In article ,
Corky Scott wrote:


Tony, it doesn't matter where the plumb bob hangs, going up means
adding some force in excees of 1G to do it. No matter how gently you
do it, a sensitive enough G meter will detect the additional force
that is required.

It's kind of like trying to fake out a bathroom scale. No matter how
gently you step onto it, it will eventually read your weight.

Climbing is like pushing against an inverted scale.

Corky Scott

Corky,

"Net force = mass times acceleration" (Isaac Newton, ~1620)

"Acceleration = rate of **change** of velocity"

"Work done = force times distance"

If you're standing on a bathroom scale in a stationary elevator at the
ground floor, the scale will read your weight. Gravity (the invisible
gravitational field) is pulling down on you with a force mg (your mass
times the acceleration of gravity); the scale is pushing back up on you
with the same force mg (and that force is what its dial reads). The
total force on you (the sum of gravity pulling down on you plus the
scale pushing up on you) is thus zero, but it's zero not because you're
stationary, that is, remaining at a constant level; it has to be zero
because you're at a constant vertical speed, namely zero; you're not
*accelerating* (changing speed) -- not at this point anyway

The doors close, the elevator starts upward. For a brief initial
period, until the elevator reaches its steady-state upward speed, the
scales read more than mg. That's because the elevator (or whoever is
pulling on the elevator cable) is both pushing you upward with a force
equal to your weight (mg), which does work and adds to your potential
energy in the gravitational field; but there's also a slight excess
force at the start which is needed to accelerate you to the steady-state
speed of the elevator (and which therefore gives you a little kinetic
energy as well as your steadily increasing potential energy).

Once the elevator reaches its steady-state speed (around the 3rd floor,
let's say) from there up to the 104th floor you're traveling at a
*constant* vertical velocity: you're *not accelerating*. Therefore
there can't be any net upward force on you; the scales read mg.

[This does leave out the fact that the value of g changes very (very!
very!) slightly between the ground and the 104th floors, but this change
is so minute in going from the ground floor to the 104th floor that it's
just not in the discussion here.]

The rest of the way up, from the 3rd to 101st floors, the scales are
pushing up on you with a constant force mg; and that force eventually
acts through a distance h, the height from the ground floor to the 104th
floor. Total work done by the elevator on you is therefore force times
distance, or mgh. That work has gone into giving you an added potential
energy equal to mgh in the Earth's gravitational field.

[As you neared the 104th floor and the elevator slowed to a stop, you
also lost the kinetic energy you had gained between the ground and third
floors. The scales showed a small reduction below mg between 101 and
104 just as they showed a small increase between first and 3rd floors.]

You now own that extra potential energy of mgh; it's yours, as you step
off the elevator on the 104th floor. Want to get it back? Step outside
on the viewing deck and pop over the railing. Leaving aside questions
of air resistance, by the time you get back down to, say, the first
floor level you'll have all that potential energy converted into kinetic
energy -- a lot of kinetic energy! Unfortunately, one floor later all
that energy energy will pretty much have been converted into heat,
slightly warming up a small patch of sidewalk and some gunk on it.

Same deal in a plane: hang a seat from a butcher's scales hung from the
ceiling of a plane, and sit in it. Have someone fly the plane in a
constant forward speed, constant upward speed, straight line climb.
Except for a slight initial transient period when they begin the climb,
the scales will read your weight, mg, no more, no less.

--"Another Tony"