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<p>Phillip Ford wrote:
<blockquote TYPE=CITE>
<br>r<sub>k</sub> is the distance Mg is from the fulcrum , not m<sub>1</sub>g.
M is the mass of the key and action for the 'real key' case, as opposed
to ye massless beam case, as Stephen refers to it, in which m<sub>1</sub>
is the action mass, since the key is massless.
<br> </blockquote>
I wrote that (m<sub>1</sub>g) wrong (looking at his first figure), and
understood it wrong to begin with. I'd thought for a bit that he was saying
more or less that r<sub>k</sub> was the distance of the << capstan
>> from the fulcrum. I found that was wrong last nite after writing. But
I am unsure of what you are saying here as well.. isnt Mg a constant (both
in quantity and position) and r<sub>k </sub>more or less the effective
balance point at any given time for any given counterleading situation
?
<br>
<blockquote TYPE=CITE>
<br>>> I am unsure of exactly what I<sub>k</sub> is... Inertia of
that point mass
<br>>> ?...Inertia at that same position ??
<p>.. Anyway, I<sub>k</sub> is the moment of inertia of the key assembly
(the key and the action components). As I understand it, Stephen
has idealized the distributed mass of the key and action parts as a point
mass M, located at a point r<sub>k</sub>, which will give the same moment
of inertia as the distributed mass of the key and action parts. So
yes, I<sub>k</sub> is the inertia of that point mass. To quote from
the paper:
<p>"Consider a real piano key and action components with distributed mass.
This combination will be called the (unleaded) reference key and represented
by a defined distributed mass beam with: (i)centre of mass (first moment
about the fulcrum) and (ii) moment of inertia (second moment)."
<br> </blockquote>
Yes... that also became clear last nite as well... grin ... helps to read
the formulas and definitions on the last page.
<br>
<blockquote TYPE=CITE>It seems a bit ambiguous to me, but as I read it,
M is an idealized mass that represents the distributed mass of the key
and action and it is located at center of mass r<sub>k</sub>. I<sub>k</sub>
is the moment of inertia of this point mass, so it should be I<sub>k</sub>=Mr<sub>k</sub>^2.</blockquote>
Hmm... I'd rather thought the M was an idealized mass as you said, but
located at the << capstan >> and the center of mass was a seperate
quantity. This would mean that the mass at the center of mass would be
the product of these two. If so the values I plugged in last nite
were more or less ok. Sort of a different way of describing the leverage
?? ... I mean in a fully balanced key r<sub>k</sub> is zero so Mr<sub>k</sub>
and for that matter Mr<sub>k</sub><sup>2</sup> become zero as well, as
they should in that case as it would take zipp diddly force to get the
key moving then :) . This would also mean that I<sub>k</sub> would be zero
there..... :)...yet M itself never becomes zero. Hmmmmm... I feel
another one of these headaches comming on ... hehe. At anyrate...
this seems to be the point where I am least certain of what Stephen means.
And I'd like to clear it up for certain as then I would know for sure how
to plug what values into the equations
<blockquote TYPE=CITE>>>And how does any of this then affect the position
or occurance of the
<br>>>break point ? I'd also like a word put to the term "C"
<p>C doesn't seem to have an explicit definition in the paper, but it seems
to be the center of mass of the key and action assembly. It's what
I'm calling CG (center of gravity). I<sub>k</sub> affects the slope
of the acceleration line and so affects the location of the break point.</blockquote>
Isnt the captilized G the symbol for the gravitational constant ?.. is
that what you mean to use here ? And I<sub>k </sub>....as I understand
it, Stephen says that the slope of the acceleration line has nothing
to do with the breakpoint location. The breakpoint location is where all
different slopes intersect... so I dont quite get what you mean by this
sentence.
<br>
<p>Cheers
<br>RicB
<p>--
<br>Richard Brekne
<br>RPT, N.P.T.F.
<br>UiB, Bergen, Norway
<br><A HREF="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A>
<br><A HREF="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broadpark.no/~rbrekne/ricmain.html</A>
<br><A HREF="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib.no/grieg/personer/cv_RB.html</A>
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