Investigating the Effect of Temperature on the Height a Squash Ball Bounce

Investigating the Effect of Temperature on the Height a Squash Ball Bounce

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Investigating the Effect of Temperature on the Height a Squash Ball Bounce

Aim: To investigate the effect of temperature on the height a squash
ball bounces.

Prediction: I think that the higher the temperature of the squash
ball, the higher the squash ball will bounce. I think that as the
temperature doubles so will the height of the bounce. I think that
they will be directly proportional.

Scientific Knowledge:

If you drop a ball onto a hard floor. It will rebound, but even the bounciest ball will not bounce back to its starting position.



The ball behaves like a spherical spring. When the ball hits the floor it exerts a force on the floor and the floor exerts a force on the ball. This force compresses the ball. The force that the ground exerts on the ball does work on the ball, since it is in the same direction as the displacement. The gravitational potential energy the ball has before it is dropped is converted into kinetic energy while the ball is falling and then into elastic potential energy as the force from the ground does work on the ball. But because the material the ball is made of is not perfectly elastic, friction converts some of the energy into thermal energy.



The elastic potential energy stored in the ball when it has lost all its kinetic energy is converted back into kinetic and gravitational potential energy. However the thermal energy is not converted back.



The ball on the floor acts like a compressed spring. It pushes on the floor with a force proportional to its displacement from its equilibrium shape. The floor pushes back with a force of equal size in the upward direction. This force is greater in size than the weight of the ball. The resultant force is in the upward direction and the ball accelerates upward. When the ball's shape is the shape it has when it is sitting still on the floor, (just slightly squashed), there is no resultant force. When the ball's shape relaxes further, the resultant force is acting downwards. But it already has velocity in the upward direction, so the ball keeps on going upward until its speed has reached zero.



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Because some of its initial gravitational potential energy has been converted into thermal energy it does not regain its initial height. So this is why even the bounciest ball will not bounce back to its starting position.



A particular ball is characterized by its coefficient of restitution, which is the ratio of its rebound speed to its collision speed just above the surface of the perfectly hard floor, (A perfectly hard floor is a floor that does not move itself).



The coefficient of restitution depends on the material the ball is made of. It is always smaller than one. The coefficients of restitution are a ration of speeds. To find the ration of the outgoing to the incoming kinetic energy we use a real surface which is not perfectly hard. This means that they distort when hit by the ball. They store energy themselves, and return some of it to the ball as it rebounds.



Squash balls are made of 2 pieces of a very durable, high quality
rubber compound. These are glued together and filled with compressed
air.

The characteristics of a squash ball are:

* As the temperature of the ball rises, so does its bounce

* Temperature rises due to repetitive impact and force of impact: i.e.
the harder the ball is hit and the longer it stays in play will result
in a higher temperature and consequently a livelier bounce. This is
why you need to 'warm up' a squash ball before a game.

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 thermal energy), 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 energy and therefore have low resilience.

Squash balls, are made of a rubber compound, and have quite a low
resilience. 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 heat has two effects: the air
inside the ball, which was originally at normal atmospheric pressure,
becomes 'pressurised', and the rubber compound from which the ball is
made becomes more resilient. Both these reasons result in the ball
bouncing higher. 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. It also explains why squash balls are
designed to have too little resilience at room temperature and
therefore why they need warming before play.


The actual temperature of the ball reached in play varies according to
two main factors:

* The temperature of the court

* The ability of the players.

The point at which the ball temperature reaches equilibrium is an
excess over the surrounding temperature of the court. So, for example,
if the court is at only 5oC, the ball may only reach 35oC.

Variables:

* Investigated variable: Temperature

* Dependant variable: The height the squash ball bounces

* Controlled variables: size and type of squash ball, height squash
ball is dropped from, the way in which the ball is dropped.

You need to keep the controlled variables the same to ensure that your
experiment is fair and also so that you can compare your results.

Apparatus:

* Yellow dot squash balls

* Water bath

* Meter ruler

* Thermometer

Method:

1. Warm a squash ball in the water bath at 30oC.

2. Fix the meter ruler to the wall.

3. Once the water bath has reached 30oC, leave the ball in the water
for 2 minutes, so that it can acclimatize to the temperature.

4. Take the squash ball out of the water bath and drop it from one
meter.

5. Record the height the ball bounces to.

6. Repeat steps one - five for the temperatures of: 35oC, 40oC, 45oC,
50oC, 55oC and 60oC.

7. Repeat the whole experiment twice more, for accuracy.

8. Record your results in a table.

Preliminaries:

We carried out preliminary experiments to test our method, to ensure
that it works. We tried to measure the height of the bounce using data
loggers, since we thought that they would give us more accurate
results. However it was not very successful because the ball had to be
at least 40cm away from the data logger before it could record the
height. Another problem was that the sensor beam was too wide spread,
which meant that the sensor picked up any other changes in height.
After having to abandon using the data loggers, since the results it
gave were inaccurate, we tried to measure the height of the bounce by
sight. However we found that this was also inaccurate. Our solution to
the problem was to record the drop and bounce with a digital camera
and then watch the film back in slow motion. This allowed us to be
accurate with our readings.

Diagram:

Results:

Height of squash ball bounce in cm.

Temperature oC

1st attempt

2nd attempt

3rd attempt.

Average

30oC

22 cm

22 cm

23 cm

22.3 cm

35 oC

27 cm

26 cm

25.5 cm

26.2 cm

40 oC

29 cm

30 cm

29 cm

29.3 cm

45 oC

34 cm

33 cm

32.5 cm

33.2 cm

50 oC

38 cm

37 cm

37 cm

37.3 cm

55 oC

41 cm

41 cm

40 cm

40.7 cm

60 oC

46.5 cm

45.5 cm

44.5 cm

45.5 cm

Conclusion:

From looking at both my graph and my results I can see that, as the
temperature increases so does the height of bounce.

My results for 30oC and 60 oC show that the results were directly
proportional, to a certain degree of accuracy. The average height of
bounce at 30 oC was 22.3 cm and at 60 oC was 45.5 cm.

The reason why the ball never bounced back to the height that it was
dropped from, i.e. one meter, was because as the ball fell through the
air and as it hit the floor, the ball lost some of the gravitational
potential energy that it started with, before it was dropped, as
thermal and sound energy. However the reason why the height of the
bounce increases as the temperature increases is because as the
temperature of the ball has increased, this heat has two effects: the
air inside the ball, which was originally at normal atmospheric
pressure, becomes 'pressurised', and the rubber compound from which
the ball is made becomes more resilient. These both result in the ball
bouncing higher.

I think the results support my prediction because they show that with
the highest temperature, 60oC, the height of the bounce was greatest,
45.5 cm, and with the lowest temperature, 30oC, the height of the
bounce was lowest, 22.3 cm.

I think that my results are reliable enough to draw and support my
conclusion because I did the experiment at each temperature three
times.

Evaluation:

I think that the results of my experiment were reliable because I
repeated the experiment an additional two times to the first time. I
repeated the experiment to make sure that my results were similar each
time and therefore reliable. I don't think that I had any anomalous
data because the results of each of the three attempts were similar
with a maximum of 2 cm between them. I felt that 2 cm was not enough
difference to repeat the experiment for a fourth time, since there was
a degree of error in the results. The error in the results was caused
by the fact that, although we filmed the drop so we could watch it
back to see the height of the bounce, there was still human error in
the reading of the results. Also there was no way that we could not be
completely sure that the squash ball was the actual temperature of the
water bath. To try and ensure that the ball was as close to the
temperature of the water as possible we left the balls in the water
for 2 minutes to acclimatise once the desired temperature was reached.
We controlled the height that the ball was dropped from, because the
further away the ball from the ground, the higher the bounce. We also
controlled the type of squash ball used, yellow dot, because different
types of squash balls behave in different ways, some are more bouncy
than others. However overall, I feel that my results were of good
quality and were reliable because we did our best to make sure that
the experiment was fair.

Although the experiment gave me reliable results and I feel the method
was suitable for a classroom based experiment, I do think that it
would be necessary to make modifications to the experiment if it was
to be done on a large scale. This would be to eliminate any
inaccuracies in the measurements if the height of the bounce and the
temperature of the squash ball.

To further my own experiment in the classroom I could now investigate
the effect of the size and type of squash ball, height squash ball is
dropped from, the way in which the ball is dropped.
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