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Re: time squared & time cubed/erratum



At 06:37 PM 1/16/02, you wrote:
At 05:09 PM 1/16/02, John Denker wrote:
>...consider the
>flexure of a springy plank, such as a high-diving board. If
>you make the board thicker by a factor of X, leaving the
>other dimensions the same, its stiffness goes up by a factor
>of X to the third power. Calling it X cubed is a bit of a
>misnomer; there is no cube of size X involved.

?
Let me amplify this idea a little - it will not fly in this form,
with electricians who bend conduit by hand - or with machinists
who know about deflection of say boring bars with force applied, e.g

<http://www.mmsonline.com/articles/060105.html >

The rule in question is:
Twice as thick, four times the cantilever deflection for constant end force:
twice as long, eight times the deflection for a constant end force.
(Notice the concrete examples?)

Brian W

Third time's a charm?

This 'rule' is wrong (though the URL is helpful - and shows a fourth power
connection between deflection and a cantilevered cylinder's diameter).

I find on rereading that John Denker is quite correct and that one can
practically confirm the relation with two feeler gage strips and a calliper,
or by referring to the properties of two steel sections of suitable weight
and depth, e.g. : W6 X 15 vs. W12 X 30 for example.


Brian Whatcott
Altus OK Eureka!