User's Manual

012–07192A Discover Density Set
7
Introduction
Developing a mathematical equation from a set of experimental data is an
extremely useful skill. The examples that follow show a method that will
work for a great many physics phenomena. Then you will be asked to apply
the method to data in a lab situation.
The mineral fluorite is often found in geometric shapes having eight faces
which are equilateral triangles. This example addresses the problem of
finding an equation that allows one to calculate the mass of such a fluorite
specimen from a measurement of one of the edges.
Experimental Data
Some data were obtained from direct measurement of five fluorite specimens:
xy
edge mass
(cm) (g)
0.8 0.8
1.3 3.3
2.0 12.0
2.7 29.5
3.7 75.9
Graphing this data in the ordinary manner is a good first step. The results
suggest an equation such as y = x
2
, or y = x
3
. Of course, a constant
multiplier would likely be present, resulting in an equation such as y =
0.57x
2
, or y = 3.9x
2
. Finally, if the exponent were a number such as (3/2) or
2.716, the same basic shape of graph would still result. Quite often in
physics, and particularly in simple situations such as this, the exponent will
be either a small integer, or a ratio of two small integers.
Data Analysis
All of the equations above are of the form y = c x
k
, where c and k are two
different constants. Many equations in physics, although certainly not all, are
of this form.
If an initial graph or other reasoning make it reasonable to assume an
equation of the form of the form y = c x
k
, the next task is to determine the
values of c and k. Several methods exist for doing this. The first might be
called “guess and test.”
The Mass
of Fluorite
Octahedra
(Pre-lab)