Physics (2007)
Sample assessment instrument and student responses
Extended experimental investigation: Sport
This sample is intended to inform the design of assessment instruments in the senior phase of
learning. It highlights the qualities of student work and the match to the syllabus standards.
Criteria assessed
• Knowledge and conceptual understanding
• Investigative processes
• Evaluating and concluding
Assessment instrument
The response presented in this sample is in response to an assessment task.
Extended experimental investigation in the context of sport
Task: Investigate how the Laws of Physics apply to a particular toy, game or sport.
The investigation will consist of:
•
review of relevant scientific literature
•
preliminary experiment that explores a physical concept linked to a game or sport
•
extended experiment that more closely models some aspect of the game or sport. This may
be a development of the simple experiment or an entirely new experiment.
Time: 4 weeks
Conditions: Word length 1000–1500 words
Instrument-specific criteria and standards
Student responses have been matched to instrument-specific criteria and standards; those which
best describe the student work in this sample are shown below. For more information about the
syllabus dimensions and standards descriptors, see www.qsa.qld.edu.au/1964.html#assessment.
Knowledge
and
conceptual
understanding
Investigative
processes
Evaluating
and
concluding
Standard A
Standard C
The student work has the following
characteristics:
The student work has the following
characteristics:
•
reproduction and interpretation of
complex and challenging motion and
energy concepts
•
reproduction of motion and energy
concepts, theories and principles
•
comparison and explanation of complex
motion and energy concepts, processes
and phenomena
•
explanation of simple motion and energy
processes and phenomena
•
linking and application of algorithms,
concepts and theories to find solutions in
complex and challenging motion and
energy situations.
•
application of algorithms to find solutions
in simple motion and energy situations.
The student work has the following
characteristics:
The student work has the following
characteristics:
•
formulation of justified significant
hypotheses which inform effective and
efficient design, refinement and
management of investigations
•
formulation of hypotheses to select and
manage investigations
•
safe selection and adaptation of
equipment, and appropriate application of
technology to gather, record and process
valid data
•
assessment of risk, safe selection of
equipment, and appropriate application of
technology to gather and record data
•
systematic analysis of primary and
secondary data to identify relationships
between patterns, trends, errors and
anomalies.
•
analysis of primary data to identify
obvious patterns and trends.
The student work has the following
characteristics:
The student work has the following
characteristics:
•
analysis and evaluation of complex
scientific interrelationships
•
description of scientific interrelationships
•
exploration of scenarios and possible
outcomes with justification of conclusions
•
description of scenarios and possible
outcomes with statements of conclusion/
recommendation
•
discriminating selection, use and
presentation of scientific data and ideas
to make meaning accessible to intended
audiences through innovative use of
range of language, diagrams, tables and
graphs.
•
selection, use and presentation of
scientific data and ideas to make
meaning accessible in range of formats.
Note: Colour highlights have been used in the table to emphasise the qualities that discriminate
between the standards.
Queensland Studies Authority December 2013 | 2
Student response — Standard A
The annotations show the match to the instrument-specific standards.
Temperature and bouncing balls
Introduction
reproduction and
interpretation of
complex and
challenging motion
and energy
concepts
When a ball bounces, it deforms and its kinetic energy is converted to
elastic potential energy (Madden, 2007). Since no ball is perfectly elastic,
this conversion is not perfectly efficient and so some energy is lost as
heat and sound. This means that a dropped ball will not return to its
original height.
The coefficient of restitution (e) is a measure of the change in velocity in a
collision. In the case of a bouncing ball, it represents the ratio of the final
speed (v2) and over the initial speed (v1):
𝑣2
𝑒=
𝑣1
For a bouncing ball:
ℎ
𝑒= � 2
ℎ
1
(Madden, 2007)
where h1 and h2 are the drop and rebound heights.
comparison and
explanation of
complex motion
and energy
concepts,
processes and
phenomena
linking and
application of
concepts and
theories to find
solutions in
complex and
challenging motion
and energy
situations
The temperature of the ball influences its coefficient of restitution. A
warmer ball will bounce higher than a cold one. There are two reasons for
this. In a hollow ball, the change in temperature causes a change in air
pressure within the ball. In an enclosed situation, air pressure is directly
proportional to temperature (Cook, 2011). Lowering the air pressure by
lowering the temperature has an effect similar to deflating the ball while
increasing the temperature has the effect of over-inflating (Portz, 2011).
Temperature also affects the elasticity of the ball.
Elasticity is a measure of how well kinetic energy is converted to elastic
potential energy; the less energy lost to heat and sound, the more elastic
the substance (Madden, 2007). Squash balls are made of rubber which is
made from long polymer chains. The molecules of these polymers are
tangled and stretch upon impact; however, they will only stretch for a
short time before atomic interactions pull them back into their original
shape, and thus transfer that elastic potential energy back to kinetic
energy (University of Virginia, 2011). When the ball is heated, the
molecules move more quickly and freely and are therefore able to stretch
more easily than those in a cooler ball. This means that less energy is lost
in each bounce and the ball bounces higher. Under cold conditions the
material can become so rigid that it becomes an ‘energy sink’ which
absorbs energy rather than transferring it (Portz, 2011).
Hypothesis
formulation of
justified significant
hypothesis
The higher the temperature of the squash ball, the greater the coefficient
of restitution as increasing temperature leads to increased elasticity and
air pressure.
Queensland Studies Authority December 2013 | 3
discriminating
selection, use and
presentation of
scientific data and
ideas to make
meaning accessible
to intended
audiences through
innovative use of
range of diagrams
Figure 1: Apparatus
selection and
adaptation of
equipment, and
appropriate
application of
technology to
gather, record and
process valid data
Notes on the method:
•
•
Yellow dot squash balls were used.
Video-analysis software was used to calculate drop and bounce
height.
Ball temperature was altered by immersion in a cold/hot water bath.
effective and
efficient design,
refinement and
management of
investigations
•
discriminating
selection, use and
presentation of
scientific data and
ideas to make
meaning accessible
to intended
audiences through
innovative use of
range of tables
Results:
selection and
adaptation of
equipment, and
appropriate
application of
technology to
gather, record and
process valid data
Refinement of the method has been documented
fully in a journal that is not included here.
Table 1: Coefficient of restitution of squash balls at varying temperatures
Temp
(°C)*
(±2)
Drop Height (m)
Bounce Height (m)
Coefficient of Restitution
(±0.05)
(±0.05)
(±0.03)
Trial
Trial
Trial
Av.
1
2
3
1
2
3
1
2
3
trial
3.61
3.47
3.54
0.90
0.96
0.90
0.50
0.53
0.50
0.51
5
3.22
3.61
3.75
0.43
0.43
0.41
0.37
0.35
0.33
0.35
15
3.71
3.65
3.65
0.49
0.55
0.53
0.36
0.39
0.38
0.38
25
3.72
3.69
3.68
0.85
0.77
0.77
0.48
0.46
0.46
0.46
35
3.41
3.62
3.64
1.10
1.09
1.12
0.57
0.55
0.55
0.56
45
3.67
3.66
3.60
1.27
1.14
1.17
0.59
0.56
0.57
0.57
* Temperature of water bath
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Figure 2: Coefficient of Restitution over Temperature (Linear Function)
discriminating
selection, use and
presentation of
scientific data and
ideas to make
meaning accessible
to intended
audiences through
innovative use of
range of graphs
0.70
Coefficient of Restitution
selection and
adaptation of
equipment, and
appropriate
application of
technology to
record and process
valid data
e = 0.0063T + 0.306
R² = 0.9555
0.60
0.50
0.40
0.30
Graph plotting software
has been adapted to show
an anomaly and
uncertainty bars
0.20
0.10
0.00
0
10
20
30
Temperature (°C)
40
50
Figure 3: Coefficient of Restitution over Temperature (Cubic Function)
systematic analysis
of primary data to
identify
relationships
between patterns,
trends, errors and
anomalies
Coefficient of Restitution
0.70
e = -1E-05T3 + 0.0008T2 - 0.0099x + 0.3779
R² = 0.9997
0.60
0.50
0.40
0.30
Graph plotting software has been
adapted to perform polynomial
regression analysis
0.20
0.10
0.00
0
10
20
30
Temperature (°C)
40
50
Note: In Figures 2 and 3, yellow point represents the initial trial assumed
to be at 25 °C.
Discussion
The coefficient of restitution of the squash balls varied between 0.35 and
0.57 as shown in Table 1. The coefficient was observed to increase as
temperature increased.
In fact, Figure 2 demonstrates a linear trend between coefficient of
restitution and temperature. The correlation of these data is strong,
2
demonstrated by the R value of approximately 0.96 which is very close to
perfect correlation. The slight lack of correlation could be due to the
uncertainty in the data as the trend line lies between the uncertainty bars
of each data point. Uncertainty in the temperature is due to the
assumption that the squash balls will be at the same temperature as the
water bath. Uncertainty in the coefficient of restitution values comes from
the fact that software used to measure distances requires human
judgements to be made about bounce heights.
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From the trend equation on Figure 2, e = 0.0063T + 0.306, it appears that
for each degree Celsius of temperature increase, the coefficient of
restitution increases by 0.0063. The trend line also suggests that at 0°C,
the coefficient of restitution would be 0.306; a reasonable prediction.
However, it is not expected that this linear trend would continue
indefinitely as ball’s elasticity has a theoretical maximum and minimum;
the maximum being perfect elasticity with a coefficient of restitution of 1
(i.e. the ball bounces back to the drop height) and the minimum being no
elasticity (i.e. the ball does not bounce), with an e value of 0. Therefore
the trend is only valid for the range 0 to 1.
systematic analysis
of primary data to
identify
relationships
between patterns,
trends, errors and
anomalies
analysis and
evaluation of
complex scientific
interrelationships
comparison and
explanation of
complex concepts,
processes and
phenomena
effective and
efficient design,
refinement and
management of
investigations
However, it is possible that a more appropriate model is a cubic one, as
shown in Figure 3. This function matches the data even more closely than
2
the linear function, with an R value of 0.9997. This trend suggests not
only a theoretical maximum and minimum value, but also physical limits. It
is possible that at the ball’s minimum coefficient of restitution, which
according to the model occurs around 0.36, temperature has little
influence and thus there is little change from 0°C (predicted to have a
coefficient of restitution of 0.36) to 15°C. From this point to approximately
35°C, temperature has a much greater influence shown by the almost
linear increase before the ball reaches it physical maximum rebound
ability with a coefficient of restitution of approximately 0.58 and once
again plateaus. However, the cubic function produced would be valid only
for a defined domain slightly outside that shown in Figure 3. At
temperatures below 0°C the cubic experiences a sharp increase, which
does not fit with the expected trend. Similarly, at temperatures greater
than 45°C the trend declines sharply; far too sharply to be explained as
the ball reaches a coefficient of restitution of 0 at only approximately
74°C. It would be necessary to complete further testing with temperatures
greater than 45°C in order to verify this trend.
The positive correlation between temperature and coefficient of restitution
is expected, as outlined in the Introduction. However, explaining possible
cubic model is more difficult and falls outside the scope of this
experiment. It could be that the squash balls are made of a material that
has a maximum and minimum elasticity and that these were reached
within the ranged tested, thus producing the flattening out shown in Figure
3. It is also possible that there is a more complex relationship between the
pressure within the ball and temperature, which could have influenced the
trend. This could be explored by using solid balls, thus eliminating the
influence of pressure on the experiment. Further experimentation is
necessary to more accurately chart the trend beyond the temperatures
tested and to determine the trend’s causes.
Initially, the ball at room temperature (estimated 25°C) was dropped
without being placed in the water/ice bath. The results that were produced
by this test were anomalous with both functions plotted (refer to Graphs 1
and 2). This anomaly was identified during the investigation, and thus
trials were performed with 25°C squash balls that were soaked in water.
This eliminated the anomaly, and the dry ball was found to have a
coefficient of restitution more than 10% higher than the wet. This is
probably because soaking resulted in the ball being surrounded by a layer
of water which absorbed some of the force and thus the ball did not
bounce as high. Other than this there are no anomalies, as all data points
are within 10% of their expected values.
A significant limitation of this experiment was the limited range of
temperatures tested. Given more time, more temperatures up to at least
100°C should be tested to provide more detail about the observed trend.
Queensland Studies Authority December 2013 | 6
exploration of
scenarios and
possible outcomes
Another extension would be to test different types of squash balls to
determine their coefficients of restitution. The balls used in this experiment
were yellow dot balls. These are often referred to as “super slow” balls,
probably due to their low coefficient of restitution. It would be expected
that double yellow dot (extra super slow) balls would have an even lower
coefficient of restitution at room temperature and that green (slow), red
(medium) and blue (fast) balls would have higher coefficients. It would
also be interesting to determine if these balls responded similarly to
changes in temperature.
Conclusion
justification of
conclusions
The results collected support the hypothesis that an increase in
temperature of a squash ball leads to an increase in its coefficient of
restitution. Both equations modelled, e = 0.0063T + 0.306 and
3
2
e = −1×10 −5T + 0.0008T − 0.0099T + 0.3779, had regression
coefficients over 0.95.
Bibliography
Cook, D 2011, Air Pressure, Newton, viewed 6 October 2011,
http://www.newton.dep.anl.gov/askasci/wea00/wea00073.htm
Madden, D et. al 2007, Physics: A contextual approach, Heinemann,
Melbourne
Portz, S 2011, Does the temperature of football affect how far it will travel
when kicked/hit, PhysLink, viewed 5 October 2011,
http://www.physlink.com/education/askexperts/ae469.cfm
University of Virginia Physics Department, 2011, The Effect of
Temperature on Bouncing a Ball, viewed 5 October 2011,
http://galileo.phys.virginia.edu/outreach/8thGradeSOL/EffectofTemper
ature.htm
Queensland Studies Authority December 2013 | 7
Appendix
To calculate the coefficient of restitution:
For Trial One at 5°C,
𝑒= �
linking and
application of
algorithms to find
solutions in
complex and
challenging motion
and energy
situations
𝑒= �
ℎ2
ℎ1
0.43
3.22
𝑒 ≈ 0.37
(Note: these calculations were performed using formulas in a spread
sheet.)
Anomaly Calculation
Percentage difference between coefficient of restitution of wet and dry
balls at 25°C
𝐷𝑟𝑦 − 𝑊𝑒𝑡
× 100
𝑊𝑒𝑡
0.51 − 0.46
× 100
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (%) =
0.46
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (%) ≈ 10.9
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (%) =
Uncertainty calculation (example)
For Trial One at 25°C,
0.05 0.05
+
� × 100% = 7%
3.72 0.85
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = �
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 7% × 0.48 = 0.03
This uncertainty will be considered typical for this experiment.
Figure 4: Software output
Queensland Studies Authority December 2013 | 8
Indicative response — Standard C
The annotations show the match to the instrument-specific standards.
Comments
Title: How Heat Affects Tennis Ball Bounce Height
Theory:
The effects studied in this EEI are, how heat affects the bounce height of
a tennis ball, and terminal velocity with tennis balls. The techniques used
are, dropping a tennis ball from the same drop height, heating a tennis ball
to the correct temperature, and using technology to help with results.
Explanation of terms:
reproduction of
motion concepts
formulation of
hypotheses to
select and
manage
investigations
selection of
equipment, and
appropriate
application of
technology to
gather and record
data
Terminal Velocity, this is the maximum speed an object can fall due to
earth’s gravitational pull, it may vary between weight and how smooth the
object is.
Hypothesis: it is believed that heat absorbed into a tennis ball will affect its
bounce height.
Equipment used:
1 Fluke mini IR thermometer with a range of -50°C to 530°C and is
accurate to .1°C
1 Regular woolworth’s tennis ball
1 Ronson mini electric oven with a temperature range of 150°C to 280°C
1 Kelvinator opal freezer with a temperature range of -30°C to -5°C
1 Faber Castle permanent maker
1 Fujifilm camera
Queensland Studies Authority December 2013 | 9
Comments
Analysis:
application of
algorithms to find
solutions in
simple motion
and energy
situations
These are the results of the bounce height from 200cm drop.
selection, use
and presentation
of scientific data
and ideas to
make meaning
accessible in
range of formats
Table 1: this table shows the different bounce heights with different
temperatures, also the table shows the percentage the ball bounced back
from the starting height.
Graph 1: this graph shows the increase in bounce height compared to the
temperature.
analysis of
primary data to
identify obvious
patterns and
trends
This graph shows that the ball bounce height decreases after 70°C thus
proving that 70°C is the optimum temperature for bounce height in tennis
balls. This was expected because after a certain amount of heat the tennis
ball must start to become not as firm and start to become almost “soggy”.
As you can see from these results the bounce height is slowly increasing
until the temperature reaches 70°C, this is when the ball starts to
decrease in bounce height. It has come the conclusion that after 70°C the
ball starts to lose elasticity instead of gaining more. This makes the ball
‘soggy’ or softer which makes the ball bounce less high.
Queensland Studies Authority December 2013 | 10
Comments
description of
scientific
interrelationships
reproduction of
energy concepts,
theories and
principles
explanation of
simple energy
processes and
phenomena
description of
scenarios and
possible
outcomes with
statements of
conclusion/
recommendation
The initial drop height of the tennis ball needed to be controlled because if
it had changed then the initial gravitational potential energy of the ball
would have changed; this would have changed the bounce height of the
tennis ball. A smaller initial gravitational potential energy would be
expected to provide a smaller bounce height. The ball drop height was
controlled by ensuring with the ruler drawn on the wall that the ball started
off at 200cm above ground where the ball would bounce for all the tests.
The main uncontrolled variable was the heat of the room in which the
heating and the dropping of the tennis ball took place, this would affect the
pressure inside the tennis ball and how fast the tennis ball decreased in
temperature during the drop. It is known from the gas equation that
pressure and temperature are directly proportional. Therefore if the
temperature on the testing day was cold then the pressure inside the
tennis ball would decrease quicker.
One source of scientific error was the starting drop height of the tennis
ball, the tape measure was quite old therefore it may have shrunk a small
proportion of the ink on the tape may have been off which would make for
inaccurate data. In future it would be better to cut a block of wood that was
exactly 200cm long and place it on a secure wall that was levelled by a
spirit level or other levelling device. Another error may include the camera
and the timing mechanism built into the camera. This would give
inaccurate readings in the overall results. In the future it would be wise to
use a higher quality video recorder and/or lens. Another scientific error
that may have occurred was that the laser thermometer may have been
badly calibrated during manufacture or the distance between the
thermometer and the tennis ball could have influenced the reading on the
laser thermometer. In the future if possible buy a new laser thermometer,
this would ensure it was calibrated to the exact temperature.
Conclusion:
This experiment was a success it got valid results. This is shown by
reading the graph and analysing the table of results, it is also shown that
the bounce height starts to drop after 70°C. The temperature which gives
the optimum bounce height is 70°C, this is proven by looking at the data
which shows that the bounce height drops after 70°C.
Acknowledgments
The QSA acknowledges the contributions of St Aidan’s Anglican Girls’ School and Gilroy Santa
Maria College, Ingham in the preparation of this document.
Queensland Studies Authority December 2013 | 11