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Re: N/kg versus m/s^2

At 08:28 PM 1/25/01 -0600, John M. Clement wrote:
The equation F=mg is calculating the gravitational force on a given mass at
the surface of the earth,

OK.

while F=ma is Ntn's 2 law.

OK.

Unfortunately the majority of texts state that g is the gravitatonal
acceleration, while it is nothing of the kind.

Huh? Nothing of the kind? It sure looks to me like something of that kind.

g = G m_earth/r_earth^2 ignoring the complications of
the Earth's rotation.

OK.

The first year physics student especially the HS student, does not
understand g in the standard text because obviously the object is not
accelerating.

I'll agree with the main parts of that sentence _except_ the "because". It
may occur that some students don't understand g. It may occur that some
object is not accelerating. The relationship between these two occurrences
is vastly more complicated than a simple cause-and-effect relationship.

Under the more rational treatment g is then stated as being 9.8N/kg at the
surface of the earth, not 9.8m/s^2.

According to physics as I understand it, 9.8N/kg is formally identical to
9.8m/s^2. The foregoing attempts to create a distinction without a
difference. Calling it "the more rational approach" doesn't make it
rational.

I assume the idea is to focus attention on the force, so that we can add
forces. We may find there are forces, but no net force, which explains why
the object mentioned above is not accelerating. On the other hand, if we
can add forces, pray tell why can we not add accelerations and come to the
same conclusion (no _net_ acceleration)?

The gravitational acceleration is still 9.8m/s^2, but that is not the same
thing as g.

This appears to be a restatement of the previous pseudo-distinction between
9.8m/s^2 and 9.8N/kg. It remains inconsistent with the laws of
physics. Indeed one need not even apply any principles of physics; just
look up the definition of the symbol "N" and apply the laws of algebra.