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Re: cantilever versus arch

At 11:08 AM 1/27/02 -0600, Jack Uretsky wrote:
Ahh, but simply stacking blocks on top of each other does
not a cantilever make.

OK, that's almost a truism. But folks do not learn much from truisms.

Was this statement offered in support of the notion that a
cantilever is half an arch, or half an arch is a cantilever?
If so, please supply the missing steps of the argument,
because I'm not getting it.

Sure, simply stack blocks on top of each other does not make a
cantilever. It also doesn't make an arch. It also doesn't make
the Taj Mahal. What does that prove?

The point is, when you state the problem please
include the constraints.

Well, that's good advice, but I say again that the
cantilever problem is well posed without any reference
to arches, contrary to what some people have repeatedly
asserted.

The usual version goes like this: Stack N uniform rectangular
blocks so that they stick out over the edge of the table as
far as possible. Then say how far that is, as a function of N.

Nitpickers are responsible for whatever additional conditions
they feel necessary: Homogeneous gravitational field, no
friction, no crazy glue, et cetera.