Extended experimental investigation: Sport

Transcription

1 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 words

2 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 Knowledge and conceptual understanding Investigative processes Evaluating and concluding Standard A reproduction and interpretation of complex and challenging motion and energy concepts comparison and explanation of complex motion and energy concepts, processes and phenomena linking and algorithms, concepts and theories to find solutions in complex and challenging motion and energy situations. formulation of justified significant hypotheses which inform effective and efficient design, refinement and management of investigations safe selection and adaptation of equipment, and appropriate technology to gather, record and process valid data systematic analysis of primary and secondary data to identify relationships between patterns, trends, errors and anomalies. analysis and evaluation of complex scientific interrelationships exploration of scenarios and possible outcomes with justification of conclusions 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. Standard C reproduction of motion and energy concepts, theories and principles explanation of simple motion and energy processes and phenomena algorithms to find solutions in simple motion and energy situations. formulation of hypotheses to select and manage investigations assessment of risk, safe selection of equipment, and appropriate technology to gather and record data analysis of primary data to identify obvious patterns and trends. description of scientific interrelationships description of scenarios and possible outcomes with statements of conclusion/ recommendation 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

3 Student response Standard A The annotations show the match to the instrument-specific standards. reproduction and interpretation of complex and challenging motion and energy concepts Temperature and bouncing balls Introduction 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 (v 2 ) and over the initial speed (v 1 ): For a bouncing ball: e = v 2 v 1 e = h 2 h 1 (Madden, 2007) where h 1 and h 2 are the drop and rebound heights. comparison and explanation of complex motion and energy concepts, processes and phenomena linking and concepts and theories to find solutions in complex and challenging motion and energy situations formulation of justified significant hypothesis 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 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

4 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 technology to gather, record and process valid data effective and efficient design, refinement and management of investigations 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. Refinement of the method has been documented fully in a journal that is not included here. discriminating selection, use and presentation of scientific data and ideas to make meaning accessible to intended audiences through innovative use of range of tables selection and adaptation of equipment, and appropriate technology to gather, record and process valid data Results: 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 trial Av * Temperature of water bath Queensland Studies Authority December

5 Figure 2: Coefficient of Restitution over Temperature (Linear Function) selection and adaptation of equipment, and appropriate technology to record and process valid data discriminating selection, use and presentation of scientific data and ideas to make meaning accessible to intended audiences through innovative use of range of graphs Coefficient of Restitution e = T R² = Graph plotting software has been adapted to show an anomaly and uncertainty bars Temperature ( C) 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 e = -1E-05T T x R² = Graph plotting software has been adapted to perform polynomial regression analysis Temperature ( C) 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, demonstrated by the R 2 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. Queensland Studies Authority December

6 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 From the trend equation on Figure 2, e = T , it appears that for each degree Celsius of temperature increase, the coefficient of restitution increases by 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. 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 the linear function, with an R 2 value of 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

7 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. justification of conclusions Conclusion 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 = T and e = T T T , had regression coefficients over Bibliography Cook, D 2011, Air Pressure, Newton, viewed 6 October 2011, 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, University of Virginia Physics Department, 2011, The Effect of Temperature on Bouncing a Ball, viewed 5 October 2011, ature.htm Queensland Studies Authority December

8 Appendix To calculate the coefficient of restitution: For Trial One at 5 C, e = h 2 h 1 linking and algorithms to find solutions in complex and challenging motion and energy situations e = 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 Difference (%) = 100 Wet Difference (%) = Difference (%) 10.9 Uncertainty calculation (example) For Trial One at 25 C, Relative uncertainty = % = 7% 0.85 Absolute uncertainty = 7% 0.48 = 0.03 This uncertainty will be considered typical for this experiment. Figure 4: Software output Queensland Studies Authority December

9 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. reproduction of motion concepts formulation of hypotheses to select and manage investigations selection of equipment, and appropriate technology to gather and record data Explanation of terms: 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

10 Comments algorithms to find solutions in simple motion and energy situations Analysis: 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

11 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: Acknowledgments 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. 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