Via the bounce height of a squash ball under various temperatures

The data that I will be analysing in this report is based upon how a rubber squash ball’s bounce height increases/decreases as the gas in the core of the ball rises in temperature.

The results from this experiment are shown below:

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Temperature (�C)

Bounce height (cm)

Test 1

Test 2

Test 3

16

23

24

28

38

43

43

42

50

53

53

53

67

68

68

67

84

72

72

73

100

76

75

75

The mean can be calculated by adding all the test results for a temperature and then dividing by 3:

Temperature (�C)

Mean

16

23 + 24 +28 = 75/3 = 25cm

38

43 + 43 +42 = 128/3 = 42.6 = 47cm

50

53 + 53 + 53 = 159/3 = 53cm

67

68 + 68 + 67 = 203/3 = 67.6 = 68cm

84

72 + 72 + 73 = 217/3 = 72.3 = 72cm

100

76 + 75 + 75 = 226/3 = 75.3 = 75cm

Method:

The ball is initially dropped from rest at 1.5m, bearing in mind that the drop is measured and recorded from the bottom of the ball.

The distance in which the ball bounces to is recorded by eyesight.

The temperature is raised by placing the squash ball into set water baths (varied by different thermometer levels as shown in the results table) for a period of time, until the ball is the same temperature as the bath.

This was carried out 3 times for each range of temperatures.

Background physics:

The property that allows the squash ball to bounce is called resilience. This is the ability to regain the ball’s original shape quickly once it has distorted after falling to the ground. When the ball hits the ground, some of its energy is lost through heat

It is therefore the resilience of the squash ball’s material that changes with temperature to create various bounce heights. This is because the particles of gas inside of the squash ball move with a greater energy when the temperature is increased. Thus increasing the chance of more particle collisions and increasing the pressure on the inner sides of the ball. As the pressure gets greater, the resilience will increase with it.

?The warmer the ball, the higher the bounce.

Analysis:

By assuming that the squash ball has a fixed volume and mass, the previous results should relate to the pressure law that says that the pressure inside of the ball is directly proportional to the absolute temperature (�K).

Pressure ? Absolute temperature

e.g. If the temperature is doubled then the pressure will also double.

In this case we do not know the pressure inside of the ball, so by assumption, the bounce of the ball will be directly proportional to the pressure in the ball provided that the volume stays the same.

The total increase in bounce height can be calculated using +273 Kelvin to find a percentage by using the following method:

Increase (temperature range)

+ 273 X 100

Original

% Increase in the bounce of the ball

% Increase in absolute temperature

75 – 25 = 50

50/25 X 100 = 200%

16 + 273 = 289

100 + 273 = 373

373 – 289 = 84

200 + 16 = 216

84/216 X 100 = 39%

Evaluation:

From the calculations used above, the results do not seem to fit the pressure rule.

The increase in bounce height was 200% and the increase in absolute temperature was 39%

200/39 = 5

This states that the bounce height went up about 5 times more than the temperature.

From the previous graph you can see that when the ball exceeds about 67?C (341?K), the gradient decreases. The pressure law should be correct so I have been led to believe that the cause for this lower gradient interfering and in turn causing inaccurate calculations is either:

* The material of the ball itself, rubber.

This must have been because the rubber somehow lost some of its resilience. Maybe by a deformation of the ball shape so that the balls pressure could not increase at its rate beforehand. The rubber itself must of hindered the energy lost on the moment of impact with the ground. However, deformation at such a low temperature (68?C) shows that the ball is not of very good quality and it may have been aged or very worn.

* The measuring technique.

Eyesight is not the most accurate or reliable method of measuring the bounce considering that a high perception is needed. E.g. a video camera with play/pause functions.

* That the apparatus was altered somehow

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