TIMETABLE LAYOUTLecture 2: Working in the Laboratory

Electricity and Measurement (E&M) BPM – 15PHF110

In This Lecture…1. Objectives

2. Using Laboratory Note Books

3. Lab Work Assessment for PHF110

4. Measuring Quantities

5. Uncertainties in Measurements

6. Plotting Graphs

Objectives

Know how to effectively maintain an experimental log book.

Know the assessment structure for lab work in this module.

Explain what is meant by the term “experimental uncertainty”.

Understand the difference between standard uncertainty and relative uncertainty.

Distinguish between random uncertainty and systematic uncertainty and recognise their sources.

Describe how to record data so that random and systematic uncertainty is accounted for and their impact reduced.

Construct graphs to present data effectively, including graphical treatment of the uncertainties in the plotted data.

The laboratory notebook is the principal tool of a scientist: maintain it professionally.

Laboratory Notebook

Record your work using neat ink only

The notebook is a working document,

in the lab,

The pen you use needs to be rugged, this means, hard wearing does not fade with time or exposure does not smudge does not run when wet

Do not use pencil except for graphs and diagrams.

on the work desk, amongst all the equipment.

Pentel Hybrid Gel Grip Rollerball Black ⟶

Sakura Gelly Roll Pen Fine Black ⟶

Record your work using neat ink only

Permanently attach loose pieces of paper, e.g. extra graphs, etc.

Cross out mistakes neatly.

Laboratory Notebook

Do not use pencil except for graphs and diagrams.

Do not tear out pages from the notebook

Do not use corrective fluid.like this

not like that

The laboratory notebook is the principal tool of a scientist: maintain it professionally.

Laboratory Notebook

Record your work using neat ink only

Permanently attach loose pieces of paper, e.g. extra graphs, etc.

Cross out mistakes neatly. Perform calculations in the

notebook

Do not use pencil except for graphs and diagrams.

Do not tear out pages from the notebook

Do not use corrective fluid. Do not use loose paper for records

aiming to write them up later.

If you have your calculations in your notebook you can easily find them.

The laboratory notebook is the principal tool of a scientist: maintain it professionally.

Laboratory Notebook

Record your work using neat ink only

Permanently attach loose pieces of paper, e.g. extra graphs, etc.

Cross out mistakes neatly. Perform calculations in the

notebook Every piece of data that is recorded

must have an estimate of uncertainty.

The result of every calculation must have an estimate of uncertainty.

Do not use pencil except for graphs and diagrams.

Do not tear out pages from the notebook

Do not use corrective fluid. Do not use loose paper for records

aiming to write them up later.

m = 1.50 ± 0.05 kg m = 1.50 kg

The laboratory notebook is the principal tool of a scientist: maintain it professionally.

Laboratory Notebook

Record your work using neat ink only

Permanently attach loose pieces of paper, e.g. extra graphs, etc.

Cross out mistakes neatly. Perform calculations in the

notebook Every piece of data that is recorded

must have an estimate of uncertainty.

The result of every calculation must have an estimate of uncertainty.

Do not use pencil except for graphs and diagrams.

Do not tear out pages from the notebook

Do not use corrective fluid. Do not use loose paper for records

aiming to write them up later. Do not simply take the

measurements with the aim of analysing later because…

when you start analysing you often find you need to take more readings or make adjustments to equipment.

The laboratory notebook is the principal tool of a scientist: maintain it professionally.

when you start analysing you often find you need to take more readings or make adjustments to equipment.

Lab Work AssessmentEach student will carry out 5 experiments during the semester. The assessment for lab work is in two parts,

1. At the end of the semester every student will present their lab book individually to one of the lab team. • A mark out of 10 will be awarded for the lab book based on its content

and the ensuing discussion.• This mark is multiplied by the number of labs completed by the student,

(maximum of 5). Any missed experiments must have a successful impaired performance claim or marks will be lost.

• Lab book total is therefore marks

2. Each student will be allocated one of their 5 experiments to type up as a formal lab report on A4 paper (usual university regulations for assessed reports) to be submitted to the Physics office by the given deadline. • Lab report total is marks.

The total lab assessment makes up of the module mark.

Measuring Quantities

All measurements are subject to uncertainty.E.g. diameter of a gold ring can fluctuate due to,• small fluctuations of temperature

from one measurement to another (thermal expansion)

• non-perfect shape of the ring• fluctuations in measurement tools etc.

𝑇 2 𝑇 3

A statement of a measured value without an

accompanying estimate of the uncertainty is useless.

diameter

circumference

Single Measurements

Never quote insignificant figures, e.g. 88.38 0.10C.

This cannot be possible as the accuracy quoted can only be as good as the uncertainty in the measurement. The correct reading of this temperature would be:

uncertainty in A

88.4 0.10C

20 22 24 26 28 30 32℃

78 80 82 84 86 88 90℃

E.g. measuring the temperature of a cooling liquid at a certain time.

θ = 25.4 0.10C, in general, A A

The uncertainty defines the number of significant figures that can be quoted, e.g.

Different Ways to Quote Uncertainty

1. Standard Uncertainty (Error) – given as a value.

i.e. A A = 25.4 0.10C

2. Relative Uncertainty (Error) – either given as a fractional or a percentage uncertainty (error).

fractional percentage

Relative Uncertainty

Standard Uncertainty

¿0.004×100=0.4 %¿0.004

The relative uncertainty is found from the standard uncertainty, i.e.

For our temperature reading, this gives,

¿∆ AA

relative uncertainty

0.125.4

Effects Leading to Uncertainty Random - where repeating the measurement gives a randomly different result. The more measurements made, the better the estimate of the true value. For example,• measuring the time of a mass falling from a fixed height,• measuring the diameter of a length of wire.

Systematic - where the same influence affects the result for each of the repeated measurements, often this is not known as it is out of the control of the experimenter. For example,• a cheap ruler that has an incorrectly marked scale,• a spring balance whose spring has stiffened with age.

Sources of Uncertainty

no parallax

parallax

parallaxparallaxparallax

no parallax

Never view at an angle when taking measurements. Move the eye into the correct position perpendicular to the scale.

Sources of Random Uncertainty• Mistakes – misreading a scale, writing the wrong number down, etc. Not a

genuine uncertainty.

Parallax error is an example of a mistake.

Sometimes there is help to do this:

mirror

image of needle

Sources of Uncertainty

Sometimes there is help to do this:

Not square on, parallax error: 0.113Too low

Not square on,parallax error: 0.120Too High

Square on, no parallax error: 0.116Correct reading

Sources of Uncertainty

Sources of UncertaintySources of Random Uncertainty• Mistakes – misreading a scale, writing the wrong number down, etc. Not a

genuine uncertainty.• Human Error – reaction time and poor observation techniques.• Binning Error – rounding off readings, this depends on the precision of the

instrument’s scale.2.5 ± 0.5 cm

= 0.025 ± 0.005 m

24.5 ± 0.5 mm = 0.0245 ± 0.0005

m

True value 0.0244 m

Sources of Uncertainty

Sources of UncertaintySources of Random Uncertainty• Mistakes – misreading a scale, writing the wrong number down, etc. Not a

genuine uncertainty.• Human Error – reaction time and poor observation techniques.• Binning Error – rounding off readings, this depends on the precision of the

instrument’s scale.• Statistical fluctuation – when taking measurements of a sample from a large

population.

Random errors are caused by sources that are not immediately obvious, For example changes in temperature, background noise, light levels, etc. can effect the measuring equipment and/or what is being measured.

Random errors can be reduced by averaging a large number of readings.

This is because the mean value gets closer to the true value as the number of readings increases.

Sources of UncertaintySources of Random Uncertainty• Mistakes – misreading a scale, writing the wrong number down, etc. Not a

genuine uncertainty.• Human Error – reaction time and poor observation techniques.• Binning Error – rounding off readings, this depends on the precision of the

instrument’s scale.• Statistical fluctuation – when taking measurements of a sample from a large

population.

Sources of Systematic Uncertainty• Instrumental error – calibration is never perfect.

Stan

dard

mea

sure

Stan

dard

mea

sure

Good Calibration

Poor Calibration

Calibration of a Ruler Zero Error on Force Meter

Correct Alignment

Zero Error

Sources of UncertaintyInstrumental error

Sources of UncertaintySources of Random Uncertainty• Mistakes – misreading a scale, writing the wrong number down, etc. Not a

genuine uncertainty.• Human Error – reaction time and poor observation techniques.• Binning Error – rounding off readings, this depends on the precision of the

instrument’s scale.• Statistical fluctuation – when taking measurements of a sample from a large

population.

Sources of Systematic Uncertainty• Instrumental error – calibration is never perfect.• Error due to Observation – the act of taking the reading changes its value.

• Cold thermometer into hot liquid will cause the liquid to cool

• The smaller the observed system is, the bigger the effect

• This becomes extremely important on atomic scales (observing in quantum physics)

• Ammeters or voltmeters in a circuit will effect the current

• Low resistance ammeters and high resistance voltmeters reduce the effect

Observation effects the Observed

Plotting Graphs

A Cartesian graph comprises of two axes (the y-axis or ordinate and the x-axis or abscissa), which cross at the origin.

Coordinates are always given in the form (x, y), e.g.

× (6, 2)

(-4, -8) ×

Plotting Graphs

• The independent variable is usually plotted along the abscissa

• The dependent variable is usually plotted along the ordinate.

Independent variable – the variable whose values were chosen by the researcher before running the experiment

Dependent variable – the variable whose values are the readings taken by the researcher during the experiment

The phrase:

“plot temperature against time”

In general it is always:

-axis against -axis

-axis -axis means:

Plotting Graphs

The uncertainty in the values plotted are shown using error bars.

±∆ 𝑦

±∆ 𝑥

Uncertainty in is ±0.6,

i.e. → 2.9 ±0.6

Uncertainty in is ±0.3,

i.e. → 3.6 ±0.3

Plotting Graphs• A fitted line passes through at least 2/3 of error bars – maximum and

minimum gradient lines give estimate of uncertainty in the gradient value.

Fitted line

Maximum gradient

Minimum gradient

Plotting GraphsIt is often useful to construct a plot to give a straight line. For example, investigating the relationship between kinetic energy and velocity,

plotting KE against velocity gives a parabola,

plotting KE against the square of velocity, v2 gives a straight line.however

All straight line graphs fit the equation, . and refer to the variables plotted, and are general constants. is the gradient of the line (it does not mean mass) and is the intercept on the -axis.

𝑦=𝑚𝑥+𝑐

𝐸

𝑣

𝐸

𝑣2

𝐸 𝑣2

0

𝐸=12𝑚𝑣2+0

Objectives

Know how to effectively maintain an experimental log book.

Know the assessment structure for lab work in this module.

Explain what is meant by the term “experimental uncertainty”

Understand the difference between standard uncertainty and relative uncertainty.

Distinguish between random uncertainty and systematic uncertainty and recognise their sources.

Describe how to record data so that random and systematic uncertainty is accounted for and their impact reduced.

Construct graphs to present data effectively, including graphical treatment of the uncertainties in the plotted data.