The Scientific Harrovian - Issue 1, June 2016

Rea da bout : L a r gea ngl eos c i l l a t i ons Thes c i enc eofbr owni ngs t ea k Mea s ur i ngt heEa r t h’ sr a di us Effec t i v enes sofha i rt r ea t ment s

From the Editor-in-Chief The Scientific Harrovian is Harrow Hong Kong’s science magazine that provides a forum for students in the Prep and Upper School to publish scientific articles or reports on scientific work and research. The magazine will be published annually and an editorial board consisting of five Year 13 students1 will be responsible for the publication.

A Scientific Harrovian article could be the result of a genuine interest a student has on a topic in the Physical and Biological Sciences or it could be the report on research that a student has carried out for a Gold CREST Project, a British Physics Olympiad Experimental Project, or a project carried out as an Extra Curricular Activity in a Science Club.

Writing an article helps a student prepare for life in higher education and beyond. In any scientific based degree students are expected to write several scientific papers and reports over the course of their degree, so learning how to do this well early will give the student the edge. Also, the publication of an article in this science magazine can be included in a student’s Personal Statement, and this will allow the student to talk about his/her research interests in a University/College interview.

Requirements for writing an article for the Scientific Harrovian • • • •

The article must be your own work and not a copyright of another person.

The article must be on a scientific topic.

The article must be factually correct.

The style of the article should be2: o Formal – avoid colloquial language; o Concise – write precisely and avoid waffling; o Structured – break the article into sections with appropriate headings o Impersonal – avoid writing in the first person; o Referenced – if you make a claim that is not your personal findings, it should be supported by reference.

Articles for publication Articles for publication in the Scientific Harrovian must be submitted to the editorial team: scientificharrovian@harrowschool.hk Editor-in-Chief

1

Editor-in-Chief Dr Michael Daniel Teacher of Physics

i

2

Student Editorial Board (2015-16) Afifa Ansari Agnes Fung Luna Hu Chloe Huang Sophie Yau

Formatting & graphics Agnes Fung

Morgan M. How to write an article for Young Scientists Journal, Young Scientists Journal, 2015

Index Letter from the Editor-in-Chief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i Large angle oscillations of a simple pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Why cooked food tastes so good – basics of the Maillard reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Measuring the radius of the Earth using a metre rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Investigation into effectiveness of keratin in hair treatment products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Front and back cover images from Britannica ImageQuest. To be used for educational purposes only.

Chambered Nautilus. Photograph. Encyclopædia Britannica ImageQuest. Web. 25 May 2016. http://quest.eb.com/search/139_1969593/1/139_1969593/cite Foucault Pendulum. Photograph. Encyclopædia Britannica ImageQuest. Web. 25 May 2016. http://quest.eb.com/search/132_1336536/1/132_1336536/cite Steak and chips. Photograph. Encyclopædia Britannica ImageQuest. Web. 25 May 2016. http://quest.eb.com/search/156_2397133/1/156_2397133/cite Earth. Photograph. Encyclopædia Britannica ImageQuest. Web. 25 May 2016. http://quest.eb.com/search/132_1230422/1/132_1230422/cite Coloured SEM of eyelash hairs. Photograph. Encyclopædia Britannica ImageQuest. Web. 25 May 2016. http://quest.eb.com/search/132_1291352/1/132_1291352/cite

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Large angle oscillations of a simple pendulum Dr Michael Daniel1, Agnes Fung2, Ralph Summers3

Introduction

θ

When a pendulum of length, l (distance between the point of support and the centre of mass of the pendulum bob), oscillates about its equilibrium position its angular acceleration satisfies the following equation đ?‘‘!đ?œƒ đ?‘” = − đ?‘ đ?‘–đ?‘›đ?œƒ đ?‘‘đ?‘Ą ! đ?‘™ where θ is the angular displacement from the equilibrium position. When θ is small enough so that θ(rad) ≈ sinθ (small angle approximation), then the above equation reduces to đ?‘‘!đ?œƒ đ?‘” =− đ?œƒ đ?‘‘đ?‘Ą ! đ?‘™ which implies that the pendulum swings with SHM with period T given by đ?‘‡! = 2đ?œ‹

đ?‘™ đ?‘”

This demonstrates that the period of oscillation is independent of the amplitude of the oscillation and the pendulum performs an oscillatory motion, which is isochronous.

We are interested in analysing the period of a pendulum when the small angle approximation is not valid.

Simple pendulum oscillating through large angles Consider a pendulum, which is set to oscillate through large angles. In this case the small angle approximation is no longer valid. The pendulum is released from rest and the initial angle is θ0. Let us denote by u the angular speed. We can write, therefore, �=

đ?‘‘đ?œƒ đ?‘‘!đ?œƒ đ?‘‘đ?‘˘ , đ?‘Žđ?‘›đ?‘‘  ! = đ?‘˘ đ?‘‘đ?‘Ą đ?‘‘đ?‘Ą đ?‘‘đ?œƒ

The pendulum equation now reads �

đ?‘‘đ?‘˘ đ?‘” = − đ?‘ đ?‘–đ?‘›đ?œƒ đ?‘‘đ?œƒ đ?‘™

Integrating the above equation gives đ?‘˘đ?‘‘đ?‘˘ = −

1

đ?‘” đ?‘™

đ?‘ đ?‘–đ?‘›đ?œƒđ?‘‘đ?œƒ

1 ! đ?‘” đ?‘˘ = đ?‘?đ?‘œđ?‘ đ?œƒ + đ?‘?

2 � The constant of integration c can be fixed by the initial conditions to give �! =

2đ?‘” (đ?‘?đ?‘œđ?‘ đ?œƒ − đ?‘?đ?‘œđ?‘ đ?œƒ! ) đ?‘™

Taking the negative square root of the above expression gives đ?‘‘đ?œƒ 2đ?‘” =− Ă— (đ?‘?đ?‘œđ?‘ đ?œƒ − đ?‘?đ?‘œđ?‘ đ?œƒ! ) đ?‘‘đ?‘Ą đ?‘™ !

By integrating the above equation and using, đ?‘?đ?‘œđ?‘ đ?œƒ = 1 − 2đ?‘ đ?‘–đ?‘›! ,  we obtain !

� �=2 × �

where T is the period of the pendulum.

Let đ?‘ đ?‘–đ?‘›

!!

đ?‘‘đ?œƒ đ?‘ đ?‘–đ?‘›!

!

đ?œƒ! đ?œƒ − đ?‘ đ?‘–đ?‘›!

2 2

đ?œƒ đ?œƒ! = đ?‘ đ?‘–đ?‘› đ?‘ đ?‘–đ?‘›đ?›ź 2 2

Clearly, when θ = 0 ι = 0, and when θ = θ0 ι = π/2. It can then be shown that !!

!

where đ?‘˜ = đ?‘ đ?‘–đ?‘›

!! !

đ?‘‘đ?œƒ đ?‘ đ?‘–đ?‘›!

đ?œƒ! đ?œƒ − đ?‘ đ?‘–đ?‘›!

2 2

=2

! !

đ?‘‘đ?›ź 1 − đ?‘˜ ! đ?‘ đ?‘–đ?‘›! đ?›ź

!

. The period of the pendulum as a function of the initial angle θ0 can now be expressed as � �=4 × �

! ! !

đ?‘‘đ?›ź 1 − đ?‘˜ ! đ?‘ đ?‘–đ?‘›! đ?›ź

with k being a function of θ0. The integral in the above expression cannot be evaluated in terms of elementary functions, because is an elliptic integral. We can approximate its value, however, by using the following expansion ! ! !

đ?‘‘đ?›ź 1−

đ?‘˜ ! đ?‘ đ?‘–đ?‘›! đ?›ź

=

! ! !

1 3 15 ! !

(1 + đ?‘˜ ! đ?‘ đ?‘–đ?‘›! đ?›ź + ! đ?‘˜ ! đ?‘ đ?‘–đ?‘›! đ?›ź + đ?‘˜ đ?‘ đ?‘–đ?‘› đ?›ź + â‹Ż )đ?‘‘đ?›ź 2 2 6Ă—2!

Performing the integration with respect to Îą we finally obtain đ?‘‡ = 2đ?œ‹

đ?‘™ 1 đ?œƒ!

9 đ?œƒ!

25 đ?œƒ!

1125 đ?œƒ! Ă— 1 + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! + â‹Ż  (1) đ?‘” 4 2 64 2 256 2 16384 2

which gives the period of the pendulum as a function of the initial angle θ0. Although this is an exact expression, being an infinite series, it does not provide a closed form solution to our problem.

In this paper we would like to report the results of an experiment designed to measure directly the period of a pendulum oscillating through large angles and investigate to what extent the first few terms in the above infinite series represent accurately the pendulum period. Before we turn to this, however, it is worth pointing out that the above expression for T yields Bernoulli’s formula (found by Bernoulli in 1749), which reads

2

đ?‘‡ = 2đ?œ‹

đ?‘™ 1 ! Ă—(1 + đ?œƒ ) đ?‘” 16

This is derived from (1) by using the expansion đ?‘ đ?‘–đ?‘›

đ?œƒ đ?œƒ đ?œƒ! = − +â‹Ż 2 2 8Ă—3!

and neglecting terms of O(θ4) or higher.

Measuring the angular amplitude The independent variable of the experiment is clearly the angular amplitude for large angles (typically greater then 100).

Using a protractor to measure the angular amplitude directly cannot give accurate results. A more accurate way of getting the amplitude is to measure lengths and use trigonometry. The length of the pendulum string (this is not the length of the pendulum) was measured with the tape to be L = 1.672 m. With the pendulum hanging in its equilibrium position the vertical height, H0, of the end of the string from the floor was measured. When the pendulum was drawn back and held in place making an angle θ0 (the angular amplitude) the end of the pendulum string rose to a vertical height H from the floor. Clearly, đ??ż − Δđ??ť đ?œƒ! = đ?‘?đ?‘œđ?‘ !! ( ) đ??ż where ΔH = H-H0.

θ0 L

-------H0

Ground level

 Â

3

H

Measuring the period of the pendulum The dependent variable of the experiment is the pendulum period. Because of the nature of what was being investigated and the presence of considerable damping for large angular amplitudes, the pendulum period was determined by measuring the time interval between the first two successive passages of the pendulum over the fiducial point, which was set at the lowest point of its circular path. This time interval corresponds to T/2.

We used a position sensor for measuring the half period. It is more accurate than using a stopwatch, as there is no human reaction time involved.

The measurement was done by putting a screen behind the plane of the pendulum oscillations and arranging the screen to be parallel to the plane of oscillations. A position sensor was put in front of the fiducial point, at a distance of about 0.5 m away from the plane of oscillations to monitor the oscillations. Every time the pendulum bob passed through the equilibrium position, the reduction in distance measured by the position sensor was recorded. By measuring the length of time between the first pulse and the second one (see the DataStudio screenshot below), the time interval corresponding to T/2 can be accurately determined.

Experimental setup

4

Data The raw data gathered following the method described above are summarised in the following table.

ΔH = H-H0 (m)

cos(theta)

theta (radians)

theta (degrees)

T/2 (s)

T (s)

T/T0

0.540

0.6770335

0.827

47.4

1.3864

2.7728

1.049507949

0.651

0.6106459

0.914

52.4

1.3922

2.7844

1.053898562

0.720

0.5693780

0.965

55.3

1.4103

2.8206

1.067600303

0.837

0.4994019

1.048

60.0

1.4220

2.8440

1.076457229

0.937

0.4395933

1.116

63.9

1.4312

2.8624

1.083421650

0.987

0.4096890

1.149

65.8

1.4293

2.8586

1.081983346

1.053

0.3702153

1.192

68.3

1.4378

2.8756

1.088417865

1.117

0.3319378

1.232

70.6

1.4680

2.9360

1.111279334

1.167

0.3020335

1.264

72.4

1.4652

2.9304

1.109159727

1.217

0.2721292

1.295

74.2

1.4640

2.9280

1.108251325

1.267

0.2422249

1.326

76.0

1.4659

2.9318

1.109689629

1.317

0.2123206

1.357

77.7

1.4920

2.9840

1.129447388

1.417

0.1525120

1.418

81.2

1.5040

3.0080

1.138531416

1.517

0.0927033

1.478

84.7

1.5115

3.0230

1.144208933

where T0 = 2.642 s, is the period of the pendulum for small (less than 100) angular amplitudes. Â

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Graphs and Conclusions Variation of the period, T, with the angular amplitude, x The graph below shows the ratio T/T0 plotted against the angular amplitude, x, measured in radians. The graph was constructed using LoggerPro. The curve represents the first five terms in the infinite series expansion for the period T. According to the series đ?‘‡ 1 đ?‘Ľ 9 đ?‘Ľ 25 đ?‘Ľ 1125 đ?‘Ľ = 1 + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›!    (2) đ?‘‡!

4 2 64 2 256 2 16384 2

Graph of (T/T0-1) vs. sin2 (x/2) T/T0-1

sin2(x/2)

(T/T0-1)/sin2(x/2)

0.049507949

0.161456743

0.306632895

0.053898562

0.194708584

0.276816567

0.067600303

0.215291562

0.313994205

0.076457229

0.250347551

0.305404343

0.083421650

0.280360324

0.297551555

0.081983346

0.295300000

0.277627315

0.088417865

0.315098804

0.280603621

0.111279334

0.333823959

0.333347355

0.109159727

0.348996945

0.312781327

0.108251325

0.363843372

0.297521772

0.109689629

0.378820636

0.289555581

0.129447388

0.393914343

0.328618114

0.138531416

0.423898764

0.326803066

0.144208933

0.453668398

0.317872995

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For values of sin2(x/2) less than about 0.4 the best-fit line gives đ?‘‡ đ?‘Ľ = 0.998981 + 0.3030Ă—đ?‘ đ?‘–đ?‘›! đ?‘‡!

2 which supports the relationship

đ?‘‡ 1 đ?‘Ľ = 1 + đ?‘ đ?‘–đ?‘›! đ?‘‡!

4 2

obtained from equation (2) by neglecting higher order terms in sin2(x/2).

Graph of ((T/T0-1)/ sin2 (x/2) vs. sin2 (x/2)

The best-fit line determined by the data gives

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đ?‘‡ đ?‘Ľ đ?‘Ľ = 1 + 0.2654Ă—đ?‘ đ?‘–đ?‘›! + 0.1196Ă—đ?‘ đ?‘–đ?‘›! đ?‘‡!

2 2 which supports the relationship đ?‘‡ 1 đ?‘Ľ 9 đ?‘Ľ = 1 + đ?‘ đ?‘–đ?‘›! + đ?‘ đ?‘–đ?‘›! đ?‘‡!

4 2 64 2 obtained from equation (2) by neglecting higher order terms in sin2(x/2).

Concluding remarks Although expression (1) is an exact solution to the period of a simple pendulum for given angular amplitude, in practice the infinite series can only be used in a truncated form. Clearly, the accuracy of the truncated form depends on the number of term incorporated in the form. The truncated expression can be made as accurate as you want by incorporating more and more terms. How many terms you need to include in order to achieve a given accuracy, however, is not obvious and it would be an interesting problem to investigate in the future.

References 1 Teacher of Physics 2 Year 13, Smith 3 Year 12, Nightingale

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Why cooked food tastes so good – basics of the Maillard reaction Luna Hu1, Agnes Fung2

Uncooked chicken. (Britannica Image Quest)

Cooked chicken. And French fries. (Britannica Image Quest)

In evolutionary terms, cooking food is selectively advantageous. Cooked foodstuffs are safer to eat, and easier to digest than raw products. The act of cooking has a lower metabolic demand than physically digesting the food raw. Cooking food allowed our early hominid ancestors to spend less time gnawing on raw material and more time for other activities, like socialization. This increased cognitive burden in turn pressured human ancestors to evolve more powerful brains, which needed a greater supply of calories, something that cooked food provides. Nutrition is a requirement for life, but many of us eat for pleasure, ‘living to eat’ rather than ‘eating to live’. What about taste? What exactly happens when we sear and sizzle our food? An understanding of browning, or the Maillard reaction, is a key component to this.

The Maillard reaction is a series of complex chemical reactions between the carbonyl group in reducing sugars and the amine group in amino acids/proteins to form compounds responsible for desirable flavours and colours in cooked foods – for example toasted marshmallows, bread crust and chocolate. Heat is obviously required, and the Maillard reaction generally only occurs above temperatures of 140°C. It is a form of non-enzymatic browning which results in the formation of unsaturated, heterogeneous, coloured polymers (melanoidins) without the help of enzymes. Thousands of taste and aroma compounds are generated in the process and combine to give characteristic flavours: sensory

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impression of foodstuffs that is mainly determined by smells (making up 95%), and taste – which explains why food does not taste half as good when you are sick.

The three main stages in the Maillard reaction are: 1. Initial: a) Carbonyl-amine reaction; formation of reversible glycosylamines b) Rearrangement (Amadori or Heyns) 2. Intermediate: complex- innumerable pathways • e.g. Sugar dehydration • e.g. Sugar fragmentation • Strecker degradation 3. Final: • Aldol condensation • Aldehyde-amine condensation

Initial stage a) The Maillard reaction is initiated by the reaction between the amine group in protein/amino acid and carbonyl in the open form of a reducing sugar. This is favoured by a high temperature of 140 – 165 °C (although it can still happen at room temperature - albeit very slowly), pH above 3, presence of water and oxygen, and a moderate water activity.

Water is produced in the Maillard reaction, but a low water activity results in poorer mixing of the reactants and a subsequently slower rate of reaction occurs between the carbonyl and amine groups. The proportion of amine- and carbonyl- containing compounds would also affect the type of non-enzymatic browning: if there were an excess of carbonyls, the system would brown mainly via caramelization, which is the thermal decomposition of sugars (not a Maillard reaction).

In the mechanism shown below, I have used an aldose (glucose). If a ketose were used, an aldosamine would have been formed instead. The Schiff base formed is able to cyclize as the functional groups are far away from each other and free rotation of the groups attached to the carbon backbone allows them to interact – though this is merely a by-product of the reaction.

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b) The Schiff base then undergoes rearrangement. The Amadori rearrangement is for aldose Schiff bases, forming ketosamines. The Heyns rearrangement is for ketose Schiff bases, forming aldosamines.

Intermediate stage Some of the most flavoursome compounds formed during hydrolysis are diacetyl (intense buttery flavour), acetol and pyruvaldehyde (sweet sherry flavour). Other compounds formed don’t possess a taste themselves but serve to amplify other tastes.

In this stage, what happens next depends on the pH. Alkaline conditions favour moderate dehydration and acidic conditions favour strong dehydration. Some of the intermediates formed (namely reductones and dicarbonyls) serve to inhibit or catalyse other reactions contributing in flavour and colour formation, though the structures of these intermediates and the pathways of their formation are complex and poorly characterized, even though the Maillard reaction has been studied for almost a century.

The intermediates then undergo Strecker degradation, a key reaction that results in the formation of many volatile aromas. The “R” group shown in the diagrams below varies with the type of amino acid that was involved in the initial stage.

11

12

Final stage In this stage, heterolytic, nitrogenous compounds are formed. Melanoidins are polymeric compounds that give cooked food their brown hue. Since aldehydes are formed in sugar dehydration, fragmentation and Strecker degradation, it is highly likely that aldol condensation and condensation between an aldehyde and amine are the reactions responsible for melanoidin formation.

By-products Despite the pleasures the Maillard reaction can bring us, it can also result in the formation of carcinogenic compounds, as well as undesirable flavour and colour. For example, furans such as hydroxymethylfurfural/furfural (hexose/pentose) formed from deoxyglucosone – although it has a buttery flavour, it is a potential toxin and carcinogen.

Acrylamide, a rodent carcinogen and neurotoxin, can also be formed at temperatures above 100°C, in the presence of Asparagine and reducing sugars, and is catalyzed by wet condition and presence of extra carbonyl group compounds such as those formed in stage 2. The presence of acrylamide was only recently discovered by Swedish scientists in 2002 in starchy foods, and there are 2 main routes to its formation, through the reaction between lipid degradation products with free ammonia liberated from deamination reactions in Maillard, and directly through Maillard: interaction between carbonyl compounds and asparagine (which provides the backbone of acrylamide). This mechanism is shown below.

The deoxyosones formed from dehydration in the intermediate stage are some of the key intermediates of Maillard reaction and can undergo further reactions – fragmentation, retro-aldolization, Strecker degradation, heterocyclization.

It is one of the reasons why cooked foods often contain about 1000 different flavour compounds.

In addition to cooking, the Maillard reaction also occurs in the body- it plays a key part in vision, and assists the formation of advanced glycation end products, which causes and accelerates degenerative diseases such as diabetes.

Who would have known the same reaction that makes us age makes cooked food taste so delicious?

1 2

Writing: Luna Hu (Year 13, Ward) Diagrams: Agnes Fung (Year 13, Smith)

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Measuring the radius of the Earth using a metre rule Hamza Apabhai (Y11, Waterman), Finn Bartlett (Y11, Lloyd), James Brammer (Y11, Cale), Eve Caplowe (Y11, Smith), Christy Cheng (Y11, Ward), Dr Michael Daniel1, Mark Gao (Y11, Cale), Andrew Hsu (Y11, Lloyd), Jeffery Kwan How (Y11, Lloyd), Lauren Lee (Y11, Tutt), Terence Lee (Y11, Waterman), Nathan David Man (Y11, Nightingale), Kalina Milenova (Y11, Ward), Tye Reid (Y11, Waterman), Jason Wong (Y11, Nightingale), Ken Zhang (Y11, Nightingale), Jenny Zhong (Y11, Smith) On the 23rd of September our school, together with many other schools round the world, participated in the Eratosthenes2 Experiment September 20153. The experiment involved measuring of a shadow produced by a metre rule at exactly the local noontime on the day of the Autumn Equinox. The solar noon at HK (latitude 22.2783o, longitude 114.1747o) on that day was at 12:16. The Year 11 students4 in 11X class, who had a Physics lesson at that time, were divided into small groups of two to three students and they were instructed to carry out the experiment at precisely the local noontime. They were given a metre rule to position in the vertical direction and had to use another rule to measure the shadow produced to the nearest millimetre. See the diagram below.

(eratosthenes.ea.gr/en/content/experiment)

Results of the experiment and analysis of data The results of the measurements taken by the 11X Physics class are shown in the following table.

Group 1 2 3 4 5 6

S, length of shadow/m 0.402 0.404 0.418 0.405 0.420 0.405

Group average value of S/m

0.409

On the Spring (21st March) and Autumn (23rd September) Equinoxes the Earth’s equatorial plane goes through the centre of the Sun. Consequently on these days, if one is standing on the equator at the time of the local solar noon, the

14

Sun will be directly overhead and it will cast no shadow. This means that, if the Eratosthenes experiment were to be performed on the equator at a point that had the same longitude as HK, the shadow of the metre rule would be zero. See the diagram below.

θ

Normal at HK

d θ

Sunrays Normal at the equator

Let us called, d, the distance between HK and the point on the equator, which has the same longitude as HK. This distance, d, is measured to be 2475 km. The angle, θ, between the vertical at the equator and the vertical at HK shown in the diagram above, is exactly equal to the angle θ shown in the experiment carried out by the students. Using the students’ data, therefore, we can calculate its value. đ?‘Ąđ?‘Žđ?‘›đ?œƒ = Therefore,

đ?‘† 0.409 = = 0.409 đ??ť 1.000

đ?œƒ (!) = đ?‘Ąđ?‘Žđ?‘›!! 0.409 = 22.24(!)

The ratio of the distance, d, to the circumference of the Earth is given by đ?‘‘ đ?œƒ = 2đ?œ‹đ?‘… 360 Therefore, 360 đ?‘… = đ?‘‘Ă— 2đ?œ‹đ?œƒ Putting d =2475 km and θ = 22.24(o) in the above equation gives the radius of the Earth to be R = 6375 km This is to be compared with the average radius of the Earth, RE = 6371 km Â

15

Uncertainties in measurements From the range of values for the measurement of the shadow we conclude that the error in S is given by S = 0.409 ¹ 0.009 m Using the above error we can work out the error in the measurement of the angle θ. and

đ?‘Ąđ?‘Žđ?‘›đ?œƒ!"# = 0.418  đ?‘”đ?‘–đ?‘Łđ?‘–đ?‘›đ?‘”  đ?œƒ!"# = 22.685(!) đ?‘Ąđ?‘Žđ?‘›đ?œƒ!"# = 0.400  đ?‘”đ?‘–đ?‘Łđ?‘–đ?‘›đ?‘”  đ?œƒ!"# = 21.801(!)

We, therefore, conclude that đ?›żđ?œƒ = Âą0.442(!)

Since đ?‘… = đ?‘‘Ă—

360 2đ?œ‹đ?œƒ

we deduce that %đ?›żđ?‘… = %đ?›żđ?œƒ + %đ?›żđ?‘‘ Since the percentage uncertainty in the measurement of d is rather small we can conclude that đ?›żđ?œƒ đ?›żđ?‘… = Ă—đ?‘… = 120  đ?‘˜đ?‘š đ?œƒ We can therefore conclude that the measurements of the 11X Physics class give the radius of the Earth to be R = 6380 Âą120 km References 1 Teacher of Physics 2 htts://en.wikipedia.org/wiki/Eratosthenes 3 eratosthenes.ea.gr/en/content/experiment 4 11X Physics Class (2015-16)

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Investigation into effectiveness of keratin in hair treatment products on hair quality improvement Katie Ip1

1. Planning my project Hair products companies often claim that their hair conditioners, which are rich in proteins, can 'deeply nourish' or 'fortify damaged/weak hair'. After primary research, however, I found that hair conditioners return fizzy, damaged hair into their original smooth and weightless state by using cationic surfactants, which have hydrophilic parts that bind tightly to the major protein keratin in hair so that the surfactants are not washed away, while their hydrophobic parts act as the new hair surfaces.

This seems to suggest that proteins in the hair conditioners, as oppose to the claims of hair products companies, play little role in restoring and maintaining hair quality, which means that thousands and thousands of consumers are being deceived. Therefore the aim of my investigation will be to find out if the proteins in hair conditioners play a significant role in improving hair elasticity, as claim by hair conditioners commonly used.

IDENTIFICATION AND SELECTION OF APPROACHES There were three reasonable ways to complete the investigation: 1. Divide volunteers into one experimental group and one control group. Only the experimental group will be given a solution of a protein commonly found in hair conditioners regularly. Compare the hair elasticity of the experimental group to that of the control group.

2. Divide volunteers into one experimental group and one control group. Only the experimental group will treat their hair regularly with hair conditioners claiming to work by using a protein it contains. The control group will use hair conditioners that don't contain the specific protein. Compare the hair elasticity of the experimental group to that of the control group.

3. Collect hair samples from different volunteers and submerge them into a solution of a protein found in hair conditioners. Compare the hair elasticity of the submerged hair to that of untreated hair.

Approach 1 & 2

Approach 3

Cons û

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Sample size is likely to be small as little people are willing to volunteer--> unreliable Difficult to achieve the controlled variables e.g length of hair, age, sex, diets.

The experiments can bring potential damage to the volunteers’ hair and health.

(Approach 2) there can be other chemicals in the hair conditioners used that cause differences in hair elasticity of volunteers in the two groups.

Pros ü

Tests are performed using humans, so the results will be directly applicable and beneficial to the public.

Pros ü

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Sample size can be very large as hair samples can be easily obtained from people's hair brushes-->reliable Controlled variables can be achieved e.g length of hair, age of volunteers from whom the hair is from etc.

No health threat will be posed to volunteers Excludes the possibility of other chemicals affecting hair elasticity, as only protein solution is used.

Experiments can be more flexible because I don't need the physical presence of the volunteers.

Cons û

Using hair only is not representative of the effect of the proteins to hair attached onto humans e.g rate of absorption can be different on real humans.

After weighing up the pros and cons of the three methods, I have chosen approach 3 because its advantages outweigh is disadvantages The fact that no human volunteers are needed in this approach has given it a huge advantage over the other two approaches, as this makes approach 3 more viable and realistic.

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2. Project process Resources and methodology Methodology The initial basic outline of my methodology was as follow: 1. Test the initial conditions of all hair samples: hair diameter, hair length and tensile strength 2. Carry out experimental hair treatment: a. Prepare a solution of the protein found in hair conditioner b. Apply protein solution to each experimental hair samples over a same period of time 3. Test final conditions of hair samples.

4. Repeat the process for 3 times. a. Testing initial and final hair condition The hair diameter is measured by using a microscope reticle to measure the width of a hair sample under the microscope and the measurements are recorded onto a logging sheet. This is assumed to be equal to the maximum diameter of the hair as any differences will be very minor.

The hair length is measured with a ruler and the length of all hair samples are set to 10 cm as a controlled variable. The measurements are recorded onto a logging sheet.

Hair tensile strength is measured using a clamp, stand and weights, please see the set-up below: Clamp

Hair used to suspend the weight.

Weight Stand

A photo showing the set-up used in the test for hair tensile strength.

A photo showing a 10g weight being suspended from the fixed glass rod by a hair sample.

Using two sets of clamps and stands, a glass rod is fixed horizontally. One end of the hair sample being tested is tied onto the glass rod firmly. Then the other end of the hair is tied to a 10 g weight. One by one, additional 10g weights are added onto the original weight until the hair breaks and the weights are no longer suspended. The maximum no. of weights that the hair can suspend before breaking are recorded, which will give indication of the hair's tensile strength.

The measurements are recorded onto a logging sheet.

The above tests are performed on randomly chosen hair strands from each set of hair samples from each volunteer (see 'resources' below), and the results are assumed to be representative of the whole set of hair sample.

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Methodology (a)- Problems and new changes After using the designed set-up to test for the initial conditions of several hair samples, the following problems were immediately observed: 1. Occasionally the weights fall due to the untying of the hair instead of the breakage of hair 2. Tying hairs around the clamp and stand is very time-consuming.

This method is deemed too inefficient, so research using the Internet was carried out in order the find a new method. By modifying the method suggested in this website, an easier and simpler test for hair elasticity is used: http://www.verticalsinhair.com/index.php?option=com_content&view=category&layout=blog&id=66 1.

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Use the thumb and forefinger of both hands to hold a strand of hair on two points that are around 1.5 inches apart.

Quickly slide apart the two hands away from each other along the hair.

The section of hair over which the fingers have slid over will become curled.

Take a photo of this section.

Hold the hair at the two ends of this curled section and gently pull the hair from both ends, aiming to straighten it. This step is set to last for 10 seconds as a controlled variable.

Compare the degree to which the section of hair has been straightened by comparing it to the photo taken in step 4. Record this as a percentage onto the logging sheet.

I have also decided to increase the no. of repeats from 3 to 9. This is because the force at which I pull the hair each time can vary greatly. Also the degree to which the hair is straightened is very subjective. Overall, the results can be very unreliable, so lots of repeats are needed to identify anomalies and to calculate a representative mean value. b. Experimental hair treatment The protein being tested is keratin. This is because after research I found that keratin comprise up to 95% of hair fibres.

Having looked at the composition of various hair conditioners, keratin is also a common component. (http://www.keratin.com/aa/aa012.shtml) In three separate beakers, an equal volume of the keratin solution of the same conc. is prepared. Three hairs from each set of hair sample are submerged into the keratin solution. One hair is removed from each beaker after 5, 10 and 15 minutes and the hairs are first blotted dry with paper towels (as presence of liquid can interfere with the test), then their conditions are tested using the same methods. All measurements are recorded onto the logging sheet. The photo on the left shows the set up of the 3 beakers.

Resources Researches were performed to find out the easiest and cheapest way to obtain material and technology required for the experiment: 1. Hair samples--- I advertised around the school seeking for volunteers that were willing to donate the hair on their hair brushes for the experiments. As controlled variables, the volunteers had to be of the same age (1516), same sex (female) and their hair had to be untreated (i.e not straightened etc.) I was able to obtain 3 sets of hair from 3 suitable volunteers.

2. Keratin--- The school provided hydrolysed keratin powder, which I could dissolve into water to make keratin solution 3. Microscope: Provided by the school

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The following table shows a summary of all the resources and where they are obtained: Resources Where to obtain 3 sets of hair samples Hair brushes of 3 volunteers Hydrolysed keratin powder Ordered by the school Microscope and immersion oil Provided by the school Other laboratory equipments Provided by the school.

Table 1: a table showing the resources required and how they are obtained.

Results Results summary table Hair diameter (mm) Hair length (cm) Other hair conditions Degree to which the hair was re-straightened before the treatment with keratin solution (%)

Degree to which the hair was restraightened after the treatment with keratin solution (%)

5 Minutes

10 Minutes

15 Minutes

Before After Before After Before After 1 2 3 4 5 6 7 8 9 Mean 1 2 3 4 5 6 7 8 9 Mean 1 2 3 4 5 6 7 8 9 Mean 1 2 3 4 5 6 7 8 9 Mean

Sample set 1 0.1 0.1 10 10 • Brown • Straight 50 60 50 50 50 60 40 40 60 51 80 90 90 80 80 70 80 80 90 82 80 90 90 90 90 80 90 90 80 87 90 90 90 90 80 90 80 90 90 88

Sample set 2 0.1 0.1 10 10 • Brown • Straight 30 30 40 30 40 50 30 40 40 37 70 70 60 70 50 60 60 70 60 63 60 60 70 70 70 70 70 60 70 67 70 70 70 70 70 60 60 70 70 68

Sample set 3 0.1 0.1 10 10 • Brown • Straight 40 40 50 50 50 30 40 40 50 43 70 70 80 60 80 70 70 80 70 72 80 80 80 80 70 70 80 70 80 77 70 80 80 70 70 80 80 80 80 77

Table 2: a table showing hair diameters, hair lengths, and results from the elasticity test for each hair set before and after keratin solution treatment.

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Results- graph

The mean degree to which the hair was re-­‐straightened after treatment with keratin solution (%)

The bar chart below shows the mean degree to which hair in each hair set was re-straightened before and after treatment with keratin solution after 5, 10 and 15 minutes.

100 90 80 70 60 50 40 30 20 10 0

Before treatment (control group) 5 minutes

Graph 1: the mean degree to which hair in each hair set was re-straightened before and after treatment with keratin solution after 5, 10 and 15 minutes.

10 minutes 15 minutes

Hair set 1 Hair set 2 Hair set 3

Results- finalisation Conclusion and implication It is clearly seen from the bar chart that hair submerged in keratin solution shows a higher percentage recovery after restraightened compared with those before treatment. As the S.D. bars of hair before treatment don't overlap with those after treatment, this shows that there are significant differences in percentage recovery after re-straightening of hair before and after treatment. Also, from the graph the longer the submergence time, the higher the percentage recovery after submergence in keratin solution. However as the S.D. bars of 5, 10, and 15 minutes overlap in all 3 hair set, there is no significant differences in their percentage recovery.

In conclusion, it can be seen from the evidence that the keratin solution treatment has improved hair elasticity, although the differences in duration of treatment produce little effect. Addressing the title of my project 'To what extend do proteins in hair conditioners improves hair strength and elasticity', I can therefore conclude that keratin in hair conditioners may improve hair strength and elasticity, yet for the same concentration of keratin the duration in which the keratin is in contact with the hair has no effect on the level of hair elasticity improvement. This implies that keratin in hair conditioners does have a role to play in improving hair elasticity as claimed by the companies Reflection The hair elasticity enhancing effects of hair conditioners might be mainly due to other substances. Also, the correlation shown between keratin treatment and hair elasticity does not imply a causal relationship. The following table shows the factors that will have effect on the results:

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Factors Only one keratin solution concentration was used Only one hair length used The actual hair conditioner is not used.

Only one investigation performed Diets of volunteers are not controlled Activities and their intensity level carried out by the volunteers daily are not controlled

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Effects Reduces reliability of the results.

The effects of other substances in the hair conditioner are unknown

Affect initial conditions of the hair samples at the start of the elasticity test each time

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How can I improve this?

Repeat the experiment using different keratin solution conc.

Repeat the experiment using hair of different lengths Repeat the experiment with a range of different independent and dependent variables.

Design a fixed daily meal plan for the volunteers--- however this can cause discontentment.

Tell the volunteers to avoid doing certain activities that might damage hair.

Table 3: a table showing the factors that will affect the outcome of the investigation, their corresponding effects and possible ways to reduce their effects.

References 1 Year 13, Tutt

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