This is an attempt to summarize the best of what has been said on this subject.
The question "what is weight" has two good answers, depending on the
level of accuracy required.
1) The ordinary, pedestrian definition of weight is simply
weight = M g
where M is the mass of the object under study and g is the acceleration of
gravity. Within the pedestrian approximation g can be taken to be a
constant, conventionally 9.8 m/s/s.
*) When I want to buy ten pounds of potatoes, this definition is the right
one to use.
*) When I want to buy a 16-pound bowling ball, this definition is the right
one to use.
*) When I stand in the terrestrial reference frame and analyze an airplane
or a baseball in flight, this definition is the right one to use.
Note: It is possible to build devices called scales that measure to high
accuracy mass and/or weight. For pedestrian purposes there is a one-to-one
correspondence between mass and weight, so in fact a device that measures
any linear combination of the form
F = (x) * weight + (1-x) * M * 9.8 m/s/s
will give the same answer for all values of x. I have seen scales that use
this trick, with interesting fractional values for x.
Refinement A) There are limits to what a scale can do. In particular,
scales by themselves do not and should not correct for buoyancy. Such
corrections, if necessary, must be made separately. For ordinary solids
and liquids, the correction is on the order of 0.1 percent, but if you want
to weigh a big bag of propane at STP, the scale-reading will need to be
substantially corrected.
Refinement B) For high accuracy, you need to account for the fact that not
all terrestrial reference frames have g=9.80665 everywhere. In particular,
you need to correct for at least
elevation (not everybody lives at sea level)
lattitude (the earth is not a sphere)
geology (the earth is not uniformly dense), and
rotation
2) [General definition] We must use a more general definition when we
consider non-terrestrial reference frames. Acceleration can introduce
large corrections -- indeed *arbitrarily* large corrections -- to the
pedestrian picture.
The definition can again be stated
weight = M * g
but to achieve full generality we must define g to be the acceleration of
the chosen reference frame, relative to an instantaneously colocated freely
falling frame.
*) When you are analyzing the flight of a turning airplane using the
pilot's frame of reference, this is the right definition to use.
*) When you are analyzing the motion of a space station inhabitant using
the station's frame of reference, it is 100% correct to say that the
inhabitant is weightless, to a verrry good level of approximation.
2a) Note that an object's weight is explicitly sensitive to the choice of
reference frame. There can be no frame-independent value of weight.
2b) Note that for any given reference frame, an object's weight is *not*
sensitive to the state of motion of the object. The motion of the
*reference frame* is the only thing that matters.
2c) Note that weight is a vector, M is a scalar, and g is a vector. The
direction of g is conventionally called "down". The direction (not just
the magnitude) depends on the choice of refernce frame. It is sometimes
helpful to use the terms N-down (Newtonian down) for the direction toward
the center of the earth, and E-down (Einsteinian down) for the direction
things go when you drop them. For an airplane in a steep turn, using the
pilot's frame of reference, the two directions are significantly different.
2d) The general definition reduces to the pedestrian definition in the
appropriate limits. The correspondence principle is alive and well.
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copyright (C) 1999 John S. Denker jsd@monmouth.com