Physics Extended Essay
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EE Extended Essay
How does the temperature of a squash ball affects the
impact time of the ball drops from a certain height
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Abstract
In this research, I investigated how temperature affects the average force of impact
when the squash ball was dropped from a height of 130cm. After collecting data; I
then applied the formula F 
m(v  u )
and calculate the average force F.
t
The research consisted of two experiments. Of which, one (a) was to find out the
impact time of the squash ball that dropped from a height of 130cm. The other one (b)
was to find out the rebound height of the squash ball from a dropping height of
130cm.
In experiment (a), I made a set up to measure the conduction time when the ball is
impacting the ground. I assume that the conduction time is equal to the impact time of
the balls. Different results were recorded from temperatures between 20oC to 100 oC
with 10 oC intervals. The results showed that the variation in impact time were very
trivial that the set up is not fine enough to sense the different.
In experiment (b), rebounds of ball of different temperatures ranged from 20oC to 100
oC with intervals of 10 oC were directly measured by measuring the rebound height.
Results showed a uprising curve with a decreasing gradient.
With the two data, I then calculated the average force act on the squash ball. A graph
was also drawn for further and deeper explanation of the effect of temperature on
average force of squash ball. Hence I can explain the application of the results to the
sport.
Finally, the limitations and errors of the experiment that could have affected the
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reliability of the results in the experiment were evaluated.
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Content
Page
Introduction
3
Hypothesis
4
Method and materials
Experiment (a)
Ways of measuring impact time
Final decision and the experimental set up
Experiment (b)
5
5
10
12
Results and Analysis
Data collection
13
Analysis
18
Discussion
21
Evaluation of the Experiment
Evaluation
22
Improvement
23
Conclusion
24
Appendix
25
References
Bibliography
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Introduction
Squash has become more and more popular nowadays. Moreover there is a growing
trend of keeping a healthy life in the modern society. Squash is one of the most energy
consuming sports. It just fits the people’s want, as time is precious in the city. For the
reason of being an enthusiastic player in squash, I investigated this sport in the field of
physics.
As we know, when squash ball is not warm, it is very inelastic and not bouncy.
Because when the ball is cold, the air pressure inside the ball is not high enough to
make the bouncy. However if we hit the ball, we do work on it. Some of the work
done is transferred to increase the particles’ kinetic energy of the ball which in turn
increases the air particles’ energy inside the ball. The air pressure in the ball increases
and pushes on the inner wall. Thus it makes the ball become bouncy.
Impact is the main constitutional element of squash games. When play, the ball often
drops on the ground where it bounces back afterward. Between the two motions is the
impact. The ball bounces back because it acquires kinetic energy which is developed
by the force acting on the impact with the ground. We have already known that squash
ball gets more elastic as its temperature increase. But what effect will it do to the
average force act on the ball when it comes to impact when temperature increases? By
knowing that, we can find out the rate of change of average force of impact when
temperature. Then we can find out at which temperature does squash ball function
most effectively.
Hypothesis
I think that as temperature increases, the average force acting on the ball by the
ground increases. Since when temperature increases, the rebound height of the ball
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will be higher. I argue that if the ball rebound higher, the net force acted on the ball by
the ground must also be greater.
According to the formula the impulse is  m(v  u )
As AverageForce 
m(v  u )
 mg ,
t
If  m(v  u ) is greater with impact time t being constant, the average must be
greater. When temperature of the squash ball is low, it is quite soft and easy to be
deformed. The impact time t is hypothesized to be longer. As temperature
increases, the squash ball will become more rigid and deform less. The impact time is
hypothesized to be shorter. Since AverageForce 
m(v  u )
 mg , when the impact
t
time is smaller with net force being constant, the average force must be greater.
Therefore, with the two effects, the average force of the impact is hypothesized to be
greater when temperature increases.
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Method and materials.
Experiment (a)
Since there is originally no any equipment that can measure the extremely short
impact time, therefore I had to develop several ideas to measure the time. These are
the six possible solutions:
1. Stroboscopic photos
The negative is put under long exposure. And the experiment is supposed to be
performed in a dark room otherwise the negative will be over expose. Stroboscope
is needed to give the flashes at a very high frequency. Under which, the images of
the falling ball including the impacting period will be taken. We will then count
the numbers of images that are touching the ground (impact period). With the
frequency shown on the stroboscope, we can then calculate the impact time of the
squash ball.
Images of
squash ball
when
dropping
Fig.1
However there is limitation of the experiment. The impacting images may pack
too close to each other that we cannot distinguish the number of them and fail to
calculate the correct value.
Moreover stroboscopic photos are difficult to be taken well. It requires skill to
control the exposure so that the photos taken will not be too bright or too dark for
observation. Therefore the suggestion was abandoned.
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2. Ultrasonic position sensor (UPS)
Place a UPS on the ground; drop the ball from certain height to it. The UPS is
connected to a computer for receiving data. A graph of distance against time will
be plotted automatically. By observing the length of time when the distance is at
zero, we can know the impact time of the ball.
Squash ball
Ultrasonic waves
To the computer
Fig.2
However, later I acknowledged that the speed of the ultrasonic waves is not fast
enough to measure the fast dropping object to give accurate results. Therefore the
suggestion was abandoned.
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3. Conduction sensor
Fix a piece of foil on a dense plate (cutting board), on the surface place another
piece of foil closely but without touching the first one. Both foils are connected to
a scalar timer with wires. The ball is then dropped onto the upper foil, pressing the
foil and closing the circuit. When the ball rebounds, the upper foil releases and
disconnects the circuit. The impact time can be indirectly collected from the
conduction time. As this experiment was easier to perform, I used the set up to
find a rough impact time of about 0.01s~0.05s. This result can be then used as a
assumption value for other suggestion.
Squash ball
Aluminium
foil
Both wires are
connected to
scalar timer
Cutting
board with
aluminium
foil on top
Fig.3
However, it was suggested that the upper foil may obstruct the falling speed of the
ball. This leads to an experimental error of the results. Moreover after the ball
rebounds and leaves the upper foil, the foil may still in touch with the lower foil
due to deformation. The impact time we get may be over estimated.
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4. Light sensor
Set up a light sensor on the table with the light beam just situate above the table
surface. Then drop the ball to cut the beam. The time that the light sensor obtains
is the impact time.
Squash ball
Light emitter
Light sensor
Beam of light
Fig.4
However, as the light beam has finite thickness, it is not accurate enough to
measure the impact time. The ball may cut the beam too early and leave too late
which over estimate the impact time. Furthermore, it is difficult to ensure the ball
drop exactly to the light beam by its lowest point. The results may not be accurate.
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5. Formula and calculation
First we need to measure the dropping height, e.g. A cm. Then we drop the ball
and at the same time start to count the time using a timer. When the ball rebounds
to the highest point we stop the timer and at the same time record the highest point
it reaches, e.g. B cm. let the total time for the process be C seconds. From the
formula s=ut +(1/2) at2. We then substitute distances B and C to find out the time
need for dropping and rebounding.
Dropping
time
Renounces
time
Fig.4
But deficiencies are still being found for this alternative. There is reaction time
error in working the timer. The reaction error is even larger than the impact time.
Also, the highest point the ball reaches may not be accurately detected. So the
measurement is considered not working.
6. Digital-video camera approach
Use the camera to take the impacting images of the ball. Then replay the film to
find out the time of impact. As we found out that the impact time is around 0.03
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Final decision
After series of consideration, I made the final choice to use the option 3. Despite its
limitation that may lead to over estimation of results, I found the problems that may
occur in No.3 least essential. Moreover stretching the upper foil a little can reduce the
deformation of the upper foil. So this measuring method was selected.
Experimental set up.
In the experiment I prepared the following material for the setting up.
Materials
Kettle, clamp, chopsticks, squash balls, stand, towel, scalar timer, aluminium foil,
aluminium tape, plastic tape, wire, clips, cutting board, a pack of unused paper card.
Methods
First of all, Impact Time Measuring Device (ITMD) was made as core of the set up:
Aluminium foil was stuck to the cutting board until its upper surface was completely
filled up by the tape. I then check the conduction of the foil to ensure no gaps between
each strip of tape. Then an 8x8cm2 hole was made from 10x10cm2 paper card. A piece
of 8x9cm2 foil was then stretched on the middle of the hole. Then I used tape to fix
the foil on two ends of the hole. The paper card with the foil on top was put onto the
upper surface (with foil) of the cutting without the two piece of aluminium touching
each other. Then both foils were connected to two separated wires with crocodile clips
and the wires were connected to the scalar timer. The ITMD was finished.
In order to test if the ITMD was reliable, I performed several dropping test for
checking. Firstly I dropped the ball at room temperature of height 140 cm;
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unfortunately the results each time collected were not consistent. They had differences
of about 50% to 200%. Therefore I changed the setting of the paper card. I used a
larger piece of foil (9x9 cm2) and stretched it to the four end of the paper hole. The
later tests showed improvement as the differences drop to about 20% to 60%. And I
thought that it may due the deformation of foil that the two foils still pressed to each
other when the ball left. So I stuck another piece of paper card with hole just right
beneath the original one. It was done to increase the distance between the two foils by
about 0.5mm so that they are more likely to separate after the ball has left. The tests
followed were more coherent as their differences were just about 10 % to 20%. Then I
varies the dropping height to see if the measurer could detect the time different (room
temperature). It showed an increasing trend of impact time when the dropping height
increase. That proved that it senses changes.
The kettle was then used to boil the water for heating up squash balls; however it is
not convenient to do in this way, so I changed to use a water bath instead. With the
water bath, I could then adjust the temperature I want easily. Clamps were used to
release the balls instead of the chopsticks. Firstly stand with clamp were put on the lab
table. I measured 130 cm from the bottom of the ball in the clamp vertically to the
centre of the cutting board. Then the squash balls were first immersed into water of
20.2oC for 10 minutes to ensure the balls were have same temperature as water. Then
I used the clamp to take one from the water bath, quickly dried it with towel and
transferred to the clamp on the stand, released it to the centre of the paper. Then I
repeated the procedure by another nine times to collect ten data at that temperature. In
between, I recorded the impact time from the scalar timer. After that I continued the
experiment with an increase of 10 oC until it reached 100 oC. For the handling of hot
balls, working gloves were needed.
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Experiment (b)
Materials
Clamp, squash balls, stand, towel, scalar timer, aluminium foil, aluminium tape,
plastic tape, wire, clips, cutting board, a pack of unused paper card, water bath,
working gloves.
1. Same platform (cutting board with paper card) in experiment (b) was used to
make the condition of two experiments more constant. Pieces of blank papers
were first placed along the drop ping track of the ball on the side of the lab table.
The balls were taken from the water bath of the temperatures as Experiment (b),
dried, transferred to clamp and dropped to the cutting board quickly. The highest
points it reached after the rebound were marked onto the papers. I repeated ten
times for each temperature. Finally measuring tape was used to measure the
rebound height of each temperature.
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Data Collection
Dropping Height=130.0 + 0.1cm
1. Temperature=20.2 + 0.4 o C
Trial
1
2
3
4
5
6
7
8
9
10
Mean
Rebound height/cm
18 18.2 18.2 18.4 18.4 18.4 18.6 18.8 19 19
18.5+0.2
Impact time/0.001s
19
0.0209
19
20
Uncertainty of height=0.1cm
20
20
20
21
22
24 24
Uncertainty of time=0.001s
Mean height = (18+18.2x2+18.4x3+18.6+18.8+19x2)/10 = 18.5 cm + 0.2cm
Uncertainty =
1
2 10
 0.2
Mean impact time = (20.9  0.8)103 s
Uncertainty =
5
2 10
 0.8
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2. Temperature=30.0+0.4oC
Trial
1
10
Mean
Rebound height/cm 27.2 27.4 27.4 27.4 27.8 27.8 28.4 28.4 28.6
28.6
27.9
Impact time/0.001s
24
16
2
19
3
20
Uncertainty of height=0.1cm
4
20
5
20
6
21
7
22
8
23
9
24
Uncertainty of time=0.001s
Mean height = (27.2+27.4x3+27.8x2+28.4x2+28.6x2)/10 = 27.9 + 0.2 cm
Uncertainty =
1.4
2 10
 0.2
Mean impact time = (20.9 + 1.3) 10-3s
Uncertainty =
8
2 10
 1.3
0.0209
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3. Temperature = 40.0+ 0.4oC
Trial
1
2
3
4
5
6
7
8
9
10
Mean
Rebound height/cm 35.8 35.8 36.3 36.4 36.4 36.4 36.4 36.4 36.6 36.8
36.3
Impact time/0.001s
21
17
19
Uncertainty of height=0.1cm
20
21
21
21
22
1
2 10
 0.2
Mean impact time =( 21+1.1) 10-3s
Uncertainty =
7
2 10
 1.1
23
Uncertainty of time=0.001s
Mean height = (35.8x2+36.3+36.4x5+36.6+36.8)/10= 36.3+0.2cm
Uncertainty =
22
24
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4. Temperature = 50.0+0.4oC
Trial
1
Rebound height/cm
41
Impact time/0.001s
18
2
3
44.6 44.8
19
19
Uncertainty of height=0.1cm
4
5
6
7
8
9
10
Mean
44.8 44.8
44.8
45
45
45.4
45.6
44.6
21
22
23
23
19
20
Uncertainty of time=0.001s
Mean height = (41.0+44.6+44.8x4+45.0x2+45.4+45.6)/10 = 44.6+ 0.7cm
Uncertainty =
4
 0.6
2 10
Mean impact time = (20.8+0.9) 10-3s
Uncertainty =
6
2 10
 0.9
24 20.8
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5. Temperature = 60.0+0.4oC
Trial
1
Rebound height/cm
Impact time/0.001s
10
Mean
51.6 51.8 51.8 52 52 52.2 52.2 52.6 52.6 54
52.3
17
Uncertainty of height=0.1cm
2
19
3
19
4
5
20 21
6
21
7
21
8
21
9
22
Uncertainty of time=0.001s
Mean height = (51.6+51.8x2+52x2+52.2x2+52.6x2+54)/10 = 52.3+0.4cm
Uncertainty =
3.4
 0.5
2 10
Mean impact time = average time = (20.4+0.9) 10-3s
Uncertainty =
5
2 10
 0.8
23 20.4
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6. Temperature = 70.0+0.4 oC
Trial
1
Rebound height/cm
Impact time/0.001s
10
Mean
60.4 60.6 60.6 61.6 61.8 61.8 62.6 62.6 62.8 63.2
61.8
16
2
19
Uncertainty of height=0.1cm
3
19
4
20
5
20
6
20
7
21
8
21
9
22
Uncertainty of time=0.001s
Mean height = (60.4+60.6x2+61.6+61.8+62.6x2+62.8+63.2)/10=61.8+0.4cm
Uncertainty =
2.8
 0.4
2 10
Mean impact time= average time = (20.2+1.3) 10-3s
Uncertainty =
8
 1.3
2 10
24 20.2
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7. Temperature = 80.0+0.4 oC
Trial
1
2
3
4
5
6
7
8
9
10
Rebound height/cm 68 68.8 69.2 69.2 69.8 70.6 70.8 71.6 72.6 73.6
Impact time/0.001s 17
17
Uncertainty of height=0.1cm
18
21
21
21
22
22
23
23
Mean
70.4
20.5
Uncertainty of time=0.001s
Mean height = (68.0+68.8+69.2+69.8+70.6+70.8+71.6+72.6+73.6)/10 = 70.4+0.9cm
Uncertainty =
5.6
 0.9
2 10
Mean impact time = average time =( 20.5+0.8) 10-3s
Uncertainty =
5
 0.8
2 10
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8. Temperature = 90.0+0.4 oC
Trial
1
2
3
4
5
6
7
8
9
10
Rebound height/cm 74.6 74.8 76.8 77 77 77.6 77.8 77.8 78.4 78.8
Impact time/0.001s
16
19
Uncertainty of height=0.1cm
20
20 20
21
21
22
23
25
Uncertainty of time=0.001s
Mean height = (74.6+74.8+76.8+77x2+77.6+77.8+78.4+78.8)/10 = 77.1+0.7cm
Uncertainty =
4.2
 0.7
2 10
Mean impact time = average time = (20.7+1.4) 10-3s
Uncertainty =
9
 1.4
2 10
Mean
77.1
1.4
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9. Temperature = 100.0+0.4 o C
Trial
1
Rebound height/cm
80
Impact time/0.001s
19
2
10
Mean
80.8 80.8 81.4 82 82.6 82.8 82.8 83.4 84
82.1
20
Uncertainty of height=0.1cm
3
20
4
20
5
20
6
23
7
21
8
21
9
21
25
21
Uncertainty of time=0.001s
Mean height = (80.0+80.8x2+81.4+82+82.6+82.8x2+83.4+84)/10 = 82.1+0.6cm
Uncertainty =
4
 0.6
2 10
Mean impact time = average time =(21+0.9) 10-3s
Uncertainty =
6
 0.9
2 10
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Observation
The size of the squash ball increased as temperature increased.
At high temperatures >80 oC, the surface of the squash ball became rough as some of
the rubber skin of the squash ball was boil away.
Analysis
The impact time against the temperature:
Time of impact 0.001s-1
25
20
15
10
5
Fig.5
0
0
20
40
60
80
o
Temperature of ball C
100
120
-1
Unlike my hypothesis, the result of the impact time of the ball showed no obvious
change when temperature increased. Moreover the pattern of the trend was not the
way I thought where it was hypothesized to increase as temperature increase.
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The graph of rebound height against temperature:
Rebound height of ball cm-1
90
80
70
60
50
40
30
20
10
Fig.6
0
0
20
40
60
80
100
120
Temperature of ball oC-1
The rebound height showed obvious increase as temperature. The results fit with the
hypothesis. The rate of increase of rebound height was quite constant from
temperature 20 o C to 80 o C. Then it started to decrease from temperature 80 o C to
100 o C.
At the time of impact, the force diagram of the ball is like this:
Force acted by the ground
Gravitational force
Fig.7
There were two forces acting on the ball, one is the normal force acted by the ground,
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the other one is the gravitational force acted by the earth. Since net force of the
ball 
m (v  u )
m(v  u )
 mg
, therefore the force acted by the ground 
t
t
Temperature of
squash ball / o
20.2
30
40
50
60
70
80
90
100
7.9
8.4
8.7
9.1
9.5
9.9
10.1
10.2
10.2
C
Average force
acted on the
squash ball by
the ground /N
The graph of average force acting on the ball by ground against temperature of the ball
12.00
10.00
Average Force
8.00
6.00
4.00
2.00
Fig.9
0.00
0
20
40
60
80
100
Temperature
From the graph of force acted on the ball against temperature. I found that the highest
increase rate of force occurring at temperature at around 20-30o C, high increase rate
continued from 20-65 o C. The rate of increase slowly decreased as it approached
temperature greater than 70 o C and finally showed no change around 100 o C. By
120
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drawing a line of symmetry from the top of the trend line, we could observe that the
highest average force the ground acting on the ball to be about 10.2N.
Discussion
Average force
As stated , the graph showed a maximum average of ~10.2N. It suggested that if the
velocity of the squash ball is hold constant, the average force that can be exerted to a
squash ball by a stationary impacting surface will be at maximum when temperature
around 95o C.
However the average force will not drop to zero when temperature drops to absolute
zero. Since the average force acted on the ball by the ground 
m(v  u )
 mg , it is
t
always >0 because the velocity of the ball is changing. According to the Newton’s
first law of motion, every body continues on it state of rest of uniform speed in a
straight line unless acted on by a nonzero force. At the point of impact, the ball
accelerates upward. The only force that points upward is the normal force by the
ground. Although there may be a possibility that the ball drops and sticks to the
ground at extreme low temperature, causing the △t to be infinite, but still there is the
opposing force acts by the ground again the weight of the ball. So the average force
by the ground must at least equal to 9.81x0.023 which is ~0.23N.
In addition, the rate of increase of average force acted by the ground is believed to fall
at the lower temperature. As shown in the graph above, the trend line is pointing
toward zero at temperature>-273. We have explained that the trend will not be zero
even when the temperature is -273. One possible way will be a turning point located
somewhere between -273 to 20o C. And if there is a turning at that certain point, the
rate of increase must be lower at that point.
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Rebound height
The rate of increase of rebound is quite constant until at 80 o C it decreased.
Theoretically the trend line will approach 130cm when temperature goes to infinity.
However it is not possible because squash ball will melt at high temperature. For the
low extreme, the squash may not rebound properly as the low temperature may
constrict the plastic layer of squash ball, making it deforms, losing it quality. It is just
a prediction and is difficult to perform in the school lab.
Impact time
The impact time showed no relation with the range of temperature set for experiment.
The set up may not be sensitive to sense the different.
Relation of force and energy at the impact
The potential energy of the ball was changed to kinetic energy before the impact;
some of the energy was lost to the air friction. At the impact, some of the kinetic
energy was transferred to heat energy of the ground and the ball. Some of it was
transferred to the sound energy. It lost his energy and rebounded to a lower height.
Those energy did lose in the impact was transferred to build up the shear modulus
(elastic energy) of the ball. The greater the elastic energy is the higher the ball
rebound.
Evaluation of the experiment
The experiment was considered successful as the data showed a direct relationship
between average force and temperature of the squash ball and a decreasing rate of
increase of average force when the temperature increases. However the impact times
collected were about the same which contradicted to my hypothesis. They were not
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even in sequence. That may due to the deficiency of the experimental set up. The foils
might still connect together a short time after the ball had left. Although the time is
short compared to the impact time, it changed for every impact. Therefore the impact
time I got was not in a trend but about the length. it may also due to the insensitivity
of the set up. After all I still managed to get the approximate impact time for the
calculation of average force.
For the rebound height experiment, it was quite good. There was little problem such
as the imprecise way of recording rebounding height by using eye observation.
On the whole, there were many systematic errors in both experiments that may affect
the results. For examples, the size of the ball increased as temperature increased, it
might have increased the impact time of the ball due to larger impacting area. It was
possible to be the reasons for the unsuccessful for the impact time results. This might
also affect the rebound height of the experiment.
The foil on the cutting board reduced the velocity before impact. It might have
reduced the rebound height and the impact time of the ball. The average force might
have been over estimated or under estimated depends on the extent of reduction of the
rebound height and impact time.
Heat lost rate increased as temperature of ball increased. That suggested that the
rebound height should be at the lower temperature. The rebound heights were over
estimated for the higher temperature. The impact times were also affected in a certain
degree.
Improvement
Renew the upper foil whenever it deforms to avoid over estimation of impact time.
However it may be inconvenient.
Change to another method in measuring the impact time. e.g. light sensor.
Physics Extended Essay
Chiu
30
Homing
For the measuring of the rebound height, we can ask a partner to observe the rebound
ball at the same level to improve accuracy. We can also do more repetitions for more
data.
Drop the squash balls directly without transferring them to the clamp on the stand.
However high delicacy is need to ensure the dropping height is right and not initial
force is applied to the ball.
Conclusion
The results of the experiment stated that there are changes of average force acted on
the ball by the impact surface with the velocity of ball hold constant. The maximum
average force will be reached at temperature around 95oC. This proved that the
hypothesis to be true. However the hypothesis for the impact time was not proven to
be true as the set up was appropriate enough to measure the data accurately.
Nevertheless, the result still showed the rate of increase in average force of impact at
different. By using the data we can know that at what temperature does the squash
ball work most effectively with the smallest force given. The data can also be useful
for the manufacture of squash ball.
Physics Extended Essay
Chiu
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Homing
Appendix
Fig
Description
1
Method of measuring with stroboscopic photos
2
Method of measuring with ultrasonic position sensor
3
Method of measuring with conduction sensor
4
Method of measuring with light sensor
5
Method of measuring with formula and calculation
6
Method of measuring with digital-video camera approach
7
The graph of rebound height against temperature
8
Average force at different temperature o f the squash ball
9
The graph of average force acted on the ball by the ground against the temperature
The graph of average force acting on the ball by ground against temperature of the ball
12.00
10.00
Average Force
8.00
6.00
4.00
2.00
0.00
0
20
40
60
Temperature
80
100
120