What
did the above experiment demonstrate? It shows that the scale on the left was
measuring the force of gravity (weight) not mass. On earth the spring was standardized
to read 100g at sea level. A true balance beam (like a triple beam balance you
use at school) measures mass by balancing the scale against a known (standardized)
mass. On the moon the mass on the left side of the balance may 'exert less force',
but then less force will be needed to balance it.

So
what is really mass and weight if they are not the same thing?

**Mass**
is defined as the amount of matter an object has. One of the qualities of mass
is that it has inertia As an example of inertia, imagine an ice puck resting on
a frozen pond. It takes a certain amount of force to set the puck in motion. The
greater the mass the more force will be needed to move the puck. The same is true
if the puck were sliding along the ice. It would continue to slide until a force
is applied to stop the puck. The more massive the puck is, the more force will
be needed to stop the motion of the puck. Mass is a measure of how much inertia
an object shows.

The
**weight **of an object on earth depends on the force of attraction
(gravity) between the object object and earth. We can express that force as an
equation:

F
= G[M m/r^{2}] ,

where F is the force of attraction, M is the
mass of the earth, m is the mass of the object, and r is the distance between
the center of mass of the two objects (G is called the Gravitational Constant)

What
does this equation show? What will cause the force of attraction to increase or
decrease? If either mass increases the force of attraction increases proportionally.
Since the moon has 1/6 the mass of earth, it would exert a force on an object
that is 1/6 that on earth.

Why
is the **1/r**^{ 2 }factor so important? This is an inverse
square relationship which seems to show up a lot in physics. How does it affect
the force?

What
is **1/r**^{ 2} when r=1, 2, 5, 10? What is the decimal equivalent?
Notice that when r=1 the value **1/r**^{ 2} is 1.0, but at
r=10 it deceases to 1/100. That means gravity gets weak 'quick' as we move away
from the earth.

To
get a real feel for the inverse square relationship, see if you can get two magnets.
Move the poles closer and closer slowly, what do you notice when r (the distance
between the poles) is very small?