Re: Gain and Mechanical advantage confusions

["John S. Denker" <jsd@MONMOUTH.COM>]

Gary Turner 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)

I've never heard of "force gain".  If the students use
this term in everyday life, or in a physics research lab,
nobody will understand them (not without help, anyway).

> Distance (or displacement) gain (=D/d)

Never heard of that either.

> Ideal gain (=D/d)

Never heard of that either, and listeners would have
a very hard time figuring it out.

> Actual (or real) gain (=F/f)

Ditto.

> Mechanical advantage (usually = F/f, but also written as D/d)

That's the term you hear on the street, and in the research
lab.  If pressed, I would define it as D:d.  If there isn't
too much friction, this is provably equal to f:F (not F:f).

> Which of these are most useful to students?  Are some terms used
> preferentially over others?
>
> Personally, I have a problem with the force - distance gain pair because
> one gains at the expense of the other.  I think this is confusing to talk
> about a 'gain' in force and a 'gain' in distance at the same time.

In (say) electrical engineering, "gain" usually refers to
energy gain, so one would say that levers do not have gain.
The electrical analogue of a lever is a transformer;  it
steps up the voltage according to the turns ratio, but it
steps down the current.

> The ideal - actual gain pair is also confusing because the "ideal"
> situation is not the ratio of distances.  If you account for stretching and
> flexing, the "distance gain" is certainly not ideal.  In some cases (such
> as a flexing lever), it seems that the imperfections related to distance
> are more significant than the imperfections related to force.  However,
> when you have a pulley with mass and friction, the imperfections related to
> force will dominate.

I consider "ideal gain" and "actual gain" to be utterly dead
horses and won't bother to flog them.

> Mechanical advantage is just outright confusing when it is sometimes used
> for distance and sometimes for force.  If we restrict it to one, what
> should we call the other one?

Do we really need fancy terminology for this?  Why not use plain
multi-word phrases such as "ratio of forces" and "ratio of
displacements"?

I agree that it is not always 1000% clear whether "mechanical
advantage" refers to D:d or d:D, but usually you can figure
it out from context.  In the real world, given a truly ambigous
question, you would just request clarification from whomever
posed the question.

You have to ask what is the objective:  understanding the physics
concepts, or rote memorization of fundamentalist definitions?
My recommendation: concepts are important;  use terminology if
and only if it helps communicate the concepts.  If the terminology
is slightly ambiguous, as it so often is, provide enough context
to disambiguate it.

> You have to assume the force and distance
> ratios are different to get efficiency.

True -- but calculating the efficiency of simple machines
in this way is academic in the worst sense of the word: it
never happens except in homework problems.  In the real world,
The ratio of distances is (usually) rather well determined
by the structure of the machine, but the ratio of forces
is not;  it depends on lots of other factors.  It might
scale with velocity in a funny way;  it might scale with
applied force in a funny way.