Re: Apparent weight

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

I don't want to get embroiled in the weight/apparent weight controversy, but
I'm curious about something that Gene Mosca wrote--specifically:
> It seems to me that the above statements fail to provide an acceptable
> definition of weight.  Consider a reference frame in which Twin A stands
> on a stationary scale (Scale A) resting on a horizontal floor and
> identical Twin B stands on a scale (Scale B) fastened to a platform that
> is accelerating down a frictionless incline, at the bottom of which is a
> loop-the-loop.  The two scales will have different readings even though
> the twins have equal masses.  In addition, Scale B's reading will vary
> dramatically as it and Twin B traverse the loop-the-loop.  Further, if the
> incline is not frictionless the readings of Scale B will be different.

I do not understand what is unacceptable about this.  Why shouldn't an
object's weight vary as for Twin B above?  An object's weight is not an
intrinsic property of the object (like its mass is).  I would expect an 
object's weight to depend on the special circumstances (e.g. the state of 
acceleration of the frame in which the object is at rest, the possible 
existence of various supporting forces deflecting the object from the 
free-fall state, etc.) that the object finds itself in when the weight 
measurement is made.

> If we agree to accept scale readings as the definition of weight then it
> seems to me that weight is a peculiar animal and one that is not commonly
> accepted anywhere.  I am not ready to pass off this definition to my
> students.  If I am somehow missing the point, please straighten me out. 

I don't know how common or not acceptence of such a definition is, but, at
least, I accept it (in a modified form).  I would modify the previous
definition so that the scale in question provides 100% of the
non-graviational force acting on the body being weighed.  If other
non-gravitational forces act on the body than that provided by the scale,
then, according to my definition of weight, the scale gives a faulty reading,
rather than the weight being what that reading is.  For instance, if I stand
on my bathroom scale in such a manner that only part of my feet are on the
scale and part of them are on the floor next to the scale, or if I lean on a
neighboring wall or partially support myself by grabbing onto a towel rack or
railing, then the reading of the scale is (according to my definition)
incorrect, rather than my weight changing according to how much of my
non-gravitational support is provided by the scale.  Since bouyancy forces of
the surrounding air support about 1 part in 770 of me when I stand on my
bathroom scale I would have to increase the scale's reading by a
corresponding amount for it to give a correct value for my weight.  Since my
scale's accuracy is far lower than the amount of the needed correction, I
do not make such a bouyancy correction when I weigh myself in air in my
bathroom.

This question of bouyancy effects reminded me of what Donald said on a 
different thread:
> ...     . And when our textbook spoke of a body immersed in liquid, and
> told us that the buoyant force was equal to the "loss of weight in the
> liquid" we realized that the loss of weight was due to the fact that the
> force required to support it (the tension in the string suspending it) is
> less when it's in liquid than when it's hanging from the string in air.
> Hence, the weight being equal to the string tension, the weight decreased
> when taken from air to liquid. We knew that mg hadn't changed.

I want to make clear that in this case my definition of the weight of the
immersed body is the same as when the body is not immersed in the liquid.
When the body is immersed in the liquid the surrounding liquid provides
some of the (non gravitational) support for the body (because the liquid
pressure exerted on the under side of the body is greater than the liquid
pressure exerted on the upper side of the body).  Because of this partial
support the tension in the string connected to the scale is reduced, and the
scale then gives a faulty reading for the object's weight.  My definition
of weight can be summarized as the magnitude of the vector sum of all of the
non-gravitational forces acting on a body which (therefore) tend to deflect
the body from a free-fall state.  So the way I see it, a neutrally bouyant
fish in a lake is *not* weightless.  Rather, the fish has the same weight
it would have if it way lying on the bottom of a fishing boat.  When the
fish is in the water its weight is supported by the perfectly form-fitting
water bed it is laying on/in.

> Oh, I know why people enjoy discussing esoteric details of mathematical
> physics which you never encounter in daily life. That's where the *fun* is!
>
>        -- Donald

How true!

> My recommendation is to avoid using the term weight.  It is a difficult
> choice, however, because it permiates most of our textbooks.  The terms
> gravitational force and normal force allow for more clarity.
>
> Gene

I agree.

David Bowman
dbowman@gtc.georgetown.ky.us