Re: The sign of g

[Larry Cartwright <exit60@CABLESPEED.COM>]

Tina Fanetti wrote:
> How do I explain to a student that when we choose up (+y) to be
> increasing, we say that the sign of g is negative, regardless of
> whether the ball is going up or going down.
> My students seem to get that when the object is going up, g is
> negative.  They want to make the ball going down positive g.
> But it stays negative because of the choice of axis.

I think the problem occurs because students think that when the ball
reaches its maximum height and its velocity vector changes from up to
down, this somehow changes the frame of reference.

I found that their perceptions "straightened out" when I started
repeatedly emphasizing that **once we have chosen a frame of reference,
that frame must stay the same from the beginning of the situation we are
analyzing to the end**.  No fair changing the reference frame in
mid-analysis.

We essentially *define* "down" by the direction of the gravity unit
vector (which describes the direction of both F_g and g).  "Up" is
defined incidentally as the direction opposite to the gravity unit
vector.  "Down-ness" is a physical construct, while "up-ness" is simply
a mathematical construct based on "down-ness".  In situations without
measurable gravity (a spacecraft in deep space), there really is no down
and up, n'est-ce pas?

Once we have defined the direction of the g vector as negative, that is
the direction it *must* retain throughout the situation regardless of
whether the ball is rising, falling, or (for an infinitesimal time
interval) motionless.  No fair changing the reference frame in
mid-analysis.

Best wishes,

Larry

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Larry Cartwright   <exit60@cablespeed.com>
Retired (June 2001) Physics Teacher
Charlotte MI 48813 USA
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