Re: Gain and Mechanical advantage confusions

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 08:16 2001/11/20, you wrote:
> I wanted to throw this out to the community, see what the general opinion
> is on gain and/or mechanical advantage for simple machines.  Here are some
> definitions I have come across-
>
> Force gain (=F/f)
> Distance (or displacement) gain (=D/d)
> Ideal gain (=D/d)
> Actual (or real) gain (=F/f)
> Mechanical advantage (usually = F/f, but also written as D/d)
>
> Which of these are most useful to students?  Are some terms used
> preferentially over others?

FWIW, older editions (3rd and earlier) of the lab manual written by Wilson
and published by Heath contained a simple-machines lab that referred to the
"ideal gain" as the "theoretical mechanical advantage" (TMA, for short) and
the "force gain" as the "actual mechanical advantage" (AMA). The
"efficiency" (e) of a simple machine was then defined as the ratio of AMA
to TMA and equated, using simple algebra and the classic (force x
displacement) definition of work, to the ratio of "output work" to "input
work". You could violate the principle of conservation of energy (i.e.,
build a perpetual motion machine) if only you could find a way to get e to
exceed unity. Some of my more careless students occasionally manage to make
measurements that lead to a calculated value of e that does exceed unity.
However, for some reason, my more careful students never obtain such a result.

Forces are determined by tying known masses (used as weights) to either end
of the machine. The AMA is determined by selecting input and output weights
that cause the machine to move slowly at constant speed. Effects of high
velocities are thus effectively swept under the rug, as are possible
discrepancies between static and kinetic friction coefficients; clearly,
the kinetic case is implicitly preferred by the author's procedure. Static
friction is dismissed by the simple expedient of giving the system a gentle
nudge at the beginning of each trial.

The experiment does not address classical first-, second, or third-class
levers. It does address pulleys (block-and-tackle systems), the
wheel-and-axle, and inclined planes. Measurable deformation (stretching) of
the string occurs with all three of these systems, but experience indicates
that it does not have a significant effect on displacement measurements,
which are made with the string fully stretched at the initial and final
positions as well as everywhere in between. It is an open question whether
deformation has a practical effect on force measurements. Frictional
forces, which are difficult to measure separately from deformation
phenomena, seem to have a much larger effect, as suggested for example by
the significant difference in results for AMA and efficiency obtained
before and after the pulleys are lubricated.

--MB