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Re: [Phys-L] the sign of g



At the risk of sounding like "me, too" I whole-heartedly agree with John Denker, Todd Pedlar, and Richard on this issue. After 30+ years of teaching, I hammer home the ideas:
1) g_vec is the gravitational field (NOT the acceleration) and it points, yea, *defines* downward. It has a magnitude which is positive, so g is *always* >0 (+9.8 m/s^2 for our introductory students).

2) You *must* draw a picture, you *must* define an origin (if position is a property you wish to investigate), and you *must* define positive coordinate directions.

3) The acceleration vector in projectile problems (the context here) happens to be the same size and direction as the gravitational field vector, so the magnitude of the acceleration is g, in the same vector direction as g_vec (downward). If you choose the +y direction as up, a_y will be -g; choose +y as down, a_y will be g. And g is always a positive number.

If you don't force them to assign/choose the positive directions of the coordinate system they wish to use ( i.e., no deliberate coordinate choice means zero on the problem), they will always be sloppy. Force them to do it and pay attention to vectors. I also emphasize to them that they may choose those positive directions.

All of John's points on this topic should be taken to heart. They are all important points. They will save a lot of confusion in the future.

-> -----Original Message-----
-> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of
-> Richard Tarara
-> Sent: Monday, May 09, 2016 12:22 PM
-> To: phys-l@www.phys-l.org
-> Subject: Re: [Phys-L] the sign of g
->
-> There are many ways to tackle this problem and others have presented
-> some. I would only emphasize that breaking the idea that 'g' carries an
-> intrinsic negative sign will help later on when you have to be careful about
-> forces between charges where students want to carry the signs into the
-> algebra. Again it is a case of setting a coordinate system and using
-> attractive/repulsive to determine the direction (and therefore the
-> sign) of the force on a given charge.
->
-> rwt
->
-> On 5/9/2016 11:28 AM, stefan jeglinski wrote:
-> > This slays large populations of students on that first exam, and seems
-> > to be a serious mental block for them: whether g = +9.8 or -9.8 (units
-> > suppressed, substitute the English version over metric if you like). I
-> > teach that the sign can't be determined unless a coordinate system is
-> > defined, which is a separate but critical step in setting up any
-> > problem, but they like to rush. Many will inadvertently (or with
-> > intent) define a coordinate system (e.g., up is positive), which
-> > naturally works the signs into the algebra, but then at the end, will
-> > say "well g is always -9.8" and introduce a sign error when they get
-> > out their calculators.
-> >
-> > I've taken to teaching that g=+9.8 or g=-9.8 is the incorrect way to
-> > think about it. Rather, g has merely a value of 9.8, and the sign is
-> > an "artificiality" that has nothing to do with g per se. The pushback
-> > I get is that "9.8 is the same as +9.8" and I push back in return on
-> > that but to skeptical looks.
-> >
-> > My question is: is there a good mathematical argument I can cite
-> > (aside from a coordinate system) for why +9.8 and 9.8 are not the same
-> > thing? Or am I myself wrong?
-> >
-> >
-> > Stefan Jeglinski
-> >
-> >
-> > _______________________________________________
-> > Forum for Physics Educators
-> > Phys-l@www.phys-l.org
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->
->
-> --
-> Richard Tarara
-> Professor Emeritus
-> Saint Mary's College
->
-> free Physics educational software
-> http://sites.saintmarys.edu/~rtarara/software.html
->
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