Re: Problem

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 7:53 -0700 9/18/01, Paul O. Johnson wrote:
> At that particular instant in time, David, the object's speed is zero;
> it is neither increasing or decreasing. At later times its speed is,
> indeed, increasing.
I haven't been following this thread carefully, since I thought I had
resolved the problem in my own mind and consistently with other
postings on the thread, but something doesn't ring true here. Just
because the object's speed is zero doesn't mean it is not changing.
In fact there is a fundamental difference between the two case that
have been discussed here. In uniform circular motion, the
acceleration is *not* constant but is constantly changing direction,
if not magnitude. In this case we have a situation where the
acceleration is *always* perpendicular to the velocity and hence
there is not a change in speed. This is very different from the
trajectory situation where the acceleration is constant and hence
able only to change the vertical component of the velocity, which is
does continuously, even when the object it at the top of its
trajectory.

My curiosity piqued, I wrote the expression for the *speed* in the
two cases, starting from the expression of the velocity in terms of
veritical and horizontal components and then taking the pythagorean
combination of the two components. In the uniform circular motion
case, it is truly constant, and hence its time derivative is zero,
and the speed is not changing. In the trajectory case, there are
terms involving *gt* in the expression for the speed, Hence the speed
is *not* constant, even if the component subject tot he acceleration
happens at some instant to be zero. The time derivative of the speed
is *not* zero, hence it *is* changing.

I haven't got a copy of HRW handy so I can't look up the problem
first-hand, but a question comes up in my mind. In what chapter is
this problem? It looks like it depends on where it is in the book
what the answer should be since it is a snapshot of a particular
situation and does not tell us what the acceleration is doing. If the
problem is in the chapter where they discuss UCM (and hence they are
imagining a UCM situation), then the answer David quoted is correct.
If it is in the chapter where they discuss trajectories (and hence
they are imagining an object at the top of its trajectory), then I
would have to say their answer is wrong. Taken out of context, this
seems to me to be an ambiguous question.

Have I missed something?

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

Let's face it. People use a Mac because they want to, Windows because they
have to..
******************************************************