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