Re: The sign of g

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

A major source of confusion in problems of this sort
has to do with blurring the distinction between _speed_
and _velocity_.   Note the contrast:
 -- The change in speed is negative during the
upward trajectory and positive during the subsequent
downward trajectory.
 -- The change in velocity is uniformly downward.

The laws of physics are most simply written in
terms of velocity, not speed.


Rick Tarara wrote:
> This is a one dimensional problem

I agree.  It is important to figure out whether you're
doing the D=1 problem or not.

But there is a downside as well as an upside to doing
the D=1 problem.  Fundamentally _g_ is a vector, and
as such cannot be positive or negative.  A particular
component of this vector might be positive or negative
in a particular reference frame, but that is not the
same thing.

> An object accelerates if it speeds up, slows down, or changes direction.

True as stated, but it brings in the notion of "speed"
which is probably a distraction....  Certainly a distraction
unless carefully discussed and systematically distinguished
from velocity.

> In one dimension, an object that speeds up has an acceleration in the
> same direction as the motion while an object that slows down has an
> acceleration opposite the direction of motion.  Now for the vertically
> thrown ball, on the way up it is slowing down, therefore the
> acceleration is opposite the direction of motion--downwards.  On the way
> down the ball is speeding up, therefore the acceleration is in the
> direction of motion--downwards.  The acceleration is always downwards.
> [Now convince them it is still accelerating at the peak of the motion.]
> You've defined DOWN as the negative direction in this problem.
> Therefore since the acceleration is always down, it must always have a
> negative value.

If I were doing this, I would make two columns, putting
all the speed-related remarks in one column, and all
the velocity-related remarks in another column, to
emphasize the contrast.

But at the end of the day, I would draw a big X through
the speed column, and exhort everybody to think in terms
of velocity not speed.

> Of course you could (and should at times) define down
> to be the positive direction.  The ball still accelerates downwards, but
> now 'g' would carry a positive sign.

Thats a separate point.  Also a good point.