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C.1: A convex die is dropped from inside an upright funnel with steep
sides. The hole in the funnel is larger than the die. The funnel
is held fixed in the air. There are no other object that intersect
the inside of the funnel, or the region below the bottom hole of the funnel
and less than the diameter of the die from the bottom hole. Infer that
the die will come out the bottom of the funnel.
Dynamics, deterministic, gravity, no external force, prediction.
C.2: In (C.1), if the die is not convex and it is dropped from nearly
level with the rim of the funnel, then it is possible but very unlikely
to bounce out the top of the funnel.
Dynamics, probabilistic, gravity, no external force, prediction.
C.3: In (C.1) if the die is dropped from above the funnel then it may
bounce out or it may fall through. The higher it is dropped and the
more elastic the die, the larger the likelihood that it will bounce
out the top.
Dynamics, comparative probability, gravity, no external force, prediction.
C.4: In (C.1), if the sides of the funnel are shallow, or if there is
a shallow shelf or pit in the side of the funnel, of a size
comparable to the die, or if the die is not convex and the side of the
funnel has irregularities, then the die may get stuck on the side
of the funnel. The shallower the sides of the funnel, or the larger the
irregularities, the more likely the die is to get stuck.
Dynamics, comparative probability, gravity, no external force, prediction.
C.5: In (C.1), if the bottom hole is too small for the die to pass through,
then it will get stuck at the bottom of the funnel.
Dynamics, deterministic, gravity, no external force, prediction.
C.6: In (C.1), if the bottom hole is large enough that the die can pass
through in some orientations but not in others, then the die may fall
through or may get stuck. The larger the range of orientations in which
the die can pass through, the more likely that it will pass through.
Dynamics, comparative probability, gravity, no external force, prediction.
C.7: In (C.1) if there is another fixed object O2 below the bottom hole of the
funnel at a distance less than the minimum width of the die, blocking
the entire hole, then the
die will end up resting on this O2 (and possibly also on the side of
the funnel), partly inside the funnel.
Dynamics, deterministic, gravity, no external force, prediction.
C.8: In (C.7), if the object blocks only part of the hole, then the die
may come out the bottom or may get stuck resting on O2. The more of
the hole that O2 blocks, the more likely that the die will get stuck.
Dynamics, comparative probability, gravity, no external force, prediction.
C.9: In (C.1), if the funnel is moved while the die is inside, then the
die may come out the top of the funnel; it may come out the bottom;
or it may remain inside the funnel as long as it is being moved. The
more vigourously the funnel is moved, the less likely it is to come
out the bottom.
Dynamics, comparative probability, gravity, external force, prediction.
C.10: In (C.1), if several objects are simultaneously dropped inside the
funnel, then one or more may bounce out. The more objects there are
and the more elastic the objects, the more likely that one will bounce
out.
Dynamics, comparative probability, gravity, no external force, prediction.
C.11: In (C.8), if the sum of the diameters of the objects is wide enough to
span the bottom hole, then some of the objects may jam the bottom of
the funnel. The broader the range of configurations that jam the hole,
the more likely that such a configuration will be attained.
Dynamics, comparative probability, gravity, no external force, prediction.
C.11.a: In (C.11), if the funnel is shaken, as in C.9, then the likelihood of a permanent jamming decreases. Dynamics, comparative probability, gravity, external force, prediction.
Funnel with crack or cracks
Open funnel on inclined plane..