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Re: cavendish expt



"C) Conclude that a round solid fiber gives
minimal stiffness for a given strength."

If "a given strength", is the same as a given cross sectional area, then
not true. Aux contraire, a cylinder has the highest stiffness strength
(tensile) for a solid member than any other simply connected
cross-sectional shape. St. Venant showed this some time ago (ca.
1855). continuing:

"B) Again split the tape, but rather than
moving them apart, move them together so they
share the same attachment point. This will
give less stiffness than the original full-width
tape."

why do you think the split tape will have significantly less stiffness
than the original?

bc who reminds all of my organization.


p.s. a quick calc. for the torsion constants (per unit length and same
shear modulus) of a cylinder (r= 0.0178 inch) and a ribbon two mills
thick and 1/2 inch wide give a factor of 120 X (the cylinder being the
more rigid)




"John S. Denker" wrote:

I wrote:

> "Videotape seems odd. Monofilament fishing line
> is pretty much standard for this application.
> Videotape will do bad things to the sensitivity."

Bernard Cleyet wrote:

> please elaborate.
1) Requirement: The support (the tape in this case)
needs to be strong enough to support the weight of
the rotor.

2) Objective: Subject to the previous requirement,
to get the most sensitivity you want the minimal
torsional stiffness.

So..... Consider a couple of possibilities:

A) Split the video tape lengthwise. Rather than
attaching the two halves side-by-side, attach them
way out at the ends of the rotor, like a swing-set.
This will give a huuuge stiffness.

B) Again split the tape, but rather than
moving them apart, move them together so they
share the same attachment point. This will
give less stiffness than the original full-width
tape.

C) Conclude that a round solid fiber gives
minimal stiffness for a given strength.

D) Think about engineering applications of
idea (A): suppose you want the _maximal_
stiffness from a given amount of material.....
-- Hollow drive shafts.
-- Hollow flagpoles (flexion not torsion).
-- I-beams.
-- Trusses.
-- Skins stretched over spars and ribs.
-- Skins stretched over honeycomb.

Designed objects are full of tricks like
this. Especially vehicles and aircraft,
where weight is at a premium.

Note that these tricks don't increase the
ultimate strength, i.e. the failure point.
But they vastly increase the stiffness for
any amount of stress short of failure.