# Investigating the Bounce of a Squash Ball

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Investigating the Bounce of a Squash Ball

This investigation is associated with the bounce of a squash ball. I
will be investigating 4 different types of squash balls, which have
different, bounce properties and compare them to each other and relate
them to why each different type of squash ball is used. The
relationship will be associated with how different balls are used at
different levels of proficiency in the game of squash i.e. the squash
balls that don't bounce much will probably used at a less proficient
level whereas the balls with the most bounce will be used at
professional level. The different coloured squash balls I will be
using are; white, yellow, red and blue, and I will be finding out what
the difference is between them.

Background Knowledge
--------------------

Pressure

The three scientists Boyle, Amontons and Charles investigated the
relationship between gas, volume and temperature. Boyle discovered
that for a fixed mass of gas at constant temperature, the pressure is
inversely proportional to its volume. So in equation form this is:

pV = constant if T is constant

Amontons discovered that for a fixed mass of gas at constant volume,
the pressure is proportional to the Kelvin temperature. So in equation
form this is:

p µ T if V is constant

Shown below this is represented on graphs in (oC) and (K).

[IMAGE] P

[IMAGE]

[IMAGE] q/oC

-273 0

[IMAGE]

P

0 T/K

Charles discovered that for a fixed mass of gas at constant pressure,
the volume is proportional to the Kelvin temperature. So in equation
form this is:

V µ T if p is constant.

The Equation Of State

These three gas laws that were proposed by Boyle, Amontons and Charles
can be summarised as follows:

For a fixed mass of gas

pV = constant if T = constant (i)

p/T = constant if V = constant (ii)

V/T = constant if p = constant (iii)

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### Popular Essays

These three laws can be used to show that the following equation
exists:

p1V1 = p2V2

T1 T2

This means for a fixed amount of gas an initial state p1, V1 and T1,
for a fixed mass of gas, will give a final state p2, V2 and T2. The
equations (i), (ii) and (iii) are obtained from this general equation
by considering what happens when the following happen:

(i) T1 = T2

(ii) V1 = V2

(iii) p1 = p2

The amount of trapped gas molecules is used to tell us the magnitude
of the constant. If there is 1 mole of gas being used then the
constant is R but if two moles of gas is being used the volume that
the gas would occupy would be double, so if there are n moles of gas
this can be shown by the following equation:

pV = nR

T

This is the equation of state for an ideal gas. R is called the
(universal) molar gas constant. A certain mass of a substance will
tell us how many moles of that substance we will have but it is
different for each substance due to its Relative Atomic Mass. 12g of
Carbon-12 will be 1 mole of carbon, the following equation is used to
calculate this:

Number of moles = mass of substance

Relative Atomic Mass

Now 1 mole of any gas will contain 6.022 x 1023 molecules and this is

The Kinetic Theory Of Gases

The kinetic theory rest essentially upon two hypotheses:

* That there are such things as molecules, and that a gas is a
collection of molecules

* That these molecules are in constant random motion, and that heat
is a manifestation of this molecular motion.

Brownian motion is the most direct visual evidence for the second
hypotheses, where smoke particles are seen to move around randomly as
they are struck by air molecules. The idea of a molecule that is of a
dense spherical body of great elasticity and rigidity, like a steel
ball bearing is useful in understanding the kinetic theory. Below are

* The molecules are of infinitesimal size, i.e. the volume of the
gas molecule is negligible compared with the volume occupied by
the gas.

* The intermolecular forces of attraction are negligible except
during a collision.

* The duration of a collision is negligible compared with the time
spent in free motion between collisions.

* A molecule moves with uniform velocity between collisions this
means gravity is not taken into account.

* The collisions between molecules and between walls are perfectly
elastic.

* All collisions obey Newtonian mechanics.

The reason the squash ball bounces higher when the pressure increases
is due to the following equation: -

P = F

A

This equation is fairly self-explanatory in explaining how the ball
bounces higher when pressure is increased. The area remains constant,
as volume isn't changed so more pressure means that there will be more
force and it is then this force that it applied in the rebounding of
the squash ball so the more force there is the higher the ball
bounces. So this equation combined with the other equation can form
the following equation: -

P1V1T2 = F

T1V2 A

More Physics Of Balls

When you hold a ball above a surface, the ball has potential energy.
Potential energy is the energy of position, and it depends on the mass
of the ball and its height above the surface. The formula for
gravitational potential energy is:

G.P.E.= Weight X Height = mgh

Where m is the mass of the ball measured in kg, g is the gravitational
acceleration constant of 9.8 m/sec2 , and h is the height of the ball
in m. As the ball falls through the air, the potential energy changes
to kinetic energy. Kinetic energy is energy of motion. The formula for
kinetic energy is:

K.E. = 1/2 mv2

Where m is the mass is kg and v is the velocity in m/sec2 . Both
potential and kinetic energy have units of Joules (J).

As the ball falls through the air, the Law of Conservation of Energy
is in effect and states that energy is neither gained nor lost, only
transferred from one form to another. The total energy of the system
remains the same; the potential energy changes to kinetic energy, but
no energy is lost. When the ball collides with the floor, the ball
becomes deformed. If the ball is elastic in nature, the ball will
quickly return to its original form and spring up from the floor. This
is Newton's Third Law of Motion- for every action there is an equal
and opposite reaction. The ball pushes on the floor and the floor
pushes back on the ball, causing it to rebound. Neglecting friction
for the ball we're using, the potential energy before you drop the
ball will be equal to the kinetic energy just before it hits the
ground.

On a molecular level, the rubber is made from long chains of polymers.
These polymers are tangled together and stretch upon impact. However,
they only stretch for an instant before atomic interaction forces them
back into their original, tangled shape and the ball shoots upward.

You may be wondering why the ball does not bounce back to its original
height. Does this invalidate the Law of Conservation of Energy? Where
did that energy go? The energy that is not being used to cause motion
is changed to heat energy, sound energy, air friction, to internal
forces within the ball and to friction between the ball and the ground
on impact. After playing a game of tennis or racquetball, you will
notice that the ball is warmer at the end of the game than at the
beginning because some of the motion energy has been changed to heat
energy. Because bouncy balls have tightly linked polymers, most of the
energy is transferred back to motion so little is lost to heat or
sound energy, and the ball bounces well.

Resilience

Ball bounce is important in many sports. The ideal height of bounce
varies for different sports with the consistency of bounce from one
part of the field to the other being of most interest. "Ball bounce
resilience" (BBR) is used as a measure of bounce and is the ratio of
the height the ball bounces to the height from which it is dropped.

Incidentally, "ball bounce resilience" is equal to the "coefficient of
restitution" squared, and then expressed as a percentage. For example,
if a ball is dropped from 3 meters, hits the ground, and bounces up 1
meter, the BBR is 33.3%.

The resilience of rubber balls is one of their most important
characteristics. This is because the
resilience of the ball material determines the "liveliness" and
"bounce" of the ball. Resilience (R) is the ratio of the work
recovered to the work required to deform the rubber.

The resilience of a compound is normally measured using a standard
rebound test. The rebound test carried out on squash balls at present
involves balls being bounced on a hard surface. The same balls are
conditioned first to 23oC and then to 45oC and dropped from a height
of 100 inches onto a concrete floor (which in both cases must be at
21-25oC). At 23oC the balls should rebound at least 12 inches and at
45oC between 26 and 33 inches to comply with regulation standards.

The Tg of rubber is related to its resilience at room temperature.
Rubbers with a low glass transition temperature have a high resilience
and rubbers with a high Tg have a low resilience.

To begin with, raw rubber from Malaysia is delivered to the Barnsley
factory in 'bales' of about 25kg - sufficient to make about 1,200
balls. In its natural state rubber is very stiff and difficult to
work, so it is first 'masticated' to a softer consistency. A variety
of natural and synthetic materials and powders are then mixed with the
rubber to give it the required combination of strength, resilience,
and colour as well as to enable it to cure (or 'vulcanise') later in
the process. The manufacturer's 'recipe' is, of course, a no less
closely guarded secret than that of Coca Cola, and different
combinations of ingredients (as many as 15 are used, including
polymers, fillers, vulcanising agents, processing aids, and
reinforcing materials) produce fast (blue dot), medium (red dot), slow
(white dot), and super slow (yellow dot) balls.

The resulting compounds are warmed and loaded into an extruder, which
forces them (rather like a mincing machine) through a 'die'. A
rotating knife cuts the extruded compound into pellets, which are then
cooled. The pellets, which now have a putty-like consistency, are
dropped into a hydraulic press which subjects them to a pressure of
1,100lb per in2 and a temperature of 140-160 C for 12 minutes. The
heat causes the material to cure and so retain its shape. Each pellet
makes half a ball, known as a 'half shell'. 50% of these are 'plains'
and 50% 'dots'. The mould for the dots has a pin in the bottom to
create the tiny dimple which takes the different coloured paints that
indicate the balls' speed. When the half shells are removed from the
press, the excess compound (called 'flash') must be cut away before
the dots can be glued to the plains to make complete balls.

First the edges of the half shells are roughened ('buffed') by a
grinding wheel to provide a key for the adhesive. The buffed edges are
then coated with rubber solution and a measured amount of adhesive is
applied in three coats at thirty minute intervals. Both the adhesive
and the dot paint are produced in a similar way to the rest of the
ball; the adhesive, for example, is also made from raw rubber mixed
with various powders before being ground, broken down into a fine web
and 'wet mixed' for several hours with a solvent. At last the half
shells can be stuck together - an operation called 'flapping'.

The flapped balls are then put through a second moulding, heating and
vulcanising process, this time subjecting them to 1000lb per in2 for
15 minutes, to cure the adhesive. Further buffing, this time of the
balls' exterior, smoothes the join and gives the balls their
characteristic matt surface. After being washed and dried each ball is
inspected. This is one of the few operations which is still carried
out by hand, by a team of four ladies, the only other manual
buffing and washing, and, most importantly, testing.

The balls are tested at every stage in the process and those that are
unsatisfactory rejected. Those that pass are stamped with the Dunlop
logo, boxed in dozens, and shipped all over the world, but a sample of
them is given a final test to ensure that they conform to WSF
standards.

Testing Of The Ball

The current WSF Specification for the Standard Yellow Dot Championship
Squash Ballas it appears in Appendix 7 of the Rules of Squash dates
from October 1990, apart from a minor amendment made in July 1995, and
determines the permitted diameter, weight, stiffness, seam strength
and rebound resilience of the championship ball. No specifications are
set for other types of ball, "which may be used by players of greater
of lesser ability or in court conditions which are hotter or colder
than those used to determine the yellow dot specification". But how
are balls tested to ensure that they meet these specifications?

The testing procedure itself states somewhat confusingly that: "For
the purposes of inspection, balls manufactured from the same mix shall
be arranged in batches of 3000 numbers or part thereof manufactured in
one shift in a day." Fifteen balls are then chosen at random from each
batch and divided into three groups of five balls. One group is tested
for diameter, weight, and stiffness; another group for seam strength;
the third group for rebound resilience.

First the 15 selected balls must be left in the laboratory for 24
hours to 'condition' them to a temperature of 23oC. Their diameter,
measured perpendicular to the seam, must be between 39.5mm and 40.5mm,
and their weight between 23 and 25g. To be measured for stiffness the
balls are held between two plates with the seam parallel to the plates
and compressed at a rate of 45-55mm per minute. They are compressed by
20mm six times, the test measurement being made on the sixth
deformation only. The stiffness of a ball is calculated by measuring
the compressive force at the point where it has been deformed by 16mm
and dividing that by 16 to give a 'force per millimetre'. The result
must be between 2.8 and 3.6N/mm at 23oC. In other words, the force
required to compress the ball by 16mm (i.e. to just over half its
original diameter) must be between 44.8 and 57.6 Newtons.

The calculation of seam strength is even more complicated. "The squash
ball is first cut into two equal halves perpendicular to the plane of
the seam." Then two strips (one from each half of the ball)
approximately 15mm wide and 60mm (roughly half the circumference) long
are cut, with the seam running across the middle. The average width of
each strip is measured before it is pulled apart at a rate of
180-220mm per minute until the seam breaks. The force at the point of
breakage is divided by the average width of the strip to give a 'force
per millimetre', which must be at least 6N/mm. So if the average width
of the test strip is exactly 15mm, the minimum force required to break
the seam must be 90 Newtons.

Rebound resilience is simply a measurement of the height a ball
bounces off a hard surface. The same balls are conditioned first to 23oC
and then to 45oC and dropped from a height of 100 inches onto a
concrete floor (which in both cases must be at 21-25oC). At 23oC the
balls must rebound at least 12 inches; at 45oC between 26 and 33
inches. (The 1995 amendment was to these figures: previously the
rebound specification at 23oC was 16-17 inches and at 45oC 26-28
inches.)

Although a compression test is no longer required by the WSF - it was
deleted from the ball specification in September 1988 - Dunlop
continue to carry out a test in which loads of 0.5kg and 2.4kg are
applied to the ball and the resulting deformation measured. The
difference in deformation under the two loads used to be specified as
between 3 and 7mm, but Dunlop aim at between 4.5 and 5.5mm, just to be
on the safe side.

Ball Behaviour

Why does a squash ball bounce higher when it's warm?
In order for a solid material to be deformed, work has to be done on
it. For that work to be done, energy must be expended (in the case of
a squash ball, it is hit by a racket). Some of this energy is
dissipated (as heat, etc.), but some is stored in the deformed
material and is released when the material relaxes. The extent to
which a material stores energy under deformation is called
'resilience'. Some materials (like sprung steel) store a lot of energy
and are described as having high resilience; others (like putty) store
very little and therefore have low resilience.

Squash balls, being made of a rubber compound, are of fairly low
resilience. Unfortunately, the lower the resilience of an object, the
higher the proportion of the energy used in deforming it must be
dissipated. When a squash ball hits the racket strings and the wall
and floor of the court, some of this energy is transformed into heat
in the strings, wall, floor, and surrounding air and some into sound,
but most of it becomes heat in the ball itself. This has two effects:
the air inside the ball (which was originally at normal atmospheric
pressure) effectively becomes 'pressurised', and the rubber compound
from which the ball is made becomes more resilient. For both these
reasons, the ball bounces higher. Obviously, the ball does not
continue indefinitely to heat up; eventually equilibrium is reached
where heat loss to strings, wall, floor, and air is equal to heat
gained from deformation. This point is normally at around 45oC, which
is why the WSF's rebound resilience specification is calculated at
that temperature. It also explains why squash balls are designed to
have too little resilience at room temperature and therefore why they
need warming before play.

But why have balls of different speeds and how are they made?
The actual ball temperature reached in play varies according to two
main factors: the temperature of the court and the ability of the
players. The point at which the ball temperature reaches equilibrium
is in fact an excess over the ambient temperature of the court. So if
the court is at only 5oC, the ball may only reach 35oC.

On the other hand, even on a warm court, if the players don't hit the
ball hard or often enough to raise its temperature to that optimum 45oC,
the ball won't perform as it should. To compensate for either factor,
players will need to use a ball of higher basic resilience, i.e. a
'faster' ball. These are produced simply by making a different mixture
of polymers. More elastic polymers create higher resilience; more
viscous polymers lower resilience.

So how can you have a ball with 'instant bounce'?
For a ball not to need warming, it must either lose as much heat as it
gains during play and therefore remain at court temperature, or it
must be made of a material whose resilience is the same at any
temperature. It remains to be seen whether Dunlop's new Max Progress
and Max balls meet either of these criteria.

Sources For Background Knowledge

* Physics 1 (Cambridge Sciences)

* Physics In Perspective

* Google search on internet for Physics - squash ball resilience

Variables
---------

Temperature

Temperature is a big variable in affecting the bounce of a squash
ball. Temperature affects the pressure within the squash ball, which
affects how much it bounces; the kinetic theory is thus used. As
temperature increases the gas molecules gain more energy due to the
heat energy and it is converted to kinetic energy. The molecules, with
more kinetic energy, have more frequent collisions with other
molecules and the walls of the squash ball, thus pressure is
increased. The increase in pressure means that the squash ball will
bounce more.

Temperature is a good variable to use in the investigation, I can use
the information that I obtain to explain why players have to hit the
ball around for a bit to get it warmed up so it bounces better! If I
decide not to use temperature as a variable though it is vital I keep
the temperature constant.

Surface The Ball Is Dropped On To

This isn't a good variable to investigate, basically different
surfaces will affect the bounce, like a spongy surface will absorb the
bounce of the ball and you won't be able to tell the difference with
each of the different balls. A hard surface will have a different
affect on how the ball bounces, it will bounce more so this is a good
surface and I will probably keep this variable constant on a hard
surface.

Height Ball Is Dropped From

This variable is a good variable to investigate e.g. dropping it at
50cm then trying 100cm and seeing how this affects the bounce of the
ball. At higher heights the bounce will bounce further than at lower
heights as the ball will have gained more velocity due to acceleration
due to gravity. If I decide not to use this variable though it will
need to be kept constant.

Rebound Height

This variable will be my dependant variable and will be used to find
out how the variable I will be using affect the bounce height of the
squash ball.

Decisions On Variables

The independent variable I will be using is temperature, I feel this
will give me good results to compare and I can do a good range of
temperature, which will give me varying results for a good conclusion.
The dependant variable I will be using is height, which will show the
bounce of the ball. Variables I need to keep constant are, the height
the ball is dropped from so I will just drop the ball from the same
height each time and also the surface the ball is dropped onto so I'll
use the same surface each time, which will be a hard surface.

Prediction
----------

I predict that as the temperature is increased the height the ball
bounces will increase. The reason for this is due to the temperature
having an effect on the pressure of the ball, which thus makes the
ball bounce higher. As the temperature increases there is heat energy
is available the gas molecules inside the ball absorb this energy and
convert to kinetic energy. This is the only way the energy can be
converted because gas molecules can't have potential energy, as there
are no intermolecular forces of attraction so it is converted to
kinetic energy. This kinetic energy means that the molecules move
around faster thus more frequent collision are made between the walls
of the ball and other molecules which creates more pressure thus the
ball bounces higher.

The equation that links pressure, volume and temperature is: -

p1V1 = p2V2

[IMAGE][IMAGE] T1 T2

This means that if the volume stays constant and temperature is
increased then the pressure must increase. The increase in pressure
means that the squash ball will bounce higher. Another equation can be
brought in here as pressure increase means a greater force is created
as the area of the ball remains the same; -

P = F

A

However the 4 different balls will obey this law but will differ in
bounce height at the different temperatures and also will show
different gradients in the area of proportionality in the graph. This
is because the balls have different resilience and this is achieved by
simply by making a different mixture of polymers. More elastic
polymers create higher resilience; more viscous polymers lower
resilience.

When the ball collides with the floor, the ball becomes deformed. The
ball is elastic in nature, the ball will quickly return to its
original form and spring up from the floor. This is Newton's Third Law
of Motion- for every action there is an equal and opposite reaction.
The ball pushes on the floor and the floor pushes back on the ball,
causing it to rebound. Neglecting friction for the ball, the potential
energy before you drop the ball will be equal to the kinetic energy
just before it hits the ground.

On a molecular level, the rubber is made from long chains of polymers.
These polymers are tangled together and stretch upon impact. However,
they only stretch for an instant before atomic interaction forces them
back into their original, tangled shape and the ball shoots upward.

My prediction for the shape of the graph is an s-shape, shown on next
page, this is because at the lower temperatures there is a slope off
from the graph because at this temperature the balls have little
resilience and thus don't bounce very high, but the balls have a
minimum bounce which means if you keep reducing the temperature the
affect temperature has, has little effect on the rebound height. This
principle is also applied at the higher temperatures where the graph
slopes off because at this high resilience the ball bounce
considerably higher than at the lower temperatures but if the
temperature keeps increasing it will have less and less of an effect
because the ball has a maximum bounce height.

[IMAGE]

Rebound

Height

(cm)

[IMAGE]

Temperature (oC)

Now my prediction for which of the balls will have the higher
gradients are those with the higher resilience which is the balls used
by the beginners who first start playing squash as the ball bounces
more it is easier to play and this is the blue ball. After this the
red ball followed by the yellow ball and finally the white ball.

Proposed Method
---------------

Firstly I will consider my heating method, to get down to the lower
temperature of 10oC I will use a beaker and ice and the squash ball
(diagram below).

[IMAGE]

For 20oC I will just use water to take the temperature down a little
from room temperature, which is slightly higher. For the rest of the
temperatures I will use a general heating method with a Bunsen burner,
heatproof mat, tripod, gauze, a thermometer to record the temperature
and a beaker with water and the squash ball to act as a water bath
(diagram shown on the next page). To get the ball to desired
temperature I will leave the ball in the water, the thermometer
showing the desired temperature, for 5 minutes so that I can be sure
that the temperature is the same all the way throughout the ball so it
will have an affect on the pressure. After I have done this I'm ready
to investigate the bounce of the squash ball, see next page for more.

[IMAGE]

I will use a metre stick that is held in an upright position and drop
the ball, using my hand, from a certain height then record how high
the ball bounces. I will take into account my eye being level in a
parallax for fair and accurate results (idea of eye being level is
shown below).

[IMAGE]

(Below shows a diagram of the apparatus)

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Preliminary Testing
-------------------

The first thing that I noticed was that by dropping it by hand it was
very hard to get from the height that I was dropping it then get down
to see how high the ball bounced. This meant I needed a method where I
could stay low down to see the bounce of the squash ball but release
the squash ball when I wanted it to. So I came up with the using some
tongs with a piece of string, the forceps to hold the ball then the
string to release the tongs so the ball drops. Also doing this method
means that it will just be the ball being dropped and no other forces
other then gravity acting on it as before I may have put some spin on
the ball making it bounce in a direction which would affect results.

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[IMAGE][IMAGE][IMAGE][IMAGE]

Squash Ball

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Tongs

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After doing this I found that I needed to take a rough bounce first to
see whereabouts the ball bounced then I could get my eye level in this
region so I will get a more accurate result for the rest of that test.
When heating the ball also I found that the ball floated and therefore
was not under the whole of the water thus not getting up to the
desired temperature so I used forceps to sink the ball into the water.

Drop Height

One of the aspects I needed to investigate in my pre-testing was the
height that I dropped the ball from, as this will need to be kept
constant to keep the investigation fair. Below is a table of results
to show how high the ball bounced when dropped from different heights
the temperature was 26oC.

Height Ball Dropped From (cm)

Bounce Height (cm)

20

4.00

40

14.00

60

19.00

80

28.00

100

32.00

As you can see at 100cm the ball bounced the highest this is because
the ball gained more velocity due to gravity as it was dropped from a
higher height. I decided to choose the 100cm because this will mean
that there will be a bigger difference between heights at different
temperature meaning that it will be easier to compare the different
balls.

How Many Temperatures

I feel to get enough points on a graph I need to do 8 different
temperatures, as a safety point I can't go above 80oC as the rubber
squash ball will start to melt. So I will do from 10oC - 80oC in 10oC
intervals. Below is a table of results to show the blue ball being
dropped from 100cm and different temperatures.

Temperature

(oC)

Rough

Test (cm)

Test 1

(cm)

Test 2

(cm)

Test 3

(cm)

Average

(cm)

40

38.00

40.00

41.00

40.50

40.50

60

48.00

50.00

51.00

52.00

51.00

80

60.00

61.00

61.00

60.00

60.67

As you can see from the results as temperature is increased the bounce
increases, and also a linear pattern can be seen suggesting it's a
proportional relationship. One of my fears was that the temperature of
the ball would drop rapidly so I would get a decrease in the bounce
height as I did each test but from these results I will be fine as
they are all consistent.

Precautions
-----------

Safety

As I'm dealing with hot water and heating apparatus I will wear safety
glasses so I don't scald or burn my eyes plus take care when handling
hot water. Also I will make sure there are no obstructions such as
chairs in my way.

Fairness

To keep the experiment fair I will only change the variable they I'm
supposed be changing which is temperature. This means that the height
that I drop the ball onto need to be consistent also that I keep my
eye level when doing this and also when taking results. Also when
taking results I must be consistent where I take the result from I
will take it from the bottom of the ball because this is the actual
distance the ball has bounced plus its easier to see this than taking
the result from the top of the ball.

Accuracy

To make the experiment accurate I will be using a thermometer to
record the temperature of the water and get it accurately to the
correct temperature. Also I will be recording to decimal places when
I've averaged them. Measuring the height is difficult however and to
get to a suitable degree of accuracy is hard that's why I'm dropping
the ball from the biggest height possible because this means if the
results are out then the other points being further apart can pull the
line of best fit better.

Reliability

To make the experiment reliable I will be taking 5 tests on each
temperature so I can be sure I have found the correct bounce height
and also I'm taking a rough bounce to start with so I can get my eye
level for the other results.

Method
------

Diagram

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Step By Step Procedure

1. Set up apparatus as shown in the diagram above

2. Get temperature of ball to 10oC

3. Bounce ball and record height once for rough result he 5 more
times.

4. Repeat steps 2 and 3 for the different temperatures

5. Repeat 2-4 for the other 3 balls

Analysis
--------

As you can see all 3 graphs have the general s-shape that I predicted
in the plan, there is a slope at the start at the lower temperatures
then a slope off at the higher temperatures, this is because at the
lower temperatures there is a slope off from the graph because at this
temperature the balls have little resilience and thus don't bounce
very high, but the balls have a minimum bounce which means if you keep
reducing the temperature the affect temperature has, has little effect
on the rebound height. This principle is also applied at the higher
temperatures where the graph slopes off because at this high
resilience the ball bounce considerably higher than at the lower
temperatures but if the temperature keeps increasing it will have less
and less of an effect because the ball has a maximum bounce height.

As the temperature is increases the height of the ball's rebound
increases. The reason for this is due to the temperature having an
effect on the pressure of the ball inside, which thus makes the ball
bounce higher. As the temperature increases there is heat energy is
available the gas molecules inside the ball absorb this energy and
convert to kinetic energy. This is the only way the energy can be
converted because gas molecules can't have potential energy, as there
are no intermolecular forces of attraction so it is converted to
kinetic energy. This kinetic energy means that the molecules move
around faster thus more frequent collision are made between the walls
of the ball and other molecules which creates more pressure thus the
ball bounces higher.

The equation that links pressure, volume and temperature is: -

p1V1 = p2V2

[IMAGE][IMAGE] T1 T2

This means that if the volume stays constant and temperature is
increased then the pressure must increase. The increase in pressure
means that the squash ball will bounce higher. Another equation can be
brought in here as pressure increase means a greater force is created
as the area of the ball remains the same; -

P = F

A

However the 3 different balls will obey this law but will differ in
bounce height at the different temperatures and also will show
different gradients in the area of proportionality in the graph as
shown on the graphs. This is because the balls have different
resilience and this is achieved by simply by making a different
mixture of polymers. More elastic polymers create higher resilience;
more viscous polymers lower resilience. So the blue ball for instant
will have a higher resilience due to having more elastic polymers and
the white ball has more viscous polymers so doesn't bounce as high.

When the ball collides with the floor, the ball becomes deformed. The
ball is elastic in nature, the ball will quickly return to its
original form and spring up from the floor. This is Newton's Third Law
of Motion- for every action there is an equal and opposite reaction.
The ball pushes on the floor and the floor pushes back on the ball,
causing it to rebound. Neglecting friction for the ball, the potential
energy before you drop the ball will be equal to the kinetic energy
just before it hits the ground.

On a molecular level, the rubber is made from long chains of polymers.
These polymers are tangled together and stretch upon impact. However,
they only stretch for an instant before atomic interaction forces them
back into their original, tangled shape and the ball shoots upward.

As you can see on my graphs they are all s-shapes, which means the
graphs confer with my original prediction and also I stated that the
blue ball would have a higher gradient due to having higher
resilience. (The gradients for each line are shown on the graph).

So now having investigated the squash balls I can now relate the balls
tp the game itself. Beginners will more than likely being using the
blue ball, this is because it has the higher resilience thus more
lively and bouncy so it will rebound of walls further making the game
easier to play. The reason it bounces away further is due to the more
elastic polymers it is made out of. The decrease in resilience of the
ball to the red ball just means a progression in performance
approaching an amateur stage where players have been playing for a
while and can play the game competently and the polymers this time
will be a little more viscous meaning the ball wont bounce as far. The
next ball would be the yellow ball and as I didn't have time to
investigate this I will give the assumption that the ball would have
less resilience again and more viscous polymers. Professional playing
will use the white ball as this has the least resilience and made out
of the most viscous polymers out of the 4 balls and this will have an
even smaller bounce. This makes it difficult for players as they are
constantly moving to get the ball and hit it with the racket.

Evaluation
----------

As a whole I am pleased with my results all points were close to the
line of best fit that I drew there were a couple of anomalous results
but not major and these w ere probably due to a slight distraction
whilst obtaining my results. The error bars show that my line of best
fit would have fitted within the error proximity meaning my error was
out because I couldn't measure the rebound to a high degree of
accuracy as it was hard to see where the ball bounced to as it was so
fast, my line of best fit goes through the +/- 0.5cm proximity meaning
the results I obtained were accurate and good which is pleasing. I
think the investigation went well as a whole but I wish I had had more
time to the fourth ball, which would be better to compare with the
other balls this would be an improvement for the future to allocate
more time to complete the collection of data. There were limitations
on the temperature also I couldn't go very high or very low with
temperatures and had to stay within a close proximity meaning I only
saw part of the graph which if I could of expanded temperatures may
have seen a different shape i.e. the line curving off more so I could
prove my theory easier.

Now the errors that could have occurred are the measuring of the
rebound height, I could only measure to 0.5 of a centimetre so the
error was +/- 0.5 cm, and the other error could have been the
measuring of the thermometer which could be read to 0.25 of a degree
so the error was +/- 0.25 oC. From this I can now calculate percentage
errors. Firstly for the rebound height my smallest rebound height was
8.1cm so:

0.5 x 100 = 6.25%

8.0

Now for the thermometer the lowest temperature was 10oC so:

0.25 x 100 = 2.5%

10

So the greatest source of error was measuring the rebound height and
it is over double the error than measuring the temperature. A new
method of trying to stop this error is to video record the experiment
up close so it can be stopped when the ball is at its highest point
and the correct measurement can be seen and will increase the
reliability of the data obtained.

I was pleased with my preliminary testing as I found some good new
aspects to add to my method there for instance using tongs at the top
of the metre stick to hold the ball in position, I got another metre
stick to measure that the bottom of the ball held at exactly 1 metre,
then using string to open the tongs which means I can have my eye at a
parallax to minimize one source of error because if my eye wasn't
level then the eye could be too low or too high: [IMAGE]

Also I was pleased with my idea of using holders, which attach to the
squash ball to hold it under water to stop it from floating meaning
the temperature would not be being applied to the whole of the squash
ball. Also I kept the ball in the water for sufficient time for the
water to heat the ball up to the desired temperature.

Sources of error could be due to the ball not being able to maintain
the correct temperature and an electric water bath would have been a
better method but this was also is a limitation, as we don't have many
at our sixth form. Really every piece of equipment including the tongs
surface the ball bounced onto would all need to be at the same
temperature for the experiment to work really accurately and fairly as
the ball gradually cooled down during the course of a test.

I feel I did enough temperatures to give me enough points for my graph
but I would like to have tried more temperatures either side of the
ones I did but there are limitations again here as for a safety reason
I cant go above 80oC as the rubber ball would start to melt and also
getting below 10oC is very difficult.

Improvements have already been stated but further testing I would like
to do is firstly the fourth ball, which I have already mentioned. I
would like to test the polymer materials of each ball individually
other than bouncing them i.e. stretching the materials.