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Re: [Phys-L] two very different "gravity" concepts

Interesting discussion (again) about gravity. Everyone has a slightly
different way of teaching this stuff, and there will never be a consensus.
I use bathroom scales to show apparent weight (normal force, support
force, etc.). Students understand the idea, and it works well when solving
F = ma problems. Regarding apparent weight, one must also consider Earth's
shape, rotation, and atmosphere (buoyant force).

I also tell the kids about Einstein's happiest thought -- a freely falling
person has no sensation of weight (and a bathroom scale would read
nothing). This was the basis for his GT of R in 1916.

Regarding antipodes, here's an interesting site I found a few months ago.
Scroll down to see a map of the Earth. Click anywhere and start digging
(through Earth's center). It tells you where you'd end up! Also says if
you drop an object, it would take about 42 minutes to make it to the other
side. I always wanted to know this value. Dos anyone know how this was
found? calculus, I presume?

www.livephysics.com/simulations/mechanics-sim/dig-hole-earth




Phys-L@Phys-L.org writes:
On 01/02/2013 04:23 PM, Ludwik Kowalski wrote:
What might be measured in a falling elevator is called apparent
acceleration.

I don't like terms such as "apparent" acceleration or "apparent"
weight. The weight measured in one frame is no more (or less)
apparent than the weight measured some other frame.

The point is, no matter what you do, it's frame-dependent.

It is the g calculated from the universal gravitational force, either
in Spain or in N.Z.

Calculating g is not so simple. In particular, suppose we have
a frame comoving with a freely-falling elevator in Spain. The
elevator is small, but we can extend the /frame/ as far as we
wish. If we extend it all the way to New Zealand, we find that
the framative g is
|g| = 0 in Spain [1]
and
|g| = 2 G M / r^2 in NZ (approximately) [2]
relative to this frame ... with a very remarkable factor of
two in equation [2].

The law of universal gravitation tells us the difference
between these two g-values, but it can't tell us either
of them separately. Einstein's principle of equivalence
guarantees that it can't.

============

Also, to save people the trouble of looking it up, I
should have mentioned that Spain and NZ are antipodes.

If you want another example, Hawaii and Botswana are
antipodes.

Examples are relatively hard to come by. Only about 4%
of the earth's land is antipodal to land.

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