Re: Pendulum acceleration

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

At 01:46 PM 10/24/01 +0200, Savinainen Antti wrote:
> If I remember correctly, less than 10% of all IB physics candidates got it
> right.

That doesn't tell us anything about the level of understanding of the
students.  In general, when a question gets such a low score, you should
suspect there is something wrong with the question.  In this particular
case, the question is grotesquely ambiguous.

There are two perfectly valid ways of analyzing the problem, the D=1 method
and the D=2 method.  They lead to the same physics, but to different ways
of wording the explanation.

In physics, the term "force" is well defined, but "net force" is not.  What
is included in the net, and what is not????

> The net force at the bottom is *not* zero because the pendulum bob is
> changing direction (a circular path). Hence there must be a net force
> acting, in this case the net force = tension - weight. So the tension
> force has greater magnitude than the weight of the pendulum bob.
> Tangential acceleration at the bottom is indeed zero but normal
> acceleration is not.

That is a fine way of starting the D=2 description.  Radial and tangential
forces are considered.

At 03:04 AM 10/24/01 -0400, Ludwik Kowalski wrote:
> In other words, the NET FORCE, and thus the acceleration,
> is zero at the bottom and non-zero at an angle, large or small.

That statement makes perfect sense in the D=1 description.  We can treat
the radial force as an uninteresting constraint and focus all our efforts
on the tangential forces and motions.

========

Test-makers should not penalize students for analyzing the system in ways
the test-makers failed to foresee.

=========================

At 07:29 AM 10/24/01 -0400, Tim O'Donnell wrote:
> Clearly it is moving the fastest at the
> bottom and an instant later it must be moving slower.

That's not true.  At the bottom, you could argue that a moment _earlier_
the speed was less, so the speed must be increasing.  You could also argue
that a moment _later_ the speed will be less, so the speed must be
decreasing.  In fact, neither statement is true to first order.  Therefore
the acceleration (in the D=1 description) is zero.  The bob flies through
the bottom at constant speed.  Acceleration has to do with first-order
changes in velocities;  changes that have higher-order dependence on the
size of the "moment" are irrelevant.

> This is a change in velocity - this is an acceleration. To
> have an acceleration, a force must be present.

In D=2 there is a change in direction of the velocity, but there is no
change in the magnitude of the velocity near the bottom.  The bob flies
through the bottom at constant speed.