Experiment to determine

acceleration due to gravity using

a Ticker tape method

By

Josh Siddons

17th June 2016

CONTENTS PAGE

Contents

contents page..............................................................................................................................2

PART A: Planning and Background Research ...................................................................4

hypothesis to be tested................................................................................................................................................... 4

Aims and Objectives ........................................................................................................................................................ 4

Limitations of the study ................................................................................................................................................... 4

Background Research and literature review ........................................................................................................... 4

Experimental plan............................................................................................................................................................. 6

Apparatus used............................................................................................................................................................. 6

Diagram of the experimental set up ...................................................................................................................... 7

Figure 1: Set up equipment.................................................................................................................................................... 7

Method with step-by-step instructions .................................................................................................................. 7

Whether repeat readings are required and how anomalies will be handled statistically..................... 8

Details of the graph that will be plotted detailing which variables will be on each axis ....................... 8

Measuring the angle of the ramp............................................................................................................................ 8

Health and Safety ........................................................................................................................................................ 8

Variable types detailing how control variables will be kept the same ........................................................ 9

How precision, accuracy, validity and reliability is addressed within the method.................................. 9

How the graph will be analyzed to obtain a value for ‘g’; and ...................................................................... 9

How sufficient data will be acquired to apply statistical techniques in your analysis ........................... 9

modifications to the Experimental plan ..................................................................................................................... 9

PART B: Results....................................................................................................................10

Description of results and issues noteD during the experiment ..................................................................... 10

Tables of all results (including units and headers).............................................................................................. 10

Table 2: g value results ......................................................................................................................................................... 11

Anomalous Data ............................................................................................................................................................. 11

Table 3: Anomalous data ...................................................................................................................................................... 11

Graphical representation of results .......................................................................................................................... 12

Table 4: Graph to show of acceleration against Sine angle of slope ............................................................................ 12

PART C: Analysis of results and discussion .....................................................................12

Interpretation of gradients of graph and intercepts (if relevant) ..................................................................... 12

statistical Analysis and interpretation ...................................................................................................................... 12

Table 5: Students t-test analysis ................................................................................................................................... 14

Procedural errors ............................................................................................................................................................ 14

Precision errors ............................................................................................................................................................... 15

Table 6: Ticker tape measurement uncertainty .............................................................................................................. 15

Table 7: Measuring height uncertainty .............................................................................................................................. 15

Table 8: Measuring length uncertainty .............................................................................................................................. 16

Table 9: Total uncertainty .................................................................................................................................................... 16

Suggested Improvements............................................................................................................................................ 16

PART D: conclusions ............................................................................................................16

References .............................................................................................................................17

BILBLIOGRAPHY..................................................................................................................18

Appendices.............................................................................................................................18

Table 10: Table of ticker tape results ................................................................................................................................. 21

Table 2: g value results ......................................................................................................................................................... 11

Table 3: Anomalous data ...................................................................................................................................................... 11

Table 4: Graph to show of acceleration against Sine angle of slope ............................................................................ 12

Table 5: Students t-test analysis ......................................................................................................................................... 14

Table 6: Ticker tape measurement uncertainty .............................................................................................................. 15

Table 7: Measuring height uncertainty .............................................................................................................................. 15

Table 8: Measuring length uncertainty .............................................................................................................................. 16

Table 9: Total uncertainty .................................................................................................................................................... 16

Table 10: Table of ticker tape results ................................................................................................................................. 21

PART A: PLANNING AND BACKGROUND RESEARCH

The purpose of the experiment is to see if there is a significant difference between

acceleration due to gravity determined by rolling a trolley down a ramp and working out the

acceleration using ticker tape. This report will present background research on the nature

and value for acceleration gravity along with a range of methods for determining its value.

Furthermore it will present results of the ticker tape experiment which took place and a

conclusion on whether the hypotheses and objectives were met.

HYPOTHESIS TO BE TESTED

There is no significant difference between acceleration due to gravity determined by rolling a

trolley down a slope using ticker tape and comparing it with the value determined using light

gates whilst rolling a trolley down a ramp.

AIMS AND OBJECTIVES

The aims and objectives were:

To find acceleration from the ticker tape and light gates from rolling a trolley down

a ramp.

To compare the value of g from two methods by applying a T-Test.

To evaluate whether my hypotheses should be accepted or rejected from the

results.

LIMITATIONS OF THE STUDY

Limitation of the study were as follows:

At college the level of equipment is at a basic level that is suitable for a student lab

rather than more advanced laboratory work. It is also old and run down over years of

use.

The ramp and trolley which was used was very old, did not have smooth surface

which could off increase the drag.

The space available was limited to a shared classroom environment with other

students other performing experimental work.

Access to college laboratory was limited which limited the time available to carry out

the experiment.

The method required access to a physics teacher in order to help with theory and

equations used.

BACKGROUND RESEARCH AND LITERATURE REVIEW

Definition of gravity:” the force that attracts a body towards the Centre of the earth or

towards any other physical body having mass”- Google

Acceleration of falling objects is due to gravity and this is the same for any object.

Newton’s law of gravitation and relation to “g”

Muncaster (1989) explains newton’s universal law of gravitation as “every particle in the

universe attracts every other with a force which is proportional to the product of their masses

and inversely proportional to the square of their separation”. This is summarised in the

equation below, where F is the gravitational force of attraction between two masses that are

a distance r apart and G is the universal constant of gravitation.

The link between Newton’s law of gravitation and “g” is also described by Muncaster (1989)

who derives the relationship as g = GM/r2 where M is the mass of the earth. This means

that gravity depends on how far away the object is from the centre of the earth.

Factors affecting the value of g at different places on earth

It is not affected by temperature but it does vary at different point on the earth due to

topography. Wikipedia (2015) states that “all small bodies accelerate in a gravitational field

at the same rate relative to the Centre of mass” providing that we ignore the air resistance.

BBC Bitesize (2014) explains that at the top of the mountain the pull of gravity is lower as

you are further away compared to being in valley or at sea level where the gravitational field

strength is much stronger.

Some factors which affect the value of g are:

Mass of the objects: Mass of the objects affects the gravitational forces as the greater the

mass the greater the attractive force between the masses.

Distance between the objects: UCL (n.d.) goes over the idea of the greater the height the

lower the level of g. So if the distance is doubled then the gravity is weaker and the force of

gravity is less than being really close. This shown in the diagram below

Shape of earth: Wikipedia (2016) explains that the shape of the earth

is not an oblate spheroid (looking similar to an American football) it means different points on

the earth’s surface will have feel a greater pull from gravity than others. At the equator where

the bulging of the earth is at its greatest then the pull of gravity is at its weakest. Saxov

(1952) explores this further and describes in more detail a selection of mathematical ways to

work out the level of “g” in different places across the earth.

Methods to determine the value of “g”

Pendulum test: Physics Classroom (n.d.) gives another test for gravity which uses objects

which are hung in midair by a fixed string, which is used for support. This method is based

on mathematical properties of objects that are in periodic or simple harmonic motion.

Muncaster (1989) give s step by step procedure in how to carry out the procedure by

determining the acceleration due to gravity.

Ticker tape: This is method to find out the motion of objects. It works by having marks on the

tape which you would attach to an object along with a piece of string. You would then pull

the string through a device which marks the tape and the dot/marks provide evidence for the

objects motion. Nuffield foundation (2012) gives a detailed procedure clearing explaining

how the procedure work and how you calculate the level of gravity through the test. Physics

Classroom (n.d.) “Ticker tape Diagrams” gives a very clear diagram in how to step the

procedure.

Magnet drop: BBC (2014) describes the method that involves dropping a magnet down the

copper tube hovering down the tube. This could take 30 seconds to travel down 1 m the

compared to it dropping straight way if it was a plastic tube. This is supported by a list

equipment you need, video of the procedure, and what to do if the experiment does not

work.

Linear air track: Physics school (n.d.) present the idea of using an air track to find the level of

g. The way in which the experiment does this is by determining the rate of acceleration of

gravity. Using the air track when carrying out calculations is a positive as there is need to

count for friction. On this sources it gives a diagram of set, a list of what you need along with

a to do list and finally a calculations.

Reasons for method selection

Having considered these methods the ticker tape method was chosen because:

It was very easy to use and set up.

The equipment needed was available in the college

It is possible to produces a large sample size and retake measurements which

reduces the number of uncertainty.

It provide a opportunity to learn to use a the ticker tape machine and analyse ticker

taper data which were techniques that were not known to the investigator.

EXPERIMENTAL PLAN

Apparatus used

1x Ramp

1x Trolley

1x Ticker tape

8x books

1x String ball

1x Spirt level

1x calculator

2x 1m rulers

1x Roll of masking Tape

1x Clamp Stand

2x Wires/cables

2x Clamp & Boss

1x Ruler

Diagram of the experimental set up

Figure 1: Set up equipment

Method with step-by-step instructions

1. Place a thread of string through the trolley.

2. Now create a ramp and note down the angle (How to work it out below), Once

completed place the trolley on the top of the ramp ensuring that all cables have no

bends or knots along and are always stretched.

Start

Ramp

Trolley Clamp & Boss Ticker tape, Connected to power supply

Books 2x 1 Meter ruler

End

3. Turn on the ticker tape to allow it to start vibrating, now remove the ticker tape to

see if the dots are all the same place.

4. Turn off the ticker timer, Now thread a piece of ticker tape through, Attach it to the

trolley and then turn it back on allowing it to vibrate

5. Now let go of the trolley from at the top of the ramp which causes the trolley to roll

down the ramp whilst pulling the ticker tape.

6. Count the first 10 dots and measure the distance.

7. Then on the same tape count another 10 dots and measure, do this 7 times and

note down the results in the table. Repeating it 7 times helps reduce anomalies.

8. Carry this out again but change the height at the top and note the results in the

table.

Whether repeat readings are required and how anomalies will be handled statistically

Noticing anomalies will be seen by noticing if the results are widely wrong (don’t follow the

trend) and how to deal with them is to ignore them when doing the data analyses. Another

way to deal with them would be to do a re-run of the tape to prevent any anomalies.

Details of the graph that will be plotted detailing which variables will be on each axis

Plotting a graph with average speed (M/S) on the X axis and on the Y axis plot cumulative

time (s). To receive the graph you will need to work out the average speed which is

length/time taken. The cumulative time+0.2 each time.

Measuring the angle of the ramp

Trigonometry was use the length to work out angles of slope. Collect two 1M meter sticks

and measure the length of the ramp, note that in a logbook. Then work out the height at

each end of the ramp (Start& End). Use a piece of string to measure the height to help

reduce uncertainties, reducing the zero errors as rulers don't start from zero. Measure the

length of string using a ruler and subtracted the “End” point from away from the “start”. Now

divide the length by the height in the calculator and you will receive an answer. Click shift,

then click Tan and receive Tan-1, Click “ans” and you should have get Tan-1(ans), Click the

“=“button and receive an answer which will be the angle of ramp.

Health and Safety

o Hand or fingers might get in the way of the trolley: Keep your hands out of the

way to prevent your hands/fingers getting hurt.

o Instability of ramp: Ensuring the ramp is secure with no wobble and area

around is tidy.

o Electrical equipment: Turn of any power supply when not in use to help

prevent the risk of any electrical shocks. No overhanging cables.

o The trolley falling off the ramp and hitting the floor: Having someone stand at

the end to catch the trolley or having a stopper to prevent it from falling off.

Variable types detailing how control variables will be kept the same

Independent: Height of Ramp, which altered the angle of slope.

Dependent: Average speed for a standard set of ticker tape (11dots or 10 gaps)

Control: same trolley and constant same start position ramp roll distance.

How precision, accuracy, validity and reliability is addressed within the method

1. When reading the ruler, reading of the mm rather than the cm to give a more

precise reading resulting in the results being more reliable.

2. Measuring the height of the ramp using string instead of a ruler as a ruler does not

start at zero. The further helps in making results more precise and reliable.

3. Reducing the drag of the ticker tape. Ensuring this is applied by ensuring the tape

can roll smoothly, this will give more accurate results meaning the data is going to

be more reliable.

4. Ensuring the ramp was level perpendicular to the roll direction of the trolley. This

will help improve the accuracy.

5. Ensuring that the trolley rolls parallel by drawing a line which it follow’s down the

ramp.

How the graph will be analyzed to obtain a value for ‘g’; and

The graph will be created using “cumulative time” along the x axis and “average speed ”

along the y Axis. Once a graph has been plotted add a trend line, click show equation and

R2 value. From that and the angle measured earlier you will need to work out the (g=a/sin A).

To work this out in the calculator you will need to use the “m” (first number on the gradient

equation) and divide it by sine ((angle/360)*2*PI()).

The final spreadsheet equation should look like =”m” value/Sin ((angle/360)*2*PI()).

The graph helps you get the gradient which then can be used receive the results of the “M”

value which is needed within the final equation.

How sufficient data will be acquired to apply statistical techniques in your analysis

The data which is collected will then be used in a student’s t-test which will compare the

values of g from your test along with the light gate results received. It will allows you to

present the two results along with standard deviation of each to show the comparison.

MODIFICATIONS TO THE EXPERIMENTAL PLAN

Decided not to use the weight to pull the trolley down the ramp.

Reason why is it makes the test simpler to analyses and carry out.

This would increase the level of accuracy as there will be less

variables involves. This will help the results be more accurate as

you will be able to achieve a more precise level g. It will also be

easier to repeat and carry out due to it being more reliable.

Find something to hold the tape to help reduce the level of drag on

the trolley. This will help improve the level accuracy as the results

received will be more accurate. The reason for this will be because

the result it will make the results more valid as there will be less

variable and you will receive a greater true value of g.

PART B: RESULTS

DESCRIPTION OF RESULTS AND ISSUES NOTED DURING THE EXPERIMENT

In summary results obtained using a slope of length 1820mm and slope angles which

ranged from 1.57-5.99 degrees, the acceleration of the trolley down the slope increased

from 0.1134-0.6634 m.s-2. This was calculated using ticker tape sections with 10 spaces of

0.02 seconds (a total time interval of 0.2 seconds), resulting in average velocity values

ranging from 0.430-1.405 m.s-1.

The ticker tapes were easy to collect and were mostly clear and easy to read, although it

was time consuming and detailed work to count each dot and measure the lengths. The

angle of the slope was worked out using trigonometry with the length and height of the

slope. The sine of the slope angle was calculated.

The main issues noted in the experiment were:

• Sometimes reading the dots were very faint which required extra time to reading and count

the dots. However none of the tapes were poor enough to be re-run.

• Regularly the ticker tape was tangled which would add extra drag and increase the effect.

This was solved by ensuring the tape was flat before the trolley was rolled and some re-

runs were needed.

TABLES OF ALL RESULTS (INCLUDING UNITS AND HEADERS)

Details of the measurements collected are presented in the appendices. A summary of the

data used to plot the graph and perform statistical analyse of calculated g values are

presented in table 1.

The table shows:

The sine of the angle of the slope for each ticker tape run,

The acceleration of the trolley down the slope determined using a graphical analyses

of the average velocity of a section of tape plotted against the cumulative time.

The value of g calculated using the equation:

Block sine (angle of

slope)

acceleration (m/s2) from graphs g (m/s2)

2 0.0275 0.1134 8.790

3 0.0412 0.1411 6.536

4 0.0554 0.3313 8.289

5 0.0723 0.4975 8.647

6 0.0876 0.6045 8.364

7 0.0952 0.6564 8.242

8 0.1044 0.6634 7.583

Table 1: g value results

ANOMALOUS DATA

Table 2: Anomalous data

(Reading Number 7)-RED

When dealing with the anomalies ignoring them from the data is the best option. The results

to left show that the 7th data was Igorned and the graph without it. Spotting anomalies is

seeing if the data received is widely wrong and when tested with a line of best fit it’s

nowhere near. Reasons why could be human error when doing the experiment or a random

error may have occurred.

Section Time taken Length(mm) Length (m) Average speed (m/s) cumulative speed (s)

1 0.2 141 0.141 0.705 0.1

2 0.2 154 0.154 0.77 0.3

3 0.2 198 0.198 0.99 0.5

4 0.2 227 0.227 1.135 0.7

5 0.2 259 0.259 1.295 0.9

6 0.2 256 0.256 1.28 1.1

7 0.2 60 0.06 0.3 1.3

Height (mm)

Length (mm)

6.898522347

Average 1.029166667

Standard Deviation 0.252416653

Mean 1.0625

Tan-1(174/1820)= 5.46(2sf)

174

0.6564/sin(5.46)

7 Block

a=g X Sin A

182

g=a/Sin A

y = 0.6564x + 0.6353R² = 0.9468

0

0.375

0.75

1.125

1.5

0 0.35 0.7 1.05 1.4

Series1

GRAPHICAL REPRESENTATION OF RESULTS

Table 3: Graph to show of acceleration against Sine angle of slope

PART C: ANALYSIS OF RESULTS AND DISCUSSION

INTERPRETATION OF GRADIENTS OF GRAPH AND INTERCEPTS (IF

RELEVANT)

The graphs show a positive correlation between the level of acceleration and the angle of

the slope. As the angle of slope increase the greater the acceleration. The graph does not

pass through the origin (0, 0) means the product would not move off as there is no energy

produced to push it off. There are also other factors such as drag on the surface which

prevent the trolley from moving off. The equation gathered from the graph is used to work

out the level of g. The R2 value of 0.97 shows that there is a high correlation as it is very

close to 1. The closer to 1 the higher the level of correlation with 1 being perfect.

STATISTICAL ANALYSIS AND INTERPRETATION

An independent two tailed student’s t-test was performed using two sets of results of data to

assess whether they are significantly different and whether the hypothesis was true. The

ticker tape results (set X) and another student data set collected using the ramp experiment

using light gates (set Y) were used for this analysis. The method used as follows:

Calculate the mean and standard deviation of (X) and (Y)

Calculate the squared values of standard deviation for each sample (these are Sx2

and Sy2 values).

Calculate the standard error (Sxy) from the equation (Sx2/sample size) +

(Sy2/Sample size).

The sample size of both data sets was 7.

Calculate the modulus of the difference of the mean’s | 𝑥̅𝑥 − 𝑥̅𝑦 |.

Calculate the T-statistic (𝑡 =|𝑥 ̅𝑥−𝑥�̅�|

𝑆𝑋𝑌) E.G value you need to divide modulus by the SXY

value = (Modulus/SXY).

Calculate degrees of freedom are then workout by adding the sample size take away

2 (14-2=12).

Used the degrees of freedom to look up critical value from table and t-value the

degrees of freedom to look up in the t-test probability table for the critical value, this

can then be Rejected or accepted.

Table 1 shows this analysis. The hypothesis has to be rejected as the t-value is above the

critical value of 2.18, which means there is a significant difference between the sets of data

at 95% confidence level.

Table 4: Students t-test analysis

PROCEDURAL ERRORS

Things to consider;

Some scatter of points on graph – procedural issues, intercept

How you measured the height of the ramp – affects the calculation of angle of slope. Adjustment for thivkness

of the ramp

Drag of ticker tape, air resistance, friction of trolley on ramp, uneveness – factors that will reduce the

acceleration measured (lower value)

Alignment of ramp and trolley roll

Calibration of ticker tape machine – assuming that each dot is ever 0.02s but could not confirm this.

Will all affect accuracy

Block/Tape Number Ticker Tape Results (X) Light gate Results (Y)

2 8.79 9.28

3 6.54 9.30

4 8.36 9.21

5 8.65 9.32

6 8.29 9.30

7 8.24 9.40

8 7.58 9.21

Mean of ticker tape results (X) 8.064

Mean of light gates (Y) 9.289

Standard Deviation of (X) 0.775

Standard Deviation of (Y) 0.066

Sx2 0.601

Sy2 0.004

Sample size (Nx) 7

Sample size (Ny) 7

Modulus 1.224

Standard Error (Sxy) 0.294

T-statistic 4.162

Degrees of freedom 12

T-test critical value 2.180

Student T-test

The R2 Value of 0.97% shows that there is a high positive correlation but it is not

perfect due to uncertainties such as drag. This in the long run will affect and reduce

the value of “g”

Not always perfectly having the alignment of the ramp and the trolley roll. This would

lead to an increase in friction as it is travelling a longer distance and this will also

affect the value of “g”.

Assuming the ticker tape was calibrated correctly and the dots were 0.02s apart.

This was never tested and would not be able to confirm if it was correct. This would

affect the overall value of “g” as the time could be wrong affecting the distance and

rate of acceleration.

Uneven surface. The surface was very bumpy which increase the level of

resistance and drag. The would further lower the level of value of “g” as there would

be an increase in drag.

PRECISION ERRORS

Measurement uncertainties were calculated for the readings taken, as shown in the tables below. Percentage

uncertainties were calculated using the equation:

% uncertainty =( ½ x Resolution / Actual Reading ) x 100

Ticker tape length

Equation

%U

(Lowest) 86mm (0.5x1)/(86)x100 0.58

(Highest) 281mm (0.5x1)/(281)x100 0.18

Table 5: Ticker tape measurement uncertainty

Tables 2 shows the percentage uncertainties for the shortest and longest ticker tape section

analysed. These were measured using a 30cm ruler which had a resolution to the nearest

mm. (Two 2 figures only)

Height

Equation

%U

50mm (0.5x1)/(50)x100 1.00

101mm (0.5x1)/(101)x100 0.50

132mm (0.5x1)/(132)x100 0.38

174mm (0.5x1)/(174)x100 0.29

191mm (0.5x1)/(191)x100 0.26

Table 6: Measuring height uncertainty

Here shows the percentage uncertainties of the height of the ramp which was measured

using string then the string was measured using a 30cm ruler with a resolution of 1mm. The

highest possible uncertainties are at the lowest height of 50mm with a percentage at 1.000

and the lowest percentage uncertainty is at the highest height with a 0.262.

Length

Equation

%U

1820mm (0.5x1)/(1820)x100 0.28

Table 7: Measuring length uncertainty

This shows the percentage uncertainty of measuring the length of the ramp. I used two 1

meter sticks with smallest resolution of 1mm. The % uncertainty for this is 0.275.

Total %U

3.457

Table 8: Total uncertainty

The Percentage uncertainties for acceleration is the same as percentage uncertainties in the

average speed (figure 5) which will be derived for percentage uncertainty in each ticker tape

section measurement.

Using the data above, the percentage uncertainty for the Sine of angle of slope was found

by adding together the percentage uncertainty for height and length of the slope, as follows:

Worst Case = 1.000(Height) + 0.275(length) =1.275%

Best Case= 0.262(Height) + 0.275(length) = 0.537%

This was then used to determine the (highest) percentage uncertainty due to measurement

instruments used, in determining the value of ‘g’:

% uncertainty in ‘g’ =% uncertainty in acceleration + % uncertainty in sine of slope

=0.581+1.275= 1.856% (approx. 2%)

SUGGESTED IMPROVEMENTS

An improvement which could be made to my Experiment could be having a set place/

run for the ticker tape to flow as when carrying out my experiment there was still drag

which could off affected my results.

Another improvement could be having a smooth running track and trolley. This would

be good as it would reduce drag and help increase the accuracy of the results as the

trolley and ramp which was used was not perfectly smooth and had bumps along the

way.

PART D: CONCLUSIONS

Figure 3 shows the table of the values of g which was received, it shows a range from 6.536-

8.790 and compared to the national accepted level of “g” at 9.811 it is not that far off from

the closest reading.

The experiment which was taken was reliable as the results was repeated at 7 different

height with 7 different read on each height giving you a final total number of reading of 49.

This helps make it reliable due to it being repeatable along with it be more precise and

accurate. This experiment which was carried out was ensured accuracy as the when reading

and measuring the height of the ramp it took in account zero errors such as the lip which

was 20mm high which has to be taken away from the final height. This was shown in the

logbook. Precision was taken into as there was a large amount of data readings there was

also instruments with a finer resolutions such as the meter rulers which was read to the mm

scale.

(Comment about precision uncertainty of 2% being a good value for a school lab

experiment).

The research which was taken out is valid as the research which was carried out as it is

reliable and used the correct physics theory with only having relevant data.

The results from the T-test the hypothesis was rejected due to the final reading being greater

than the critical value of 2.18. This showed that there was no significant difference between

the two pieces of data a confidence level.

All objectives were met as the hypothesis was tested to see if it was accepted or rejected,

there was a comparison between two methods by applying statical values and the level of

acceleration was found from rolling a trolley down a slopes using ticker tape and lights

gates. These are shown in figure 1 and 2.

ADD MORE HERE

REFERENCES

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Thorne's

Journal sources:

• Saxov, S (1952), “Variation of gravity within earth”, Danish Geodetic Institute, pp:138-140,

Available at http://onlinelibrary.wiley.com/doi/10.1111/j.2153-3490.1952.tb00998.x/epdf

(Accessed 19/01/16)

BILBLIOGRAPHY

APPENDICES

Block sine (angle of

slope)

acceleration (m/s2) from graphs g (m/s2)

2 0.0275 0.1134 8.790

3 0.0412 0.1411 6.536

4 0.0554 0.3313 8.289

5 0.0723 0.4975 8.647

6 0.0876 0.6045 8.364

7 0.0952 0.6564 8.242

8 0.1044 0.6634 7.583

Table 2:

Table 3:

Table 4:

2 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 86 0.086 0.43 0.1

2 0.2 89 0.089 0.445 0.3

3 0.2 94 0.094 0.47 0.5

4 0.2 108 0.108 0.54 0.7

5 0.2 112 0.112 0.56 0.9

6 0.2 106 0.106 0.53 1.1

7 0.2 111 0.111 0.555 1.3

3 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 108 0.108 0.54 0.1

2 0.2 113 0.113 0.565 0.3

3 0.2 128 0.128 0.64 0.5

4 0.2 135 0.135 0.675 0.7

5 0.2 145 0.145 0.725 0.9

6 0.2 155 0.155 0.775 1.1

7 0.2 127 0.127 0.635 1.3

6 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 112 0.112 0.56 0.1

2 0.2 153 0.153 0.765 0.3

3 0.2 169 0.169 0.845 0.5

4 0.2 192 0.192 0.96 0.7

5 0.2 220 0.22 1.1 0.9

6 0.2 244 0.244 1.22 1.1

7 0.2 260 0.26 1.3 1.3

Table 9: Table of ticker tape results

5 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 111 0.111 0.555 0.1

2 0.2 139 0.139 0.695 0.3

3 0.2 160 0.16 0.8 0.5

4 0.2 173 0.173 0.865 0.7

5 0.2 197 0.197 0.985 0.9

6 0.2 218 0.218 1.09 1.1

7 0.2 225 0.225 1.125 1.3

4 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 137 0.137 0.685 0.1

2 0.2 149 0.149 0.745 0.3

3 0.2 162 0.162 0.81 0.5

4 0.2 177 0.177 0.885 0.7

5 0.2 196 0.196 0.98 0.9

6 0.2 208 0.208 1.04 1.1

7 0.2 210 0.21 1.05 1.3

7 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 141 0.141 0.705 0.1

2 0.2 154 0.154 0.77 0.3

3 0.2 198 0.198 0.99 0.5

4 0.2 227 0.227 1.135 0.7

5 0.2 259 0.259 1.295 0.9

6 0.2 256 0.256 1.28 1.1

7 0.2 60 0.06 0.3 1.3

8 Block

Section Time taken Length(mm) Length (m) Average speed (m/s) Cumulative time (s)

1 0.2 103 0.103 0.515 0.1

2 0.2 136 0.136 0.68 0.3

3 0.2 199 0.199 0.995 0.5

4 0.2 198 0.198 0.99 0.7

5 0.2 224 0.224 1.12 0.9

6 0.2 228 0.228 1.14 1.1

7 0.2 281 0.281 1.405 1.3