practical work for a level physics

11AS and A Level Physics © Cambridge University Press Study skills

Why spend time doing practical work?

‘Practical work is time consuming for both students and teachers.’‘Practical work requires laboratories which are well equipped.’‘It is more important that students are drilled in the basic facts, rather than spending time playing at doing practical work.’‘My students do not see the point of doing practical work, they want something more concrete.’

Th ese are all comments that teachers have made regarding the role of practical work. It cannot be denied that practical work does require planning by the teacher and that it does consume a lot of the students’ time. Nevertheless, the benefi ts of doing relevant, well-planned practical work far outweigh the disadvantages. Sophisticated equipment may help, but basic apparatus gives plenty of scope for interesting and challenging practical work. Th ere may be a role for drilling students, but there is not much point if they do not understand the basic concepts. If students do not see the point in doing practical work, then does this not refl ect on their past experiences?

So let’s look at some reasons for doing practical work:

it’s fun• it brings the theory to life• it develops cross-curricular skills• the skills learnt are relevant in a changing world• it teaches persistence• it aids learning and develops understanding• it is key to being successful in practical • examinationsphysics is a practical as well as a theoretical science.•

Some of these reasons might seem rather nebulous. However, as we go down the list we begin to see more immediate reasons for practical work. Research shows that understanding comes from doing practical work and seeing phenomena for yourself, rather than from just being told about things or just reading about them. How many of us remember

the excitement of fi rst experiencing the magic of a magnet picking up a steel ball bearing, even when some distance from it? Or the amazement when two like poles repel? To describe an interference pattern is drab and of little interest; to see a pattern through an already set-up microscope is infi nitely more real and exciting, but this pales into insignifi cance when a student discovers for him or herself the diff raction pattern produced by a distant light when viewed through a (not so) narrow slit!

It is this fi rst-hand experience which makes science so exciting and which captures students’ imagination, making them want to learn more.

It is also clear, as an examiner, that some groups of students are much more successful at practical work than other groups. Th is is not coincidence; regular, well-planned practical work is central in gaining the self-confi dence, the manipulative skills and the ability to overcome diffi culties to succeed in practical examinations.

Th e last point in our original list, however, is the key. Practical examinations are required because sciences, by their very defi nition, are practical as well as theoretical. If a theory is put forward which cannot be disproved by practical experiment, it becomes philosophy not science. It is this intertwining of experiment and theory which makes science unique in the academic spectrum.

So, we have decided that practical work is an integral and necessary part of our teaching strategy; we must now ensure that the practical work we do is relevant and eff ective.

Effective practical workWe should be wary of doing practical work merely for the sake of it, or because it has ‘always been part of our scheme of work’. When we plan practical work we must be aware of our aims; very often it might be a short experiment, or even a demonstration to illustrate a particular point – an example of which might be the demonstration of electric fi elds (Chapter 9, Practical 3).

At other times the primary aim might be to develop the students’ specifi c abilities to satisfy Assessment Objective C in the examination.

1AS and A Level Physics © Cambridge University Press 11Introduction to practical work

hy spend time doing the excitement of fi rst experiencing the magic of a

Introduction to practical work

AS and A Level Physics © Cambridge University Press Introduction to practical work2

of readings. For example, they may be asked to investigate the period of vibration of a 30 cm long, cantilevered hacksaw blade as the overhanging length of the blade is varied. It would be folly to take fi ve or six readings with lengths varying from 10 to 15 cm; a full range from about 5 to 25 cm would give much more information. Also the gaps between the diff erent lengths should be roughly equal.

Th ey need to recognise when repeat measurements are required. Th ey should be aware of the limitations of their measurements and the uncertainties in them. Th ey need to learn that when there is a reading which appears anomalous, it should be checked; if the reading is the same when repeated, then they should investigate it further, perhaps taking a series of readings close to the original value.

If you are unsure of the backgrounds of your students it is a good idea to set up a circus of diff erent tasks and sets of apparatus for them to put together and take simple readings from. Appendix 1 gives an example of some suitable experiments.

Presentation of data and observationStudents need to be able to present their observations in an intelligible manner. Often this will require the drawing of tables. Th ese observations should be recorded straight into the students’ fi les – rather than on scraps of paper which subsequently get lost or are used as spills to light Bunsen burners!

Each column (or row) in a table should be labelled with the quantity and the unit in which it is measured. Th e recognised way of doing this is to write the quantity followed by a solidus and the unit, e.g. Potential diff erence / mV, or V / V.

All raw data should be measured to the same degree of precision, and a precision which is commensurate with the measuring instrument being used or the task being undertaken. Generally the precision to which we can measure a quantity is determined by the scale on the measuring instrument. Students are expected to measure to the nearest scale division of the instrument and are not expected to estimate to a greater precision than this. However, there are exceptions: modern digital stopwatches will give readings to one hundredth of a second precision, but the reaction time means that times can only be accurate to the nearest one tenth of a second, at best.

Th e precision of the reading should be made clear in the way the reading is recorded, so that if the time of

However, this will generally have the parallel aim of illustrating the theoretical work that has recently been covered. An example of this is Chapter 13, Practical 1, where the exercise is designed to give the opportunity to develop measurement skills, but also to reinforce the ideas of internal resistance.

Where students move from feeder schools to a sixth form college for their A level courses they will have diff erent experiences of practical work; some may have been fortunate enough to have experienced a previous course (such as IGCSE or O level) where a practical approach to the subject was taken; others will not have been so fortunate and their practical skills may be very limited. It is therefore essential that there is work for both the experienced and the inexperienced – without making the former feel they are wasting their time doing trivial exercises or the latter feel overwhelmed by the complexity of the material.

Requirements for the AS courseTh e syllabus specifi es that the following areas will be tested in the practical paper, Paper 3:

manipulation, me• asurement and observationpresentation of data and observation• analysis, conclusions and evaluation•

Manipulation, measurement and observationTh is requires that students are able to set up basic apparatus from written or verbal instructions, and to ‘get it to work’ so that they can take measurements of reasonable quality. Th ey should be able to design and set up simple circuits and to build more complex ones from circuit diagrams. Virtually every experiment that we set gives practice to a greater or lesser degree in handling apparatus. Th e more that is done, the greater the students’ confi dence will become.

Students, above all, need to be able to use basic instruments such as electric meters, vernier scales and micrometer scales, as well as more mundane instruments such as timers and rulers.

Students need to learn and appreciate the range of measurements that is required for a particular task and, within that range, to use a sensible spread

AS and A Level Physics © Cambridge University Press Introduction to practical work 3

20 swings of a pendulum is being measured with a hand-held stopwatch then every measurement should be recorded to the nearest 0.1 of a second. A result such as 21 s should be written as 21.0 s to show the precision of the measurement.

Students need to learn when readings need to be repeated. Generally the readings in an experiment in which there is the greatest percentage uncertainty should be repeated. In a simple pendulum experiment, the timing of the oscillation, partly because of the dynamic nature of the reading, is likely to have the greatest uncertainty and should be repeated.

Students should be able to plan ahead, so that they can draw tables with columns available for calculated quantities, such as the period and the period squared of the simple pendulum. Calculated quantities should be given to the same number of signifi cant fi gures as the least precise measurement. Using the fi gures above, there is only one measured quantity and the calculated value of the period would be to three signifi cant fi gures: 1.05 s. Likewise the period squared would be 1.10 s2, not 1.1025 s2.

Th e example below shows a table showing the data from an experiment to investigate the variation of the period of a simple pendulum as the length is changed.

Note how the times are all measured to three signifi cant fi gures and quantities that are calculated from them are also calculated to same number of signifi cant fi gures.

GraphsAnother way of presenting data is by drawing a suitable graph. Graphs should have axes which are clearly labelled with the quantity and the unit, using the same conventions as for tables. Scales should be chosen so that most of the paper is used, but beware of ‘awkward scales’ – scales which are multiples of odd numbers such as 3, 7, 9, 11, 13, etc. Not only is this bad practice, but it also leads to errors in plotting the points.

Pendulum

length / cm

Time for 20

swings / s

Time for 20

swings / s

Average time for

20 swings / s

Period / s (Period)2 / s 2

30.0 21.6 22.0 21.8 1.09 1.19

40.0 25.1 25.2 25.2 1.26 1.59

50.0 28.0 28.2 28.1 1.41 1.99

60.0 30.6 31.0 30.8 1.54 2.37

70.0 33.2 33.2 33.2 1.66 2.76

Points should be clearly plotted, using small crosses, rather than dots – which tend to either become indeterminate ‘blobs’ or, if small, disappear into the drawn line.

Students should develop their skills in the drawing of straight lines and smooth curves. At AS students will be expected to be able to identify the best fi t line and to draw it using a sharp pencil and a ruler. Similarly they will be expected to be able to draw a smooth curve without wobbles or ‘feathering’; they also need to be able to draw tangents to curves. Th ese are skills that require practice.

Analysis, conclusions and evaluationProbably the fi rst method of analysing results that students meet will be from calculating the gradients of straight-line graphs. Th is is a fairly straightforward task, but it should be emphasised that points at the two extreme ends of the line should be used to calculate the gradient. Th is reduces, as far as possible, the introduction of unnecessary uncertainties.

Where a false origin is used on a graph, students should be able to calculate the intercept. Students should be able to use the gradient and the intercept to fi nd the values of m and c in the equation of a straight line, y = mx + c.

It is important to emphasise that whenever calculations are done the working must be shown.

Th e evaluation of an experiment is the most challenging aspect of practical work that students will meet at AS. It is a high-level skill and students need practice to develop this skill.

Th e fi rst stage is the recognition of uncertainties. Students should be able to assess the uncertainty in their measurements and be able to express these in absolute, fractional and percentage terms. Th ey should recognise that in cases where a quantitative fi nal result is required, its precision is limited by the measured quantity with the greatest fractional (or percentage) uncertainty.

AS and A Level Physics © Cambridge University Press Introduction to practical work

path and learn the hard way that careful thought is needed!

Th e fi rst stages in planning an investigation are to:

identify the independent variable in the experiment• identify the dependent variable in the experiment• identify the variables that are to be controlled.•

For example, consider the investigation of the force between two charged spheres as the distance between them is varied (Chapter 23, Practical 1).

Th e independent variable, the one which we control, is the distance between the two charged spheres, and the dependent variable is the force between the two spheres. When considering this experiment we need to ensure that the charges on the two spheres remain the same throughout the experiment – this is a variable which must be controlled.

Once the decision regarding variables is decided then students must:

determine and describe the method to be used to • vary the independent variabledetermine and describe how the independent and • dependent variables are to be measureddetermine and describe how other variables are to be • controlleddescribe, with the aid of a clear labelled diagram, the • arrangement of apparatus for the experiment and the procedures to be followeddescribe how the data should be used in order to • reach a conclusion, including details of derived quantities to be calculatedassess the risks of the experiment• determine and describe precautions that should be • taken to keep risks to a minimum.

In the example described above the independent variable is varied by mechanically moving the free sphere and clamping it in position before each reading. Th e independent variable is the reading on the balance (assuming the balance to have been zeroed when the test sphere is not present, otherwise we are into derived data). Th ere are various ways that the charges may be kept constant: ensuring that the experiment is done in a dry atmosphere might be one way, charging the spheres from the same source each time is another.

Th e student needs to be aware of suitable graphs to draw in order to fi nd the relationship between the

Th e next stage is to be able to identify where uncertainties in measurement are introduced and to recognise inherent weaknesses in the experimental procedure. Students who have a wide experience of practical work will develop these skills much more quickly than those who learn by rote.

Requirements for the A2 courseTh e A2 course builds on the AS course and all the skills developed at AS are taken further in A2. Th is particularly applies to analysis and evaluation, where the treatment of uncertainties is taken to another level.

In addition, the A2 course introduces aspects of planning experiments. Whereas at AS students will generally be told the variables to measure and what graphs to plot, by the end of the course students should be able to choose the variables for themselves and to plot appropriate graphs.

Th e ‘practical paper’ at A2 does not require students to actually use any apparatus. It might be tempting to abandon class practicals altogether. Th is approach, however, would be disastrous. Planning exercises, where students just do the planning part of the experiment, might have a role to play, as might data analysis exercises, but if students do these in isolation it will stifl e their understanding of the processes and their creativity when confronted with novel situations. For students to gain a full understanding of the processes required they need to experience for themselves the satisfaction (and the frustrations) of completing full investigations.

PlanningTh e skills which are to be developed in the fi nal year of the A level course may well have been gently introduced at the AS stage. Students’ ability to plan will not yet have been formally assessed, but in plenary sessions before the start of practical work you may well discuss possible variables to measure and guide students into making sensible choices. Students who have had some introduction to this in the previous year will be well prepared to go on to the next stage. Even so, in the early days they will need guidance, although sometimes it can be a salutary lesson for them to be allowed to go along the wrong

4

AS and A Level Physics © Cambridge University Press Introduction to practical work

UncertaintiesStudents need to be able to:

express a quantity as a value, an uncertainty • estimate and a unitshow uncertainty estimates, in absolute terms, • beside every value in a table of resultsshow uncertainty estimates in derived quantities• convert absolute uncertainty estimates into • fractional or percentage error estimates and vice versashow uncertainty estimates as error bars on a graph• estimate the absolute uncertainty in the gradient of • a graph using: absolute uncertainty = (gradient of best fi t line) − (gradient of worst acceptable line)estimate the absolute uncertainty in the • y-intercept of a graph using absolute uncertainty = (y-intercept of best fi t line) − (y-intercept of worst acceptable line).

Even at a fairly elementary level students should have been introduced to the idea that no quantity can be measured exactly, so there is always an uncertainty in our measurement. We now go on to develop the analysis of uncertainties, starting with the conversion of absolute uncertainties into fractional or percentage uncertainties, a prerequisite of being able to estimate the uncertainty of a quantity derived from the product of two other quantities.

Students need to be taught and reminded that if quantities are added (or subtracted) the absolute uncertainties are added. If there is a 0.5 mm uncertainty at either end when the length of a rod is measured, it is fairly intuitive that the overall absolute uncertainty is 1 mm.

It is not so intuitive that if the quantity is derived from multiplying or dividing two quantities that the overall uncertainty is the sum of the percentage uncertainties. Consider the experiment where we are investigating the power dissipated in a heater. If the p.d. across the heater is 12.0 ± 0.2 V (a percentage uncertainty of 1.7%) and the current is measured as 2.8 ± 0.1 A (a percentage uncertainty of 3.6%), the overall percentage uncertainty is 5.3%, giving a fi nal answer of 33.6 ± 1.8 W.

Past examinations have also demanded the calculation of uncertainties in the logarithm of a measured quantity. Th e only way of fi nding this is to fi nd the diff erence between the logarithm of the measured value and the logarithm of the maximum (or minimum) value. Th is

variables. With our experience we would expect an inverse square law. However, there is no reason for the student to be aware of this and the sensible course of action is to plot a log–log graph. Th is is explored further in the next section.

Analysis and evaluationTh e syllabus clearly lists the forms of mathematical equation that the students should be familiar with, be able to handle and be able to test for by plotting suitable graphs.

Th ey should be able to

rearrange expressions into the forms • y = mx + c, y = axn and y = a ekx

plot a graph of • y against x and use the graph to fi nd the constants m and c in an equation of the form y = mx + cplot a graph of ln • y against ln x and use the graph to fi nd the constants a and n in the equation of the form y = axn

plot a graph of ln • y against x and use the graph to fi nd the constants a and k in an equation of the form y = a ekx

decide what derived quantities to calculate from • raw data in order to enable an appropriate graph to be plotted.

Analysis of this sort is a challenge to all students and they need careful guidance and help to develop their skills. Where possible it is best to develop them as the theory is met. Students will meet equations of the form y = a ekx when looking at radioactive decay, and generally they will plot the well-recognised decay curve. However, an interesting exercise is to plot the graph of time against the logarithm of activity. Th is should give a straight line, the gradient of which will give the decay constant. Th is can be returned to in the medical imaging chapter when looking at the attenuation of γ-rays.

Very often raw data is not suitable for direct use in analysis and students need to be able to decide what derived quantities need to be found. An example might be investigating the energy dissipated by a heater as the potential diff erence across it is varied. Th e measured quantities might be the potential diff erence across the heater and the current through it. Th e former is the independent variable, while the dependent variable is the power, which is the product of the potential diff erence and the current.

5


diff erence is the uncertainty in the logarithm of the measured quantity.

Th e use of error (or uncertainty) bars on graphs and the best fi t and worst acceptable lines on graphs takes the analysis of uncertainties a stage further. By this stage students will be familiar with the best fi t line, but the idea of the worst acceptable line – the line which just touches all error bars and has the most extreme gradient – is new to them and needs careful introduction. Similarly, care is needed when introducing students to the calculation of uncertainty in the gradient and in the intercept.

How do we achieve this?Students learn best and understand most thoroughly when they are given the opportunity to learn by assimilation.Th ey need to:

be helped to work with progressively less help• evaluate and refl ect on their work• learn to assess risks to themselves and others and to • work safelylearn to put their plans down in writing in a way • that makes sense to othersextend the range of equipment with which they are • familiar.

You can help achieve this by:

setting part experiments aimed at developing • particular skillsdiscussing the skill being worked on beforehand• aiming whole practicals to develop specifi c skills• discussing the skills you are concentrating on before • the experimentbuilding these into your scheme of work.•

Th e experiments detailed on this disc will form the basis of a practical course. However, the list does not aim to be exclusive. Th ere are many other activities which can be done and with the websites that are increasingly available there are many other activities which can be introduced.

AS and A Level Physics © Cambridge University Press Introduction to practical work 77AS and A Level Physics © Cambridge University Press Study skills

In this circus of experiments it is important that you record every measurement you take.

a Set up a hacksaw blade to vibrate as shown in the diagram.

G-clamphacksaw blade

bench weight

Measure the period of the vibration and record all the measurements you make. Measurements made:

Period = s

b Draw a circuit to measure the current through a lamp and the potential diff erence across it.Circuit diagram:

When you have drawn your diagram, ask your teacher to check if it is correct.When it has been checked, build the circuit.Measure the current through a lamp and the potential diff erence across it.

Current = A Potential diff erence = V

7AS and A Level Physics © Cambridge University Press 77Introduction to practical work

In this circus of experiments it is important that you record every measurement you take.y

Appendix 1: Introductory experimental circus


c i Use the vernier callipers to measure the internal and external diameters of the pipe.Measurements taken:

Internal diameter = mm External diameter = mm

ii Use the micrometer screw gauge to measure the diameter of the length of wire.Measurements taken:

Wire diameter = mm

d Set up the apparatus as in the diagram so that the band is just tight without the mass holder. Hang the mass holder from the centre of the bottom part of the band. Add a 100 g mass and measure the extra distance the holder moves downwards.

rubber band

dowel

mass holder

clamp stand

G-clampbench

Measurements:

Distance moved = mm

8 AS and A Level Physics © Cambridge University Press Introduction to practical work


e Use the Geiger–Müller tube and counter to fi nd the rate of radiation from the source when the tube is 15 cm from the radioactive sample.Measurements:

Count rate =

f Set up the metre rule on the fulcrum. Place the 1.0 N weight at the 10 cm marker. Where must you put the unknown weight, W, in order for the ruler to balance?

Position of W: cm mark.Draw your experimental setup.

Calculate the weight of W.

Weight N

9Introduction to practical work 9AS and A Level Physics © Cambridge University Press


Teacher’s notesa Apparatus

1 × hacksaw blade 1 × G-clamp 1 × stopwatch 1 × set of weights

Th e weights can be made from steel or lead, rectangular blocks drilled so that set screws and nuts can be used to attach the weights to the blade, as shown. Alternatively, slotted masses can be taped to the blade. Care needs to be taken to ensure the period is in the region of 0.5 to 2 seconds.

Detail of weights (End elevation)

set screw

nuts

steel/lead blockshacksaw blade

b Apparatus

1 × power supply unit or battery 1 × lamp 1 × ammeter 1 × voltmeter 5 × leads

Any lamp will suffi ce as the power/voltage is immaterial. Th e practical is testing whether the student can correctly build the circuit. Th e battery, ammeter and voltmeter should be chosen so that they are compatible with the lamp – preferably so that it is impossible to blow the lamp!

c Apparatus

1 × vernier callipers 1 × length of copper (or other material) pipe of external diameter about 1 to 2 cm and

length 5 to 10 cm 1 × micrometer 1 × length of wire, diameter approximately 1 mm

Th e exact dimensions of the pipe and wire are not critical. Th e aim of the experiment is to give the students practice using vernier callipers and micrometers.

d Apparatus

1 × rubber band 1 × mass holder and 100 g masses 2 × stands and bosses 2 × lengths of dowel (or the ‘wrong ends’ of stand clamps could be used) 2 × G-clamps


e Apparatus

1 × GM tube and counter 1 × radioactive source (beta or gamma) 1 × hazard notice suitable stands for holding the GM tube and the radioactive source

Th e apparatus should be set up so the students only need to switch on the counter and take the required readings. Th is is a fun experiment – probably the fi rst time that students have worked closely with radioactive sources.

Care must be taken that local regulations regarding the use of radioactive sources are followed.

f Apparatus

1 × metre rule 1 × 100 g mass labelled 1 N 1 × fulcrum/knife edge 1 × loop of cotton 1 × 50 g mass labelled W

Students need to be told that the ruler is uniform and that its centre of gravity is at its centre point. Th is type of experiment should be familiar, but it is a good exercise in setting up apparatus. Th e best students will recognise that if the weight is suspended from the ruler using the cotton, not only can you get a more precise reading of the weight position, but also the apparatus is more stable. Do not tell them this before they attempt the experiment, let them fi nd out for themselves, or bring it out in discussion after the experiments are completed.



Exercise 1A steel ball bearing is rolled down a ramp and is launched horizontally as in the diagram.

l is the horizontal distance that the ball bearing travels from its launch point to where it hits the ground and h is the height above the bench from which it is released.

Values of h and l are given in the table.

h / cm l / cm l 2 / cm2

10.0 20 ± 1

20.0 29 ± 1

30.0 35 ± 1

40.0 41 ± 1

50.0 45 ± 1

60.0 50 ± 1

It is suspected that l and h are related by the equation:

l 2 = Kh + C

where K and C are constants.

a Calculate values of l 2. Include in your table the absolute uncertainties in l 2.b i Plot a graph of h on the x-axis, against l 2 on the y-axis. Include error bars for l 2. ii Draw the best fi t line and the worst acceptable straight line on your graph. Clearly

label the lines.

Exercise 1

Appendix 2: Data analysis exercises

ball bearing

ramp flight path of ball bearing

h

table

l



iii Determine the gradient of the best fi t line. Include the uncertainty in your answer.

Gradient = unit

iv Determine the y-intercept. Include the uncertainty in your answer.

y-intercept = unit

c Use your answers to b iii and b iv to fi nd the values of the constants K and C.

K = C =

Teachers’ notesTh e question is modelled on the type of question set in Paper 5 and could be set as a pure data analysis problem. However, by allowing the students to actually carry out the experiment fi rst – and even allowing them to go through it and to complete the work using their own fi gures, rather than those in the table – it will bring the whole thing alive. Th e fi gures in the table could then be used as a back up for those students who are unable to get meaningful results, or they could be used as reinforcement material for all students.

Exercise 2A student is going to use a thermistor as a thermometer. She initially investigates the variation of resistance of the thermistor with temperature.

Th e table shows the values of the resistance at diff erent temperatures.

T / K R / Ω ln T ln (R / Ω)

200 22 000 ± 2%

250 4 230 ± 2%

300 463 ± 2%

350 167 ± 2%

400 39 ± 2%

450 12 ± 2%



It is suspected that R and T are related by the equation:

R = KT n

where K and n are constants.

a Determine the absolute uncertainty in R when the temperature is 300 K.

Absolute uncertainty = Ω

It is proposed to draw a graph of ln T (x-axis) against ln R (y-axis).

b Explain how values for K and n can be obtained from this graph.

c Calculate and record the values of ln (T / K) and ln (R / Ω) and record them in the table.

Th e absolute uncertainty in the values of ln (R / Ω) can be found by fi nding the value of ln (R + ∆R / Ω) and subtracting ln (R / Ω) from it (where ∆R = the absolute uncertainty).

d Calculate the absolute uncertainty of ln (R / Ω) when T = 300 K.

Uncertainty =

e i Plot a graph of ln (T / K) (x-axis) against ln (R / Ω) (y-axis). Use a false origin on the x-axis in order to make reasonable use of the graph paper.

ii Draw the best fi t line and determine its gradient.

Gradient =



iii Calculate the y-intercept.

y-intercept =

f Use your answers to e ii and e iii to determine the values of K and n.

K = n =

Teachers’ notesIn order to put this analysis exercise into context it would be best done after practical work investigating the characteristic curve of a thermistor. Th e aims in this particular exercise are to highlight the use of a log–log graph and to show how to fi nd the absolute uncertainty in the logarithm of a quantity. It is felt that detailed analysis of uncertainties of the fi nal quantities would obscure the primary aims, and so we leave the analysis at this stage. It might be felt appropriate to do a full analysis, with error bars, worst acceptable line and consequent uncertainties in K and n at a slightly later stage.

Exercise 3: Analysis of solar systemKepler theorised that the relationship between the length of a year and the orbital radius of a planet was of the form A = Krn where K and n are constants.

Th is exercise takes information about the planets and allows you to fi nd a value for n.Th e planetary data are given in the table. Orbital periods are given in Earth years.

Planet Mass / kg Orbital radius / m × 1011 Orbital period / yearsMercury 3.30 × 1023 0.58 0.074

Venus 4.87 × 1024 1.08 0.240

Earth 5.98 × 1024 1.50 1.000

Mars 6.42 × 1023 2.28 1.881

Jupiter 1.90 × 1027 7.78 11.86

Saturn 5.69 × 1026 14.3 29.46

Uranus 8.69 × 1025 28.7 84.02

Neptune 1.03 × 1026 45.0 164.8

Draw a suitable graph to show the relationship between the lengths of the planets’ years and their orbital radii.

Calculate K and n.

Teachers’ notesTh is exercise does not enter into the realms of uncertainties; it is a straightforward exercise to show the power of the method of plotting log–log graphs to fi nd the relationship between variables.


practical work for a level physics

Documents