13
CORE BIOLOGY PRACTICALS You will need to know these practicals as the exam board may ask you questions based on them. Below is a summary of each one. Name of practical and independent & dependent variables Other variables to be controlled Other equipment Method and outcome Possible evaluation issues Effect of caffeine on Daphnia heart rate Independent: caffeine concentration Dependent: heart rate of Daphnia Temperature Volume of solutions Stress of Daphnia Size of Daphnia Time of acclimatisation Microscope, counter, cavity slide, dropping pipettes, stop clock, distilled water, test tubes, stop clock Method: Remove 1 Daphnia and place in cavity slide. Remove pond water and replace with distilled water. Leave for 5mins to acclimatise then observe & count heart rate under microscope for 30s, multiply number by 2 to calculate beats/min. Repeat with 2 more Daphnia. Repeat again, this time with small concentration of caffeine solution in place of distilled water. Carry out for 5 concentrations of caffeine = 3 repeats at 3 concentrations. Outcome: as caffeine concentration increased, heart rate increased Ensuring Daphnia were same size If left too long under microscope, temp increases (due to lamp) = increased heart rate Ensuring enough data is collected Too high concentration of caffeine kills Daphnia Counting of heart beat can be inaccurate Measuring the content of Vitamin C in fruit juice Independent: fruit juice Dependent: volume of juice required to decolourise 1cm 3 of DCPIP Temperature Concentration of DCPIP solution (1%) Shake each tube same number of times Same end point colour. i.e. until the blue colour of DCPIP just disappears 1% DCPIP solution, 1% vitamin C solution, range of fruit juices, test tubes/conical flasks, beakers, pipette accurate to 1cm 3 , burette, safety goggles Method: pipette 1cm 3 blue DCPIP into test tube. Using burette (or accurate pipette) add 1% vitamin C solution drop by drop. Shake tube gently after each drop. Continue until the blue colour just disappears. Record volume of solution needed to decolourise the DCPIP. Repeat further 2 times and calculate mean result. Repeat procedure with different fruit juices. Calculations: 1cm 3 of 1% vitamin C solution contains 10mg Vitamin C, therefore mass in 1cm 3 = 10mg x volume of 1% vitamin C to decolourise 1cm 3 of DCPIP. Mass in sample = mass of vitamin C to decolourise 1cm 3 DCPIP volume of sample required to decolourise 1cm 3 DCPIP Difficulty in controlling temperature Amount of shaking (too much adds oxygen which will slightly restore the DCPIP to blue) End point difficult to judge as needs to be just when blue colour disappears especially in highly coloured juices Some loss of solution when transferring from one beaker to another Accuracy of measuring equipment The effect of temperature on cell membranes Independent: temperature of water Dependent: % transmission of light through resulting solution Volume of distilled water Time left in water Size of beetroot piece Raw beetroot, size 4 cork borer, white tile, knife, ruler, beaker, forceps, water baths, boiling tubes, thermometer, colorimeter & cuvettes, stop clock, distilled water, syringe Method: using cork borer and knife, cut pieces of beetroot into 1 cm length cylinders. Place in distilled water overnight to remove any dye released on preparation. Wash and blot dry. Place 8 boiling tubes of distilled water into 8 water baths of different temperature. Once at temperature, add a piece of beetroot to each and leave for 30 mins. Remove beetroot and shake tubes to disperse dye. Set colorimeter to % absorbance on blue/green filter. Calibrate using distilled water in a cuvette first then add 2cm3 of beetroot solution from the first temp to a new cuvette. Place into colorimeter to read % absorbance. Repeat for all other pieces. Calculations & outcome: to calculate % transmission = 100-%absorbance. As temperature increased, % transmission slightly increased to a point at which it greatly increased due to membrane molecules gaining more heat energy, vibrating more to a point where the vibrations caused large gaps in the membrane enabling the release of dye also proteins in membrane denatured leaving large pores. Some beetroot may have skin on affecting surface area. Difficulty in maintaining temperature Accurate reading of the colorimeter Accurate size of beetroot From the different parts of the root Ensuring same amount of time at the different temperatures The effect of changing enzyme concentration on rate of reaction. Independent: concentration of enzyme dependent: time taken for enzyme to break down substrate Temperature Volume of enzyme Volume of substrate Concentration of substrate pH Protease e.g.1% trypsin, casein solution, small beakers, thermometer, distilled water, syringes, stopclock, large beaker Method: make up different concentrations of enzyme using distilled water. Ensure different syringes for different chemicals to prevent cross contamination. Set up water bath for temperature to keep constant. Place 1 test tube of 5cm 3 casein solution into water bath alongside second tube containing 2cm 3 of 0.2% trypsin. Allow to acclimatise for 3 mins so that at same temperature then add trypsin to casein, start stop clock. Time how long it takes for casein solution to turn transparent. (mark a ‘X’ on the other side of tube, as soon as seen through solution stop clock). Repeat a further 2 times then repeat for next concentration. Calculations & outcome: rate = 1 time As concentration of enzyme increases, rate of reaction increases until a plateau point where all enzyme has metabolised all substrate immediately. Maintaining constant temperature Accurately making up the different concentrations Identifying end point consistently Difficult to see the cross through the solution Using catalase in yeast and hydrogen peroxide Method: using first concentration of yeast solution, acclimatise to desired temperature alongside separate tube of hydrogen peroxide. Set up gas syringe and set to 0. Quickly add peroxide to yeast and attach gas syringe. Read off the volume of oxygen gas produced every 10 mins until 3 readings are the same. Repeat 3 times for each concentration of yeast solution. Calculations & outcome: rate = initial rate of reaction = gradient at steepest point from graphs of volume against time for each concentration. Outcome as protease above Attaching syringe can be slower allowing loss of gas Inaccurate reading of gas syring Inaccurate reading of syringes in making up dilutions Reaction going too quickly to read

AS Biology Core Practicals and AS/A2 Physics Experimental Work Guidelines

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Summary of AS Core Practicals for Biology, together with details of controlled variables, errors in experiment and the details of the experiment itself.Experimental guidelines for the practical papers of GCE AS and A2 Physics are also available here. The document includes advice on error calculations and how accuracy/reliability can be improved in the experiment.

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  • CORE BIOLOGY PRACTICALS

    You will need to know these practicals as the exam board may ask you questions based on them. Below is a summary of each one.

    Name of practical and independent & dependent

    variables

    Other variables to be controlled

    Other equipment Method and outcome Possible evaluation issues

    Effect of caffeine on Daphnia

    heart rate

    Independent: caffeine concentration

    Dependent: heart rate of Daphnia

    Temperature

    Volume of solutions

    Stress of Daphnia

    Size of Daphnia

    Time of acclimatisation

    Microscope, counter, cavity slide, dropping pipettes, stop clock, distilled water, test

    tubes, stop clock

    Method: Remove 1 Daphnia and place in cavity slide. Remove pond water and replace with distilled water. Leave for 5mins to acclimatise then observe & count heart rate under microscope for 30s, multiply number by 2 to calculate beats/min. Repeat with 2 more Daphnia. Repeat again, this time with small concentration of caffeine solution in place of distilled water. Carry out for 5 concentrations of caffeine = 3 repeats at 3 concentrations. Outcome: as caffeine concentration increased, heart rate increased

    Ensuring Daphnia were same size

    If left too long under microscope, temp increases (due to lamp) = increased heart rate

    Ensuring enough data is collected

    Too high concentration of caffeine kills Daphnia

    Counting of heart beat can be inaccurate

    Measuring the content of

    Vitamin C in fruit juice

    Independent: fruit juice Dependent: volume of juice

    required to decolourise 1cm3 of DCPIP

    Temperature

    Concentration of DCPIP solution (1%)

    Shake each tube same number of times

    Same end point colour. i.e. until the blue colour of DCPIP just disappears

    1% DCPIP solution, 1% vitamin C solution, range

    of fruit juices, test tubes/conical flasks,

    beakers, pipette accurate to 1cm3,

    burette, safety goggles

    Method: pipette 1cm3 blue DCPIP into test tube. Using burette (or accurate pipette) add 1% vitamin C solution drop by drop. Shake tube gently after each drop. Continue until the blue colour just disappears. Record volume of solution needed to decolourise the DCPIP. Repeat further 2 times and calculate mean result. Repeat procedure with different fruit juices. Calculations: 1cm3 of 1% vitamin C solution contains 10mg Vitamin C, therefore mass in 1cm3 = 10mg x volume of 1% vitamin C to decolourise 1cm3 of DCPIP. Mass in sample = mass of vitamin C to decolourise 1cm3 DCPIP volume of sample required to decolourise 1cm3 DCPIP

    Difficulty in controlling temperature

    Amount of shaking (too much adds oxygen which will slightly restore the DCPIP to blue)

    End point difficult to judge as needs to be just when blue colour disappears especially in highly coloured juices

    Some loss of solution when transferring from one beaker to another

    Accuracy of measuring equipment

    The effect of temperature on cell

    membranes

    Independent: temperature of water

    Dependent: % transmission of light through resulting solution

    Volume of distilled water

    Time left in water

    Size of beetroot piece

    Raw beetroot, size 4 cork borer, white tile, knife, ruler, beaker,

    forceps, water baths, boiling tubes, thermometer,

    colorimeter & cuvettes, stop clock, distilled

    water, syringe

    Method: using cork borer and knife, cut pieces of beetroot into 1 cm length cylinders. Place in distilled water overnight to remove any dye released on preparation. Wash and blot dry. Place 8 boiling tubes of distilled water into 8 water baths of different temperature. Once at temperature, add a piece of beetroot to each and leave for 30 mins. Remove beetroot and shake tubes to disperse dye. Set colorimeter to % absorbance on blue/green filter. Calibrate using distilled water in a cuvette first then add 2cm3 of beetroot solution from the first temp to a new cuvette. Place into colorimeter to read % absorbance. Repeat for all other pieces. Calculations & outcome: to calculate % transmission = 100-%absorbance. As temperature increased, % transmission slightly increased to a point at which it greatly increased due to membrane molecules gaining more heat energy, vibrating more to a point where the vibrations caused large gaps in the membrane enabling the release of dye also proteins in membrane denatured leaving large pores.

    Some beetroot may have skin on affecting surface area.

    Difficulty in maintaining temperature

    Accurate reading of the colorimeter

    Accurate size of beetroot

    From the different parts of the root

    Ensuring same amount of time at the different temperatures

    The effect of changing enzyme

    concentration on rate of reaction.

    Independent: concentration of

    enzyme dependent: time taken for

    enzyme to break down substrate

    Temperature

    Volume of enzyme

    Volume of substrate

    Concentration of substrate

    pH

    Protease e.g.1% trypsin, casein solution, small

    beakers, thermometer, distilled water, syringes, stopclock, large beaker

    Method: make up different concentrations of enzyme using distilled water. Ensure different syringes for different chemicals to prevent cross contamination. Set up water bath for temperature to keep constant. Place 1 test tube of 5cm3 casein solution into water bath alongside second tube containing 2cm3 of 0.2% trypsin. Allow to acclimatise for 3 mins so that at same temperature then add trypsin to casein, start stop clock. Time how long it takes for casein solution to turn transparent. (mark a X on the other side of tube, as soon as seen through solution stop clock). Repeat a further 2 times then repeat for next concentration. Calculations & outcome: rate = 1 time As concentration of enzyme increases, rate of reaction increases until a plateau point where all enzyme has metabolised all substrate immediately.

    Maintaining constant temperature

    Accurately making up the different concentrations

    Identifying end point consistently

    Difficult to see the cross through the solution

    Using catalase in yeast and hydrogen peroxide

    Method: using first concentration of yeast solution, acclimatise to desired temperature alongside separate tube of hydrogen peroxide. Set up gas syringe and set to 0. Quickly add peroxide to yeast and attach gas syringe. Read off the volume of oxygen gas produced every 10 mins until 3 readings are the same. Repeat 3 times for each concentration of yeast solution. Calculations & outcome: rate = initial rate of reaction = gradient at steepest point from graphs of volume against time for each concentration. Outcome as protease above

    Attaching syringe can be slower allowing loss of gas

    Inaccurate reading of gas syring

    Inaccurate reading of syringes in making up dilutions

    Reaction going too quickly to read

  • Name of practical and independent & dependent

    variables

    Other variables to be controlled

    Other equipment Method and outcome Possible evaluation issues

    Observing Mitosis

    Chromosomes stained blue using

    orcein ethanoic stain

    Garlic roots, sharp knife, 1M hydrochloric acid,

    Ethanoic alcohol, Orcein ethanoic stain, ice-cold distilled water, water bath @ 60C, 2 watch glasses, test tube, 2

    pipettes, microscope slides, forceps, mounted

    needle, filter paper, microscope with mag

    x100 & x400

    Method: place test tube of 2cn3 1M HCl into 60C waterbath. Cut off 1-2cm of root tip from garlic root. Put in watch glass containing 2cm3 of acetic alcohol for at least 12 mins. Remove then place into another watch glass containing 5cm3 ice cold distilled water. Leave for 4-5 mins, then remove and dry. Place tips into heated HCl for 5mins then repeat process again by placing tips back into acetic alcohol etc. Tips will be very fragile at this point. Transfer 1 tip to microscope slide, cut 4-5mm from growing tip (site of mitosis) and keep the tip. Gently break up (macerate) with mounted needle, add 1 small drop of orcein ethanoic stain and leave for 2 mins. Add coverslip and blot with filter paper. View under microscope and identify the stages of mitosis. Calculations: percentage of cells in each stage of mitosis Mitotic index: number of cells containing visible chromosomes total number of cells in the field of view

    Resolution of microscope

    Human error in counting numbers of cells

    Enough time in the solutions to enable successful maceration or staining.

    Totipotency & Tissue Culture

    Seeds of white mustard, agar, distilled water,

    damp sponge, cling film, McCartney bottles,

    weighing scales, plastic tray, 250ml beaker, glass

    rod, scissors, sunny window sill

    Method: sprinkle seeds on damp sponge and allow to germinate. Use when just starting to unfold their cotyledons (seed leaves). Make up Agar gel and pour 2cm height of gel into McCartney bottles and allow to set. With sharp scissors, cut the tops off just below the shoot apex (including the cotyledons). This is called an explants. Push the stem of the explant into the gel (making sure cotyledons dont touch agar) cover with cling film and place on sunny windowsill. Observe over 10 days. Outcome: explant grows roots and leaves continue to grow. You need to be able to explain why they are covered in cling film and why they continue to grow even when covered. Also why they shouldnt be opened again.

    Unwanted pathogens growing in the gel as it is a good source of water and nutrients

    Wrong part of the plant cut and inserted into gel.

    The strength of plant fibres

    Independent: source and type of

    fibre Dependent: mass that can be

    held

    Length of fibre

    Size of each individual mass

    Stems of stinging nettles or celery, bucket, gloves,

    paper towels, clamp stands, slotted masses and holders, white tile,

    sharp knife

    Method: plant material should be left to soak in a bucket of water for about a week in order for the fibres to be easily extracted (called retting). Or celery stalks should be left in beaker of coloured water in order for fibres to be easily seen and pulled out. Once fibres removed, connect between 2 clamp stands and gradually add mass in the middle until the fibre snaps. Try with individual fibres from different plants and different ways of combining fibres eg twists and plaits. Can also compare stem to individual fibres. Outcome: the more fibres combined together the stronger it is.

    Maintaining length of fibres

    Ensuring consistency when twisting or plaiting

    Using fibres of the same age (as they get older they become more brittle)

    Extracting whole fibres that are useful

    Investigating plant mineral

    deficiencies

    Independent: minerals present Dependent: physical

    characteristics of the plant

    Volume of mineral solution

    Species of plant

    Size of container

    Amount of light received

    Mexican hat plantlets or geranium leaves, 7 test tubes, test tube holder,

    different mineral solutions:- each lacking

    1 nutrient and 1 containing all, aluminium foil

    Method: half fill a tube with the all nutrients present solution. Cover the top of the tube with foil or paraffin and push down on covering so that there is a well in the centre. Gently push the geranium stem/roots of Mexican hat plantlet through the hole so it is in solution below. Repeat with solutions lacking in nitrogen or phosphate or potassium or magnesium or calcium or lacking all. Wrap all tubes in aluminium foil and place in tube holder on sunny window sill. Observe regularly. Outcome: the all nutrients present plant will look healthy whereas the others will all have some abnormality. Make sure you know what nutrient deficiencies affect plants.

    Ensuring accurate measurement of solutions

    No air bubble caught in xylem of geranium

    possible microorganism growth in nutrient solution

    insufficient time to see an effect.

    Effect of garlic and mint on

    bacterial growth

    Independent: presence of garlic or mint

    Dependent: zone of inhibition around disc

    concentration of plant material

    lawn of bacteria on petri dish

    contamination of petri dish by other microbes

    same volume of plant material on each disc

    Agar plate seeded with bacteria, plant material e.g. garlic & mint, pestle

    & mortar, 10cm3 industrial denatured

    alcohol, sterile pipette, paper discs, sterile petri

    dish, sterile forceps, hazard tape, marker

    pen.

    Method: make plant extract by crushing 3g of plant material with 10cm3 industrial denatured alcohol. Shake occasionally for 10 mins. Pipette 0.1cm3 of extract onto sterile paper disc. Allow to dry on sterile petri dish. Meanwhile label agar plates with date and split into 4 sections. 1 for each type of plant extract. Place 1 disc of each extract in each quadrant of the agar plate, close and tape with hazard tape. Leave to incubate over night and observe zone of inhibition. Carry out controls with just distilled water on discs. Outcome: the control discs completely covered with bacteria, some plant extracts will create larger zones of inhibition than others, meaning they are more effective at lower concentrations.

    Growth of unwanted microbes on agar plates due to bad aseptic techniques

    Not shaking extract enough to ensure enough active ingredient

    Inconsistency when adding plant extract to paper discs.

    Contaminating controls

    Using wrong species of bacteria for lawn

  • Guidance notes on experimental work.

    Section 1 Treatment of uncertainties in Physics at AS and A2 level

    Preamble

    One of the main aims of the practical work undertaken in GCE Physics is for candidates to develop a feeling for uncertainty in scientific data. Some of the treatment that follows may appear daunting. That is not the intention. The estimates of uncertainties that are required in this specification are more in the nature of educated guesses than statistically sound calculations. It is the intention that candidates be introduced early in the course to estimating uncertainties so that by the time their work is assessed, they have a relaxed attitude to it. The sections in PH1 on density determinations and resistivity are ideal for this.

    DefinitionsUncertaintyUncertainty in measurements is unavoidable and estimates the range within which the answer is likely to lie. This is usually expressed as an absolute value, but can be given as a percentage. The normal way of expressing a measurement x0, with its uncertainty, u, is x0 u. This means that the true value of the measurement is likely to lie in the range x0 u to x0 + u.

    Note: The term error is used in many textbooks instead of uncertainty. This term implies that something has gone wrong and is therefore best avoided.

    Uncertainties can be split up into two different categories:

    - Random uncertainties These occur in any measured quantity. The uncertainty of each reading cannot be reduced by repeat measurement but the more measurements which are taken, the closer the mean value of the measurements is likely to be to the true value of the quantity. Taking repeat readings is therefore a way of reducing the effect of random uncertainties.

    - Systematic uncertainties These can be due to a fault in the equipment, or design of the experiment e.g. possible zero error such as not taking into account the resistance of the leads when measuring the resistance of an electrical component or use of a ruler at a different temperature from the one at which it is calibrated. The effect of these cannot be reduced by taking repeat readings. If a systematic uncertainty is suspected, it must be tackled either by a redesign of the experimental technique or theoretical analysis. An example of this sort of uncertainty, the origin of which remains mysterious, is in the determination of stellar distances by parallax. The differences between the distances, as determined by different observatories, often exceeds the standard uncertainties by a large margin.

    Percentage uncertaintyThis is the absolute uncertainty expressed as a percentage of the best estimate of the true value of the quantity.

    ResolutionThis is the smallest quantity to which an instrument can measure

  • MistakeThis is the misreading of a scale or faulty equipment.

    Suspect resultsThese are results that lie well outside the normal range e.g. points well away from a line or curve of best fit. They often arise from mistakes in measurement. These should be recorded and reason for discarding noted by the candidate.

    How is the uncertainty in the measurement of a quantity estimated?

    1. Estimation of uncertainty using the spread of repeat readings.Suppose the value a quantity x is measured several times and a series of different values obtained:x1, x2, x3..xn. [Normally, in our work, n will be a small number, say 3 or 5].

    Unless there is reason to suspect that one of the results is seriously out [i.e. it is anomalous], the best estimate of the true value of x is the arithmetic mean of the readings:

    Mean value 1 2........ nx x xx

    n+ +

    =

    A reasonable estimate of the uncertainty is the range:

    i.e. max min2x xu = , where maxx is the maximum and minx the minimum reading of

    x [ignoring any anomalous readings]

    Example The following results were obtained for the time it took for an object to roll down a slope.

    4.5 s, 4.8 s, 4.6 s, 5.1 s, 5.0 s

    The best estimate of the true time is given by the mean which is:

    4.5 4.8 4.6 5.1 5.0 4.8s5

    t + + + += =

    The uncertainty, u, is given by: 5.1 4.5 0.3s2u = =

    The final answer and uncertainty should be quoted, with units, to the same no. of decimal places and the uncertainty to 1 sig. fig

    i.e. t = 4.8 0.3 sNote that, even if the initial results had be taken to the nearest 0.01 s, i.e. the resolution of an electronic stopwatch, the final result would still be given to 0.1 s because the first significant figure in the uncertainty is in the first place after the decimal point.

    The percentage uncertainty, p 0.3 100% 6%4.8

    = = . Again, p is only expressed to 1 s.f.

  • 2. Estimation of uncertainty from a single reading

    Sometimes there may only be a single reading. Sometimes all the readings may be identical. Clearly it cannot be therefore assumed that there is zero uncertainty in the reading(s).With analogue instruments, it is not expected that interpolated readings will be taken between divisions (this is clearly not possible with digital instrument anyway). Hence, the uncertainty cannot be less than the smallest division of the instrument being used, and is recommended it be taken to be the smallest division. In some cases, however, it will be larger than this due to other uncertainties such as reaction time [see later] and manufacturers uncertainties. If other sources of random uncertainty are present, it is expected that in most cases repeat readings would be taken and the uncertainty estimated from the spread as above.

    Advice for Specific apparatus

    Metre Rule

    Take the resolution as 1 mm. This may be unduly pessimistic, especially if care is taken to avoid parallax errors. It should be remembered that all length measurements using rules actually involve two readings one at each end both of which are subject to uncertainty. In many cases the uncertainty may be greater than this due to the difficulty in measuring the required quantity, for example due to parallax or due to the speed needed to take the reading e.g. rebound of a ball, in which case the precision could be 1 cm. In cases involving transient readings, it is expected that repeats are taken rather than relying on a guess as to the uncertainty.

    Standard Masses

    For 20g, 50g, 100g masses the precision can be taken as being as being 1g this is probably more accurate than the manufacturers [often about 3%]. Alternatively, if known, the manufacturers uncertainty can be used.

    Digital meters [ammeters/voltmeters]

    The uncertainty can be taken as being the smallest measurable division. Strictly this is often too accurate as manufacturers will quote as bigger uncertainty. [e.g. 2% + 2 divisions]

    Thermometers

    Standard -10 C to 110 C take precision as 1CDigital thermometers uncertainty could be 0.1C. However the actual uncertainty may be greater due to difficulty in reading a digital scale as an object is being heated or cooled, when the substance is not in thermal equilibrium with itself let alone with the thermometer..

  • The period of oscillation of a Pendulum/Spring

    The resolution of a stop watch, used for measuring a period, is usually 0.01s. Reaction time would increase the uncertainty and, although in making measurements on oscillating quantities it is possible to anticipate, the uncertainty derived from repeat readings is likely to be of the order of 0.1 s. To increase accuracy, often 10 (or 20) oscillations are measured. The absolute error in the period [i.e. time for a single oscillation] is then 1/10 (or 1/20 respectively) of the absolute error in the time for 10 (20) oscillationse.g. 20 oscillations: Time = 15.8 0.1 s [0.6%]

    Period 15.8 0.1

    20

    = s = 0.790 0.005 s

    Note that the percentage uncertainty, p, in the period is the same as that in the overall time.

    In this case, 0.1 100% 0.6%15.8

    p = = (1 s.f.)

    Digital vernier callipers/micrometer

    Precision smallest measurable quantity usually 0.01mm

    Measuring cylinder / beakers/ burette

    Smallest measurable quantity e.g. 1 cm, but this depends upon the scale of the instrument. In the case of measuring the volume using the line on a beaker, the estimated uncertainty is likely to be much greater.Note candidates must be careful to avoid parallax when taking these measurements, and should state that all readings were taken at eye level. They should also measure to the bottom of the meniscus.

  • Determining the uncertainties in derived quantities.

    Please note that candidates entered for AS award will now be required to combine percentage uncertainties.

    Very frequently in Physics, the values of two or more quantities are measured and then these are combined to determine another quantity; e.g. the density of a material is determined using the equation:

    mV

    =To do this the mass, m, and the volume, V, are first measured. Each has its own estimated uncertainty and these must be combined to produce an estimated uncertainty in the density. The volume itself may have been determined by combining several independent quantity determinations [e.g. length, breadth and height for a rectangular solid or length and diameter for a cylindrical wire].

    In most cases, quantities are combined either by multiplying or dividing and this will be considered first. Multiplying by a constant, squaring (e.g. in 343 rpi ), square rooting or raising to some other power are special cases of this and will be considered next.

    1. Multiplying and dividing:The percentage uncertainty in a quantity, formed when two or more quantities are combined by either multiplication or division, is the sum of the uncertainties in the quantities which are combined.

    Example

    The following results were obtained when measuring the surface area of a glass block with a 30cm rule, resolution 0.1cm

    Length = 9.7 0.1 cmWidth = 4.4 0.1cm

    Note that these uncertainties are estimates from the resolution of the rule.This gives the following percentage errors:

    Length: L0.1 100% 1.0%9.7

    p = =

    Width W0.1 100% 2.2%4.4

    p = =

    So the percentage error in the volume, V 1.0 2.2 3.2%p = + =Hence surface area = 9.7 4.4 = 42.68 cm 3.2 %The absolute error in the surface area is now 3.2% of 42.68 = 1.37 cmQuoted to 1 sig. fig. the uncertainty becomes 1 cmThe correct result, then, is 43 1cm - Note that surface area is expressed to a number of significant figures which fits with the estimated uncertainty.

    2. Raising to a power (eg x2, x1, x )

    The percentage uncertainty in xn is n times the percentage uncertainty in x. e.g. a period (T) is as being 31 seconds with a percentage uncertainty of 2 %,

  • So T2 = 961 4%. 4% 961 = 40 (to 1.s.f)So the period is expressed as T = 960 40 s.

    Note: x1 is the same as 1/x. So the percentage uncertainty in 1/x is the same as that in x. Can you see why we ignore the sign?Note: the percentage uncertainty in x is half the percentage uncertainty in x.

    3. Multiplying by a constantIn this case the percentage uncertainty is unchanged. So the percentage uncertainty in 3x or 0.5x or pi x is the same as that in x.

    Example: The following determinations were made in order to find the volume of a piece of wire:Diameter: d = 1.22 0.02 mmLength: l = 9.6 0.1 cm

    The percentage uncertainties are: pd = 1.6%; pl = 1.0%.

    Working in consistent units, and applying the equation 2

    4dV lpi= , we have:

    V = 448.9 mm3 The percentage uncertainty, pV = 1.6 2 + 1.0 = 4.2 % = 4 % (to 1 s.f.)[Note that pi and 4 have no uncertainties.]So the absolute uncertainty u = 448.9 0.04 = 17.956 = 20 (1 s.f.)

    So the volume is expressed as V = 450 20 mm3.

    Multiply the percentage uncertainty

    4. Adding or subtracting quantities [A2 only]If 2 quantities are added or subtracted the absolute uncertainty is added. This situation does not arise very frequently as most equations involve multiplication and division only. The e.m.f. / p.d. equation for a power supply is an exception.

    In all cases, when the final % uncertainty is calculated it can then be converted back to an absolute uncertainty and quoted 1 sig. figure. The final result and uncertainty should be quoted to the same number of decimal places

  • Notes for purists: 1. When working at a high academic level, where many repeat measurements are taken,

    scientists often use standard error , a.k.a. standard uncertainty. Where this is used, the expression x0 is taken to mean that there is a 67% probability that the value of x is in the range x0 to x0 + , a 95% probability that it lies in the range x0 2 to x0 + 2 , a 98% probability that it is between x0 3 and x0 + 3 , etc. Our work on uncertainties will not involve this high-level approach.

    2. The method which we use here of estimating the uncertainty in an individual quantity takes no account of the number of readings. This is because it is expected that only a small number of readings will be taken. Detailed derivation of standard uncertainties (see above) involves taking the standard deviation of the readings and then dividing this by 1n , so taking 10 readings would involve dividing by 3.

    3. The above method of combining uncertainties has the merit of simplicity but it is unduly pessimistic. If several quantities are combined, it is unlikely that the actual error (sic) in all of them is in the same direction, i.e. all + or all . Hence adding the percentage uncertainties overestimates the likely uncertainty in the combination. More advanced work involves adding uncertainties in quadrature: i.e. 2 2 21 2 3 ......p p p p= + + + . This is normally done when standard uncertainties are employed (note 1 above).

    It is not intended that candidates pursue any of these courses!

  • GRAPHS [derivation of uncertainties from graphs is only expected in A2]

    The following remarks apply to linear graphs:

    The points should be plotted with error bars. These should be centred on the plotted point and have a length equal to ymax ymin [for uncertainties in the y values of the points]. If identical results are obtained the precision of the instrument could be used. If the error bars are too small to plot this should be stated. If calculating a quantity such as gradient or intercept the steepest line and a least steep line should be drawn which are consistent with the error bars. It is often convenient to plot the centroid of the points to help this process. This is the point ( ),x y , the mean x value against the mean y value. The steepest and least steep lines should both pass through this point.

    .The maximum and minimum gradients, mmax and mmin, [or intercepts, cmax and cmin] can now be found and the results quoted as:

    gradient = max maxmin min2 2m m m m+

    intercept = max maxmin min2 2c c c c+

    Scales

    Graph should cover more than of the graph paper available and awkward scales [e.g. multiples of 3] should be avoided. Rotation of the paper through pi /4 [90 !] may be employed to give better coverage of the graph paper.

    Semi-log and log-log graphs [A2 only]

    Students will be expected to be familiar with plotting these graphs as follows:Semi-log: to investigate relationships of the form: xy ka= .

    Taking logs: log log logy k x a= + or ln ln lny k x a= + [It doesnt matter which]So a plot of log y against x has a gradient loga and an intercept logk .Examples: Radioactive or capacitor decay, oscillation damping

    Log-log: to investigate relationships of the form: ny Ax=Taking logs: log log logy A n x= + [or the equivalent with natural logs]So a plot of log y against log x has a gradient n and an intercept log A .Examples: Cantilever depression or oscillation period as a function of overhang length, Gallilean moon periods against orbital radius to test relationship.

    Note that Log-log or semi-log graph paper will not be required.

    Uncertainties from Log graphs: Candidates will not be expected to include error bars in log plots.

  • Section 2 Ideas for practical work

    Prac ContextDensity of regular solids [cuboids, cylinders]Identification of material using density.

    Use of metre rule, callipers, micrometer, balanceInitial work on uncertainties

    Density of liquids and irregular solids Use of measuring cylindersWeighing a rule by balancing a loaded rule Use of P of MAcceleration of a trolley on a ramp [lots of variants here]

    Use of equations of motion graphs to determine acceleration

    Determination of g by simple pendulum N.B. Not on spec but a useful intro to oscillation period measurements

    Investigation of a compound pendulum or a pin and pendulum

    Ditto

    I-V characteristics of diodes, lamps etc. Use of ammeters, voltmeters, variable resistors, potentiometers [pots].

    Identification of the material of a wire by determination of its resistivity

    Various ways single measurements / R against l. Uncertainty combinations.

    Variation of resistance with temperature for a metal wire [copper is good] and/or thermistor

    Thermistor not on spec but it doesnt matter here. Could tie in with potential dividers to design a temperature sensor.

    Determination of resistance of a voltmeter by use of a series resistor.

    !

    Investigation of currents in series and parallel circuitsDetermination of internal resistance of a power supply

    Direct use of V = E Ir or use of 1 1 rV E ER

    = + - use of reciprocals in graphical

    work.Sonometer variation of frequency with length determination of the speed of transverse waves on the metal wire

    Use of reciprocals in graphical work

    Measurement of the wavelength of microwaves by standing wavesMeasurement of the wavelength of microwaves by Double slit (or Lloyds mirror)Measurement of wavelength of a laser by Youngs slitsMeasurement of wavelength of a laser pointer using a diffraction gratingMeasurement of refractive index of glass or water by real and apparent depthMeasure refractive index of a semicircular glass block using ray box [or pins!]Measurement of the speed of sound in air using a double beam CRO and two microphones

  • Section 3 Experimental techniques

    The following is a selection of experimental techniques which it is anticipated that candidates will acquire during their AS and A2 studies. It is not exhaustive, but is intended to provide some guidance into the expectations of the PH3 and PH6 experimental tasks.

    Measuring instrumentsThe use of the following in the context of individual experiments:

    micrometers and callipers. These may be analogue or digital. It is intended that candidates will have experience of the use of these instruments with a discrimination of at least 0.01 mm. A typical use is the determination of the diameter of a wire. digital top-loading balances. measuring cylinders and burettes. This is largely in the context of volume and density determination. force meters (Newton meters). stop watches with a discrimination of 0.01 s. It is also convenient to use stopwatches / clocks with a discrimination of 1 s. rules with a discrimination of 1 mm. digital multimeters with voltage, current and resistance ranges. The following (d.c.) ranges and discriminations illustrative the ones which are likely to be useful:2 V 0.001 V20 V 0.01 V10 A 0.01 A2 A 0.001 A2 k 1 200 0.01 Students should be familiar with the technique of starting readings on a high range to protect the instrument. liquid in glass thermometers. -10 110C will normally suffice, though candidates can be usefully introduced to the advantages of restricted range thermometers. Where appropriate, digital temperature probes may be used.

    Experimental techniques

    The purpose of PH3 is to test the ability of the candidates to make and interpret measurements, with special emphasis on:

    combining measurements to determine derived values, eg density or internal resistance

    estimating the uncertainty in measured and derived quantities investigating the relationships between variables

    These abilities will be developed by centres, using all the content of PH1 and PH2. They can and will be assessed using very simple apparatus which can be made available in multiple quantities. Hence it is not foreseen that apparatus which centres are likely to possess in small numbers, if at all, will be specified, e.g. oscilloscopes, data loggers, travelling microscopes.

    The following list may be found useful as a checklist. Candidates should be familiar with the following techniques:

    connecting voltmeters across the p.d. to be determined, i.e. in parallel;

  • connecting ammeters so that the current flows through them, i.e. in series; the need to avoid having power supplies in circuits when a resistance meter is being

    employed; taking measurements of diameter at various places along a wire / cylinder and taking

    pairs of such measurements at right angles to allow for non-circular cross sections; determining a small distance measurement, e.g. the thickness or diameter of an object,

    by placing a number of identical objects in contact and measuring the combined value, e.g. measuring the diameter of steel spheres by placing 5 in line and measuring the extent of the 5;

    the use of potentiometers (N.B. not metre wire potentiometers) and variable resistors in circuits when investigating current-voltage characteristics;

    the determination of the period and frequency of an oscillating object by determining the time taken for a number of cycles [typically 10 or 20]; N.B. Although the concept of period is not on the AS part of the specification, it is likely to be used in PH3;

    the use of fiducial marks and no-parallax in sighting against scales and in period determinations.