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Re: g



One thing that can sometimes be useful for getting the signs right in
problems such as these is the extensive use of velocity time graphs. A
carefully plotted graph of this type can easily be reversed to show the
show the possibility of different conventions.
Simple calculations from raphs can also often help solve seemingly complex
problems.
Here simulations such as Interactive Physics can also be useful for the
students to quickly create graphs

Simon Lorimer

On Mon, 10 Sep 2001 21:44:05 -0400, Ludwik Kowalski
<kowalskiL@MAIL.MONTCLAIR.EDU> wrote:

In learning dynamics students will become aware that the sign
of acceleration is always the same as the sign of the net force.
Now we are discussing an object moving along a vertical line.
Here g is negative when the y axis is pointing up and g is
positive when the y axis is pointing down. As emphasized
by others, we are free to choose the orientation of the y axis.

The difficulties described by Michael are likely to be reduced
when elements of dynamics are presented to students when
they learn kinematics. It is not a crime to start talking about
the "no F no a" idea at the level at which F is conceived only
as "a pull or push of some kind". We should not be separating
kinematics from dynamics too much. Students know that
objects are attracted down and this is sufficient to see why g
must be down. Then "down" can be made either + or ? by
introducing a convenient y axis.

In other words "the down" is absolute while "positive and
negative" are arbitrary.
Ludwik Kowalski

Michael Edmiston wrote:

After my original post, and a reply from Tina about the problems her
students seem to be having, I don't think the problem is actually a
problem
of whether g is positive or negative. Therefore, even though this
thread is
interesting, I don't think it is solving the original problem.

I think the original problem stems from the common feeling among students
that positive acceleration means "speeding up" and negative acceleration
means "slowing down." This preconceived notion is strong and for some
students I never succeed at getting them beyond it. Another way to say
this
is that if acceleration is in the same direction as the velocity, then
the
acceleration is perceived as positive. If the acceleration is opposite
the
velocity, the acceleration is perceived as negative. Of course these
preconceived notions about acceleration are incorrect... or at least
these
notions are contrary to how practicing physicists view it.

I wrote an e-mail about this, but it never came back to me, so I wonder
if
anybody got it. I'll repeat it now with apologize to any of you who
might
have already received it.

* * * speeding up and slowing down * * *

Some students have the gut feeling that acceleration is negative when the
object is slowing down, and the acceleration is positive when the object
is
speeding up. This is not true. Objects with negative acceleration can
just
as likely be speeding up as slowing down. Objects with positive
acceleration can just as likely be slowing down as speeding up. Students
need to learn to disconnect the sign of acceleration from the sign of the
velocity. These signs are determined by the choice of coordinate system;
they are not determined by each other.
I find it useful to point out that the signs of acceleration/velocity
can be
+/+ or +/- or -/+ or -/-. Then I point out that when the signs are the
same, the instantaneous speed (magnitude of velocity) is increasing.
When
the signs are opposite then the speed is decreasing. I also point out
that
in the opposite-sign situation it can't stay that way for too long
because
the object will eventually come to rest then reverse direction and the
signs
will become the same.
If you can get students to understand the previous paragraph then they
will
have "seen the light." I certainly don't have 100% success with this,
but I
keep trying.