Re: Poms view of the Gilly debate

On May 12, 1:50 am, a...@xxxxxxxxxxxxxxxxxx (Dr A. N. Walker) wrote:
In article <1178901858.079763.189...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Gavin Cawley <g...@xxxxxxxxxxxxx> wrote:

If you lot could manage to re-phrase your comments in terms
of impulse, momentum, restitution and centres of percussion, rather
than in terms of energy and power, it might make a lot more sense,
and might even turn into proper mechanics.
At which point, I'd have an audience of one (very knowledgable though
he may be ;-).

Well, OK, but although I don't recall much mention of
cricket [or football, tennis, golf, ... for that matter] in the
writings of Galileo and Newton, this is basically pure Galileian
mechanics with a dash of Newtonian, and well within the bounds
of A-level maths+physics. Doesn't even need calculus. There
must be a reasonable number of readers with that knowledge, and
many more who could at least appreciate the results.

Yes, but why needlessly limit the audience to those who have the
background rather than those who might be interested? Also (being the
product of a more modern education) I have never really studied
classical mechanics (although I expect there are subjects that I have
studied and you have not), so I'm not keen on making myself look more
expert than I actually am by pretending that I have.

Here is your starter for ten. A brick wall will work quite
well at "hitting" a ball bowled at it. Would you expect a rubber
wall to work better, or worse? Give reasons.
Not so sure how that is relevant.

Well, for a start, there is *no* [relevant] energy or
power stored in the wall, so it's a simpler problem -- always
a good starting point.

Yes, it is simpler, but perhaps the simplification changes the problem
in such a way that the important element of the discussion (stored
energy) is no longer relevant (and so neither is the example). For a
start, a bat is not moving with constant velocity w.r.t. the ball, but
should be accelerating through it under force supplied by the
batsman. Secondly, the ball does not make an instantaneous perfect
contact with the bat (because the blade is relatively soft and there
is a bit of give in the handle), which I would have thought would give
opportunity for stored energy to come into play. Of course I may be
wrong, but an over-simplified example doesn't really help.

Secondly, a Galileian transformation*
turns it into a moving wall.

Except that as I have pointed out, there is energy being put into the
system whilst the experiment is in progress, which may be relevant.

After that, you can start to
think about a *light* moving wall, which you can call a "bat"
[or a "club"] if you like. Mere words

Except that a in the case of a bat, the ball does not have negligible
mass compared to the bat and the bat is not an independent object, but
is anchored to a more substantial object at one end via a stiff
flexible hinge (at least approximately), which affect what will
happen.

For example, you can "easily" find the angle of loft
at which you need to hit the ball -- cricket or golf -- for a
drive to have maximum range. Left as an exercise. You lose
most of the marks if you assume the answer involves 45 degrees.

Depending on where you play, you seem to be rather selective in your
simplifications ;-)

As to the rubber -- would you expect a ball to bounce
further off a brick wall or one made of squash balls [which
would therefore compress and store energy,

dropping onto a stationary wall, the brick one. Now if it were an
ideal rubber wall that released all of its stored energy back into the
ball... ;-)

and, according to
the arguments up-thread, enhance the power of the wall]. Why?
What determines the strength of bounce? [You can use a floor
rather than a wall, if it helps you to find rubber ones. Mere
words again.]

Are you sure the simplifications you have made are valid?

What kind of rubber? What
configuration of wall? How do you mean "better"?

Sorry, those are unbounded questions, you'll have to
ask elsewhere. [Didn't they teach you not to argue with the
examiner?]

No, but I have learned to set assignments that are well posed unless I
deliberately intend them to be ill-posed.

* This is just Galileo's observation that mechanics on board
a smoothly-moving ship is exactly the same as it is on land --
you could play [French?] cricket in your cabin and not notice
the difference.

not the same on an accelerating ship, which is a valid point re.
cricket.

So if you know what happens to a ball and a
stationary wall/bat/club, you can just add the same velocity
to every part of the experiment to know what happens if the
wall/bat/club is moving.

A simplification too far IMHO.

How about this, propel a snooker ball towards a normal cushion on a
snooker table and it will rebound nicely. Take the rubber out of the
cusion, how far does it rebound now? As Albert Einstein would say
"Make everything as simple as possible, but not simpler".

If a hard brick wall is better than a soft springy rubber one, why is
the blade of a cricket bat made out of soft, springy Willow, rather
than hard Oak (note the main function of the handle is to absorb the
vibrations)?

Having said which, if stored energy plays a part it will be absolutely
minimal (if at all - I may well be wrong), the point is there will be
far more energy stored in the handle than there would be in the squash
ball in Gilly's glove (if he chose to use it that way in the first
place).

.

Relevant Pages

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