User's Manual

Discover Density Set 012–07192A
14
Your instructor may tell you which method(s) to use.
6. Check the accuracy of the equation by using the following data from
published sources:
volume of a sphere = (4/3)π r
3
radius = diameter / 2
density of the sphere material = 1.18 g/cm
3
density = mass / volume
7. Algebraically combine this information to produce an equation giving
the mass of these spheres in terms of their diameter.
8. Compare this result with the equation you determined experimentally.
Are they in agreement, taking into account uncertainty?
Introduction
Mathematical equations of several variables are common in physics. Some
examples are;
F= m a, Newton’s Second Law of Motion,
F = G (m
1
m
2
) / d
2
, The gravitational force between two point objects,
a = v
2
/ r, a formula for centripetal acceleration, and
T
2
= (4 π / G) r
3
/ M, an equation relating orbital time of a satellite to the
radius of its path and the mass of the body it orbits.
These equations and others may be discovered by organizing and analyzing
experimental data. The example that follows leads you through the process
of discovering a mathematical equation that describes experimental data.
You will follow the same process in a lab activity that follows.
Pre-Lab Exercise: The Mass of Cones
Suppose you are given a variety of solid cones made of a certain type of
metal. You are then asked to discover a formula that will allow you to
calculate the mass of any cone of this metal, from measurements of the
diameter of the base and the height. You are free to make measure the mass
and other dimensions of the cones you have been given. You should
assume that you do not know any special mathematical formulas regarding
cones.
First, you recognize that there are three variables involved: mass, diameter,
Discovering
a
Mathematical
Equation
That
Describes
Experimental
Data
(Pre-lab)