Topicmd743ba61d3e7d613_1528449000663_0Topic

Measurement uncertaintymeasurement uncertaintyMeasurement uncertainty

Levelmd743ba61d3e7d613_1528449084556_0Level

Second

Core curriculummd743ba61d3e7d613_1528449076687_0Core curriculum

I. Using physical concepts and quantities to describe phenomena and to indicate their examples in the surrounding reality.

I. Cross‑sectional requirements. The student:

5) uses the concept of measurement uncertainty; saves the measurement result together with its unit and including information on uncertainty.

Timingmd743ba61d3e7d613_1528449068082_0Timing

45 minutes

General learning objectivesmd743ba61d3e7d613_1528449523725_0General learning objectives

Familiarizing with the concept of measurement uncertainty.

Key competencesmd743ba61d3e7d613_1528449552113_0Key competences

1. Determining the causes of measurement uncertainty.

2. Writing the measurement result with a specified accuracyaccuracyaccuracy.

Operational (detailed) goalsmd743ba61d3e7d613_1528450430307_0Operational (detailed) goals

The student:

- uses the concept of measurement uncertainty,

- writes the measurement results with a specific approximation.

Methodsmd743ba61d3e7d613_1528449534267_0Methods

1. Learning by observation.

Forms of workmd743ba61d3e7d613_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionmd743ba61d3e7d613_1528450127855_0Introduction

[Ilustration 1]

Task 1

Look at the picture and answer the question:

What is the air temperature in this shop?

Answer:

Thermometers indicate different air temperatures in the shop. The thermometer readings shown in the figure are between 22°C and 25°C.

Therefore, based on the indications of these thermometers you cannot give one temperature value as the air temperature in the shop. It can only be stated that the temperature is in the range of 22°C to 25°C.

Conclusion:

The measurement results never give absolute certainty as to the value of the measured quantity (in this case - temperature). We are talking about the so‑called measurement uncertaintymeasurement uncertaintymeasurement uncertainty.

The measurement uncertainty is defined as the smallest readable scale unit.

Proceduremd743ba61d3e7d613_1528446435040_0Procedure

Experiment 1

Research problem:
Indicating sources of measurement uncertainty.

Hypothesis:
The measurement uncertainty is related to the characteristics of the measuring instrumentmeasuring instrumentmeasuring instrument.

What you will need:

a) laboratory thermometer
b) medical thermometer
c) room thermometer
d) a beaker with tap water

Instruction:

1. Insert three thermometers at the same time into the same beaker with water
2. Read the temperature value on each of the thermometers,
3. Write the results of the measurement in the table:

[Table 1]

4. Calculate the averageaverageaverage water temperature in the beaker using the formula:

Round the result of the calculation to the first decimal place and write it in the table.

Summary:
Each measuring instrument has a certain accuracy (precision) of measurement. When measuring, for example, temperature, we read the result and we need to determine with what accuracy the measuring instrument (in this case the thermometer) allows us to give it (specify).

Task 2

Answer the question:

Why do you think that thermometers that we hang outside the window are not used to measure body temperature?

Thermometers which are used to measure the body temperature have a different scale and different measurement accuracy from the window ones. We expect that the thermometer which is used to measure the body temperature may indicate the temperature from the range of 34 to 42°C with an accuracy of 0,1°C. The thermometers which are used to measure the air temperature do not need such accuracy. They have to be able to indicate temperatures from -50 to +50°C. The thermometers used, for example, in ovens or in technical processes have the other measuring range and accuracy.

Experiment 2

Research problem:
Indicating sources of measurement uncertaintymeasurement uncertaintymeasurement uncertainty.

Hypothesis:
The measurement uncertainty is related to the accuracy of the scale and the smallest readable scale of the measuring instrument.

What you will need:

a) stick
b) ruler
c) rolled construction tape
d) sewing centimeter

Instruction:

1. Perform a five‑fold measurement of the stick length using ruler, a sewing tape measure and a rolled construction tape.
2. Record the results obtained by all group members in the table.

[Table 2]

3. Calculate the averageaverageaverage cord length ($l_{\mathrm{average}}$) using the formula:

Round the result of the calculation to the first decimal place and write it in the table.

Summary:
The reason for differences in the length of the stick read from the measuring instruments was the accuracy of their performance. The smallest readable scale units are almost (but not exactly) equal. Therefore, the reason for measurement uncertainty in this case was the accuracy of reading, the accuracy of the measuring instrument and its correct application.

[Interactive illustration]

Observation:

a) Measuring a single time interval always gives an error of 0.1 s to 0.5 s. b) When measuring 10 measuring signal cycles, the absolute error is the same as when measuring only one measuring signal cycle. However, the error in measuring one cycle of the measurement signal is now 10 times smaller, and is within 0.02 s 0.05 s.

Conclusion:

a) We ourselves (i.e. the characteristics of the experimenter, called the observerobserverobserver) are the reason for the measurements uncertainty.
b) The measurement error of a recurring phenomenon can be reduced by making a single measurement of a whole series of recurring phenomena.

Lesson summarymd743ba61d3e7d613_1528450119332_0Lesson summary

There are no perfect measurements! Each measurement has limited accuracy and is subject to measurement uncertainty resulting from the accuracy (quality) of the measuring instruments used. Of course, we can reduce this uncertainty by improving instruments and measuring methods, but we will never eliminate it completely. We do not always need measurements with very high accuracy.
For example, there is no sense in providing distance on road signs expressed in millimeters, centimeters and even in meters.SummaryThere are no perfect measurements! Each measurement has limited accuracy and is subject to measurement uncertainty resulting from the accuracy (quality) of the measuring instruments used. Of course, we can reduce this uncertainty by improving instruments and measuring methods, but we will never eliminate it completely. We do not always need measurements with very high accuracy.
For example, there is no sense in providing distance on road signs expressed in millimeters, centimeters and even in meters.

[Illustration 2]

If you measure the length of the same object several times and get several different values (numbers), the average of the results will be closest to the actual length.
The measurement error of a recurring phenomenon can be reduced by making a single measurement of a series of recurrent events.SummaryIf you measure the length of the same object several times and get several different values (numbers), the average of the results will be closest to the actual length.
The measurement error of a recurring phenomenon can be reduced by making a single measurement of a series of recurrent events.

Selected words and expressions used in the lesson plan

accuracyaccuracyaccuracy

averageaverageaverage

measurement uncertaintymeasurement uncertaintymeasurement uncertainty

measuring instrumentmeasuring instrumentmeasuring instrument

observerobserverobserver

sensessensessenses

sensitivitysensitivitysensitivity