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Experimental Uncertainty and Error Analysis
Introduction:
In the physical sciences as well as in engineering, we depend on accurate measurements of realworld
objects to test our theories and to design the things we build. In this lab we will study the accuracy of measurements
and how this accuracy affects things we calculate from measured values.
All measurements are subject to "experimental uncertainty", sometimes called "experimental error". These terms do
not refer to any kind of "mistake" or “blunder”
1
in making measurements. It is simply an observed fact that when
repeated, independent measurements are made on a physical system, the measured values will not generally all be
exactly the same. (We will see this happen in this lab.) To make progress in experimental science and engineering, it
is important to strive to reduce these measurement errors, and to be able to calculate the effect they will have when
we use measured values to calculate desired quantities and results.
The mathematics of error analysis, or error
propagation, gives us a systematic way to determine from our data itself, how confident we should be of our results;
that is, how far from the "correct" or "actual" value our results are likely to be. In this lab the whole class will work
as a large group, each person measuring the diameter and the mass of a metal object. We will study the spreads of
the measured values and relate them to characteristics of the measurement tools. We will see graphically how certain
mathematical quantities such as mean (or average) value and standard deviation can be used to describe the set of
measured values.
Next we will calculate the volume and density of the object from our measurements, and observe
the spreads of these "derived quantities".
Mathematical formulae of error propagation which should predict the
spreads in the derived quantity, will be checked against the observed spreads.
Figure 1.
S
teel ball,
triple beam balance
, a
ruler and
a Vernier Caliper. Metal calipers are sharp. Use with CUATION.
Vernier Micrometer
s
are also shown and often used to make precise measurements.
Equipment:
1.
Vernier Caliper.
2.
Triplebeam balance.
3.
Steel ball (one for entire class).
Theory:
This experiment is somewhat different as the theory is mathematical, though we will approach it from a physical
point of view.
The theory we shall discuss will be spread throughout the Procedure and Analysis sections.
1
In fact, we tacitly assume all human blunder has been removed from the experiment.
LAB# 2
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Procedure:
In this part of this lab we will study the measurement process itself. That is, the fact that each and every
measurement ever made has some uncertainty.
There is no such thing as a “Perfect Measurement”.
You can see
one aspect of this inability to make a perfect measurement quite easily.
What if a measurement comes out between
the finest markings on your measurement scale?
What value would you assign to this measurement?
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 Fall '08
 RABE
 Physics

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