Is there general agreement that little-g is the measured acceleration of
the net gravitational field on the surface of the earth, and not simply
a shorthand calculation of GM/r^2? (M is mass of Earth, r is average
radius.) Thus, g can vary over the surface of the earth. Anywhere else,
'g' should have a subscript, i.e., g<moon>.
If you're standing on a scale up to your neck in water, your feet feel
less weight, your spine is under less compression, but your liver is
unaffected. Parts of you weight less, and parts of you stay the same?
Therefore, buoyancy should not be a factor in computing weight.
If you're in a rotating, orbitiing space station, like in "2001", you
are in free-fall, yet you feel the "centrifugal" weight, and a scale
would show that you had weight. You can jog around the circular rim. Do
you have weight in this case?
A comment was made about the term "microgravity". There's plenty of
gravity in low earth orbit, but microgravity refers to the small change
in gravity between the side of the ISS closer to Earth and the side
further away, due to the r-squared difference. An object will experience
a tidal force along its radial direction directed at the center of the
earth. See the section "Microgravity" in
http://en.wikipedia.org/wiki/International_Space_Station
This isn't something that was mentioned in this thread yet, but since
the vomit comet has been mentioned, I have seen the misconception that
you are "weightless" on the way down, and under higher G's on the way
up. For an ideal parabola, you are floating over the entire top half of
the parabola (including the uphill side), and heavier in the bottom half
(including the last half of the downhill side).
For the other topic about acceleration vectors, that's why I like to
progress from statics into dynamics. Statics encompasses forces,
vectors, compression, tension, support, Newton's 3rd, torque, gravity,
mass, weight, frames of reference, maybe even electrostatics and
springs, all under conditions where Fnet = 0 and net torque=0.
After that comes constant velocity motion, and velocity vectors.
Relative velocity and two-dimensional constant velocity (boat moving
across a moving stream, airplane in the wind) are considered.
Then you move into what happens in straight line motion when Fnet is
constant, but not zero. Since vectors are already firmly established,
along with what we consider the positive and negative directions in one
dimensional motion, it becomes easy to equate positive acceleration with
positive net force, and negative acceleration with negative net force. I
like the suggestion to have the positive force rocket and the negative
force rocket, but I worry that the students will confuse the direction
of the exhaust with the direction of the force. Free fall is introduced
as a special case of vertical acceleration.
Then you need to have the students graph the position, velocity and
acceleration vs. time motion graphs for the nine case matrix of
positive, negative and zero net force crossed with positive, negative
and zero velocity. That's 27 graphs. Maybe velocity vs. position as
well. Mastery includes being able to draw all of these graphs.
Then you can combine non-accelerated motion and accelerated motion and
get into projectiles. Mastery includes being able to graph position,
velocity and acceleration vs. time, as well as velocity vs. position for
the horizontal and vertical motions.
Later, you can get into acceleration when the force varies, in
particular, simple harmonic motion.
It's got to be a long, slow build-up, with each concept spiraled in in
multiple contexts, and viewed in real life environments, not just
textbook problems.