Ed Schweber (edschweb@ix.netcom.com)
Physics Teacher at The Solomon Schechter Day School, West Orange, NJ
To obtain free resources for creative physics teachers visit: http://www.physicsweb.com
----- Original Message -----
In reference to Atwood Machines Ludwik Kowalski writes:
There are two possible approaches to pulley
problems. One is to consider the total mass (m1+m2)
accelerated by the net force. In our example (Atwood's
machine) it was the difference between two weights.
I am very much in favor of this approach, at least in a introductory
course -even though the professor of my Lagrangian mechanics course railed
against it -especially if you consider several masses and ask for the
tensions in the connecting strings as well as the acceleration.
It force students to think about what is meant by the system and how the
system is chosen arbitrarily to make forces either internal or external
depending on what we are solving for. The free body approach is more easily
turned into a mechanical algorithm.
The system approach also allows students to build up a quantitative
intuition in other ways. Think of a hanging block connected by a string over
a pulley to another block on a frictionless horizontal surface. What happens
to the tension and the acceleration if we increase the mass of the block on
the table.?
The acceleration decreases - easy enough. But students will then
frequently focus on the block on the table and become stymied. Its
acceleration is less so they typically think the tension is less. But then
they come to realize that the mass is also greater and they don't know which
effect is more important.
If they focus on the hanging block, it has less acceleration but the same
mass. So the upward tension in the string must have increased.
In other words, thinking like this forces students into a mode of
thinking where they must find the part of the system where only one variable
has changed (acceleration, but not mass for the hanging block). This is an
important lesson in itself.