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

["John Clement" <clement@hal-pc.org>]

Since the force is proportional to the distance from the center assuming a
homogeneous distribution of mass you can apply algebra.  Just use the
formulas for simple harmonic motion.  Of course they are derived using
calculus.

As to a proposal to label one force law as the acceleration force law, that
is a bad idea.  Students are already confused about the F_g = mg where g is
an acceleration.  They know it resembles NTN2, but an object at rest is not
accelerating so the acceleration is zero.  This causes all kinds of
conceptual problems.  Labeling it the "local" gravitational law valid on the
surface of a planet is just fine.  But if you take a Modeling approach, the
students should become accustomed to the idea that laws can be modified or
remade for new situations.  Students need to be reminded that many laws are
limited or are even approximate.  The local law can be easily "discovered"
by hanging various masses from a spring scale and then after graphing the
data find the "law" or equation for the force when you know the mass.  When
we get to the NTN general law they model the force using a simulation that I
created of a planet pulling on a mass.  They graph the force vs distance
from the center and figure out the new general law.

John M. Clement
Houston, TX


> 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?