Re: How does a see-saw really work?

Date: Mon Jan 15 22:09:10 2001
Posted By: Vernon Nemitz, , NONE, NONE
Area of science: Physics
ID: 969407309.Ph
Message:
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Greetings, Jake:

different ways can you apply a force to it?  For the most part, you
already know that pushing or pulling constitute the main types of
application of force.  But what about variations on those themes?
Depending on where a force is applied to the stick, or how much is
applied, or even how rapidly it is applied, very different results
can occur.

If the stick is secured so that one end cannot move, then if you
try to pull the other end directly away, the stick experiences
"tension".  Molecular bonds become stressed (and stretched a bit)
throughout the length of the stick.  If you push the free end
directly toward the secured end, the stick experiences
"compression".  Molecules resist being squished into each other, as
you may expect.  Different substances respond to different degrees;
wood is not as responsive to forces of tension and compression as
is, say, a stick of rubber, but be assured that wood IS affected.

Next, suppose the stick of wood is placed horizontally, supported
at both ends, with nothing under its middle (like a miniature
bridge).  If you apply a force to its middle, pushing downwards,
the stick may flex a bit.  (Very likely, it flexes a minute amount
anyway, thanks to the force of gravity.)  The wood may withstand a
considerable amount of force before it breaks; we say that a
"shear" force has been applied.  As mentioned above, the rapidity
of application of a force can be as important as the total amount
of force:  Consider a mini-bridge that can support a slowly-
accumulated mass of 1000 kilograms -- yet it may break if a karate
chop is instead applied, even though the "normally computed"
maximum force is less than that associated with 1000Kg of resting
mass.  (In the field of engineering, the INITIAL application of a
force has effects that are usually described with such terms as
"jerk", "kick", or "starting transient".  Physicists generally
don't pay a lot of attention to these effects, because they are
difficult to measure precisely and consistently -- and they only
last for milliseconds at best.  What evidence there is suggests
[and this qualifies as Mad Science!] that while forces are normally
computed in association with "acceleration", which is "a rate of
change in velocity", there MAY be additional forces associated with
"a rate of change in acceleration".  It would be these additional
forces that let the karate chop -- or kick -- break the wood.)

You're probably wondering when I'll get to the topic of see-saws.
In a way, I just did!  Take that mini-bridge above and turn it
upside-down, and you GET a see-saw, with the 1000Kg mass in the
middle becoming the fulcrum, and the bridge-support points becoming
the kids on each end.  Obviously, if there are too many kids at
each end there will be too much mass, and the see-saw will break in
the middle (shear force again).  So as we detour into the topic of
geometry, keep in mind that see-saws aren't being neglected.

Below is a sketch of several arcs:

1 - - - - - - - - - - - -
2 - - - - - - - - - - -       -
3 - - - - - - - - - -       -      -
4 - - - - - - - - -       -      -     -
5 - - - - - - - -       -      -     -     .
6 - - - - - - -       -      -     -     .    .
7 - - - - - -       -      -     -     .    .
-      -     -     .    .       .
-     -     .    .       .
-     .    .       .      .
.    .       .      .
.       .      .
.      .        .
.      .        .
.        .
.        .       .
.       .
.       .
.       .      .
.      . .
.      . . .
.      . . . .
. . . . .
. . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
7 6 5 4 3 2 1

By simple inspection of these arcs, it is obvious that #1 is longer
than any of the others, and #7 is the shortest.  Now suppose you
take a thin stick and bend it into an arc.  The OUTSIDE edge of the
bent stick might correspond to arc #1 above, while its inside edge
might correspond to #2.  Because the stick is thin, the difference
in distance bewteen #1 and #2 is quite small, and you are able to
bend the stick easily.  Now ask yourself, "When I let go of one end
of the bent stick, what causes it to straighten out again?"

To reach the answer, let us pretend we have a big magnifying glass,
and look at the bent stick.  NOW the stick may look as thick as the
distance between arcs #1 and #7 above, instead of arcs #1 and #2.
Arc #4, of course, corresponds to the MIDDLE of the bent stick.

Note that when the stick was straight, all edges were the same
length.  When bent, however, one edge has been forced to imitate
arc #1 (stretched under tension), and one edge has been forced to
imitate arc #7 (squished under compression).  Without needing a lot
of math, it is reasonable to state that arc #4 is close to the
original length of the stick.

So:  If bending the stick involves forces that cause parts of it to
compress and parts of it to stretch, any resistance to those forces
is going to reverse that compression and tension.  THIS is what
causes the stick to straighten out again.

Now take away the big magnifying glass, and remember that you only
have a thin stick.  What if you had a thick stick, that really was
equal to the distance between #1 and #7?  You can't bend that so
easily at all!

One of the differences here is simply that the thick stick has a
lot more material (wood) in it than the thin stick.  Trying to bend
it means compressing and tensioning much more material than before
-- and this is naturally associated with much more resistance to
those forces.  Furthermore, the greater distance outside and inside
edges of a thick stick, the greater the DIFFERENCE in the lengths
of the arcs they would form when bent.  That is, much more tension
and compression must be applied, to cause the edges to imitate arcs
#1 and #7, than to cause those edges to imitate arcs #1 and #2.

Perhaps now it is pretty obvious why one end of a see-saw goes up
when the other end goes down.  It is made of pretty thick wood, or
even steel, after all.  As you press down on one end, a force of
tension grows along the top surface, and a force of compression
grows along the bottom surface.  These two forces work together to
lift the other end of the see-saw.

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With respect to constraints on motion, that will entirely depend on
how the see-saw is mounted.  As a child I encounterd an unusual
type of see-saw that was cone-shaped.  The fulcrum was at the top
of a short tower, just under the top of the cone, and seats for
kids were spaced along the lower circular edge of the cone.  The
whole cone could sway in any direction, and it could also rotate
around the fulcrum.

With respect to predictive formulae, there are almost certainly
heavy-duty equations in the literature describing the tension and
compression effects in vastly more detail than presented here.  You
would primarily use them to determine how much a see-saw (or a
bridge) would flex under a given load.  Feel free to pursue those

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