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Samuel Pius

Physics Extended Essay

003810 0013

Title Page

Extended Essay

To what extent does the change in the diameter and height
or volume of the water in the measuring cylinder affect the
angle of inclination, which changes the Centre of Gravity
(Stability)?

By Samuel Pius

Word count: 3788
excluding abstract, contents, tables, appendix, references, figure labels
...
The investigation was thought of after observing
a rollover accident of a heavy-duty truck in an inclined highway
...
The accident was simulated by using
a measuring cylinder in an inclination test to determine that the diameter of the cylinder and
volume of liquid does affect the measuring cylinder’s stability
...
At the tipping point, the bosses were tightened and
the tilt angle was measured
...
Moreover,
the absolute and relative uncertainties were found out through which the percentage
uncertainties for each graphs were found
...
The errors were identified for which few improvements
were suggested and employed
...


Word count: 284
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Samuel Pius

Physics Extended Essay

003810 0013

Contents
Title Page
...
2
Introduction:
...
5
Equilibrium:
...
7
Independent variable:
...
8
Controlled variable:
...
8
Methodology:
...
8
Setup 2:
...
14
Case3:
...
17
Data Presentation and Analysis:
...
18
Calculations:
...
19
Case 3 processed data tables:
...
21
Firstly, comparing different models for the 2000ml processed data table
...
23
Comparing the different models for the 500 mL processes data table:
...
26
Comparing the different models for the 100 mL processes data table:
...
35
Terms, which will be frequently used in the inferences, are defined below:
...
37
Evaluation:
...
41
The errors that may have occurred in the Experiment are as follows:
...
42
Methods already employed:
...
44
Appendix: Reviewing the parametric estimates for the angle of tilt vs diameter of the measuring
cylinder graphs
...
47

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Samuel Pius

Physics Extended Essay

003810 0013

Introduction:
When a Truck filled with huge oil-tankers travel through a region with constant
inclination, the stability of the truck goes haywire and probably topples over
...
The reason why these trucks roll
over is due to the Centre of Gravity (COG) moving upwards or changing its position
horizontally
...
” This influenced me to make a
mechanical device with variable parameters through which we can alter the diameter
(width), height or volume of the container, which will display and alarm the heavyduty truck drivers when there is a possibility for the truck to topple over while
travelling on an inclined highway
...
Hence the
research question is: To what extent does the change in the diameter and height or
volume of the water in the measuring cylinder affect the angle of inclination,
which changes the Centre of Gravity (Stability)?

Theory of Stability:
Stability of an object is the measure of how likely it is for an object to topple over
when pushed or moved
...
The higher it is, the more likely the object is to topple over if
it is pushed
...

c) Height of the object: Altering the height of the object will also affect the
stability of an object, the shorter the height more stable the object and viceversa
...

Therefore, if an object is pushed, it will rollover, if a vertical line from its centre
of gravity falls outside its base
...

Hence, these conditions are as follows:
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Samuel Pius

Physics Extended Essay

003810 0013

(a) Stable Equilibrium is when the object tilts and then return to its original position
...

(c) Neutral Equilibrium is when the objects centre of gravity remains the same even after a
forced is applied
...
Hence, the selection
and control of variables are essential before starting the experiment
...

Case 2: Height of the measuring cylinder:
In this case, the measuring cylinder of different height will be used accordingly in
order to investigate the stability of the cylinder
...

(Note: In this essay, I have investigated only Case 1 and Case 3 because Case 2
and 3 are almost the same since as volume increase height increases too
...
)

Dependent variable: Angle of tilt:
The angle of tilt is required to determine how stable the cylinder is
...

b) Position of the measuring cylinder on the plank: The positon of the measuring
cylinder must be kept on the centre of the plank in order to distribute the force
applied on the wooden plank evenly, reducing the error possibilities
...


Uncontrolled Variable:
There were no uncontrolled variable
...

c) Then keep a 2000ml measuring cylinder on a fixed position parallel to the 90degree mark of the protractor
...


Figure 3

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Samuel Pius

Physics Extended Essay

003810 0013

e) However, while performing this trial it was not possible to tilt the measuring
cylinder and record the angle of tilt at the same time
...


Setup 2:
a) Apparatus used:
For this experiment,


A basic set up of a stand, a clamp and bosses were used to hold the
wooden plank such that it can be displaced from the surface from one end
...




5- measuring cylinders (2000mL, 1000mL, 500mL, 400mL, 100mL), each
of different heights and base diameters must be used
...




Sufficient amount of water supply in order to use for the measuring
cylinders
...




Ruler to measure the height of the measuring cylinders
...


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Samuel Pius

Physics Extended Essay

003810 0013

Figure 4
b) Experiment Procedure:


Take a wooden plank, which will be used to incline a measuring cylinder
and attach a wooden scale in the middle of the plank using a cello-tape so
that the measuring cylinder does not slip down the plank when raised
...




Connect the wooden plank to the bosses on both the sides of the plank
...




Raise the plank in order to find the angle at which the measuring cylinder
topples over
...


11

Samuel Pius

Physics Extended Essay



003810 0013

Repeat the experiment for the same cylinder by altering the volume of
water (50mL, 100mL, 150mL, 200mL, 250mL, and 300mL) with five
trials for each
...
1cm, 8
...
0cm and 6
...


After designing both the experiment, I found out that the first trial turned out to
be a very inadequate way of recording the angle
...
Hence, I carried out
the experiment using the trial 2 design
...
_ (_____mL)
Diameter: ___ cm; Mass: ____g (without any liquid added)
Tilt Angle/ ± 0
...
This is because we can extract the
readings for Case 1, which has fixed volume of 50mL, which will be executed
graphically wherein the diameter is the independent variable, the angle of tilt will
be the dependent variable, and the controlled variable will be the volume of water
added
...
1 (2000mL)
Diameter: 12
...
2g (without any liquid added)
Tilt Angle/ ± 0
...
0

20
...
0

20
...
0

100

20
...
0

21
...
0

21
...
0

24
...
0

24
...
0

200

26
...
0

28
...
0

27
...
0

29
...
0

28
...
0

300

28
...
0

29
...
0

29
...
5 ˚
Table 1
...
1 cm ; Mass: 236
...
5 ˚ (Degree)

Volume/ ±
5 mL

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

0

24

24

23

24

24

50

24

25

26

25

25

100

25

25

26

26

26

150

28

27

28

28

28

200

29

29

28

30

29

250

31

30

31

31

30

300

33

32

32

31

32

Choice of uncertainty:
volume: least count/2:- 10mL/2= 5mL
Tilt angle: least count/2:- 1 ˚ /2= 0
...
3 (500mL)
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Samuel Pius

Physics Extended Essay

003810 0013

Diameter: 8
...
74 g (without any liquid added)
Tilt Angle/ ± 0
...
5 mL

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

0

21

21

22

21

21

50

22

23

22

23

23

100

23

24

24

24

23

150

26

25

25

26

25

200

26

27

26

25

26

250

26

27

25

26

26

300

23

24

25

25

25

Choice of uncertainty:
volume: least count/2:- 5mL/2= 2
...
5 ˚
Table 1
...
1 cm; Mass: 106
...
5 ˚ (Degree)

Volume/ ±
1
...
0mL
Tilt angle: least count/2:- 1 ˚ /2= 0
...
5 (100mL)
Diameter: 6
...
87g (without any water added)
Tilt Angle/ ± 0
...
5 mL

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

0

28

28

27

28

28

10

28

29

29

28

29

20

29

30

30

30

31

30

32

33

33

33

33

40

33

34

34

34

35

50

35

36

36

36

36

60

37

37

37

37

38

Choice of uncertainty:
volume: least count/2:- 1
...
5mL
Tilt angle: least count/2:- 1 ˚ /2= 0
...
5 ˚ (Degree)

Diameter/ ±
0
...
70

35

36
...
0

36
...
0

8
...
0

24
...
0

24
...
70

22

23
...
0

23
...
0

11
...
0

26
...
0

25
...
80

19
...
0

20
...
0

21
...
1cm/2= ±0
...
5˚

Data Presentation and Analysis:
Processing:
The raw data collected in the data tables does not constitute the average tilt angle
...

Calculations:
I
...

Average Tilt angle = (Trial 1 + Trial 2 + Trial 3 + Trial 4 + Trial 5)/5
II
...
1
...
8 cm; Mass: 410
...
5 ˚ (Degree)

Volume/ ± 10 ml

Average Tilt angle

Uncertainty in the tilt angle

0

17
...
5

50

20
...
0

100

20
...
5

150

24
...
0

200

27
...
75

250

28
...
0

300

28
...
5

Table 1
...
2 (1000mL)
Diameter: 11
...
00 g (without any liquid added)
Tilt Angle/ ± 0
...
8

±0
...
0

±1
...
6

±0
...
8

±0
...
0

±1
...
6

±0
...
0

±1
...
1
...
7 cm; Mass: 153
...
5 ˚ (Degree)

Volume/ ± 10 ml

Average Tilt angle

Uncertainty in the tilt angle

0

21
...
5

50

22
...
5

100

23
...
5

150

25
...
5

200

26

±1
...
0

300

24
...
0

Table 1
...
4 (400mL)
Diameter: 8
...
42 g (without any liquid added)
Tilt Angle/ ± 0
...
2

±0
...
6

±0
...
6

±0
...
2

±0
...
8

±0
...
1
...
7 cm; Mass:46
...
5 ˚ (Degree)

Volume/ ± 10 ml

Average Tilt angle

Uncertainty in the tilt angle

0

27
...
5

10

28
...
5

20

30
...
0

30

32
...
5

40

34
...
0

50

35
...
5

60

37
...
5

Case 3 Reviewing and comparing the parametric estimates:
Reviewing the estimates for the coefficients for the quadratic, cubic and quartic
models, their root mean square error and standard deviation
...
Smaller the root mean
square values better the modelling of the fitted line graph
...
This is because the RMSE (Root mean square) is the lowest
for the cubic model
...
This is because the RMSE (Root mean square) value is the
lowest for the quadratic model
...
This is because the RMSE (Root mean square) value is the
lowest for the cubic model
...
This is because the RMSE (Root mean square) value is the
lowest for the cubic model
...
This is because the RMSE (Root mean square) value is the
lowest for the cubic model
...
The uncertainty in each trial is showed with the help of the
error bars in each graphs
...
0°
Therefore, the uncertainty =

Percentage uncertainty =

Percentage uncertainty =

11
...
5
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑖𝑙𝑡

5
...
80

× 100

× 100 = 23
...
2°
Therefore, the uncertainty =

Percentage uncertainty =

Percentage uncertainty =

8
...
1
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑖𝑙𝑡
4
...
69

× 100

× 100 = 14
...
8°
Therefore, the uncertainty =

Percentage uncertainty =

Percentage uncertainty =

4
...
4
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑖𝑙𝑡
2
...
17

× 100

× 100 = 9
...
8°
Therefore, the uncertainty =

Percentage uncertainty =

Percentage uncertainty =

3
...
9
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑖𝑙𝑡
1
...
91

× 100

× 100 = 8
...
0°
Therefore, the uncertainty =

Percentage uncertainty =

Percentage uncertainty =

10
...
0
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑖𝑙𝑡

5
...
23

× 100

× 100 = 15
...
5 ˚ (Degree)

Uncertainties in the angle

6
...
8

±0
...
10

23
...
5

8
...
6

±0
...
10

25
...
5

12
...
0

±0
...
05 cm

After reviweing and comparing the parametric estimates, the quartic curve is the best
fit for this relation
...


35

Samuel Pius

Physics Extended Essay

003810 0013

The uncertainty in the angle of tilt is:
(Range of angle of tilt)/2
Range of angle of tilt = ∆Θ
∆Θ = 15
...
9
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

Percentage uncertainty =

Percentage uncertainty =

15
...
9
25
...
10%

Terms, which will be frequently used in the inferences, are defined below:
1
...

2
...


36

Samuel Pius

Physics Extended Essay

003810 0013

Inferences:
From the graphs above we can see the relation between the angle of tilt versus the
volume of water added to the measuring cylinder in Case-3 and angle of tilt versus
the diameter of the measuring cylinder where the volume of the water added is
constant (50mL) in Case-1
...
This is because
the volume of water added to the measuring cylinder affecting the stability is very
less; compared to the case when the range of the angle of tilt is low
...


Range of tilt angle/ ∆Θ

1 (2000mL)

11
...
2

3 (500mL)

4
...
8

5 (100mL)

10
...
Here, we can immediately spot that there is an
anonymous state point that is the ∆Θ value of 100mL measuring cylinder
...
Thus, we can deduce that the
∆Θ value depends upon the proportions of the diameter and capacity of the
measuring cylinder
...
Hence, even though the
2000mL cylinder is the tallest and 1000mL cylinder is relatively shorter the
2000mL is more stable
...

Moreover, we can determine the relation between variable capacity addition (xaxis) and the tilt angle (y-axis) of a fixed capacity-measuring cylinder
...
1
...
1
...
1
...
1
...
1
...
Here I have taken data for four different
capacities of cylinder and neglected 100ml because as mentioned above the
100mL measuring cylinder produces an anonymous state of readings, which
cannot be collaborated with other sets of readings to determine the relationship
...


38

Samuel Pius

Physics Extended Essay
Capacity

003810 0013

2000

1000

500

400

410

236

154

106

1000mL 500 mL

400 mL

Empty
cylinder/
gms
x-axis

2000 mL
50

19

24

22

23

100

20

25

23

24

150

24

28

26

24

200

26

29

26

23

250

28

31

26

22

300

28

33

23

20

0
...
99

0
...
78

R

Here ‘r’ is found using Microsoft Excel by plotting the above processed data table
onto a graph, wherein the line passes through all the points of the graph unlike the
other graphs plotted above
...

For example, for the 1000mL cylinder r=0
...
Here 0
...
Therefore, by
calculating r, I can infer that the tilt angle increases as you decrease the capacity
of the measuring cylinder
...


39

Samuel Pius

Physics Extended Essay

003810 0013

The data tabulated above and its inferences is plotted onto a graph to give a clear
incite about the investigation
...
Then
the angle at which the truck will topple over will depend directly upon how we are
altering the volume of liquid in the container
...
The angle of tilt affects the stability because the
truck tilts beyond its centre of gravity
...
Moreover, in Case-1 the diameter

40

Samuel Pius

Physics Extended Essay

003810 0013

Evaluation:
Error analysis:
In this investigation, uncertainties were observed in each section of the
experiment
...

The percentage uncertainties of the graph plotted for the five measuring cylinder
with different capacities are as given below:
for 2000mL = 23
...
80%,
for 500mL = 9
...
30%,
and for 100mL = 15
...
(anonymous state reading)
The high uncertainty in the 2000mL cylinder is probably because of the multiple
errors caused due to bad human handling
...
There is
exception, which is to be marked as an anonymous state reading for the 100mL
cylinder
...


41

Samuel Pius

Physics Extended Essay

003810 0013

2) It is the same case for the measuring the angle of tilt where it was difficult to
keep the head still while reading the angle of tilt from the protractor
...

4) It is assumed that the tilt angle measured has lot of errors because there was a
lot difficulty while measuring it
...

5) Even after keeping a wooden scale to avoid the cylinder from slipping it
would slip and topple over in other direction when the wooden plank is
displaced
...
They are as listed below:
1) We can use tilt sensors and inclinometers, which will create an artificial
horizon to measure the angle of tilt subject to this horizon
...

2) Instead of using a measuring cylinder, we can use a beaker glass pitcher since
it is a perfect cylinder with fixed diameter unlike the measuring cylinder,
which has a bigger base, making it more stable
...

3) Get the eye level perpendicular to the protractor lines while measuring the tilt
angle
...


This will make the previous issue of keeping the head still while measuring
the angle
...


Methods already employed:
1) Used a wooden plank as a base instead of a fixed base, to elevate it from one
of its side in order to improve the experiment by making the measurement of
tilt angle more accurate
...


Further investigation:
In this, essay certain parts constraints, which are possible to investigate but are not
investigated
...

This experiment uses a measuring cylinder as a simulation for the truck
...

The other part that could have been investigated too is deriving the mathematical
equation in alarming the truck drivers to be cautious about toppling
...
Even after the keeping a
thick wooden scale in the centre in order to avoid slipping, the cylinder would slip and
topple over in various other undesired directions
...

Quadratic model:

Cubic model:

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Samuel Pius

Physics Extended Essay

003810 0013

Quartic model:

After reviewing the plotted graph, I have concluded that the quartic model is the best for
modelling the graphs for the relationship between the volume of water added and the tilt
angle of the measuring cylinder
...


46

Samuel Pius

Physics Extended Essay

003810 0013

References:
1
...
com/metrology/measuring-instruments-metrology/
2
...
slopeindicator
...
php
3
...
xtremepapers
...
pdf
4
...
xtremepapers
...
pdf
5
...
tutorvista
...
php
6
...
howstuffworks
...
htm
7
...
tutorvista
...
html
8

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