Physics Unit 6 Source Book

AAKC PHYSICS ©

Unit 6 | Notes

1.

All non-zero numbers (1, 2, 3, 4, 5, 6, 7, 8, 9) are always significant.

2.

All zero between non-zero numbers are always significant.

3.

All zeroes which are simultaneously to the right of the decimal point and at the end of the number are always significant.

4.

All zero which are to the t he left of the written decimal de cimal point and are a number >= 10 are always significant.

Number

S.F

48923

5

3.967

4

900.06

5

0.0004

1

8.1000

5

501.040

6

3000000

1

Prefix pico nano micro milli centi deci kilo mega giga tera

Symbol P n μ m c d k M G T

Base quantity Length Mass Time Current Temperature interval Amount of substance

Multiple -12 10 -9 10 -6 10 -3 10 -2 10 -1 10 3 10 6 10 9 10 12 10

Base unit Metre Kilogram Second Ampere Kelvin

Symbol m kg s A K

Mole

mol

Page 1 | Azman Anju Khan Chowdhury | (880) 1842 584 134

AAKC PHYSICS ©

Unit 6 | Notes

Quantity Speed Acceleration Force Pressure Work Power Charge Potential difference Resistance

Derived units

newton (N) pascal (Pa) joule (J) watt (W) coulomb (C) volt (V) ohm (Ω)

Base units -1 ms -2 ms -2 kgms -1 -2 kgm s -2 -3 kgm s -2 -3 kgm s As -2 -1 -3 kg m A s -2 -2 -3 kg m A s


AAKC PHYSICS ©

Unit 6 | Notes

Section 1 – Treatment of uncertainties in Physics at AS and A2 level Preamle

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 this spec specifi ifica catio tion n are more more in the the natu nature re of educ educat ated ed guess guesses es than than stati statist stica icall lly y sound sound calculations. t is the intention that candidates !e introduced early in the course to estimating uncertainties so that !y the time their work is assessed" they have a rela#ed attitude to it. The sections in P$% on density determinations and resistivity are ideal for this. !efinitions "ncertainty &ncertainty in measurements is unavoida!le and estimates the range within which the answer is like likely ly to lie. This This is usua usuall lly y e#pr e#press essed ed as an a!sol a!solut utee valu value" e" !ut !ut can !e give given n as a percentage. The normal way of e#pressing a measurement x measurement x'" with its uncertainty" u" is x is x' ( u. This means that the true value of the measurement is likely to lie in the range x range x' − u to x to x' ) u.

*ote+ The term ,error- is used in many te#t!ooks instead of uncertainty. This term implies that something has gone wrong and is therefore !est avoided. &ncertainties can !e split up into two different categories+

-

-

#andom uncertainties  These occur in any measured quantity. The uncertainty of each reading cannot !e reduced !y repeat measurement !ut the more measurements which are taken" the closer the mean value of the measurements measurements is likely to !e to the ,true- value of the quantity. Taking repeat readings is therefore a way of reducing the effect of of random uncertainties. Systematic uncertainties uncertainties  These can !e due to a fault in the equipment" or design of the e#periment e.g. possi!le /ero 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 cali!rated. The effect of these cannot !e reduced !y taking repeat readings. f a systematic uncertainty is suspected" it must !e tackled either !y a redesign of the e#perimental technique or theoretical anal analys ysis. is. 0n e#am e#ampl plee of this this sort sort of uncer uncerta tain inty ty"" the the orig origin in of whic which h rema remain inss mysterious" is in the determination of stellar distances !y paralla#. The differences !etween the distances" as determined !y different o!servatories" often e#ceeds the standard uncertainties !y a large margin.

Percenta$e uncertainty This is the a!solute uncertainty e#pressed as a percentage of the !est estimate of the true value of the quantity. #esolution This is the smallest quantity to which an instrument can measure


AAKC PHYSICS ©

Unit 6 | Notes

%istake This is the misreading of a scale or faulty equipment. Suspect results These are results that lie well outside the normal range e.g. points well away from a line or curve of !est fit. They often arise from mistakes in measurement. These should !e recorded and reason for discarding noted !y the candidate. &ow is the uncertainty in the measurement of a 'uantity estimated( 1. )stimation )stimation of of uncertai uncertainty nty usin$ usin$ the spread spread of of repeat repeat readin$s readin$s.. Suppos Supposee the value value a quanti quantity ty x is x is measured several times and a series of different values o!tained+ x%" x1" x233.. x xn. 4*ormally" in our work" n will !e a small num!er" say 2 or 56.

&nless there is reason to suspect that one of the results is seriously out 4i.e. it is anomal anomalous ous6" 6" the !est estimate estimate of the true value value of x is x is the arithmetic mean of the readings+ x% + x1 + ........xn n 0 reasona!le estimate of the uncertainty is 8 the range+

7ean value x =

xma# − xmin " where xma# is the ma#imum and xmin the minimum reading of 1 x 4ignoring x 4ignoring any anomalous readings6 i.e.

u=

)xample The following results were o!tained for the time it took for an o!9ect to roll down a slope. :.5 s" :.; s" :.< s" 5.% s" 5.' s

The !est estimate of the true time is given !y the mean which is+ t =

:.5 + :.; + :.< + 5.% + 5.' 5

The uncertainty" u" is given !y+ u =

= :.;s

5.% − :.5 = '.2s 1

The final answer and uncertainty should !e quoted" with units" to the same no. of decimal places and the uncertainty to % sig. fig i.e. t = = :.; ( '.2 s *ote that" even if the initial results had !e taken to the nearest '.'% s" i.e. the resolution of an electronic stopwatch" the final result would still !e given to '.% s !ecause the first significant figure in the uncertainty is in the first place after the decimal point. The percentage uncertainty" p uncertainty" p

=

'.2 :.;

× %''> = < >

. 0gain" p 0gain" p is is only e#pressed to % s.f.


AAKC PHYSICS ©

Unit 6 | Notes

2. )stimation )stimation of uncer uncertain tainty ty from from a sin$le sin$le re readin$ adin$

Sometimes there may only !e a single reading. Sometimes all the readings may !e identical. Clearly it cannot !e therefore assumed that there is /ero uncertainty in the reading?s@. Aith analogue instruments" it is not e#pected that interpolated readings will !e taken !etween divisions ?this is clearly not possi!le with digital instrument anyway@. $ence" the uncertainty cannot !e less than 8 the smallest division of the instrument !eing used" and is recommended it !e taken to !e ( the smallest division. n some cases" however" it will !e larger than this due to other uncertainties such as reaction time 4see later6 and manufacturerBs uncertainties. f other sources of random uncertainty are present" it is e#pected that in most cases repeat readings would !e taken and the uncertainty estimated from the spread as a!ove.

Advice for Specific apparatus %etre #ule

Take the resolution resolution as (% mm. This may !e unduly unduly pessimistic" pessimistic" especially if care is taken to avoid paralla# errors. t should !e remem!ered that all length measurements using rules actually involve two readings  one at each end  !oth of which are su!9ect to uncertainty. n many cases the uncertainty may !e greater than this due to the difficulty in measuring the required quantity" for e#ample due to paralla# or due to the speed needed to take the reading e.g. re!ound of a !all" in which case the precision could !e ( % cm. n cases involving transient readings" it is e#pected that repeats are taken rather than relying on a guess as to the uncertainty. Standard %asses

or 1'g" 5'g" %''g masses the precision can !e taken as !eing as !eing (%g this is pro!a!ly more more accurat accuratee than than the manufa manufactu cturerB rerBss 4often 4often a!out a!out 2>6. 2>6. 0ltern 0lternativ atively" ely" if known known"" the manufacturerBs uncertainty can !e used. !i$ital meters *ammeters+voltmeters, *ammeters+voltmeters,

The uncertainty can !e taken as !eing ( the smallest measura!le division. Strictly this is often too accurate as manufacturers will quote as !igger uncertainty. 4e.g. 1> ) 1 divisions6 Thermometers

Standard D%' C to %%' C take precision as %C Figital thermometers uncertainty could !e ( '.%C. $owever the actual uncertainty may !e greater due to difficulty in reading a digital scale as an o!9ect is !eing heated or cooled" when the su!stance is not in thermal equili!rium with itself let alone with the thermometer..


AAKC PHYSICS ©

Unit 6 | Notes

The period of oscillation of a Pendulum+Sprin$

The resolution of a stop watch" used for measuring a period" is usually '.'%s. eaction time would increase the uncertainty and" although in making measurements on oscillating quantities it is possi!le to anticipate" the uncertainty derived from repeat readings is likely to !e of the order of '.% s. To increase accuracy" often %' ?or 1'@ oscillations are measured. The a!solute error in the period 4i.e. time for a single oscillation6 is then %H%' ?or %H1' respectively@ of the a!solute error in the time for %' ?1'@ oscillations e.g. 1' oscillations+ Time = %5.; ( '.% s 4'.<>6 %5.; ± '.% ∴ Period = s = '.IJ' ( '.''5 s 1' *ote that the percentage uncertainty" p" in the period is the same as that in the overall time. n this case" p =

'.% %5.;

× %''> = '.<>

?% s.f.@

!i$ital vernier callipers+micrometer

Precision smallest measura!le quantity usually ( '.'%mm %easurin$ cylinder + eakers+ urette

Smallest measura!le quantity e.g. ( % cmK" !ut this depends upon the scale of the instrument. n the case of measuring the volume using the line on a !eaker" the estimated uncertainty is likely to !e much greater. *ote candidates must !e careful to avoid paralla# when taking these measurements" and should state that all readings were taken at eye level. They should also measure to the !ottom of the meniscus.


AAKC PHYSICS ©

Unit 6 | Notes

!eterminin$ the uncertainties in derived 'uantities. Please note that candidates entered for AS award will now e re'uired to comine percenta$e uncertainties.

Lery frequently in Physics" the values of two or more quantities are measured and then these are com!ined to determine another quantityM e.g. the density of a material is determined using the equation+ m ρ = V To do this the mass" m" and the volume" V " are first measured. Each has its own estimated uncertainty and these must !e com!ined to produce an estimated uncertainty in the density. The volume itself may have !een determined !y com!ining several independent quantity determinations 4e.g. length" !readth and height for a rectangular solid or length and diameter for a cylindrical wire6. n most cases" quantities are com!ined either !y multiplying or dividing and this will !e 2 considered first. 7ultiplying !y a constant" squaring ?e.g. in 2: π r @" square rooting or raising to some other power are special cases of this and will !e considered ne#t. 1. %ultiplyin$ and dividin$The percentage uncertainty in a quantity" formed when two or more quantities are com!ined !y either multiplication or division" is the sum of the uncertainties in the quantities which are com!ined. )xample

The following results were o!tained when measuring the surface area of a glass !lock with a 2'cm rule" resolution '.%cm Nength = J.I ( '.% cm Aidth = :.: ( '.%cm *ote that these uncertainties are estimates from the resolution of the rule. This gives the following percentage errors+ '.% × %''> = %.'> J.I '.% pA = × %''> = 1.1> Aidth :.: So the percentage error in the volume" pL Nength+

pN

=

= %.' + 1.1 = 2.1>

$ence surface area = J.I × :.: = :1.<; cm ( 2.1 > The a!solute error in the surface area is now 2.1> of :1.<; = %.2I cm uoted to % sig. fig. the uncertainty !ecomes % cm The correct result" then" is :2 ( %cm D *ote that surface area is e#pressed to a num!er of significant figures which fits with the estimated uncertainty. 1. #aisin$ to a power e$ x 2/ x 1/

x

0

The percentage uncertainty in xn is n times the percentage uncertainty in x. e.g. a period ?T @ is as !eing 2% seconds with a percentage uncertainty of 1 >"


AAKC PHYSICS ©

Unit 6 | Notes

So T 1 = J<% ( :>. :> × J<% = :' ?to %.s.f@ So the period is e#pressed as T = J<' ( :' s. −

*ote+ x % is the same as %H x. So the percentage uncertainty in %H x is the same as that in x. Can you see why we ignore the − signQ *ote+ the percentage uncertainty in x is half the percentage uncertainty in x. . %ultiplyin$ y a constant n this case the percentage uncertainty is unchanged. So the percentage uncertainty in 2 x or '.5 x or π x is the same as that in x. )xample- The following determinations were made in order to find the volume of a piece of wire+ Fiameter+ d = %.11 ( '.'1 mm Nength+ l = J.< ( '.% cm

The percentage uncertainties are+ pd = %.<>M pl = %.'>. 1

Aorking in consistent units" and applying the equation V

=

π d

:

l " we have+

V = ::;.J mm 2 The percentage uncertainty" pV = %.< × 1 ) %.' = :.1 > = : > ?to % s.f.@ 4*ote that π and : have no uncertainties.6 So the a!solute uncertainty u = ::;.J × '.': = %I.J5< = 1' ?% s.f.@ So the volume is e#pressed as V = :5' ( 1' mm 2. 7ultiply the percentage uncertainty . Addin$ or sutractin$ 'uantities *A2 only, f 1 quantities are added or su!tracted the a!solute uncertainty is added. This situation does not arise very frequently as most equations involve multiplication and division only. The e.m.f. H p.d. equation for a power supply is an e#ception.

n all cases" when the final > uncertainty is calculated it can then !e converted !ack to an a!solute uncertainty and quoted % sig. figure. The final result and uncertainty should !e quoted to the same num!er of decimal places


AAKC PHYSICS ©

Unit 6 | Notes

3otes for purists%. Ahen working at a high academic level" where many repeat measurements are taken" scientists often use ,standard error- ε , a.k.a. ,standard uncertainty-. Ahere this is used" the e#pression x' ( ε is taken to mean that there is a pro!a!ility that the value of x is in the range x' − ε to x' ) ε " a J5> pro!a!ility that it lies in the range x' − 1ε to x' ) 1ε " a J;> pro!a!ility that it is !etween x' − 2ε and x' ) 2ε " etc. Our work on uncertainties will not involve this highDlevel approach. 1. The method which we use here of estimating the uncertainty in an individual quantity takes no account of the num!er of readings. This is !ecause it is e#pected that only a small num!er of readings will !e taken. Fetailed derivation of standard uncertainties ?see a!ove@ involves taking the standard deviation of the readings and then dividing this !y n − % " so

taking %' readings would involve dividing σ !y 2. 2. The a!ove method of com!ining uncertainties has the merit of simplicity !ut it is unduly pessimistic. f several quantities are com!ined" it is unlikely that the actual error ? sic@ in all of them is in the same direction" i.e. all ) or all −. $ence adding the percentage uncertainties overestimates the likely uncertainty in the com!ination. 7ore advanced work involves adding uncertainties in quadrature+ i.e. p =

p%1

+

p11

+

p2 1

+ ......

. This is normally

done when standard uncertainties are employed ?note % a!ove@. t is not intended that candidates pursue any of these coursesR


AAKC PHYSICS ©

Unit 6 | Notes

G#AP&S *derivation of uncertainties from $raphs is only expected in A2,

The following remarks apply to linear graphs+ The points should !e plotted with error !ars. These should !e centred on the plotted point and have a length equal to yma# − ymin 4for uncertainties in the y values of the points6. f identical results are o!tained the precision of the instrument could !e used. f the error !ars are too small to plot this should !e stated. f calculating a quantity such as gradient or intercept the steepest line and a least steep line should !e drawn which are consistent with the error !ars. t 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 !oth pass through this point. . The ma#imum and minimum gradients" mma# and mmin" 4or intercepts" cma# and cmin6 can now !e found and the results quoted as+ gradient = intercept =

mma#

+ mmin

1 cma#

+ cmin

1

m ma# − m min 1 c ma# − cmin ± 1 ±

Scales

Graph should cover more than 8 of the graph paper availa!le and awkward scales 4e.g. multiples of 26 should !e avoided. otation of the paper through π H: 4J'° R6 may !e employed to give !etter coverage of the graph paper. Semi4lo$ and lo$4lo$ $raphs *A2 only,

Students will !e e#pected to !e familiar with plotting these graphs as follows+ x SemiDlog+ to investigate relationships of the form+ y = ka . Taking logs+ log y = log k + x log a or ln y = ln k + x ln a 4t doesnBt matter which6 So a plot of log y against x has a gradient log a and an intercept log k . )xamples- adioactive or capacitor decay" oscillation damping n NogDlog+ to investigate relationships of the form+ y = Ax Taking logs+ log y = log A + n log x 4or the equivalent with natural logs6 So a plot of log y against log x has a gradient n and an intercept log A . )xamples- Cantilever depression or oscillation period as a function of overhang length" Gallilean moon periods against or!ital radius to test relationship. *ote that 5o$4lo$ or semi4lo$ $raph paper will not e re'uired. "ncertainties from 5o$ $raphs + Candidates will not !e e#pected to include error !ars in log plots.


AAKC PHYSICS ©

Unit 6 | Notes

Section 2 – 6deas for practical work

Prac Fensity of regular solids 4cu!oids" cylinders6 dentification of material using density.

Conte#t &se of metre rule" callipers" micrometer" !alance nitial work on uncertainties Fensity of liquids and irregular solids &se of measuring cylinders Aeighing a rule !y !alancing a loaded rule &se of P of 7 0cceleration of a trolley on a ramp 4lots of &se of equations of motion  graphs to variants here6 determine acceleration Fetermination of g !y simple pendulum *.. *ot on spec !ut a useful intro to oscillation period measurements nvestigation of a compound pendulum or a Fitto pin and pendulum DL characteristics of diodes" lamps etc. &se of ammeters" voltmeters" varia!le resistors" potentiometers 4pots6. dentification of the material of a wire !y Larious ways  single measurements H  determination of its resistivity against l . &ncertainty com!inations. Lariation of resistance with temperature for a Thermistor not on spec !ut it doesnBt matter metal wire 4copper is good6 andHor thermistor here. Could tie in with potential dividers to design a temperature sensor. Fetermination of resistance of a voltmeter !y R use of a series resistor. nvestigation of currents in series and parallel circuits Fetermination of internal resistance of a Firect use of V = E − Ir or use of power supply % % r = + D use of reciprocals in graphical V E ER work. Sonometer  variation of frequency with &se of reciprocals in graphical work length  determination of the speed of transverse waves on the metal wire 7easurement of the wavelength of microwaves !y standing waves 7easurement of the wavelength of microwaves !y Fou!le slit ?or NloydBs mirror@ 7easurement of wavelength of a laser !y oungBs slits 7easurement of wavelength of a laser pointer using a diffraction grating 7easurement of refractive inde# of glass or water !y real and apparent depth 7easure refractive inde# of a semicircular glass !lock using ray !o# 4or pinsR6 7easurement of the speed of sound in air using a dou!le !eam CO and two microphones


AAKC PHYSICS ©

Unit 6 | Notes

Section  – )xperimental techni'ues

The following is a selection of e#perimental techniques which it is anticipated that candidates will acquire during their 0S and 01 studies. 6t is not exhaustive " !ut is intended to provide some guidance into the e#pectations of the P$2 and P$< e#perimental tasks. %easurin$ instruments The use of the following in the conte#t of individual e#periments+ • micrometers and callipers. These may !e analogue or digital. t is intended that candidates will have e#perience of the use of these instruments with a discrimination of at least '.'% mm. 0 typical use is the determination of the diameter of a wire. • digital topDloading !alances. • measuring cylinders and !urettes. This is largely in the conte#t of volume and density determination. • force meters ?*ewton meters@. • stop watches with a discrimination of '.'% s. t is also convenient to use stopwatches H clocks with a discrimination of % s. • rules with a discrimination of % mm. • digital multimeters with voltage" current and resistance ranges. The following ?d.c.@ ranges and discriminations illustrative the ones which are likely to !e useful+ 1L '.''% L 1' L '.'% L %' 0 '.'% 0 10 '.''% 0 1 k Ω %Ω 1'' Ω '.'% Ω Students should !e familiar with the technique of starting readings on a high range to protect the instrument. • liquid in glass thermometers. D%' − %%'°C will normally suffice" though candidates can !e usefully introduced to the advantages of restricted range thermometers. Ahere appropriate" digital temperature pro!es may !e used.

E#perimental techniques The purpose of P$2 is to test the a!ility of the candidates to make and interpret measurements" with special emphasis on+ • com!ining measurements to determine derived values" eg density or internal resistance • estimating the uncertainty in measured and derived quantities • investigating the relationships !etween varia!les These a!ilities will !e developed !y centres" using all the content of P$% and P$1. They can and will !e assessed using very simple apparatus which can !e made availa!le in multiple quantities. $ence it is not foreseen that apparatus which centres are likely to possess in small num!ers" if at all" will !e specified" e.g. oscilloscopes" data loggers" travelling microscopes. The following list may !e found useful as a checklist. Candidates should !e familiar with the following techniques+ • connecting voltmeters across the p.d. to !e determined" i.e. in parallelM


AAKC PHYSICS ©

• • • •

• •

•

Unit 6 | Notes

connecting ammeters so that the current flows through them" i.e. in seriesM the need to avoid having power supplies in circuits when a resistance meter is !eing employedM taking measurements of diameter at various places along a wire H cylinder and taking pairs of such measurements at right angles to allow for nonDcircular cross sectionsM determining a small distance measurement" e.g. the thickness or diameter of an o!9ect" !y placing a num!er of identical o!9ects in contact and measuring the com!ined value" e.g. measuring the diameter of steel spheres !y placing 5 in line and measuring the e#tent of the 5M the use of potentiometers ?*.. not metre wire potentiometers@ and varia!le resistors in circuits when investigating currentDvoltage characteristicsM the determination of the period and frequency of an oscillating o!9ect !y determining the time taken for a num!er of cycles 4typically %' or 1'6M *.. 0lthough the concept of period is not on the 0S part of the specification" it is likely to !e used in P$2M the use of fiducial marks and noDparalla# in sighting against scales and in period determinations.


AAKC PHYSICS ©

Unit 6 | Notes

Plan List all the materials that you require for your experiment. State how you will measure two different types of quantities using the most appropriate instrument. For example, you could write: •

I will use a top pan balance to measure the mass.

•

I will use a micrometer screw gauge to measure the diameter of the wire.

Explain why you have chosen two of the measuring instruments that you have list ed. For example, you could write: •

•

I will use vernier callipers to measure the internal diameter of the test tube as no other instrument has this facility. I will use a multimeter to measure the resistance of the thermistor since it has a variety of ranges so I will be able to select the one that gives me the best precision.

Describe at least two measuring techniques that you have used to make your measurements reliable. For example, you could write: •

•

I will look horizontally across the wire with the metre rule behind in order to measure the position of the node. I will remove the Bunsen to slow the rate of heating as I measure the temperature of the thermistor. This will allow it to come to thermal equilibrium.

You need to identify other variables that could affect your results and state how these were controlled to ensure that you carried out a fair test. For example, you could write: •

I increased the pressure of the gas slowly so that the temperature stayed the same.

If you will not be taking repeat readings you should explain why. For example, you could write: •

I will be recording the temperature of the liquid as it warms up the thermistor so it will not be able to repeat my readings. I will check each reading carefully before replacing the bunsen.

Identify any safety hazards in your experiment and any precautions you may take. For example, you could write: •

I will use a stand to make sure the beaker of boiling water is kept securely on the tripod and gauze.

Indicate how you intend to use the data that you collected. For example, in an experiment to find out how the period, T , of a pendulum varies with its length, l , you could write: I will plot the log of the time against the log of the length and find the gradient to give me the n value of n in the equation T = kl . Include a diagram showing the arrangement of the apparatus that you will use. Mark important distances on this diagram and, in particular, mark any distances that you will measure.


AAKC PHYSICS ©

Unit 6 | Notes

The sources of uncertainty and error should be commented on. For example you could write: •

•

The uncertainty in my measurement of the period comes from the range of my repeated readings. It is caused by my judgement of when the pendulum actually stops. The thermometer might introduce a systematic error since I am unable to check whether i t reads 00C in melting ice. I will get an indication when the water boils and I can see if it reads 1000C even though the water is not pure.

Finally, remember that your plan should show logical thought by describing what you intend to do in sequence. The plan should be written in the future tense but this is not essential.

Implementation and measurements Record all your results in an appropriate table. If you take the average of, say three readings, then you should ensure that you write down each individual reading, not just the average value to show the examiner that you have taken an appropriate number of measurements. If you are plotting a graph then you should aim to take at least six readings and repeat these if necessary. It is a good idea to draw a rough graph as you are taking the measurements so that you can investigate anomalous readings or to take extra readings near any turning points in any curves that you obtain. Make sure that you take measurements over as wide a range as possible. For example, if you are determining the distance between two nodes that are separated by a few centimetres then you should not measure the distance between two nodes only. Instead, measure the distance occupied by several nodes and then calculate the average distance between two of these nodes. Think critically about your plan as you carry it out. Record any changes that you make to the plan with a reason. Record any techniques that you use but might not have written in your plan.

Analysis When you draw your graph, you should use more than half the graph paper in both the x and y directions. The graph need not necessarily include the origin; this depends on the measurements that you are carrying out. Use a sensible scale; for example avoid the use of a scale that goes up in steps of three as this will make it difficult for you to process any readings that you take from your graph. Make sure that you label each axis with the quantity being plotted (or its symbol) and its units if it has any, eg log (T/s). Plot points accurately, using either a dot surrounded by a small circle or a small cross. Make a brief comment on the trend shown by your graph, eg as temperature increases, resistance increases linearly. Remember that a straight line graph must pass through the origin to confirm a directly proportional relationship. If you need to obtain the gradient of your graph you should draw as large a triangle as possible on your graph paper to show how you worked out a value for the gradient. If the gradient is to be used to calculate a value for a physical quantity then you must read the units carefully from the axes.


AAKC PHYSICS ©

Unit 6 | Notes

You will need to discuss the sources of error and calculate the uncertainties that these contribute to the result(s) of your experiment. At A2 you will need to compound your errors to estimate their combined effect on the final result. You might use error bars on your graph to do this. You should comment on the precision of your measurements and how these contributed to the precision of your result. It might be that some of your readings were more precise than others in which case the least precise determines the result. The likely accuracy of your result might be commented on by reference to the uncertainties or by numerical comparison with the accepted value of a quantity such as the acceleration due to gravity. Suggest at least one realistic non-trivial modification that you could make to reduce the errors in your experiment or to improve your experiment. Trivial suggestions such as if I had more time I would have taken more readings will not score this mark. Vague suggestions such as I would use a digital meter are only of use if they go on to describe how they improve the experiment. Considering the precision of your readings is an appropriate way to do that. Similarly you might consider using a more sensitive device. Certainly the accuracy of your result merits comment. You should suggest further work that will develop the investigation that this work started, often it will involve changing different variables with the same apparatus. You should explain how this work will add to your understanding of the investigation and what you might expect to find.

Conclusion It is important to make a clear concise statement of your final conclusion. Make sure it is easy to find the conclusion in your report. For example, draw a box round it, give it a prominent heading, or underline it in a bright colour. The conclusion should relate your results to the original aim of the experiment and should include your final numerical result with its uncertainty. For example you could write: From my measurements I found a value of 6.2 +/- 0.5 x 10 -34 J s for the Planck constant. or The results from these experiments indicate that there is a power-law relationship between wave speed v and tension T : v = kT a where a = 0.48+/- 0.03. Theoretical analysis suggests that a = 0.5 (ie v = k √T ), which is consistent with the data. Briefly mention any physics principles that you use in your calculations and/or conclusion. This might involve algebraic manipulation of equations or a discussion of the phenomenon you have been investigating. For example why the wire was resonating at all in an experiment to measure resonant lengths.


AAKC PHYSICS ©

Unit 6 | Notes

Uncertainties in measurements

What are uncertainties? Why are they important? When you repeat a measurement you often get different results. There is an uncertainty in the measurement that you have taken. It is important to be able to determine the uncertainty in measurements so that their effect can be taken into consideration when drawing conclusions about experimental results.

Calculating uncertainties Example: A student measures the diameter of a metal canister using a ruler graduated in mm and records three results:

66 mm, 65 mm and 61 mm.

The average diameter is (66 + 65 + 61) / 3 = 64 mm.

The uncertainty in the diameter is the difference between the average reading and the biggest or smallest value obtained, whichever is the greater. In this case, the measurement of 61 mm is further from the average value than 66 mm, so the uncertainty in the measurement is: 64 – 61 = 3 mm.

Therefore the diameter of the metal canister is 64 + 3 mm. -

Even in situations where the same reading is obtained each time there is still an uncertainty in the measurement because the instrument used to take the measurement has its own limitations. If the three readings obtained above were all 64 mm then the value of the diameter being measured is somewhere between the range of values 63.5 mm and 64.5 mm.

In this case, the uncertainty in the diameter is + 0.5 mm. Therefore the diameter of the metal canister is 64.0 + 0.5 mm. -


AAKC PHYSICS ©

Unit 6 | Notes

Calculating percentage uncertainties The percentage uncertainty in a measurement can be calculated using: Uncertainty of measurement x 100% Measurement taken

The percentage uncertainty in the measurement of the diameter of the metal canister is: Uncertainty of measurement x 100% = 0.5 Measurement taken 64

x 100% = 1 %

The radius of the canister = diameter/2 = 32 mm.

The percentage uncertainty for the radius of the canister is the same as its diameter ie 1%.

Compounding errors Calculations often use more than one measurement. Each measurement will have its own uncertainty, so it is necessary to combine the uncertainties for each measurement together to calculate the overall uncertainty in the result of the calculation.

The total percentage uncertainty is calculated by adding together the percentage uncertainties for each measurement if (1) all the measured quantities are independent of one another AND (2) they are multiplied together.

Example 1: Calculating the percentage uncertainty for the area of a square tile.

A student using a rule to measure the two adjacent sides of a square tile obtains the following results: Length of one side = 84

+ -

0.5mm

Length of second side = 84

+ -

0.5mm

Show that the percentage uncertainty in the length of each side of this square tile is about 1%. Calculate the area of the square. (The above two calculations are left as an exercise for the student.) [Area of square A = 84 x 84 = 7100 mm] The percentage uncertainty in the area of the square tile is calculated by adding together the percentage uncertainties for its two sides.


AAKC PHYSICS ©

Unit 6 | Notes

Percentage uncertainty in the area of the square tile is:

Δ A/A = 1% + 1% = 2%

Example 2: A metallurgist is determining the purity of an alloy that is in the shape of a cube by measuring the density of the material. The following readings are taken:

Length of each side of the cube l = 24.0 + 0.5mm Mass of cube m = 48.230+ 0.005g Calculate (i) the density of the material (ii) the percentage uncertainty in the density of the material. Solution 2:

(i) Density of alloy = mass/volume = 48.230 x 10 -3 kg/ (24.0 x 10 -3)3 = 3500 kg m -3. (ii) Percentage uncertainty in the length of each side of the cube

Δl/l

= 0.5 24

x 100% = 2 %

Percentage uncertainty in mass of cube

Δm/m = 0.005 x 100% = 0.1 % 48.2

Therefore total percentage uncertainty = 2% + 2% + 2% +0.1% = 6.1% We normally ignore decimal places in calculating uncertainties so the percentage uncertainty in the density of the material is 6%.

Example 3: Calculating the percentage uncertainty for the cross sectional area of a canister.

If the student determines that the radius of the metal canister is 36 mm with an uncertainty of 1% then the cross sectional area A of the canister is: A = π r 2

A = π (36) 2

A = 4.1 x 10 3 mm2.

Notice that the result has been expressed using scientific notation so that we can write down just two significant figures. The calculator answer (4071.5...) gives the impression of far greater precision that is justified when the radius is only known to the nearest mm.


AAKC PHYSICS ©

Unit 6 | Notes

The cross sectional area was calculated by squaring the radius (ie multiplying the radius by the radius). Since two quantities have been multiplied together, the percentage uncertainty in the value of the cross sectional area is found by adding the percentage uncertainty of the radius to the percentage uncertainty of the radius:

Percentage uncertainty in cross sectional area

Δ A/A = 1% + 1% = 2%

Using error bars to estimate experimental uncertainties The equation v = kT a relates the speed of a wave, v in a string to its tension, T . In an experiment to verify this relationship, a graph of ln ( v/ms-1) against ln (T /N) is plotted and the gradient of the straight line is the constant a. To determine the uncertainty in constant a, the uncertainties in v and T can be compounded by considering the difference between the best fit and worst fit lines that can be plotted through the data using error bars. To produce error bars in ln(T /N) you need the uncertainty in T . You then calculate the logarithm of your data point with the uncertainty applied and draw the error bar to this value. Suppose you measure T as T = 3.4N +/- 0.2N. Then the length of the error bar is [ln(3.6N)-ln(3.2N)]. This need only be calculated for one data point and the same size error bar used for each value of T . The uncertainty in ln (v/ms-1) can be calculated in the same way and error bars drawn in that direction to give, in effect, an error box around each plot. The best fit line is the line that passes closest to all the plots. The worst fit line just passes through all the error boxes. It is not intended that this should be a particularly lengthy procedure but it is one way of finding an estimate of the uncertainty in an experiment.

Carrying out the practical work Students must carry out the practical work individually under supervised conditions. It is advisable to have spare parts available, particularly for vulnerable components. It should be possible for students to set up their equipment and record all necessary measurements in one normal practical session. If it is not possible to complete the practical in one session then the teacher may decide to use the following session to complete the practical. The unmarked plan should be returned to students at the beginning of the lesson. Teachers may give students a copy of the assessment criteria (marking grids) from the specification and briefing documents at the start of the session; students must not bring their own copies of any documents to the session to prevent them from accessing annotated versions that they may produce. Teachers may provide students with any formula that are needed during the session without penalty.


AAKC PHYSICS ©

Unit 6 | Notes

Glossary Accuracy

The degree to which a measurement matches the true value of the quantity that is being measured. This is a qualitative term only.

Dependent variable

A variable physical quantity, the values of which are not chosen by the person doing the experiment, but change with another variable ie the independent variable.

Error

An offset or deviation (either positive or negative) from the true value.

Independent variable

A variable physical quantity, the values of which are chosen by the person doing the experiment.

Percentage uncertainty Percentage uncertainty =

Uncertainty of measurement x 100% Measurement taken

Precision of an instrument

This is a term meaning 'fineness of discrimination'. In practice, it is the smallest scale division on an instrument that can be read.

Random error

An unpredictable error that has no pattern or bias. To reduce the effects of random errors when measuring a quantity it is necessary to take the mean of several values.

Range

The difference between the smallest value and the largest value of a set of readings.

Reliability

The extent to which a reading or measurement gives the same value when a quantity is measured several times under the same conditions.

Sensitivity

The change in response of an instrument divided by the corresponding change in stimulus. For example, the sensitivity of a thermometer is expressed in mm/oC

Systematic error

An error that has a pattern or bias, for example, errors caused by background lighting. This type of error adds or subtracts the same value to each measurement that is taken.

True value

The value that would be obtained if there were no errors in the measurement of that value.

Uncertainty

A range of values which are likely to contain the true value.

Validity

The level of confidence that is associated with a measurement or conclusion.

Zero error

An error that is caused when an instrument does not read true zero, eg a spring balance may not read zero when there is nothing hanging from it. This type of error is a form of systematic error.


AAKC PHYSICS ©

Unit 6 | Notes

Plan for experiment for interacting magnetic fields Apparatus Flat coil of wire Small bar magnet Ammeter Dc psu Thread Stopclock Two retort stands

Method 1

Suspend the magnet using thread so that it lies in the centre of the coil. Rotate the magnet, release it and take measurements to find the period T of the resulting oscillation of the magnet about its centre. It will oscillate due to the Earth’s magnetic field.

2

Turn on the power supply unit and increase the current to 0.50 A and repeat 1 above.

3

Repeat 2 up to 5.0 A to enable you to plot a meaningful graph.


AAKC PHYSICS ©

Unit 6 | Notes

Plan for experiment for guitar strings Apparatus Bench mounted pulley Moveable bridge - support for the wire 1.2 m length of 32swg constantan wire Low voltage ac power supply unit 2 blocks of soft wood G clamp 2 magnadur magnets and yoke – to produce magnetic field Slotted masses and hanger Metre rule Crocodile clips and connecting leads Ammeter.

Method 1

The wire is to be stretched across the bench so that it hangs over the bench mounted pulley. The other end is held between two blocks of wood by a G clamp. Hang 100 g on the end of the wire to tension it.

2

Place the moveable bridge under the wire near the blocks of wood. The distance l between the bridge and pulley should be about 1 m.

3

Use crocodile clips at each end of the wire to connect the power supply unit to the wire and pass an alternating current of less than 1 A through it.

4

Place the yoke and magnets around the wire so that the wire passes through the magnetic field.

5

Turn on the power supply unit and increase the voltage until the wire clearly vibrates.

6

Adjust the position of the moveable bridge until resonance is found. Measure the length l .

7 Vary T by increasing the hanging mass and measure the new resonant length. Do this until you have enough data for a graph and record your data in a table.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 1 Momentum and momentum conservation – large trolleys Purpose

Safety

The aim of this experiment is to study momentum

Lift the large wooden runway with care.

and its conservation in an inelastic collision.

Set up the experiment away from the edges of the bench so that the trolleys do not fall off.

You will need: •

Two trolleys

•

Plasticene®

•

Two light gates and suitable interface

•

Drawing pin

•

Eight 100 g slotted masses

•

Adhesive tape

•

Wooden runway

•

Means of tilting the runway

light gate 1

light gate 2

Plasticene®

trolley A

trolley B

Figure 1: Arrangement of large trolleys to investigate momentum and momentum conservation

Experimental instructions Set up the apparatus as shown in the diagram with five slotted masses fixed onto trolley A. Compensate for friction by tilting the runway slightly. Check by giving one trolley a small push and confirming that it r uns down the runway with constant speed. Soften the Plasticene ® and stick it to the front of one of the trolleys. Fix the drawing pin to the front of the other trolley with the adhesive tape, so it is facing out from the trolley as shown. Put the two light gates quite close together. This is to minimise the effects of friction as the trolleys collide. Set the interface unit to record the speed of trolley A before the collision and the speed of the two trolleys (A and B joined together) after the collision. Put trolley A at one end of the runway and trolley B just before light gate 2. Give trolley A a push (not too large) so that it runs down the track, cutting through the light beam of light gate 1 and colliding with, and sticking to, trolley B. The two trolleys will now travel on, the mask on trolley A cutting through the light beam of light gate 2. Repeat the experiment for differing initial speeds and trolley masses. Do not allow the trolleys to fall off the bench.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 1 (cont.) Momentum and momentum conservation – large

trolleys

Analysis and conclusions Use your results to test the law of conservation of momentum. Calculate the total momentum of both trolleys before and after the collision. Comment on the most important sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 2 Momentum and momentum conservation – small trolleys Purpose

Safety Lift the wooden support board with care.

The aim of this experiment is to study momentum and its conservation in an inelastic collision.

You will need: •

Two trolleys

•

Eight washers

•

Two pieces of Velcro® strip

•

Two light gates and suitable

•

Plastic runway

•

Means of compensating the

interface

•

Wooden support board

light gate 1

runway for friction

light gate 2

mask size 1 cm trolley A trolley B washers

Velcro® strip

Velcro ® strip

Figure 1: Arrangement of small trolleys to investigate momentum and momentum conservation

Experimental instructions Set up the apparatus as shown in the diagram with four washers on each trolley. Compensate for friction by tilting the r unway slightly. Check by giving one trolley a small push and confirming that it runs down the runway with constant speed. Mount a piece of Velcro ® on each trolley so that the trolleys stick together when they collide. Set the interface unit to record the speed of trolley A before the collision and the speed of the two trolleys (A and B joined together) after the collision. Put trolley A at one end of the runway and trolley B just before light gate 2. Give trolley A a push (not too large) so that it runs down the runway, cutting through the light beam of light gate 1 and colliding with, and sticking to, trolley B. The two trolleys will now travel on, the mask on trolley A cutting through the light beam of light gate 2. Repeat the experiment for differing initial speeds and trolley masses.

Analysis and conclusions Use your results to test the law of conservation of momentum. Calculate the total momentum of both trolleys before and after the collision. Comment on the most important sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 3 Momentum and momentum conservation using a linear air track Purpose The aim of this experiment is to study momentum and its conservation in an inelastic collision between two riders using a linear air track.

You will need: •

Linear air track

•

Additional masses

•

Air blower

•

Pin attachment

•

Two riders

•

Plasticene®

•

Two light gates and suitable interface

light gate 1

light gate 2

mask rider A

rider B

pin attachment Figure 1: Using a linear air track to investigate momentum and momentum conservation

Experimental instructions Set up the apparatus as shown in the diagram. Compensate for friction by tilting the air track slightly. Check by giving one rider a small push and confirming that it runs along the air track with constant speed. Put some Plasticene ® in the hole on one rider and fix the pin attachment to the other rider. Set the interface unit to record the speed of rider A before the collision and the speed of the two riders (A and B joined together) after the collision. Put rider A at one end of the linear air track and rider B just before light gate 2 and switch on the air blower. Give rider A a push (not too large) so that it runs along the air track, cutting through the light beam of light gate 1 and colliding with, and sticking to, rider B. The two riders will now travel on, the mask on rider A cutting through the light beam of light gate 2. Repeat the experiment for differing initial speeds and rider masses. The mass of the rider can be changed by fitting additional masses to it.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 3 (cont.)

Momentum and momentum conservation using a

linear air track

Analysis and conclusions Calculate the total momentum of both riders before and after the collision. Use your results to test the law of conservation of momentum. Comment on the most important sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 4 Rate of change of momentum using a linear air track

Purpose The aim of this experiment is to investigate rate of change of momentum using a linear air track.

You will need: • Linear air track • Air blower • Rider • Two light gates and suitable interface

light gate 1

• • •

Pulley suitable for xing to the air track Thread Set of slotted masses (10 g)

light gate 2

mask

rider

slotted masses Figure 1: Using a linear air track to investigate rate of change of momentum

Experimental instructions Set up your apparatus as shown in the diagram. Compensate the air track for friction by raising one end slightly. Check by giving the rider a gentle push and measuring its velocity through both light gates – it should move along the air track at a constant velocity when there is no accelerating force on it. Set your interface unit to measure velocity at both gates and the time taken to travel between them. Start with six of your ten masses on the rider and the other four (including the hanger) on the thread hanging down. The mass to be accelerated is the mass of the rider and the set of slotted masses while the accelerating force is the weight of the four suspended slotted masses (0.4 N). Hold on to the rider. Switch on the air blower and timing devices. Release the rider and allow it to accelerate down the track. Do not allow it to crash into the end of the track. Record the velocities of the rider as it passes through light gates 1 and 2 and the time taken for the rider to travel between the gates. Repeat the readings and take an average.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 4 (cont.)

Rate of change of momentum using a linear air

track Vary the accelerating force but keep the total mass constant by putting masses on the rider if they are removed from the hanger and vice versa. Record the values of accelerating force, velocity and momentum values at gates 1 and 2, the momentum change and the time between the light gates in a table.

Analysis and conclusions Calculate the rate of change of momentum for each accelerating force. Plot a graph of rate of change of momentum against accelerating force. Comment on the shape of graph and deduce the relationship between rate of change of momentum and accelerating force.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 5 Rate of change of momentum using a trolley

Purpose The aim of this experiment is to investigate rate of change of momentum using a trolley on a runway.

You will need: • Trolley • White plastic track • Board • Two light gates and suitable interface • Bench pulley

• •

•

Thread Twelve washers (mass 10 g each) (a set of slotted masses could be used instead of the washers) Sponge to put on oor below the masses

mask size 1 cm light gates

trolley washers

accelerating washers Figure 1: Using a trolley to investigate rate of change of momentum

Experimental instructions Set up your apparatus as shown in the diagram. Compensate the runway for friction by raising one end slightly. Check by giving the trolley a gentle push and measuring its velocity through both light gates – it should move along the runway at a constant velocity when there is no accelerating force on it. Set your interface unit to measure velocity at both gates and the time taken to travel between them. Start with ten of your twelve washers on the trolley and the other two on the thread hanging down. The mass to be accelerated is the mass of the trolley and twelve washers while the accelerating force is the weight of the two suspended washers (0.2 N). Allow the trolley to accelerate down the runway. Record the velocities of the trolley as it passes through light gates 1 and 2 and the time take for the trolley to travel between the gates. Repeat the readings and take an average.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 5 (cont.)

Rate of change of momentum using a trolley

Repeat the procedure by taking one washer off the trolley and adding it to the suspended washers – the accelerating force is now 0.3 N (same total mass). Carry on until you have only two washers left on the trolley. Record the values of accelerating force, velocity and momentum values at gates 1 and 2, the momentum change and the time between the light gates in a table.

Analysis and conclusions Calculate the rate of change of momentum for each accelerating force. Plot a graph of rate of change of momentum against accelerating force. Comment on the shape of graph and deduce the relationship between rate of change of momentum and accelerating force.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 6 Centripetal force – whirling bung

Purpose

Safety

The aim of this experiment is to verify the equation for centripetal force using a whirling bung.

Do not swing the bungs round too fast and avoid collisions between bungs and people! Keep away from windows. Wear eye protection.

You will need: • Rubber bung with a hole through it • Length of string (about 1.5 m) • Washers or 10 g slotted masses and hanger

• • •

Stopwatch or stop clock Metre ruler Short length of glass tube with the ends burred over (or a short metal tube)

• •

Access to a balance Eye protection

Experimental instructions

R

Tie the piece of string to a rubber bung and then thread it through a short length (10 cm) of glass tube. Fix a small

rubber bung mass M glass tube

weight (such as a few washers with a mass a little greater than the mass of the bung) to the lower end of the string. Whirl the bung round in a horizontal circle (radius approximately 80 cm) while holding the glass tube so that

washers or slotted masses (weight mg)

the radius of the bung’s orbit is constant. (A mark on the string will help you see if the radius of the orbit remains the same.)

Figure 1: Whirling bung arrangement

Measure the mass of the bung ( M ), the total mass of the washers (m), the radius of the orbit ( R) and the time for ten orbits (10

3

T ).

Repeat the experiment with different numbers of washers, different orbit radii and bungs of different masses.

Analysis and conclusions

(

Calculate the period of the orbit ( T ), the velocity of the bung in the orbit v then work out the centripetal force F 5 ____ . R

(

Mv2

5

2 R ____ and p

T

)

)

Compare this value with the weight of the washers ( mg ). (The centripetal force should be equal to the weight of the washers. This will only be the case if the system is frictionless.) Plot a graph of m against v2. Comment on the most important sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 7 Centripetal force – rotating trolley

Purpose

Safety

The aim of this experiment is to verify the equation for centripetal force.

Do not allow the rotating table to turn too fast!

You will need: • Trolley • Spring • Plastic runway • Wooden support • Washers • Rotating table

• • • • • •

Power supply (0–12 V) Ruler Stop clock Newtonmeter Balance G clamps

spring washers

trolley R

runway

rotating table

Figure 1: Rotating trolley setup

Experimental instructions Set up the apparatus as shown, clamping the rotating table firmly to the bench. Carefully increase the speed of the motor until the trolley just touches the stop at the end of the runway. Measure the rotation rate and use it to calculate the speed ( v) of the trolley in a circle of radius

R.

Measure the mass of the trolley and its load ( m) and hence calculate the theoretical value of

(

the centripetal force needed to keep it in the orbit at that speed centripetal force

5

mv2 ____ . R

)

Using a newtonmeter, measure the force required to extend the spring by the amount needed for the trolley to touch the end of the runway. Compare your two values and comment on your findings. Repeat the experiment for different values of the load on the trolley.

Analysis and conclusions Plot a graph of the measured force against

mv2.

Use the graph to verify the equation for

centripetal force. Comment on the most important sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 8 Measuring the charge stored by a capacitor

Purpose

Safety

The aim of this experiment is to measure the charge stored by a capacitor using a coulombmeter and to investigate the formula charge Q capacitance 5 ________ C 5 __ . potential V

(

If you are using an electrolytic capacitor, take care to connect

)

You will need: • Capacitors (0.1 mF, 0.22 mF, 0.047 mF)

•

it with the correct polarity.

Power supply (0–6 V dc) (or 6 V battery pack and a 10 V rheostat)

1

V

Digital coulombmeter Digital voltmeter SPDT switch

2

C

1

• • •

Q

Circuit using battery pack and rheostat

Q

Circuit using variable voltage power supply

2



y l p p ) u s V r 6 e – w 0 ( o p c d

V

C



Figure 1: Circuit for measuring the charge stored by a capacitor

Experimental instructions Connect up the circuit shown in the diagram using the 0.1

mF

capacitor, with the switch in

position 1. Switch on the power supply and adjust the output so that the voltmeter reads 0.5 V. Move the switch to position 2 and record the reading of charge on the coulombmeter. Return the switch to position 1, and adjust the voltmeter to read 1.0 V. Move the switch to position 2 and again record the charge. Repeat the procedure in 0.5 V steps up to a maximum of 6.0 V. Record all your results in a table showing capacitor voltage and charge. Repeat for different values of capacitance.

Analysis and conclusions For each capacitor plot a g raph of capacitor voltage against charge. Calculate the gradient of each of your graphs and compare this with the stated value of the capacitor.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 9 Effect of length and current on the force on a wire in a magnetic field Purpose The aim of this experiment is to investigate how the force experienced by a c urrent-carrying wire in a magnetic eld depends on the length of the wire and the current passing through it.

You will need: • Electronic balance • Length of thin copper rod • Power supply (0–12 V dc, 0–5 A) • 4 mm connecting leads • Strong U-shaped magnet (two magnadur magnets on a yoke can be used if the balance is sufciently sensitive)

• • • • •

Two crocodile clips Ammeter (0–5 A dc) 30 cm ruler Two retort stands Bosses and clamps

to power supply copper rod

magnets fixed to metal yoke

245

side view

front view Figure 1: The experimental arrangement

Experimental instructions Set up the apparatus as shown with the crocodile clips a measured distance apart (say 4 cm). Take the reading on the balance and then switch on the power supply so that a current of 5 A flows through the rod. If necessary, change the direction of the current flow so that it causes an increase in the balance reading. Record the new reading of the balance. Change the separation of the crocodile clips and repeat the reading, keeping the cur rent constant. Note that the separation of the crocodile clips must not be greater than the length of the magnet poles. Repeat for a number of different crocodile clip separations. Return the crocodile clips to their original separation and repeat the experiment with a new value of the current. Repeat this for a number of different currents.


AAKC PHYSICS ©

Unit 6 | Notes

Effect of length and current on the force on a wire in a magnetic field Practical 9 (cont.)

Analysis and conclusions Calculate the force on the current using the equation F

5

BIl (if B is known) and compare it

with the increase in the balance reading. If the value of B is not known, use the increase in balance reading (

5

mg ) to calculate it.

Plot graphs of force against crocodile clip separation and force against current. Comment on your graphs.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 10 Specific heat capacity of a liquid

Purpose

Safety

The aim of this experiment is to measure the specic heat capacity of a liquid using an electrical method.

Do not heat the contents of the calorimeter above 50 °C.

You will need: • A copper or aluminium calorimeter with a volume of between 250 and 400 ml • Insulating jacket with a hole for the thermometer or sensor • Electrical immersion heater • Voltmeter • Ammeter

• Low-voltage power supply (0–12 V) • Thermometer (0–50 °C) • Stop clock (A temperature sensor and data logger can be used instead of the thermometer and stop clock.)

Stirrer insulating muff

heater water

Figure 1: Calorimeter setup for measuring the specific heat capacity of a liquid

Experimental instructions Set up the apparatus as shown in the diagram. Measure the mass of the calorimeter ( mC) and fill it with a known mass of water ( mW). There must be enough water to cover the immersion heater when it is put in the calorimeter. Place the muff over the calorimeter. Switch on the heater. Set the voltage ( V ) to a convenient value and record this with the value of the current ( I ). Measure the initial water temperature ( u ) using a thermometer and start the stop clock (or use a temperature sensor and data logger). Record the temperature at oneminute intervals, stirring just before the thermometer is read. Switch off the heater when the temperature reaches 50 °C. (You may need to adjust the value of

V during

the experiment so that the power input

remains constant.)


AAKC PHYSICS ©

Unit 6 | Notes

Practical 10 (cont.)

Specific heat capacity of a liquid

Analysis and conclusions Plot a graph of temperature against time and choose a section of the graph where the temperature is rising steadily. In this area find the temperature rise ∆u in a time ∆t . Calculate the electrical energy supplied to the heater ( VI ∆t ). Assume that there are no heat losses during the experiment. Calculate the specific heat capacity of water ( c W) from the equation: VI ∆t 5 mCc C∆u 1 mWc W∆u

where c C is the specific heat capacity of the material of the calorimeter. (The value of be found from a data book.) Repeat the experiment with other liquids. Record any sources of error which you consider will affect your result. Predict the effect on your answer of significant heat loss.


c C can

AAKC PHYSICS ©

Unit 6 | Notes

Practical 11 Specific heat capacity of a solid

Purpose The aim of this experiment is to measure the specic heat capacity of a solid using an electrical method.

You will need: • Aluminium (or other metal block) with a mass of 1 kg • Heat-resistant mat • Low-voltage heater and suitable power supply • Ammeter and voltmeter • Thermometer (0–50 °C)

• •

Stop clock Insulating jacket with a hole for the thermometer or sensor • Silicone grease (A temperature sensor and data logger can be used instead of the thermometer and stop clock.)

immersion heater

heat-resistant mat

metal block insulating jacket

Figure 1: Setup for measuring the specific heat capacity of a solid

Experimental instructions Measure the mass of the metal block ( m). Put the thermometer in the small hole in the metal block. Place the heater in the large hole in the block and switch it on. A small amount of silicone grease in the holes in the block can improve thermal contact. Place the insulating jacket around the apparatus. Set the voltage (V ) to a convenient value and record this with the value of the current ( I ).


AAKC PHYSICS ©

Unit 6 | Notes


Specific heat capacity of a solid

Measure the initial temperature ( u ) and start the stop clock (or use a temperature sensor and data logger). Record the temperature at one-minute intervals. Switch off the heater when the temperature reaches 50 °C. (You may need to adjust the value of

V during

the experiment so that the power input

remains constant.)

Analysis and conclusions Plot a graph of temperature against time and choose a section of the graph where the temperature is rising steadily. In this area find the temperature rise ∆u in a time ∆t . Calculate the electrical energy supplied to the heater ( VI ∆t ). Calculate the specific heat capacity ( c ) of the metal of your block using the formula: c

5

VI ∆t ______ m∆u

where m is the mass of the block. Assume that there are no heat losses during the experiment. Predict the effect on your answer of significant heat loss. Suggest the most likely sources of error in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 12 The relationship between the pressure and temperature of a gas Purpose

Safety

The aim of this experiment is to investigate how the pressure of a gas changes when it is heated at a constant volume.

You will need: • Round-bottomed ask • Temperature sensor and probe (or 0–100 °C thermometer) • Rubber bung with a short length of glass tube tted through it

• • • •

Wear eye protection if your face is to be close to the hot water.

Length of rubber tubing Pressure sensor (or Bourdon gauge) Bunsen burner, tripod, gauze and mat Glass beaker

• • •

Water Ice Eye protection

Experimental instructions Set up the apparatus as shown in the diagram with some ice in the water to cool it to near 0 °C. Record the temperature of the water (effectively the temperature of the air in the flask) and the pressure of the air as shown on the Bourdon gauge. Light the Bunsen burner and heat the water slowly. Record the pressure and temperature of the air at 10-degree intervals until the water temperature reaches 80 °C. (The temperature

air Bourdon gauge water

sensor may record temperatures at equal time intervals.)

Analysis and conclusions Plot a graph of the pressure of the trapped air ( y-axis)

heat

against the temperature of the trapped air ( x-axis). (Make sure that the pressure you record is the pressure of the trapped air, not just the excess above atmospheric pressure).

Figure 1: Investigating the relationship between temperature and pressure

It is assumed that the temperature of the trapped air will be the same as that of the water in the beaker.

Draw a second graph with the temperature axis showing minus 300 °C to plus 100 °C and find the intercept on the pressure axis (when the gas has zero pressure). This should be at absolute zero. Record your value for absolute zero, suggesting any inaccuracies in your experiment and how they might be reduced.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 13 The relationship between the pressure and volume of a gas Purpose

Safety

The aim of this experiment is to verify the relationship between the pressure ( p) and volume (V ) for a gas.

The apparatus should include a protective plastic screen around the glass tube. However, a safety screen is advisable. Do not increase the pressure to more than 300 kPa.

You will need: • Boyle’s law apparatus • Bicycle pump

•

Length of thick-walled rubber tubing

• •

Thermometer Safety screen

Experimental instructions Use the special apparatus shown in the diagram. trapped air

Using the bicycle pump, pump up the oil until the volume of trapped air is less than half the original value as shown on the vertical scale. Record the pressure ( p) and volume ( V ). The tube containing the air can be taken as having a uniform bore, so the length of the trapped air column is proportional to its volume.

oil

Slowly reduce the pressure by opening the valve at the base of the apparatus after disconnecting the pump. Close the valve after the oil level has fallen a little, wait for any excess oil to drain down the sides, and then take another reading of p and V . kPa

Repeat the procedure to gain as many readings as possible as the pressure of the trapped air, and therefore the oil level, falls. to pump

Take readings of the air temperature next to the apparatus to make sure that it does not alter significantly during the experiment.

Figure 1: Boyle’s law apparatus

Analysis and conclusions Plot two graphs: 1 one of p against __ . V From your graphs, deduce the relationship between pressure and volume of a gas at a a

one of p against V and

b

constant temperature.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 14 Measurement of the activity of a radioactive source

Purpose

Safety

The aim of this experiment is to investigate the activity of a radioactive source.

Use the recommended safety precautions associated with the handling of radioactive sources when carrying out this experiment. Because the Geiger–Müller tube operates at a high voltage, check the condition of the connecting leads before you start.

You will need: • Geiger–Müller (GM) tube, lead and stand • Source holder • Beta source (usually strontium-90, 185 kBq) • Pair of long forceps (the source should be at least 100 mm from the hand)

•

•

Counter/scaler and stop clock (a ratemeter could be used, in which case the counts per second are displayed directly) Ruler

radioactive source

GM tube

Figure 1: Apparatus for measuring the activity of a radioactive source

Experimental instructions Set up the apparatus as shown in the diagram but without the source in place. Carefully place the source in the holder using the pair of forceps, taking care to keep the source at arm’s length and well away from others in the laboratory. Switch on the GM tube power supply and adjust the voltage to the correct value for your tube. Record the number of counts in a period of five minutes. Repeat the experiment and obtain an average value for the count rate (counts per second). Return the radioactive source to its protective box. When you have done this, measure the distance ( R) between the source holder and the GM tube window. Measure the diameter of the GM tube window (2 r ).


AAKC PHYSICS ©

Unit 6 | Notes


Measurement of the activity of a radioactive

source

Analysis and conclusions Calculate the surface area of the sphere radius

R (4p R 2)

and the area of the GM tube

window (p r 2). Calculate the activity of the source using the equation: activity of the source

5 count

rate

3

4p R 2 _____ p r 2

You will have to ignore the absorption of the intervening air and the GM tube end window.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 15 Simulation of radioactive decay

Purpose

The aim of this experiment is to simulate the decay of a radioactive source using a large number of small wooden blocks or dice.

You will need: • A large number (at least 100) of small (1 cm sided) wooden cubes. One side of each cube should be coloured. Alternatively, dice can be used. • Large plastic beaker • Large plastic tray • Computer

Figure 1: You can use dice to simulate radioactive decay

Experimental instructions Collect your set of wooden blocks (or dice) and beaker. Record the initial number of blocks. Place them in the beaker and then tip them into the tray. Remove any that fall with the coloured side up, and return the remainder to the beaker. Tip these into the tray again and, as before, remove those that fall with the coloured side up. Repeat the process about 20 times, until very few blocks remain. If dice are used, then each time remove any that fall with the six (or any other chosen number) uppermost.

Analysis and conclusions Combine your results with those of the rest of the class in a spreadsheet and plot a graph of the number of blocks remaining after each throw ( N ) against the number of throws. Plot a further graph of ln N against the number of throws. Use the graph to calculate the ‘half-life’ of the blocks. What is the advantage of using a large number of blocks or dice? Suggest how you might modify the experiment to simulate a source with a different half-life.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 16 Graphical representation of simple harmonic motion

Purpose

The aim of this experiment is to generate graphs of some of the different properties of a system undergoing simple harmonic motion. This can be done using a motion sensor and data logger.

You will need: • Helical spring • Motion sensor • Suitable data logger

• • •

Set of slotted masses and hanger (100 g each) 30 cm ruler Retort stand, boss and clamp

helical spring

Experimental instructions Set up the apparatus shown in the diag ram with the motion sensor positioned below the slotted masses and in line with the direction of oscillation. The exact arrangement will depend on the design of your motion sensor. slotted masses

Five experiments should be performed to enable you to plot graphs of: a

acceleration against distance from the centre of oscillation

motion sensor b

velocity against distance from the centre of oscillation

c

distance against time

d

velocity against time

e

acceleration against time.

Use the data logger to display and record the Figure 1: The experimental arrangement

graphs.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 17

Forced oscillations

Purpose

Safety

The aim of this experiment is to investigate how the amplitude of a system subjected to a forced oscillation varies with the driving frequency.

Wear eye protection in case the hacksaw blade snaps.

You will need: • 30 cm ruler • Vibration generator • Signal generator • Frequency meter • Hacksaw blade

• • • • •

Lump of Plasticene® Base clamp (channel base) 2 G clamps Two large blocks of wood Eye protection

Plasticene®

hacksaw blade

vibration generator

Figure 1: Using a weighted hacksaw blade to investigate forced oscillations

Experimental instructions Set up the apparatus as shown with the end of the vibration generator pressing against the hacksaw blade and a known mass of Plasticene® on the end. Adjust the oscillator frequency until the hacksaw blade oscillates with maximum amplitude. This is resonance. Record the mass of Plasticene ® (m) on the end of the hacksaw blade and the signal generator frequency ( f ). Repeat for a series of different values of m.


AAKC PHYSICS ©

Unit 6 | Notes

Practical 17 (cont.) Forced oscillations

Analysis and conclusions Plot a graph of the mass of Plasticene ® (m) against the resonant frequency ( f ). Plot a graph of log m against f . Attempt to suggest an equation relating m and f . Comment on the most important sources of error in your experiment and suggest how they might be reduced.


Physics Unit 6 Source Book

Recommend Documents