# AS and A Level Physics (9702)

### About Cambridge International AS and A Level Physics (9702)

Cambridge International AS and A Level Physics builds on the skills acquired at Cambridge IGCSE (or equivalent) level. The syllabus includes the main theoretical concepts which are fundamental to the subject, a section on some current applications of physics, and a strong emphasis on advanced practical skills. Practical skills are assessed in a timetabled practical examination.

The emphasis throughout is on the understanding of concepts and the application of physics ideas in novel contexts as well as on the acquisition of knowledge. The course encourages creative thinking and problem-solving skills which are transferable to any future career path. Cambridge International AS and A Level Physics is ideal for learners who want to study physics or a wide variety of related subjects at university or to follow a career in science. Please note that the Scheme of Assessment has changed since 2005.

# AS Level Physics Practical Paper 3

### Paper format:

There are two questions in each paper. Each question should take one hour as both questions are of 20 marks.

**Question number 1:**

Outline: it requires candidate to collect data, plot a graph and draw simple conclusions.

**Question number 2:**

Outline: No graph will be required. It will require candidates to follow an inaccurate method, take several readings and then evaluate the results. It requires candidates to identify the problems faced in experiment and suggest improvements that can be made.

Now, before starting on the tips to ace the **Physics Practical Paper 3**, you should keep this thing in mind that most of the marks are for working, presentation and conclusions. So even if your practical work is not very accurate you should move to the tables, graph and working without wasting time in making it more accurate. There are only 2 marks of quality on whole paper. Why lose rest of the marks due to 2 marks only? Don’t get me wrong though. I don’t mean that don’t do the practical accurately but I mean to say that don’t waste extra time in making it more accurate and leaving no time to complete rest of the paper.

I will discuss each point given in the **Mark Scheme** below.

### Question 1:

In this question, first set up the apparatus in exactly the same manner as shown on the question paper. The first part of this question usually involves measuring something like diameter of a wire, length of some part of experiment apparatus, potential difference, current etc. While measuring you should ensure that you present the data to the appropriate number of significant figures so that if reflects the least count of the device being used for example:

**Micrometer Screw Gauge***: 0.01 mm**Meter rule:**0.5 mm-
**Vernier Caliper**:**0.1 mm **Protractor:**0.5 degrees-
**Graduated cylinder:**1/2 of the least count **Time:**1 decimal place

And, yes, represent your all data in the SI units..meter (m) for length, radius e.t.c

***** Below is the animation, showing: *How to use Micrometer Screw Guage?*

****** Below is the animation, showing: *How to use Vernier Calipers?*

In some cases, you have to measure something and judging by the space provided you have to show the evidence that you have taken repeated readings and averaged them out. Say you have to measure the diameter of a sample of wire, so using the micrometer screw gauze take 3 readings in three different parts along the length of the wire and show:

**d = (d1+d2+d3)/3**

and show the value calculated. Also remember to add appropriate units along with the individual readings you measure.

Then it says to repeat the procedure and get six different sets of data in a table. Students often have this thing out of their mind that the presentation is important and CIE in its examiner’s report terms such students as ‘*weak candidates*’. So first thing first, know how many variable you have to measure and/or calculate so you could draw appropriate columns.

Now before moving onto how to construct a ‘nice’ table, let’s first consider what actually is demanded by the examiner in the table. A ‘nice’ table should have these features:

**1) Range and distribution**

Largest possible range is required. It means that for example if you have to measure length (L) from 0-100 cm, so we must take highest range while keeping the difference constant and getting 6 set of readings. The difference you can take here is 15, so the readings of L you’ll take will be: *15 cm, 30 cm, 45 cm, 60 cm, 75 cm, 90 cm*. These values of L you have cover almost the whole range of values possible from minimum to maximum. Same applies if you have set of resistors and you are asked to make different combinations of resistors to yield different values of resistances. These values of resistance must cover the whole range possible, like from minimum to maximum value possible (here keeping the difference between individual values of resistance for different combinations common is not necessary!)

**2 ) Quality of data**

In a nutshell this one mark is for how close your readings are to the readings of supervisor and does your readings have the points which make them look actual readings instead of made-up readings such as: (1) scatter of points about the graph, due to random error the points will never lie on a straight line (2) the trend is correct like dependent variable increasing with increasing independent variable and so on.

You will get accuracy marks if you actually write the values which are there on the equipment instead of making your own and if you did the experiment as accurately as supervisor.

**3 ) Table**

**(i) Layout:**

You will draw one single table with headings. Each heading will have the name or symbol of quantity with it’s standard units in brackets of after slash such as “L /m” or “Temperature (K)”. using T can cause confusion so better write temperature or time instead of T or t unless the question explicitly says something like “ t=time period”. Writing “L m” or “temperature K” is not accepted.

**(ii) Raw data**

The data must be up to to the same precision. All the raw readings of a particular quantity should be recorded to the same number of decimal places which should in turn be consistent with the precision of the measuring instrument.

**(iii) Calculated quantities**

For example, you record the values for current (*I*) using the ammeter. Then the question asks you to include the values of *1/I* in your table. That *1/I *is calculated from *I*.

Lets say, *I* was given to 3sf. Then the calculated form (*1/I*) must have same number of sf, i.e. 3sf or one more sf, i.e. 4sf. These number of significant figures for calculated quantity should be kept same throught out the colum for that quantity.

However, if you are to calculate resistance from p.d and current, and the p.d was up to 2 significant figures while current was up to 3 significant figures. Then the number of sf in the calculated quantity must be equal to the least number of sf used in the calculation or one better. Therefore, the resistance calculated can only be given to either 2 sf (least sf used in calculation) or 3 sf (1 better sf).

Now after this discussion of what are the features of a nice table, lets move on to : ** HOW** to draw the table?

Use the full space provided. First draw a rectangle covering whole of the space and then draw a upper row relatively wide. Then draw a narrow column headed, S.No. (serial number), then draw equal sized columns for the variables, then draw equal sized 6 rows below the heading row the column heading carries one mark ‘quantity/unit’. Finally, record your raw data in to the table which is obtained from the experimental procedure. Afterwards, use this data to calculate other quantities. A ‘nicely’ made table looks like this (Here, I have taken the table from a question which involved measure of two quantities,* x/m & I/A*, and then involved a calculated quantity, *1/I)* :

S.No. | X/m | I/mA | 1/I / 1/mA |

1 | 0.100 | 1.1 | 0.9 |

2 | 0.250 | 1.0 | 1.0 |

3 | 0.400 | 0.9 | 1.1 |

4 | 0.550 | 0.8 | 1.3 |

5 | 0.700 | 0.7 | 1.4 |

6 | 0.850 | 0.6 | 1.7 |

However, if you have to measure time period of an oscillating pendulum, make sure that the amplitude is not greater than 5 cm, then display 3 sets of data in 3 small columns for 10 oscillations **10t1 **,**10t2**,** 10t3** and show in a separate column the calculated value of ‘*t*’ stating the formula in the column heading. Again significant figure of the raw data should represent the precision of the instrument used, and s.f of any calculated value from those data should be in same or one more s.f – correct calculation carries one mark!

**DO NOT** panic if your data has some flaws; inform the supervisor and if he gives replacement of some instrument carry on or if he doesn’t, hit him with the same instrument!! Just kidding. Any type of malfunctioning of instrument will be reported to CIE and you are not penalized for it as your practical skills are being assessed here.

After this comes the graph.* Now what is required for the graph?* Read it below!

**Graph**

**Layout:**

The axes must be labeled with their appropriate units (same as the headings of table). The scale must not be odd such as each 1 cm block = 3 N. Appropriate scales are 1,2 and 5 units = 1 block. Scale must be chosen to give at least 50% of the graph in both of x- & y- directions. On the graph grid provided, there are about 8 big boxes horizontally & 12 big boxes vertically (when the paper is viewed in portrait form). Therefore, the graph you draw must cover **ATLEAST** 4 boxes horizontally and 6 boxes vertically – appropriate scales must be chosen to ensure this. The line drawn must be extended beyond the points to occupy full graph. False origin should be used if the values start far away from the origin. The numerical labels must be regularly spaced. Scale markings should be no more than three large squares apart so to be on the safe side label all the

marks.

**Plotting:**

All points must be plotted accurately so they are not more than 1mm away from where they must be plotted(slight offsetting is pardoned). The point must be plotted sharply. If the points are not visible due to sharp lead then cross them or encircle them. Personally, I recommend using small crosses instead of dots (points), because blobs (points with diameter > 0.5 small square) are not accepted. Otherwise, if you find it easy to work with dots, use them, but make sure they are not blobs.

**Trend:**

The graph is a straight line. But it is not possible that all points lie on the line. A best-fit line has to be drawn. Most people don’t get the idea of best-fit line. By best-fit we mean ‘*average of all **points*‘ line. There must be even distribution of points above and below the line. The scattering of points around the line is due to random errors.

Best fit line must have the balance of at least 5 points which means you can ignore any one point which does not fit into a trend . There must be an even distribution of points either side of the line along the full length, as we can call the best fit line ‘*Insaaf Wali Line*’ in Urdu, which means line doing fair treatment to all the points. So the vector displacement of the points from the line should cancel out to zero . Lines must not be kinked. Lines thicker than half a small square are not accepted so I recommend a sharp lead pencil and a transparent ruler for this job. All points in the table (minimum 5) must be plotted for this mark to be scored. All points must be within 2 cm (to scale) in x direction of a straight line.

When finding gradient from the line draw the triangle with the hypotenuse at least 70% of the graph. Label the points with their coordinates.

**Analysis conclusion and evaluation**

**Finding gradient and y-intercept:**

First you will need to revise the equation of linear lines if you don’t remember them. A linear line can be written in equation as: *y=mx+c*

*y **is dependent variable, **x **independent variable, **c **is point where line touches y-axis(a constant), **and **m **is gradient of graph.*

To find gradient. From your points which you found by drawing triangle on the line, you can find gradient by this equation:

(Y2 – Y1) / (X2 – X1)

Both read-offs must be accurate to half a small square and sensibly quoted on the graph and in the calculations as well.

Finding the Intercept:

Either: Check correct read-off from a point on the line, and substitution into y = mx + c. Read-off must be accurate to half a small square.

Or: Check read-off of intercept directly from graph. then a calculation follows which requires you to substitute the values obtained in previous calculation of gradient and intercept. A method mark and a accuracy mark for the new calculated value.

### Question 2:

This question is more accurately described as an ‘error-question’ – meaning that this question depends on how accurately you work, and in case your accuracy is compromised, how can you improve the experiment to avoid it. Throughout this question you should think: Why I am feeling that this is difficult? What is the problem with this experiment? How can I modify it to take better readings? This critical thinking is very important to do the last part of this question, but the observations are made while doing experiment and setting up the apparatus.

This question usually has something ‘vulnerable’ to error to be measured so in this case a repeated reading is required. Same as the method described in question 1 of this guide, take several readings (2-3 readings would be enough) and take their average. Proof of repeated readings is mostly required in marking schemes. Keep in mind! A consistent unit must be quoted with the appropriate number of significant figures.

The types of ‘vulnerable-to-error’ questions which may come include: finding maximum height after rebound, measuring the angle at which a water-filled bottle falls, timing the falling body in a fluid (like oil) etc.

After measurements follow the calculations for finding out the uncertainty in the readings or calculating another value using a given formula by putting in the measure values. Usually the absolute uncertainty is the least count of the device, but in most cases it is greater – for example, the least count of a digital stop watch is 0.01s, but it will not make sense if you quote the absolute uncertainty to be 0.01 s because human error is quite large here; therefore, you must write a sensible value (a range of values is given in the marking scheme, in most of the cases 0.2s to 0.5s – but once again it totally depends on the experiment. As a certain answer you can just put it to be 0.2 s ).

For finding the percentage/absolute uncertainty, keep in mind the following rules:

- in case of addition / subtraction:
- we add the
**individual uncertainties**of the quantities added or subtracted. Take the following example:*a = 5 ± 0.2 & b = 2 ± 0.3**We are given, c = a + b*c = 5 + 2 = 7**Find the absolute uncertainty & percentage uncertainty in c.**absolute uncertainty in c = 0.2 + 0.3 = 0.5

percentage uncertainty in c = 0.5/7 * 100 = 7.14% (up to 3 sf.)**Note:**whatever the case (subtraction or addition), the individual uncertainties are always**ADDED**never subtracted!

- we add the
- in case of multiplication / division:
- we add the
**fraction uncertainties**of the involved quantities. Take the following example:**a = 2 ± 0.2 & b = 3 ± 0.3****We are given, c = b/a****Find the absolute uncertainty & percentage uncertainty in c.**c = 3/2 = 1.5

fractional uncertainty in a = Δa/a = 0.2/2 = 0.1

fractional uncertainty in b = Δb/b = 0.3/3 = 0.1

fractional uncertainty in c = (Δa/a + Δb/b) = 0.1 + 0.1 = 0.2

absolute uncertainty in c = (Δa/a + Δb/b) * c = (0.1 + 0.1) * 1.5 = 0.3

percentage uncertainty in c = (Δa/a + Δb/b) * 100 = 0.2 * 100 = 20%

- we add the
- in case powers are involved:
- when powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:

P = I^{2}R

when finding the percentage uncertainty of P, we’ll do it like this:

percentage uncertainty in P = (2 (ΔI/I) + ΔR/R) * 100

Just see how everything is done exactly the same, except that inclusion of power 2. I hope this clears the concept of uncertainty calculations of quantities involving powers.

- when powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:

After calculations involving a given formula to find a certain value, the candidate is usually asked to ‘*justify the number of significant figures*‘ in the final answer to the value you were asked to calculate. Here you need to keep in mind that when you are calculating a certain value, its significant figures must be equal to or 1 more than the significant figures in the raw data. Let’s take an example here (using **May/June 2018 Paper 3 Variant 3**, Question 2 as an example):

In the example question, you are initially asked to measure angle A in part b(i). In part c(ii), you are asked to calculate a value ‘*d*‘, using the formula:

**d = sin A/sin 45°**

In c(iii), you are asked to justify your number of significant figures for value of ‘*d*‘. The calculation for ‘*d*‘ involves the raw data, ‘angle A’, that you measured. Let’s say the number of s.f. for ‘*A*‘ were 2. Then the number of s.f. for ‘*d*‘ that you give **MUST** be equal to 2 s.f or 1 more (i.e. 3 s.f.). This is the justification you are supposed to provide for this type of questions.

The example question involved only ONE measured quantity; what if there are more than one? In that case, your significant figures for the calculated quantity (in the example, value ‘d’), must be equal to the smallest number of significant figures in the raw data or 1 more than that.

Following this type of question, you are usually asked to alter the apparatus in some way, and record set of values, and do calculations for the new arrangement.

Finally, a relationship is usually suggested between the values you calculated in previous parts, and you are required to find 2 different values of a constant ‘k’ for the respective data sets using the given relationship. In the part following it, you are asked ‘*Explain whether your results support the suggested relationship’.* Here you need to set a certain criterion for yourself. Let’s say you set the criterion to be : “*The suggested relationship will be valid, if the percentage difference between the two values of ‘k’ is less than 10%*“.

Suppose the values of ‘k’ you calculate come out to be :

k_{1} = 0.456 and k_{2}=0.461

Percentage difference between these values of ‘k’ is:

% difference = (k_{2}-k_{1})/k_{1} * 100 = (0.461-0.456)/0.456 * 100 = 1.09% (which is <10%)

Therefore, as 1.09% is less than 10%, according to given criterion, the suggested relationship is valid.

A thing to keep in mind is that there is no specified criterion to judge the validity of a relationship; it is entirely up to the the candidate to set it. A candidate can set the criterion to be <20% or <5%; it is entirely up to the candidate! However, setting a criterion like <50% difference for the relationship to be valid is totally stupid. So set a sensible criterion. You may sometimes be asked to justify the number of s.f. used in values of ‘k’ calculated; again give the same justification as described previously relating the s.f. in ‘k’ to the s.f. in raw data.

This last part is worth 6 marks which asks you to describe four sources of error and suggest the appropriate remedies. At the start of this guide for question 2, we mentioned this :

*“Throughout this question you should think: Why I am feeling that this is difficult? What is the problem with this experiment? How can I modify it to take better readings? This critical thinking is very important to do the last part of this question, but the observations are made while doing experiment and setting up the apparatus.”*

If you thought about these points while performing, you would have definitely no problem dealing with this part of the question. There are no set “errors and improvements”, as the errors are specific to a particular experiment you perform. However, some general errors and improvements are given below:

(*Pro-Tip: The first error and improvement works for ALL experiments. So better memorize it as it is 😉*)

**Error:**- Two readings are not enough to draw a (valid) conclusion

**Improvement:**- Take many readings and plot a graph or take more values of ‘k’ and compare.

**Different Experiment Scenarios (and their potential errors and improvements):**

**A) Water related experiment:**

**Error:**

(1) Hard to see water surface due to refraction effects/ meniscus effect

(2) Labels get wet/ink runs

**Improvement:**

(1) Use coloured liquid

(2) Use waterproof labels/ink

**Rejected:** Bottle not vertical

**B) Ball related experiment**

**Error:**

(1) Locating the centre of the ball when reading rule

(2) Inconsistent bounce

**Improvement:**

(1) Mark the centre of the ball with marker

(2) Use a flat surface/ Turn off fan

**C) Fast- moving object experiment**

**Error:**

(1) Difficult to judge when the ball is at its (maximum displacement, highest point etc)

(2) Hard to see when object strikes floor.

(3) Difficult to judge end point

(4) Difficulty in deciding the toppling point

**Improvement:**

(1) Position sensor above or below with data logger/ Video camera to play back frame by frame.

(2) Use pressure sensor to stop timer.

(3) Mark distance with lines on ramp (to eliminate parallax)

(4) Move by increments

**Rejected:**

Reject reaction time ideas/difficult to release from the same point each time.

**D) Releasing object from rest experiment**

**Error:**

(1) Difficulty in releasing the object due to (applied force etc)

(2) (Object) falls at an angle due to wind.-Light object

(3) Rod falls sideways/not entering sand vertically. – Heavy object

**Improvement:**

(1) Use a remote-controlled clamp to release the object/ slot in tube + card/electromagnet

(2) Turn off fans

(3) Practical method to keep rod vertical e.g. guide for rod.

**E) Oscillation experiment**

**Error:**

(1) T or time short/large uncertainty in T

(2) Object does not swing freely/ friction between pivot and object

(3) Not swinging in one plane only/idea of non-uniform oscillation (Light object only)

(4) Oscillations die out quickly/ heavy damping (Light object only)

(5) Difficult to judge end/start/ centre of swing/difficult to judge complete swing

**Improvement:**

(1) A marker to time as reaches maximum displacement with (motion sensor) at end with video with timer (playback) in slow motion/ Increase the magnitude of the independent variable

(2) Make hole bigger/bush or bearing idea

(3) Turn off fan(Light object only) * For heavy object, no improvement available.

(4) Use increased thickness of object

(5) Use of fiducial marker/pointer

**Rejected:** Do the experiment in a vacuum, switch the fans off, not just ‘use video’, light gates, Camera, High speed camera, Too fast, Time too fast, Time more swings , Time large no. of swings,not ‘repeated readings’, not just ‘use computer/data logger’, Difficult to release from same point each time/human error/reaction time/unqualified use of light gates/sensors

**F) Electricity experiment**

**Error:**

(1) Resistance / current fluctuating

(2) Voltmeter scale not sensitive enough

(3) Wires not straight

**Improvement:**

(1) Clean contacts

(2) Use digital voltmeter

(3) Method of keeping wire (during experiment) straight e.g. tape to ruler, hang weights off end, clamp wire.

**Rejected:** Voltmeter not accurate enough. More accurate voltmeter/ Parallax error/zero error on meters/heating effects of wire

**G) Force experiment **

**Error:**

(1) Maximum force reached without warning

(2) Weights move.

**Improvement:**

(1) Practical method of recording maximum value e.g force sensor with data logger

(2) Method of fixing cotton loop to rule e.g. tape, glue.

**Rejected:** Increase force slowly/reaction time error

**H) Pulley experiment**

**Error:**

(1) Masses hit each other

(2) Friction at pulley

(3) Uncertain starting position

**Improvement:**

(1) Use larger pulley

(2) Lubricate pulley

(3) Method of fixing rule e.g. clamp rule/electromagnetic with steel /magnetic material ball) release mechanism

Rejected: Friction between pulley and string

**I) Moment experiment**

**Error:**

(1) Rule hits bench

(2) Ruler slips on support

**Improvement:**

(1) Method of preventing rule hitting bench, e.g. project end of cylinder over bench or elevate apparatus.

(2) Glue support to block

**Rejected:** Difficult to start at the same amplitude each time

**J) Magnetism experiment**

**Error:**

Glass may affect magnetic force / effect of surrounding magnetic materials

**Improvement:** Use a variety of materials to separate magnets and test if material affects results

**Rejected:** Reference to Earth’s field/Move object further away

**K) Bench/ Ramp (Surface) related experiment**

**Error:**

(1) Some parts of board rougher than others/surface of board is uneven/board not flat

(2) Board tends to slip/board not stable/supporting block can topple

**Improvement:**

(1) Method to ensure same section of board used in each experiment (e.g. mark one section)

(2) Method described to secure board/block/support e.g. clamp the board, fix the supporting block to the bench with tape/blu-tack

**Rejected:** Board is rough/there is friction between the block and the board/use a smoother surface/references to oil/lubricants

**L) Heat loss experiment**

**Error:**

(1) Heat lost through sides and /or Bottom

(2) Low precision of thermometer

(3) Bulb of thermometer is not completely immersed

(4) Resistor continues to give out heat when switched off/ temperature continues to rise after switching off

**Improvement:**

(1) Method to reduce heat loss/lag/insulate/polystyrene container

(2) Thermometer with specified better precision, e.g. 0.1oC, 0.5oC

(3) Use larger volume of water/use of thermocouple/other small temperature sensor(e.g. probe)

(4) Wait until temperature reaches a maximum before reading

**Rejected:** Switch off fans to reduce convection/Just “weigh water”/ different starting temperatures of water; uneven temperature distribution in beaker/ parallax errors in reading volume or temperature/use of lid/heat loss in warming bowl/cup/draughts/heat loss to surroundings/use more accurate thermometer/thermometer not precise enough/not just ‘digital thermometer’

**M) Terminal velocity experiment**

**Error:**

(Object) may not have reached terminal velocity.

**Improvement:**

Time constant over three markers

**N) Light dependent experiment**

**Error:**

External light affects (LDR)

**Improvement:**

Conduct experiment in dark room.

**Errors and improvement of common apparatus**

**A) Metre rule**

**Error:**

(1) Ruler not vertical

(2) Parallax error

(3) Difficult to hold rule still

(4) Difficult to take measurements because the ruler moves / is not vertical

(5) Reason for difficulty in measuring d e.g. viewed through ruler/parallax error in d

(6) String too wide for markings on rule

(7) Rules have different thicknesses /different lengths so not a fair test

**Improvement:**

(1) Sensible method to ensure ruler vertical

(2) Put coloured paper behind (object) /Description of method of reducing parallax error requiring additional equipment, e.g. !shadow projection/ extend mark to wood or track / pointer on rule / travelling microscope*)

(3) Mount ruler in stand

(4) Clamp rule / ensure rule is vertical using a set square on the bench

(5) Method to improve measurement of d e.g. travelling microscope

(6) Use thinner string

(7) Use rulers of similar thicknesses/ readings/method to take thickness into account /use rulers of the same length

* If the diameter is quite wide, meter rule is prefer over calipers! Accuracy of metre rule is increased by using set square held against ruler.

**Rejected:** View at eye level.

**B) Newton metre**

**Error:**

(1) Difficult to pull newton-meter parallel to ruler/bench

(2) Difficult to judge reading on newton-meter when detaches with reason e.g. ruler moves suddenly/without warning (so difficult to read newton-meter at the instant the ruler starts to move)/force drops to zero immediately after detachment

(3) Difficult to zero newton-meter when used horizontally

**Improvement:**

(1) Method to ensure force is parallel to ruler e.g. use a long string/pulley and weights*

(2) Method to read force at detachment e.g. newton meter with a ‘max hold’ facility/video and playback or freeze frame/ use system of pulley and weights or sand to measure F*/ use force sensor and data logger or computer*

(3) Improved method to measure F: e.g. use system of pulley and weights or sand*/use force sensor with datalogger or computer*

**Rejected:** Video to take reading/digital (electronic) newton meter/parallax related to newton meter/difficult to measure force/issue of viewing ruler and meter simultaneously/zero error in newton-meter/just a pulley

**C) Slotted mass**

**Error:**

Labelled values of mass may not be accurate.

**Improvement:**

Use balance/method of weighing mass.

**Rejected:** Weigh mass.

**D) Objects with unfixed diameter (Circular objects)**

**Error:**

(1) Difficult to measure diameter because (object) is flexible/not circular.

(2) Difficult to form a perfect sphere or disc/diameter of sphere or disc varied

**Improvement:**

(1) Measure diameter of (object) in two directions and average/ Use vernier calipers or micrometer screw gauge to measure average diameter

(2) Method to make uniform spheres/discs e.g. moulds

**E) Protractor**

**Error:**

(1)Protractor “wobbles” when being held by hands/ Difficulty in measuring θ owing to container not perfectly right angled (curved) at the bottom/difficult to line up protractor/horizontal line of protractor not on table

(2) parallax error in θ measurement

(3) θ (or reading) is difficult (or inaccurate, or imprecise) because pointer is thick

**Improvement:**

(1) use protractor with horizontal line flush to table top/freestanding or clamped protractor.

(2) use mirror scale

**Rejected:** View at right angles

#### General Tips For Errors and Improvements Experiments:

- If the value of the quantity measured is very small, can write increase the magnitude of the quantity of the independent variable.
- Credit is not given for suggestions that should be carried out anyway, such as repeating measurements and calculating average or avoiding parallax errors by looking at an instrument “square on”.
- Ask yourself whether the improvement is practical or not.
- Common answers that are rejected by mark scheme :
- Repeat experiment
- Human error
- Use a computer to improve the experiment
- Use assistant
- If clay/plasticine/heavy object is used in the experiment, wind movement doesn’t affect it anymore.

(Think whether turning off fan will make a difference or not).

# A Level Physics Paper 5 – Planning, Analysis and Evaluation

Paper 5 is a written paper to test the practical skills that you acquired during your Cambridge International A Level course.

## Question 1: [Planning – 15 marks]

This question of paper 5 tests your ability to plan experiments. If you have done a good amount of practical work during your A Levels, this question won’t be much of a concern for you (especially if you paid good attention to your paper 3 of Physics). Whatever you practically perform in your paper 3, you have to write it in this paper.

While solving this question, keep these pointers in mind:

- Defining the problem [3 marks]
- Methods of data collection [4 marks]
- Setup for the apparatus [1 mark]
- Method of Analysis [2 marks]
- Safety considerations [1 mark]
- Any additional details [4 marks]

We’ll now describe these pointers one by one. The experiment described in this paper 5, question 1 : (**May/June 2018 Paper 5 Variant 2**) is used as an example for an explanation of the above pointers in the sections that follow.

### Defining the problem:

Here you are required to identify the variables in the experiment:

**Independent variable:**it is a variable whose variation does not depend on that of another.**Dependent variable:**it is a variable whose value depends on that of another.

In simpler terms, the independent variable is the variable you are going to *vary* in the experiment, and the dependent variable is the variable you are going to *measure* in the experiment (pay attention to the words ‘vary’ and ‘measure’).

After the identification of variables, you are required to identify the quantities you are going to keep constant. Any quantity which may vary your results, other than quantities involved in the experiment, must be kept constant. Mention ‘how’ you are going to make sure it does not change, and ‘why’ you think it should be kept constant. While you do this, keep in mind one thing that there may be a lot of such quantities that need to be kept constant; always mention that quantity which DIRECTLY affects the variables being measured.

### Methods of data collection:

Now that you have mentioned the variables, you need to describe how to measure them. Describe the method to vary the independent variable, and a method to measure the effect on the dependent variable. State all instruments used.

In the example question, two variables are involved in the experiment, λ (independent) and h (dependent). λ can be *varied* by using different colored LEDs/lasers (red, green, blue, etc) and using the values for λ given on these LEDs/lasers for any calculations/analysis. The corresponding values of ‘h’ can be measured using a meter rule/plastic ruler.

As you can see now, I described above ‘HOW’ I am going to vary the independent variable, and ‘HOW’ I am going to measure the dependent variable. I also stated all the instruments used too. Along with all this, you are also required to mention the SETUP (discussed below) for the experiment; for instance, how you are going to place the LEDs/lasers (any appropriate method to support the light source, like clamping the light source using a retort stand, etc.), how you are going to place the ruler (placing the ruler close to the maxima on the screen).

You also need to describe how any errors possible may be prevented; these points you mention are counted as *additional details*.

Also include details on how you are going to keep constant quantities you mentioned before constant (In the example experiment described above, the constant quantity was the angle of the incident light. It can be kept constant by holding the light source using a retort stand, and not changing its position the entire experiment)

In some cases, there are no proper instruments available for the measurement of dependent quantity. For example, resistance cannot be measured using a conventional piece of apparatus directly. So for that purpose, mention all the measurements you need to take for its calculation and the instruments used (ammeter used for measurement of current, voltmeter used for measurement of p.d. across the resistor. R is then calculated using the equation: R = V/I).

### Setup for the apparatus:

Draw a diagram with all the equipment you mentioned / might use during the experiment. A basic, well-labeled diagram could score many marks; even if the explanation is weak! Therefore, don’t think that the diagram is of little importance.

### Method of analysis:

In all papers, an equation is given which you need to test or experiment about. Algebraically manipulate the given equation to form a linear relationship (Y = mX + c) – choose what quantity should be on each axis to give a straight line graph.

Relationship | Linear form | Graph | Gradient | y-intercept |

y = mx + c | y = mx + c | y against x | m | c |

y = ax^{n} | g y = (n)lgx + lg a | lg y against lg x | n | lg a |

y = ae^{kx} | ln y = kx + ln a | ln y against x | k | ln a |

Once you are done algebraically manipulation the equation into a linear form, describe what the graph will look like if the given relationship is true, e.g.

Relationship given is : y = ax^{n} ; linear form : lg y = (n) lgx + lg a

The graph will be linear if lg y is plotted against lg x.

Also mention, where the line will intersect the y-axix, and what will the gradient of the plotted relationship.

If quantities are asked to calculated, as in the example question given above, that can be done as follows:

The equation given in the example question is:

h = n λ/d + B

Converting this linear form; (y = mx + c) form, we get:

(*the given equation is already in the linear form, so I’m just making it look like one by the use of brackets*)

h = n/d (λ) + B

h is plotted on the y-axis against λ on the x-axis.

By comparing it with linear form, we know that, n/d = m = gradient, and B = c = y-intercept.

Therefore,

d = n/gradient

and

B = y-intercept

These all steps of conversion to linear form, graphical form, gradient, y-intercept, and calculation of quantities come under ‘*Analysis of Data*’.

### Safety considerations:

Any hazards/harms involved while performing the experiment go here; for every hazard/harm, mention a way to avoid it.

For the example question, the safety precautions needed are:

- Looking directly at the bright light source may damage your eyes [safety precaution: wear goggles, do not look directly, safety screens, etc.]

Other common safety issues for other experiments may be:

- In electricity experiments, electrocution may occur [safety precaution: wear gloves]
- If heating is involved, burns may occur; fire [safety precaution: wear gloves, use holders for picking up hot objects; turn off heating instruments between taking measurements]
- For experiments involving heavy objects, moving objects, they may fall on your foot if slipped from bench/table, sand bucket for falling masses or moving objects may hit you, resulting in eye injuries or other face injuries [make sure heavy objects not placed near edges, supports are strong, wear goggles to prevent moving objects hitting your eyes]

There may be many more such harms possible, and many more precautions necessary depending on the experiment.

### Additional details:

All the improvements possible, preventions of errors, etc. come under this heading.

Make yourself acquainted with the following list of apparatus (these apparatus/additional details are taken from Znotes – https://znotes.org/cie-a2-physics-9702/)

#### General Experiments Apparatus:

**Signal generator:**can be used to produce a sound/voltage/current and can vary frequency settings on the device**Micrometer:**can be used to measure small distances**Vernier calipers:**can be used to measure small distances**Set square:**used to make sure apparatus perpendicular**Magnets:**can be used with metal objects in the experiment**Balance:**can be used to weigh a mass**Burette:**accurately measuring the volume of liquid**Diffraction grating:**can be used to measure the wavelength of a monochromatic light source

#### Additional Details:

**Measuring amplitude and period using a c.r.o**- Adjust time-base and 𝑦-gain to achieve a suitable waveform
- Calculate amplitude by finding height in terms of boxes on a grid of waveform and multiplying by 𝑦-gain
- Calculate period by counting boxes of grid occupied by a full waveform and multiply by time-base setting

**Measuring diameter:**repeat measurements in different positions and average- Wear safety goggles/use a safety screen to protect eyes when heating/pouring liquids or handling stretched wire
- Ensure apparatus stable & not easily knocked over by placing weights (e.g. on retort stand) and working on a flat surface
- Use a sand tray under heavyweights and make sure weights don’t fall on your foot
- Keep radioactive substances in a lead-lined container
- To ensure the surface is horizontal, use a spirit level
**Sound experiment:**perform the experiment in a quiet room**Light experiment:**perform the experiment in a dark room- Repeat experiment & determine the average

#### Pressure Experiments Apparatus:

**U-Tube (manometer):**measures pressure difference between two fluids**Bourdon gauge:**measuring the pressure of a gas or liquid**Pump:**can be used to alter the pressure in a container

#### Electrical Experiments Apparatus:

**Variable resistor (rheostat):**can be used to alter voltage/current supplied in a circuit or can be used to keep current constant**LDR:**resistance decreases with increasing light intensity**Photocell:**sensors that allow you to detect light – generate an e.m.f when light is incident

#### Additional Details:

- Use a protective resistor to reduce current
- Switch off currents when not in use so that wires/coil do not overheat
- Use microammeter and galvanometer for small voltages and currents
- When using an ammeter and voltmeter to measure resistance, a power supply is required
**Type of current to use:**- Large current to create a large magnetic field
- Large current to produce measurable e.m.f./voltage
- Small current to reduce the heating effect

#### Magnetic Field Experiments:

**Hall probe:**used to measure magnetic fields- Keep Hall probe at right angles (perpendicular) to the magnetic field by fixing to rule
- Calibrate Hall probe in a known magnetic field
- Repeat experiment with Hall probe reversed and average
- In magnetic experiments, avoid external alternating magnetic fields

#### Falling Bodies & Oscillations Experiments

**Measuring velocity using light gate:**- Measure distance between light gates
- Connect light gates to time loggers
- Calculate the time of fall by using data from loggers – time difference between when the first and second beam is broken

- For experiments with light weights or wind, close windows & switch off the air conditioning to avoid draughts
- For measuring the time period of oscillations, find time for 10 oscillations and then divide
- Use fiducial markers to time oscillating objects
- To measure quantities in an experiment with fast motions, record the experiment with a video camera and playback in slow motion
- In an experiment with an object being dropped, make sure the object released with no/constant velocity. Can use electromagnets or a spring-loaded device
- For falling objects, use a guide to keep motion in the correct direction

An example question 1 solved is provided at the following link:

## Question 2: [Analysis – 15 marks]

This question has a number of parts. For solving this question, you need to have a strong grip on the following things. Using the same paper for explanations:(**May/June 2018 Paper 5 Variant 2**).

### Conversion to linear form:

Firstly, you should be comfortable with transforming ANY given equation to linear form (Y = mX + c). Make yourself familiar with the logarithmic rules to help you in this.

In the example paper, the equation given in question 2 is:

It can be arranged into linear form like this (t is *measured*, hence a dependent quantity, and resistance (nR) is *varied*, hence an independent quantity):

Taking ln on both sides,

Using the power rule of logarithm on the right side, we get,

Comparing this final equation with linear form (Y=mX + c),

This shows that if a graph of ‘t’ against ‘nR’ is plotted, we will obtain a straight line graph passing through the origin (it can then be deduced that ‘t’ is *directly proportional* to ‘nR’)

### Treatment of uncertainties and significant figures:

Secondly, you should be familiar with the treatment of uncertainties and significant figures.

For finding the percentage/absolute/fractional uncertainty, keep in mind the following rules:

- in case of addition / subtraction:
- We add the individual uncertainties of the quantities added or subtracted. Take the following example:

a = 5 ± 0.2 & b = 2 ± 0.3

We are given, c = a + b

Find the absolute uncertainty & percentage uncertainty in c.

c = 5 + 2 = 7

absolute uncertainty in c = 0.2 + 0.3 = 0.5

percentage uncertainty in c = 0.5/7 * 100 = 7.14% (up to 3 sf.)

- We add the individual uncertainties of the quantities added or subtracted. Take the following example:

Note: whatever the case (subtraction or addition), the individual uncertainties are always ADDED never subtracted!

- in case of multiplication / division:
- We add the fraction uncertainties of the involved quantities. Take the following example:

a = 2 ± 0.2 & b = 3 ± 0.3

We are given, c = b/a

Find the absolute uncertainty & percentage uncertainty in c.c = 3/2 = 1.5

fractional uncertainty in a = Δa/a = 0.2/2 = 0.1

fractional uncertainty in b = Δb/b = 0.3/3 = 0.1

fractional uncertainty in c = (Δa/a + Δb/b) = 0.1 + 0.1 = 0.2

absolute uncertainty in c = (Δa/a + Δb/b) * c = (0.1 + 0.1) * 1.5 = 0.3

percentage uncertainty in c = (Δa/a + Δb/b) * 100 = 0.2 * 100 = 20%

- We add the fraction uncertainties of the involved quantities. Take the following example:
- in case powers are involved:
- When powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:

P = I2R

when finding the percentage uncertainty of P, we’ll do it like this:

percentage uncertainty in P = (**2**(ΔI/I) + ΔR/R) * 100

Just see how everything is done exactly the same, except that inclusion of power 2.

- When powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:
- in case of logarithmic uncertainties:
- We are given: a = 2 ± 0.2

log a = log 2 = 0.301

uncertainty in log = log (2+0.2) – log(2) = 0.0414

log (2±0.2) = 0.301 ± 0.041

- We are given: a = 2 ± 0.2

Calculate all the data in 3 significant figures (generally done) or to one s.f. more or equal to the s.f of the raw data.

However, in the case of logarithmic calculations, the number of d.p for the calculated log is the number of s.f in the raw data. Hence for raw data of 3 s.f. the log should be calculated to 3 d.p.

The significant figures of uncertainty are usually ignored in the marking scheme but stick to 1 or 2 s.f.

### Graphs:

Thirdly, make sure you know how to draw the graphs for this question.

The general instructions for drawing graphs are:

- Use small encircled dots or crosses to plot the points.
- Use a sharp pencil.
- If a gradient is to be calculated, draw a triangle and mentioning the points of the vertices on the best-fit line. The hypotenuse should be greater than half the length of the best-fit line.

#### Drawing worst-fit lines:

Once you are done plotting the best-value points, add or subtract the error from the best point, and plot this above or below, or left or right the best-value point, depending on the question.

Join the three points together to form the error bar.

The worst-fit line can then either be the shallowest (*drawn by joining the bottom of the topmost bar, and top of the bottommost bar*) or steepest (*drawn by joining the top of the topmost point’s error bar and the bottom of the bottommost error bar*) possible line that passes through every error bar.

Draw either the shallowest or steepest worst-fit line, NOT both. Both lines should be clearly labeled.

For calculation of error in gradient, calculate the gradients for both lines by drawing triangles with hypotenuses greater than half the lengths of both lines and mentioning the points of vertices on both the best and worst fit lines. Find error by subtracting the gradient of best-fit from worst-fit. All calculations should be to 3 s.f.

Take special care of units and powers of tens. Don’t forget to mention the units along with answers!

This was all about paper 5 of A Level Physics. We really hope it proves useful.

# Motion in a circle | A Level Physics Notes

### Kinematics of uniform circular motion

**a) Define the radian and express angular displacement in radians.**

**Radian** is the angle subtended at the center of a circle by an arc length equal to the radius of a circle is one radian.

Radian (rad) is the S.I. unit for angle, θ and it can be related to degrees in the following way. In one complete revolution, an object rotates through 360°, or 2π rad.

**Angular displacement** is the angle, θ, through which an object moves as it performs circular motion.

**s = rθ**

(*θ* is the angular displacement; *s* is the arc length; *r* is the radius of the circle)

**b) Understand and use the concept of angular speed to solve problems.**

**Angular velocity (ω)** of the object is the rate of change of angular displacement with respect to time.

**ω = θ t = 2π/T**

**Uniform circular motion** is the motion of a particle along a circular path with constant speed. It is accelerated motion; although speed is constant, velocity changes as direction changes.

**c) Recall and use v = rω to solve problems**

**Linear velocity, v,** of an object is its instantaneous velocity at any point in its circular path.

**v = arc length/time taken = rθ/t = rω**

**Important points to note:**

(i) The direction of the linear velocity is at a tangent to the circle described at that point. Hence it is sometimes referred to as the tangential velocity.

(ii) ω is the same for every point in the rotating object, but the linear velocity v is greater for points further from the axis.

### Centripetal acceleration and centripetal force

**a) Describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle.**

A body moving in a circle at a constant speed changes velocity (since its direction changes). Thus, it always experiences an acceleration, a force and a change in momentum. The direction of resultant force (and hence acceleration) is directed towards the center.

**Centripetal force** is the force acting on an object in circular motion. It acts along the radius of the circular path and towards the center of the circle. It’s responsible for keeping the body moving along the circular path. It is the resultant of *all* forces that act on a system in circular motion.

When asked to draw a diagram showing all the forces that act on a system in circular motion, it is wrong to include a force that is labelled as ‘*centripetal force*‘.

**b) Recall and use centripetal acceleration equations a = rω^2 and a = v^2/r.**

Self-explanatory.

**c) Recall and use centripetal force equations F = mrω^2 and F = mv^2/r.**

Self-explanatory.

**Additional information:**

Orbital Speed:

Equate, mv^2/r = mg,

=> v = sqrt(rg)

# A Level Physics Paper 5 – October/November 2008 [Solved]

**Question:**

*A student wishes to investigate how the resistance R of a light-dependent resistor varies with the distance d from an intense light source.*

*It is believed that the relationship between R and d is*

*R = kd ^{n}*

*where k and n are constants.*

*Design a laboratory experiment to test the above relationship. The light-dependent resistor has a resistance of 100 Ω when it is in bright light and a resistance of 500 kΩ when no light falls on it.*

*You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to*

*(a) the procedure to be followed,**(b) the measurements that would be taken,**(c) the control of variables,**(d) how the data would be analysed,**(e) any safety precautions that you would take.*

**Solution:**

In this experiment, ‘d’ is the independent variable and ‘R’ is the dependent variable. A variable which needs to be kept constant is the power of the light source (this can be achieved by connecting an ammeter in the light source circuit together with a rheostat and then adjusting the rheostat during the experiment to keep the current constant).

The apparatus will be set up as per diagram and light source will be turned on. Distance d will be measured using a meter rule and it will be recorded. The resistance R of the LDR corresponding to this value d will also be measured using an ohm meter.

While measuring d, it should be ensured that parallax error is avoided. One way to do this is to place the LDR and the light source over a meter-rule fixed to the bench and then the light source can be moved over the meter rule (along it) to vary d. In this way, distance between LDR, the light source and the meter rule will be decreased enough to avoid parallax error. The above procedure will be repeated until we have at least 6 different readings for R and d.

The readings will be tabulated and values of lg(R) and lg(d) will be calculated.

R = kd^{n }=> lg(R) = lg(k) + nlg(d)

A graph of lg(R) against lg(d) will be plotted. If the suggested relation is correct, then the graph will be a straight line. It will be possible to find the value of k using:

K = 10^{y-intercept}

and value of n by calculating the gradient of the graph.

The experiment must be performed in a dark room where there are no other light sources than the one being used in the experiment. Ohm-meter must be able to measure resistances in the range 50Ω to 500KΩ.

The light source may be very bright and may therefore affect experimenter’s eyes. So goggles must be worn throughout the experiment.