Is weight determined strictly by the distance between and mass of two objects, or are other factors figured in; i.e. can a person be considered weightless underwater?

Is weight determined strictly by the distance between and mass of two objects, or are other factors figured in; i.e. can a person be considered weightless underwater?

Asked by: Chris Smallwood

Answer

Your question is as much about symantics as physics, so
I'm afraid the answer depends on your definition of the
term 'weight'.

If weight is defined as the gravitational force on a body,
then your statement that it depends only on the masses
of the two objects and the distance between them (actually,
the distance between their respective centers of gravity),
is correct. But that definition implies that conditions
we ordinarily call 'weightless' are not. Everything from
orbiting astronauts to people in falling elevators have a gravitational
force acting upon them. This definition implies they
all have weight in spite of the fact we ordinarily consider
them 'weightless'.

If you use a more specific definition of weight as 'the
amount of external force required to keep a body at rest
in its inertial frame of reference', you come closer to
the more common understanding of 'weightlessness'. In this case
an astronaut needs no further 'upward' force to remain
stationary in his spacecraft and can be considered
'weightless'. Similarly, an object submerged under water
would only weigh the difference between its gravitational
force and the upward buoyant force.

Using this second definition, a person underwater wearing
just enough weights to establish neutral buoyancy CAN
be considered weightless since no additional external
force is required to keep him at rest relative to the
bottom. Of course, his internal organs still experience
a net downward force and require support from within, so
the feeling does not exactly duplicate the weightlessness of
an orbiting astronaut.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'