NOTES ARE SUPPLEMENTS, NOT SUBSTITUTES FOR BOOKS!

Quazi Rafquat Hossain

Important terms to remember

Precision: The precision of an instrument depends on the smallest change that it can record. A micrometer screw gauge has a higher precision than a vernier caliper while a vernier caliper has a higher precision than a metre rule. On the other hand, the precision of a measurement is the degree of exactness (the number of significant figures) to which the measurement of a quantity or value can be obtained and reproduced consistently

Accuracy: A result is said to be accurate if it is close to the actual value. A result can be accurate without being precise and vice versa.

Reliability: Results are said to be reliable when they are internally consistent. For instance if repeated measurements gives approximately the same results, the readings can be considered reliable.

Range: The range of a set of readings is the difference between the smallest and the largest values.

Uncertainty: The uncertainty of a measurement is the range in which the actual value is expected to exist. Therefore,

Uncertainty = max – min 2

At this point it should be mentioned that uncertainty and percentage uncertainty should never be confused

Percentage Uncertainty: _____Uncertainty______ x 100% Average Measured value

When two quantities are in a multiplication or division form, the total percentage uncertainty is found out by adding their individual percentage uncertainties. This will be further illustrated with examples in later sections.

Percentage Difference: Difference between the actual and measured value x 100%Actual value

If both the values are experimental, Difference between the two values x 100%

Average of the two values

While taking measurements several types of errors can contribute to an inaccurate result. The most common types of errors are described below:

Random error: Random errors are errors with no pattern or bias. Readings with random errors vary in an unpredictable manner with no discernable pattern or trend. The effect of random variations in measurements of a quantity is reduced by taking more readings and finding a mean value. Some common examples of random errors include – ● The height a ball bounces to when dropped from the same height.● The small variations in voltage when repeating a reading on the same length of wire

Systematic error: Systematic errors in measurements are errors which show a pattern or a trend. Systematic errors can result from an instrument calibration error (eg zero errors), from incorrect use or reading of instruments (eg parallax errors) or be caused by another factor changing the quantity in an unknown or unrecognised manner. Systematic errors can be minimized by drawing a suitable graph. Some common examples of systematic errors include – Zero error on an instrument making all readings too large or small by a set amount ● Not realising a 30cm ruler has an extra few mm before the scale starts.● A set of scales that has not been zeroed first Calibration of an instrument giving false readings ● An ammeter consistently giving reading that are too high● A measuring tape becoming stretched over years of useExperimental design flaws● Friction on a sloping runway not being accounted for● Errors in measurements of temperature due to poor thermal contact

The paper constitutes four main segments –

□ Comparing instruments and methods

▫ choosing instruments with reference to instrumental precision▫ draw comparison between analog and digital devices▫ discuss the advantages and disadvantages of different methods for the same measurement

□ Planning

▫ identify the apparatus required �▫ discuss calibration of instruments, e.g. whether a meter reads zero before measurements are made▫ describe how to measure relevant variables using the most appropriate instrument and correct measuring techniques▫ identify and state how to control all other relevant variables to make it a fair test �▫ discuss whether repeat readings are appropriate �▫ identify health and safety issues and discuss how these may be dealt with �▫ discuss how the data collected will be used �▫ identify possible sources of uncertainty and/or systematic error and explain �▫ how these may be reduced or eliminated▫ comment on the implications of physics (e.g. benefits/risks) and on its context (e.g. social/environmental/historical).

□ Implementation and measurements

You will be given details of an experiment carried out by an inexperienced student. You may be asked to▫ comment on the number of readings taken �▫ comment on the range of measurements taken �▫ comment on significant figures �

▫ check a reading that is inconsistent with other readings, e.g. a point that is not on the line of a graph — students may be shown a diagram of a micrometer that is being used to measure the diameter of a wire and be expected to write down the reading to the correct number of significant figures

▫ comment on how the experiment may be improved, possibly by using additional apparatus (e.g. to reduce errors) — examples may include using a set square to determine whether a ruler is vertical and to aid the measurement of the extension of a spring.

□ Processing results

In this section, you will be provided with a set of experimental results that were obtained by a more experienced student conducting an experiment. You may be asked to ▫ perform calculations, using the correct number of significant figures �▫ plot results on a graph using an appropriate scale �▫ use the correct units throughout �▫ comment on the trend/pattern obtained ▫ determine the relationship between two variables or determine a constant with the aid of a graph, e.g. by determining the gradient using a large triangle▫ suggest realistic modifications to reduce errors ▫ suggest realistic modifications to improve the experiment ▫ discuss uncertainties, qualitatively and/or quantitatively (students will be expected to determine the percentage uncertainty of a single measurement).

□ Drawing conclusions

▫ Processing results and providing a final conclusion for the experiment based on their quantitative evidence

Let’s put the theories to the test

KEY POINTS TO REMEMBER

● Make sure the decimal places in your answers are consistent with the question. P.S don’t forget to discard anomalous value(s)Example – Calculate the mean value of the set of readings and state the uncertainty:

24.5 24.6 26.9 24.3

It should be obvious that 26.9 is an anomalous value and all further calculations should be executed after discarding it. Now you might be temped to state the mean value as 24.467 because 3 decimal places seem pretty legit. However this would cost you a mark! Your answer must be consistent with the number of decimal places in the question. Therefore the answer should be 24.5

● You must be able to recall the precisions of the common measuring devices along with the units

COMPARING INSTRUMENTS AND METHODS

You will have to remember that an experiment can be performed in two different methods with the same instrument. For instance, if you want to measure the thickness of a coin, you can either measure the thickness of a single coin OR measure the thickness of a stack of coins and divide by the number of coins in the stack. You must be wondering which method should you choose. We always want to minimise the percentage uncertainty of our measurements. If you recall the equation, percentage uncertainty = (uncertainty/average measured value) x 100. Therefore, the greater the measured value, the lower will be the percentage uncertainty. Thus in this scenario, the stacking method is more suitable.

The paragraph above discusses how a same instrument can be used in two different methods. In certain cases, you will also have to compare different instruments available for the same experiment. Lets look at it from the context of a common question. You will be often asked to calculate the resistivity of a piece of wire. The resistance (which will be used to calculate resistivity) can be found out directly using a digital meter (multimeter) or voltages and currents can be measured using analog ones (ammeter and voltmeter). The pros and cons are discussed below –

Idea Analog Digital

Equipment /cost two meters needed / may be more expensive only one meter needed / may be cheaper option

Ease of reading two readings must be taken one reading only / fluctuates

Parallax needs to be considered digital display / no parallax error

Systematic errors zero errors /contact resistance zero error / contact resistance

Scales fixed variable/can be changed

Sensitivity limited by size of scale divisions two decimal places

Setting up requires both series and parallel connections only requires series connection

Heating effect of current heating may change resistance of wire unlikely to be much heating effect

Power supply meters do not require individual batteries internal battery required

Uncertainties greater since two readings smaller since only one reading

Data needs calculation from two readings no calculation required

Graphical method possible less simple for a fixed wire

Device PrecisionMetre rule 1mmVernier Caliper 0.1mmMicrometer Screw Gauge 0.01mmStopwatch 0.1sProtractor 1o

Balance 0.1gVoltmeter 0.1VAmmeter 0.1AThermometer 1 o

Lets take a look at some of the most common experiments -

● Experiment to determine the Young’s modulus ● Experiment to determine the spring constant/stiffness ● Experiment to verify Hooke’s law ● Experiment to determine the acceleration due to gravity ● Experiment to determine the viscosity of a liquid

● Experiment to determine the Planck’s constant● Experiment to determine the refractive index of a medium ● Experiment to determine the internal resistance of a cell● Experiment to determine the resistance/resistivity of a piece of wire

● Experiment to investigate the relationship between temperature and resistance of metal/thermistor● Experiment to investigate the relationship light intensity and resistance of LDR ● Experiment to investigate the relationship between voltage current and resistance (keeping one constant)

PLANNING

In this segment you will be asked to design an experiment. You will be provided with a number of points to address in your planning. Make sure you answer them in the same order as the question. These questions come in parts (a, b, c, d …..) and should be answered one part at a time. DO NOT WRITE A WHOLE PARAGRAPH!

Some of the most common parts of the planning questions are discussed below

● list any (additional) apparatus required● quantities to be measured● choice of measuring instrument● comment on repeat readings● how the data collected is used ● main sources of uncertainty and/or systematic error● safety aspects

IMPLEMENTATION AND MEASUREMENTS

In this section you will be asked to criticize the measurements of an inexperienced student. The most common points are -

● There is a missing unit. ● There are only N sets of results/too few results. ● No repeats/mean shown. ● Inconsistent intervals/ large gap between readings ● Small range ● There is inconsistent precision in measurements of X

This section also asks how measurements can be taken more accurately. For instance, in the experiment to determine the spring constant/young’s modulus, a set square should be used to keep the ruler vertical. The most common improvements in measurements are repeat and average.

PROCESSING RESULTSThis section might appear independently or as a part of the previous section

This segment requires you to answer why the graph of two certain quantities should be a straight line. All you have to do is recall the equation that links the two quantities. The equation should be consistent with the equation of a straight line – y = mx + c. After comparing the two equations you must also mention the quantities that can be found out from the gradient of the graph and the Y intercept.

You will be required to plot a graph. Always ensure that you’re being consistent with the axes. Use 2/3 of the graph on both axis.

Once you have calculated a value from the graph, you might be asked why there is a difference between your value and the accepted value. You will have to point out the uncertainties in the measurements of the determining factors.