This investigation will be looking at what factors affect the performance of a squash ball (in terms of how high it bounces).

Paul Dunn Physics Coursework Helsby High School

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Squash Ball Investigation

Aim

This investigation will be looking at what factors affect the performance of a squash ball (in terms of how high it bounces).

My personal aim is to investigate exactly what effect temperature has on the bounce of a squash ball.

Introduction

When a squash ball is held above a surface, the ball has potential energy. The amount of potential energy (measured in Joules (J)) depends mainly on two factors: the mass of the ball and the ball’s height above the surface. The higher the ball and the greater the mass of the ball, the more potential energy it possesses. When the ball is allowed to drop and travel through the air a rule called the Law of Conservation of Energy takes place. This law establishes that through the process of the ball being dropped, energy is neither gained nor lost, only transferred from one form to another, in this case from potential energy to kinetic energy.

When the ball collides with the floor, the ball becomes deformed (changes shape or ‘flattens’). If the ball is elastic, it quickly returns to its original form and rebounds faster of the floor. The ball pushes the floor and the floor pushes back on the ball, causing it to rebound. Solid objects have well-structured molecules and atoms that line up in an even pattern and give the object a fixed, specific shape. A solid’s molecules never move closer together or further apart. The object may break, but the molecules never move - an incompressible object. Gases, like air, (inside the ball) have less organized molecules. Gases take the shape of the containers that they fill, expanding or contracting to fill that container. A gas can be expanded or compressed: as the squash ball bounces off the floor, the part of the ball in contact with the floor is pushed upwards whilst the rest of the ball is still travelling downwards, resulting in the ball flattening slightly. The material is pliable - it can bend. The compressed ball has less volume than the original uncompressed ball but as the ball completely bounces of the floor, the gas in the ball acts in a similar way to a spring, returning the ball to it’s original shape.

Prediction

Now I can begin to explain my prediction that increasing the temperature of a squash ball will affect its bounce. A theory linked with this prediction is the Kinetic Theory. The Kinetic Theory deals with molecules vibrating and bonds breaking as they receive more energy. In the case of a squash ball, the air molecules are moving and colliding inside the ball pushing against the surfaces with which they make contact. The air molecules, bouncing around inside the ball, push hard enough on the walls of the round ball to enable it to keep its shape, even after it hits the floor. These small pushes, over the entire surface, are defined as pressure. The pressure is maintained by the constant collisions of air molecules. The pressure inside the ball depends on the speed at which the air molecules are travelling and how often they hit the inner walls of the ball - the more collisions that occur in the ball, the greater its air pressure. When the ball is heated therefore, the air molecules inside it will possess more energy, move faster and collide more frequently. This will result in more collisions of the air particles with the inner surface of the ball consequently increasing the ball’s overall air pressure.

As the air pressure within the ball increases, the ball is more able to keep its shape when it comes into contact with the floor than it would be if it had a lower air pressure - constant, rapid collisions of the air molecules inside the ball help maintain the shape of the ball better at a higher pressure. Because the ball deforms (or flattens) less, it loses less sound and heat energy when it comes into contact with the floor and therefore retains more energy resulting in the ball being able to bounce higher. When the ball is cooler or at a lower temperature, the air pressure inside the ball is less - the air molecules have less energy, move slower and collide less frequently resulting in the ball deforming (flattening) more as it hits the grounds and resulting in greater loss of heat and sound energy. This means the ball has less energy to use during motion and is therefore unable to bounce as high as balls warmed to a greater temperature.

Having reflected on the principles discussed above, I predict that as the squash ball is heated, the height of bounce will increase to a point where the temperature rises to such an extent that I would expect the reaction to produce the same results over and over (providing that that specific temperature is not too high that the squash ball proceeds to melt). Conversely as the squash ball is cooled the height of bounce will decrease. I also predict that the graph line will begin to straighten into a horizontal line after a certain time, as after a certain temperature the results will become less distinguishable and the ball may also begin to melt (obviously resulting in a ‘stickier, less bouncy’ ball). This melting process would eventually take place because the atoms would gain so much energy that they would break free from bonds with other atoms changing the solid into a liquid.

Preliminary Work

Preliminary work has to be completed in order to determine the final experimental method and how it will be conducted. This work helps to decide appropriate measurements that need to be taken during the experiment to make results more reliable, sensible and accurate and also to ascertain appropriate testing period times.

During preliminary testing, I needed to decide from what height the squash ball should be dropped. The final height needed to give a large ‘bounce back’ height and produce few inaccuracies. In order to do this, a range of heights was tested from 25cm to 200cm:

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Having evaluated the results, I believed that a fixed height of one metre would be appropriate with the resultant heights covering a greater range than if a fixed height of say 50cm was used. On the other hand, if I dropped the ball from 2 metres it would not only be awkward to reach that high but the results would cover too great a range and the resultant graph would become impractical. In fact, any height over one metre would be difficult to measure and consequently may produce less accurate results.

The next set of preliminary results I collected involved the temperature variable (the independent variable):

From these results, I could see that any temperature under the standard room temperature of 20ºC would be ineffective if used in the final experiment as all the results were too close together. Temperatures above 20ºC seemed most suitable and I therefore chose to begin my experiment at a temperature of 20ºC and conclude it at a temperature of 100ºC (perhaps reaching the final temperature in steps of 10ºC).

Variables and Fair Test

To make the test a fair one, certain variables have to be fixed at a constant otherwise the results would not be accurate or conclusive. All the variables listed will be kept constant apart from the temperature variable -the variable under investigation.

Force used to Drop Ball:

According to the amount of force applied when the ball is dropped, it will bounce higher or lower. An automated ‘ball-dropping’ process, with the ball being mechanically dropped from a given height would be most suitable. This would completely eliminate the possibility of any human error. Unfortunately however, with no such equipment being available the ball will have to be dropped by hand from the fixed height, with no force applied, allowing gravity to pull the ball to the surface below. This is the approach I intend to use in relation to this variable to ensure the fairest possible results.

Pressure:

Squash balls all contain air and are not always at exactly the same pressure. This could affect the test as it could make the ball lighter or heavier so this should be kept constant by using the same ball right through the experiment.

Height of Drop:

As discovered in preliminary experiments, the greater the height from which the ball is dropped, the higher it will bounce back - at different heights the ball possesses more/less potential energy, gains more/less kinetic energy concluding in a harder/softer impact with the surface below, producing a higher/lower bounce. Throughout the experiment, the height will be kept at a constant. At each temperature the ball will be dropped three times from the same fixed height to ensure a fair result.

Equipment Usage:

The same equipment should be used throughout the experiment i.e. the same surface (reasons discussed above), same metre rule etc. Also, one individual will be appointed to read off values from the metre rule for the bounce back height of the ball as different people will approximate the separate height values differently making the results slightly anomalous.

Material of Ball:

This variable affects the bounce of a ball in a number of ways:

According to what material it is made of, its molecules may melt and reduce the height of the bounce earlier or later than other balls.

Some materials may insulate better (heat-wise), e.g. hard rubber, meaning that those balls would bounce higher than balls made from materials such as soft plastic (which is a poor insulator), as they will not loose the heat energy as quickly.

Some materials may have a molecular structure that allows a lot of space for air molecules which would result in an increase of air pressure within the ball affecting its bounce back height (the higher the air pressure, the higher the bounce back height).

To ensure balls are tested fairly, I will use the same ball throughout the experiment ensuring that the material of the ball is not different and therefore giving more accurate, more reliable results.

Ball Mass:

The heavier an object is, the faster its acceleration rate. Knowing that the mass of the ball will affect the results, I will use the same ball throughout the experiment to ensure that its acceleration rate will be constant throughout the experiment.

Ball Diameter:

A larger ball with a larger diameter will have a bigger surface area meaning that when it hits the floor, more of its area will be in contact with the floor at impact thereby affecting its bounce back height. For this reason, to make the test fair, the same ball will be used throughout the experiment to eliminate this problem.

Surface Type:

Different surfaces have different exterior textures. Changing the surface during the experiment may make the test unfair - some surfaces will allow a neat bounce whereas other surfaces will alter the bounce (possibly due to indentation in the surface, bumps etc). If a ball were bounced on a soft surface, the surface may cushion the ball, removing its kinetic energy therefore making the bounce weaker. To make the test fair, all testing will be done on the same bench surface throughout the experiment.

Ball Temperature:

As the temperature of a squash ball increases, the atoms in the ball vibrate more as due to them having more energy to move about in a freer fashion. Consequently, when the ball is dropped and hits the surface, the atoms push each other way forcing the ball to bounce higher. When the temperature is lowered the opposite occurs - the atoms have less heat energy, the particles vibrate less and the ball compresses much more easily.

The variables listed below are known as the input variables. Temperature is the variable I intend to investigate. Since this is the variable I am testing, I can now refer to it as my Independent Variable. The Dependent Variable is the bounce height of the ball - it is dependent on the ball temperature in the experiment.

Type of Surface
Material of Ball
Mass of Ball
Diameter of Ball
Temperature of Ball
Pressure of Air in Ball
Height of Drop
Force used to Drop Ball
Equipment

Method

Having conducted the preliminary tests, certain measurements were established which would be suitable for use in the final method. By using these measurements, a good set of results relating to the bounce back height of a squash ball should be achieved. I am optimistic that the method below will supply me with clear, accurate results.

Assemble all equipment.
Using tongs to hold the ball under the water, heat the ball to the desired temperature (20ºC is the first temperature to test).
Accurately measure temperature with the use of a thermometer.
Set up a metre rule in a clamp (to keep ruler stationary).
Drop the ball from the one metre height.
Record maximum rebound height.
Repeat steps 3 to 6 three times for each temperature.
Arrange collected data from the whole experiment in a table.

To make the test fair, I will reheat the ball for each individual drop of the ball. Whilst heating the squash ball, it will be held under the water using a pair of tongs to keep it from surfacing above the water. The temperature will be measured accurately by using a thermometer. The height of the squash ball bounce will be measured as accurately as possible (to the nearest centimetre) using a metre rule. For every temperature the ball will be dropped three times and the average of the three results calculated.

Safety

To make this experiment as safe as possible I will need to make sure that all bags and stools are safely under benches so that no one is able to trip over them. I need to wear goggles at all time as they protect the eyes from hot water as well as the Bunsen flame. The main safety points are listed below:

Place glassware such as beakers away from edges of tables.
Wear protective eyewear at all times.
Tie back long hair.
Place all bags under benches.
Use an orange Bunsen flame when not in use.
Do not leave hot water in beakers near electrical equipment such as sockets.

Apparatus

1 metre rule
Clamp to hold the metre rule
Large beaker
Stop clock
Squash ball
Area of floor space to bounce ball on
Bunsen Burner
Thermometer
Pair of tongs

The large beaker will contain 200ml of water.

Results

To calculate an average height, I added up the results from the three different experiments for each temperature row and divided by the result by three.

Conclusion

Looking at the graph it is clear that as the temperature is increased, the height of bounce of the ball also increases proving the first part of my prediction correct. As the ball is heated, the increased energy affects the air molecules inside it, giving them more energy to collide and travel faster. With this increase of air pressure within the ball, the ball deforms (flattens) to a lesser extent when it comes into contact with the floor than it would if it had a lower air pressure - constant, rapid collisions of the air molecules inside the ball help maintain the shape of the ball better at higher pressure. Due to the ball deforming less, it loses less heat and sound energy and consequently retains more energy to be put to use in the motion field, resulting in it bouncing higher.

When observing points on the graph in relation to the line of best fit, it is quite evident that the increase in temperature is not proportional to the height of bounce. For example at 200C, the ball’s bounce back height is 19.7cm – according to the line of best fit, the ball’s bounce back height should be nearer to 18cm.

From analysis of the results I can conclude my prediction was in the main correct and that:

The ball’s bounce increases as the temperature increases. This is explained by the Kinetic Theory.
At higher temperatures the ball does in fact stop bouncing as high due to excessive heat melting the atoms of the ball (as more and more energy is given to them to break their bonds), resulting in a curve on the graph proving this part of my prediction to be correct.

The graph line did not begin or go through the origin, as there is still molecular activity happening. Only if I look at negative temperature values will I be able to see exactly where the molecular activity stops/begins.
That I was wrong in thinking that the effect of doubling the temperature would double the bounce of the ball. In fact, when the temperature doubles the bounce less than doubles due to significant energy loss through heat and sound as the ball hits the surface.

Ideally, heights above one metre would have produced better results with even larger bounce back heights of the ball but because we were limited to perform the test on a bench surface, measuring any height above one metre would have proved too difficult as a device similar to a ladder would have been needed to help drop the ball. This was not practical in the lab where I was conducting the experiment.

From this experiment and the resultant graph I have learnt that when the temperature of a squash ball is increased, the bounce height also increases.

When the squash ball is dropped, and is in contact with the surface, it is compressed and the particles of gas are pushed closer together. This increases the pressure inside the squash ball; consequently the particles of gas cause the ball to harden further, causing the squash ball to bounce higher. Therefore when the temperature is decreased the reverse effect happens.

Evaluation

I will evaluate the evidence obtained from my experiment in different ways, covering the accuracy and reliability of results and examining as to how the results could be made more precise by making alterations to the method.

The quality of the results I have collected appears to be good as the graph produced shows that nearly all points plotted follow the positive trend line of best fit, supporting my prediction that states ‘as the temperature of the squash ball increases, it’s bounce will also increase’. Since all the points are situated close to the line of best fit, it can be concluded that they are of a high quality.
Since the experiment was conducted in a classroom by pupils and wasn’t automated by a machine, inevitably some results were likely to finish slightly away from the best-fit line. However as they are situated fairly close to the best-fit line, they are not anomalies, merely less accurate results.
Every effort was made to make the testing of the ball fair. One individual ball was used throughout the experiment resulting in consistency with regard to material, internal pressure, external measurements and mass. The same surface was used and the ball was dropped (with no force being exerted) from the same height each time. The experiment was conducted in the same lab with air resistance and altitude remaining constant. Keeping these variables as constant as possible was not easy but ensured that the results obtained from the experiment were more precise, reliable and fair.

My method made sure that all results would be accurate by testing the ball’s bounce at each temperature three times so that a more conclusive average could be established, lessening the effect of any anomalies. I can confidently say that the results achieved were precise, especially taking into consideration that the process wasn’t automated and therefore possessed the chance of human error.

There were however elements that could have affected the results:

The mass of the ball - because the ball was heated underwater in a beaker, water droplets may have remained on the ball when it was bounced adding to its mass and resulting in a difference in its acceleration speed – the greater the mass, the higher the rate of acceleration.
Room temperature - because the lab I worked in was crowded with students (most using heating equipment such as Bunsen burners) as the experiment progressed, the room increased in warmth. This may have affected the air molecules in the room, which in turn could have affected the speed of the squash ball when dropped due to the change in air resistance.
Force given to the ball when dropped – I believe that the method I applied to drop the ball from one metre above the surface was as fair as it could possibly have been. However, some drops may have had more force applied to them than others resulting in the ball achieving a greater bounce back height.
The surface on which the ball was tested - Ideally, it would have been best to have as smooth a surface as possible on which to test the ball, so ensuring that indentations could not change the angle of the ball’s bounce. However, because we were using an older bench surface, there were inevitably scratches, marks, dips and other such distortions on the surface that may have affected the bounce back height of the ball. Using an immaculately smooth surface would decrease the chance of anomalies, as it would ensure that the ball bounced onto the surface at the same angle each bounce, thereby producing more accurate results.
Bounce height reading - Even though a metre rule was used to ensure that the height of a bounce could be measured to the nearest centimetre, when the ball was bounced it bounced back at a fast speed. For that reason, to read the height to which the ball bounced back proved very difficult. All efforts were made to ensure that the reading was as accurate as possible. Once again, I believe that the procedure could have been made much more efficient by using an automated machine to measure each bounce back height.
Water temperature – This variable proved to be difficult to control as the water temperature inside the glass beaker fluctuated, rising and dropping rapidly.
Height at which ball dropped - A one metre rule set up on the bench via a clamp stand to hold the ball at exactly a metre. Some drops of the ball may have been done at a distance slightly less/more than a metre affecting the first bounce height of the ball.

I think that the most obvious reason as to why most of the results are reliable is that wide ranges of results were collected - in total, nine different temperatures were each tested three times. This greatly reduced the chance of inaccurate results affecting the overall average. However, there were various problems that I encountered during the experiment. One such problem occurred as I was recording my results: no human eye would be able to accurately record the height of the responding bounce of the ball. This restriction meant I was forced to record each of my results to the nearest centimetre. A solution to this could be to use a video camera.

The method used to record results was obviously good since the majority of the results were consistent. There were no anomalous results in the results table for this experiment and consequently the graph shows trends that were expected. Even though the method did not supply any false results, it could still be further improved upon. The bounce height of the ball was measured alongside a metre rule and was recorded by the human eye. This procedure unavoidably involved human error since it is extremely hard to accurately measure the bounce height with the naked eye. If I were to repeat this test I would use light gates that are able to measure the height that the beam of light had been broken. The equipment is technical but the final results would be far more accurate. If all the equipment could have been more advanced, for example electronic water baths, lasers to measure heights, machines to drop the ball with the same force, electronic thermometers to record temperatures, light gates etc, the results would have been far more accurate and the chance of producing anomalous results would decrease further.

Extension Work

For future investigations I could use balls made of different materials to see how they would affect the bounce of the ball.
I previously mentioned that if the whole procedure were automated using a machine, the ball would drop at exactly a metre, applying the same force whilst measuring the bounce height using a laser or a similar device. These points would all help to make the results even more accurate as human error would be eliminated - if an electrical water bath were used, keeping the temperature of the water would be far easier and would eliminate the possibility of human error when reading thermometers, as the water bath would accurately heat the water to the right temperature. It would also keep the temperature constant ensuring that the ball receives exactly the amount of heat required for the next test. To make the measuring of the heights even more accurate, we could use a camera that captures images at very high speeds, for example a repeat flash camera.
If enough balls of the same type were available, I could repeat the experiment, using a different ball for each temperature so that the same ball would not become overheated by constantly re-heating it. Every ball is different though so that procedure could provide inaccuracies in itself.
Other further work could include investigating at what temperature molecular activity ceases. This would have to be done by an automatic device because at negative temperatures the ball would bounce less than 10 cm making it extremely difficult to measure its height with accuracy. I could try increasing the number of temperatures used within the range, experimenting degree by degree so that a clear, gradual change in bounce height could be seen, proving that even at negative temperatures there is still molecular activity in progress.
A greater number of repeats at the same temperature could gain more precise results, for example, I used three bounces and created an average from those three so using more than three bounces would produce an even more accurate average still.
I could create a separate investigation involving how a ball’s pressure increases/decreases when heated. I could aim to find out if a relationship exists between the heights to which a squash ball bounces based on internal air pressure. Then I could analyse and plot the results to see what the trend is (if there is a trend) and how it compares with that of the ball’s bounce and the temperature.
Balls of different materials could be heated and then tested to see how their material affects their bounce height.
This experiment involves a variety of variables all of which could be tested if there were no time constraints:

What results are obtained if different sized balls are heated to the same temperature and dropped from the same height?
To what angle would the surface have to be altered to significantly affect the height of the bounce?
Does heating the ball before changing the angle of the surface affect how it bounces off the surface?

Endless other such experiments could be conducted at different altitudes, in areas of different atmospheric pressure etc.

Bibliography

GCSE Physics Guidebook - Puffin
The Way Things Work - Michael Roberts
Various Science Revision Guides - Lonsdale
GCSE Bitesize Revision Website
GCSE Bitesize Revision Programmes (BBC2)

I obtained most of the information that I have included from my teacher and exercise book. I also collected information from several science textbooks and computer encyclopaedias. I found a small amount of information from various Internet sites similar to the GCSE Bitesize Revision Website I have listed above.