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Re: A weighty subject



Timothy Folkerts wrote:
Let me define two quantities
    g(1) = GM/R^2    = gravitational field strength
    g(2) = dv/dt     = acceleration of falling object in lab frame

These differ by up to about 0.03 m/s^2, depending on latitude, so
    g(1) = g(2) + v^2/R

Who votes for W = mg(1) and who votes for W = mg(2)?  You seem to be saying
that weight is mg(2).  Or specifically, weigh is the force of gravity minus
centripetal effects due to the rotation of the earth.  So at the poles, W
= mg(1) = mg(2) but at the equator, W = mg(2) = mg(1) - 0.03 m/s^2.

And by the way, which of these two is officially 9.81 m/s^2 ???

Is the definition of g to be decided by secret ballot? Can we not agree on the very lucid and reasonable distinction in Resnick, Halliday, Walker, 5th ed., p. 326, viz,

"The gravitational acceleration a sub g computer from F = GMm/r^2 is not the same as the free-fall acceleration g that we would measure for a falling object (and that we have approximated as 9.80 m/s^2 near Earth's surface)."

"The two accelerations differ for three reasons: (1) Earth is not uniform, (2) it is not a perfect sphere, and (3) it rotates. Moreover, because g differs from a sub g, the weight mg of the object differs from the gravitational force of the object for the same three reasons."

That makes sense to me. What else is there to say?

poj