Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] the sign of g



Weirdly enough I actually now care a little bit about this. I can make an argument for the -ive sign to wit:

g is the local scalar value of the Earth’s gravitational field strength at the Earth’s surface, but F_vec = mg_vec is a vector equation and the negative sign use reminds us that the field points down. I feel that negative downwards (towards the Earths center) ’s a favored co-ordinate system for energy.

The negative is important to my students conceptual development to keep track of energy: Displacing an object with mass (or charge or whatever) AGAINST the direction of a force stores positional energy we standardly call potential energy. Displacing an object in the direction of the field releases that field stored energy (often as kinetic energy). So think it’s important to keep in mind that gravitational field and resulting force(s) have direction at the Earth’s surface and the direction matters. A classroom analogy I often use is a stretched rubber band, you can see and feel the energy storage and release shooting a rubber band. If you rotate the band vertically, g can be pictured as conceptually akin to invisible rubber band pulling an object down to the center of the earth. Lift a lab weight from the floor to a table top and you have stored energy by stretching the “g rubber band” if you will. Push the lab weight off the table and the U_grav is recovered as KE. Similar arguments repeat with U_electrostatic and U_magnetic later on in the intro course.

Making the direction of g explicit as much as possible helps me later with consistency describing spring (elastic potential) energetics, gravitational orbital energetics, electric field energetics, chemical bonding etc.

Dan M


On May 9, 2016, at 11:28 AM, stefan jeglinski <jeglin@4pi.com> 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
http://www.phys-l.org/mailman/listinfo/phys-l