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[Phys-l] pin-connected constraints



http://www.av8n.com/physics/img48/pin-connected.png

On 08/15/2007 10:45 AM, Jeffrey Schnick wrote:

pin-connected

This is great fun. Pin-connected mechanisms are common in
the real world. Often they are more precise and more robust
than other designs for solving the same problem.

There is an elegant way to think about such things ... and
thinking of the force as being "in the direction of the strut"
is *not* the elegant way ... nor even the correct way, except
in the simplest cases.

Please refer to the four versions of a pin-connected apparatus
in
http://www.av8n.com/physics/img48/pin-connected.png
The green anvil-shaped thing would be free to slide on the base,
except that it is pin-connected by the red strut as shown. The
pins are represented by black dots.

Assume the strut has negligible mass and negligible compliance
(inverse spring constant).

The version in the upper-left corner is the "standard" version.
This should generally be the first versions students see, because
even this will scare them and confuse them at first. Eventually
they will figure out that the force is "in the direction of the
strut".

At that point you can challenge them with the upper-right version
and/or the lower-left version. A lot of students who thought they
understood the physics (but didn't really understand it) will have
to re-think what pin-connectedness means.

The version in the lower-right corner doesn't introduce any new
physics, but it does impose a higher penalty on those who don't
see the correct and elegant way to analyze the situation.
Those who don't understand the physics will perceive the problem
to be harder than it really is.