be set to compensate for the drag
balancing the system against gravity.
Then the only effect of drag that we
would see is the torsional force of the
drag on the pencil itself which we are
resisting with our fingers. The system is
now "balanced". But if we took our
fingers off the pencil the drag exerted
by the bearing on the pencil would be
reduced as the pencil itself began to
rotate pulled by the drag. As the
frictional loss to drag is eliminated the
top speed of the bearing (now solid)
would increase exponentially and it
would slowly fall off the bottom of the
belt no matter how high you turned the
speed. There must be a calibrated
uniform drag designed into the system
to limit the speed of the rotating
member so that energy is removed
equal to compensate for the
gravitational acceleration of the rotating
mass. Air resistance will not provide
this drag unless the angle, and thus the
speed are very low. Much more
complicated than it seems and it would
make great material for a college level engineering contest (who could make
the fastest, or most stable perpetual
||can we do this with meatballs in marinara making a stationary meatfall?
||If one uses expandable cylinders or spheres rotational
energy can be used to expand them rather than
speeding up the rotation. If they're quite heavy on
the outside they could absorb quite a bit of energy
as momentum. Alternatively one could increase air
||//Alternatively one could increase air friction.// Now there's something. If only you had benouilli-er with that post.
||If anybody remembers Tribbles, I could see a bunch of those things "jogging" on a propery adjusted treadmill.
||A soft belt (carpet or similar) would work to increase the rolling friction of the ball, helping to balance it.