Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

physics of bouncing



Hi Folks --

We have begun a discussion of the physics of bouncing.
There have been some controversial statements.
It should not be too hard to resolve the controversies.

As a possible way to reduce some of the confusion, let's analyze a few
variations of the situation shown in
http://www.monmouth.com/~jsd/physics/ballistic-pendulum.gif

Basically we have
a) An anvil. This is very hard and rather heavy (20kg). It is supported
by a string from the ceiling. An anvil suspended in this way is easier to
analyze than one resting on the floor, because we can observe any
horizontal momentum transferred to it.

b) A ball. It is also supported on a string. It is relativly light
(20g). In one version of this apparatus, the ball is a superball. It is
fairly hard and extremely bouncy.

This seems to be within the spirit of previously proposed demonstrations,
in that you can let the ball swing down from a height, converting
gravitational potential energy into kinetic energy, which then is involved
in a collision.


The following facts can be easily verified:

A) If we remove the anvil and let the ball swing freely, eventually the
motion decays. Air resistance is obviously the dominant dissipative
mechanism.

B) If we replace the anvil and let the ball bounce against it, eventually
the motion decays.

I assert:
B1) The decay with the anvil is only slightly faster than the decay without
the anvil.

B2) Air resistance remains the dominant dissipative mechanism.

B3) Internal friction within the ball is the second most important
dissipative mechanism. This friction applies to internal modes excited by
the collision process.

B4) You can glue half a superball to the anvil in such a way that the
collision physics is locally left/right symmetric. This slightly changes
assertion B5 but does not significantly change any of the assertions (B1
through B6).

B5) When the moving ball (momentum p, energy E) hits the stationary anvil,
it transfers 200% of p to the anvil. It transfers less than 1/2% of E to
the anvil.

B6) Placing a card between the ball and the anvil provides no information
whatsoever about the magnitude of the p transfer or the E transfer.

B7) Placing a card between the ball and the anvil provides no reliable
information about the magnitude of the energy dissipation process (B2 or B3).

===========

In another version of the demonstration, you can replace the ball by a wad
of putty of comparable dimensions. The putty is so gooey that it sticks
when it hits the anvil.

In this case:

C1) Internal friction in the putty is the dominant form of dissipation.

C2) You can symmetrize the situation by putting a wad of putty on the
anvil. This greatly changes assertion C3 but doesn't significantly change
any of the other assertions.

C3) When the moving putty (momentum p, energy E) hits the stationary anvil,
it transfers 100% of p to the anvil. It transfers about 0.1% of E to the
anvil. The rest is dissipated within the putty.

C4) Placing a card between the ball and the anvil provides no information
whatsoever about the magnitude of the p transfer or the E transfer.

C5) Placing a card between the ball and the anvil provides no reliable
information about the magnitude of the energy dissipation process.

===========

Let us consider a third version, namely steel ball hitting steel anvil.

D1) I am not 1000% sure, but I suspect that this case is closely analogous
to the superball on superball case.

D2) I don't know what is being measured when the card is placed between the
steel ball and the steel anvil, but I strongly suspect it is measuring a
process that does not take place unless the card is there. It does not
measure the amount of energy transferred from the ball to the anvil. It
does not measure the amount of dissipation, except for dissipation in the
card, in which case it has nothing to say about the normal (cardless)
bouncing situation.

If anybody believes that the card measures anything significant about the
normal (cardless) bouncing situation, please explain what process is being
measured, and how the card measures it.