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Physics295Introductory Laboratory I
Partners
Section
Date
LABORATORY
Ib:
MEASUREMENT
AND
UNCERTAINTY
[
j
l
j~
"When you can measure what you are speaking about and express it in numbers,
you know something about it; but when you cannot measure
it, when you cannot
express it in numbers, your knowledge is of the meager and unsatisfactory
kind.
" 
Lord Kelvin
IOBJECTIVES
1.
Understand
the
difference
between
accuracy
and
precision
in
physical
measurements.
2.
Learn one method for determi.ningthe uncertainty of a measurement.. Determine
the uncertainty associated with the Motion Detector used in this lab.
3.
Learn how to propagate uncertainty to other measurements.
Introduction:
Measurement
and Uncertain
All measurements carry an element of uncertainty.
Improving your knowledge of the
uncertainties in your measurements improves the quality of inferences which can be
drawn from these measurements.
Today you will investigate uncertainties in the measurements made in Phys 295 lab.
Page 1 of Ib
Real Time Physics:
Active Learning Laboratory: Lab Ib Measurement and Uncertainity
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There are two main types of uncertainty encountered in experiments: uncertainty related
to
precision,
and uncertainty related to
accuracy.
Precision
Precision refers to the
width of the range of values that can
be the result of a
measurement.
It is an indicator of how
fine
your measurement is. If a measurement is
precise, you will be able to repeat it many times and always find approximately the same
result.
Examples.
I have a meter that displays a digital readout. The position of the rightmost digit typically
determines the precision.
Let's say my meter reads
3.101.
This really means that the
measured value lies somewhere between 3.1005 and 3.1015, so it really represents a
measurement of 3.1010 plus or minus 0.0005. The uncertainty due to limits in precision
is 0.0005.
When you measure a length or distance using a ruler, you can usually measure well to the
limit imposed by the most fine markings on the measuring stick.
For example, when
using a meter stick, the most fine marking is typically the mm. Thus, with a meter stick,
you can usually set an uncertainty due to the limit on precision of :!::0.0005m, assuming
your eyes can distinguish the markings satisfactorily.
Another common means of determining uncertainty due to the limit in precision is to
repeat a measurement a number of times and determine the standard deviation of the
measurements.
This standard deviation is a measure of the uncertainty due to limits in
precision.
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 Fall '07
 Brown
 Physics, Standard Deviation, real time, Motion detector, Ultrasonic Motion Detector

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