In order to obtain results showing the correct trend in how the bounce height of a table tennis ball changes as the height from which it is dropped changes, a minimum of three records (at different heights) are required. However, the more records are obtained, the greater the accuracy is likely to be. It was decided that 20 centimetre intervals between recordings was the smallest distance that could accurately show a difference in bounce heights, so as many recordings will be taken as is possible with a 20 centimetre gap between each. We found that 20 centimetres is the lowest drop height we will be able to read a bounce height from (to a sufficient level of accuracy) and 172 centimetres is the highest due to the ceiling. We will take three recordings at every height in order to maximise accuracy (more would be even better, but we will be limited by the amount of time made available to us).
Apparatus:
- tape
- retort stand
- two clamps
- desk
- table tennis ball
- a hard area (i.e. not carpeted) of flat floor
- three metre rules
A table tennis ball will be dropped from heights at 20 centimetre intervals. Three drops at each height will be made and the results recorded. I will release the ball at each height and Jake Grave will look horizontally at the bottom of the ball at the peak of its bounce to measure its bounce height against the ruler behind it (as the bottom of the ball will hit the ground, we will drop it with the bottom of the ball at the measured mark, i.e. 20cm, 40cm, etc.). We will measure the height using metre rules stuck firmly together with tape, the second rule directly on top of the first. The lower rule will be taped to the side of a desk, exactly perpendicular to the floor; the second will be held in place by clamping it to a retort stand carefully positioned on the edge of the desk to ensure the rule is in line with the first. Care will be taken to keep them completely vertical throughout the experiment in order to measure the vertical drop of the ball as accurately as possible.
We decided that a human hand might not have the capability to maintain complete consistency in dropping the table tennis ball throughout the experiment. To overcome this problem, another clamp will be attached to the metre rule against which the drop and bounce heights will be measured. By setting the end which is not attached to the rule to the right size, the clamp will loosely grip the ball without deforming it. Therefore, by simply flicking the tightening screw which controls the width of the end of the clamp holding the ball, the clamp marginally loosens its grip on the ball, thereby releasing it.
The experiment will be conducted in a classroom, so there is a restriction as to how high it will be possible to drop the table tennis ball from. As the drop heights become progressively higher, eventually we will be unable to drop the ball 20cm higher than the last recording, so for the final recording we will drop the ball from the nearest centimetre mark under the ceiling (allowing for the height of the ball), which is 272cm.
For dropping the table tennis ball from between 2 metres and the ceiling (272cm) a third metre rule is required; however, there will not be room to place it directly on top of the second rule. Therefore, we will tape the third rule to the back of the second with the 21cm mark of the third rule exactly at the 100cm end of the second and take the 21cm mark as 0cm of the third. This means a drop from 61cm on the third rule will actually be from 240 centimetres – 100 centimetres from each of the first two metre rules plus 40 centimetres on from the third.
To ensure a fair test is carried out, certain measures will have to be applied. The same table tennis ball will be used every time, and the drop will always be from directly above (therefore aimed at) the same bit of the floor. The windows will always be closed to avoid draughts, which could affect the flight of the ball thereby altering the results, and also to maintain a steady temperature throughout the experiment (no radiators will be on for the same reason). Drop consistency will be maintained (to the greatest possible extent) by using a clamp to release the ball, as described earlier.
However, certain problems are unavoidable. Ideally we would use an electronic measuring device to measure the height of the bounce, but such sophisticated pieces of equipment are not available to us. We will be forced simply to measure it by eye, being careful to look directly horizontally with the bottom of the ball at the peak of its bounce in order to take a correct reading.
Diagram
Prediction – I think that the height of the table tennis ball’s bounce will always be below the height from which it is dropped due to the loss of energy, predominantly through air resistance (transferred to heat energy due to friction with the air and kinetic energy by moving air out of its way), but also partly through transfer to sound and heat energy on impact with the floor. I think the bounce height will increase with the drop height, but at a slowing rate, i.e. the distance between drop height and bounce height will increase as the drop height increases. I think that once the ball is dropped from a height from which it can accelerate to its terminal velocity, a drop from any height above that will produce the same bounce height, as no further energy will be carried in the ball on impact with the floor.
Analysis
Table of Results
This table shows a complete list of all the results gained in this investigation, all of which are illustrated in the following graph. No bounce height is higher than its drop height, as I stated in my prediction.
This scatter graph compares the bounce height of the ball against the drop height. The addition of a trend line illustrates several things. It shows a predicted bounce height for any drop height between 0 and 300 centimetres, not only the ones we were capable of measuring accurately. The curvature of the trend line shows how the bounce height’s rate of increase slows as the drop height increases, as I stated in my prediction. By projecting the trend line, the height from which the ball’s terminal velocity can be achieved is shown, which this graph shows to be about 300 centimetres.
By finding the mean bounce height at each drop height (this is done by dividing the sum all the values by the number of values, i.e. three), the nature of the ball’s bounce height compared to its drop height can be illustrated further. Subtracting the mean bounce height from the drop height calculates where the ball fell but did not bounce to (this represents the energy the ball has lost since its drop). Dividing the mean bounce height by the drop height and multiplying this by 100 calculates the bounce height as a percentage of the drop height.
The calculations for this table were made before the numbers were rounded to the nearest whole number for greater accuracy, so calculations made from the numbers shown might not appear accurate. For example, if the formula was 5.4 + 5.4, if these numbers were rounded before the answer was calculated the answer would be 10, but rounded after the calculation and the answer is 11.
Evaluation
We wanted to be as consistent as possible, so the same table tennis ball was used throughout. This experiment was conducted recording the lowest height’s bounce first, with each drop height 20cm higher than the last. It is possible that the table tennis ball ‘lost its bounce’ the more it was used, like a tennis ball, if it was pressurised at the start of the experiment but gradually leaked air, in which case the ball’s natural bounce at higher drop heights may be represented lower in this experiment. However, it is also a possibility that the table tennis ball ‘warmed up’ and increased in bounce the more it was used, like a squash ball, if it heated up due to friction and this heat made its atoms vibrate more giving it a bigger ‘push’ off the floor, in which case the ball’s natural bounce at higher drop heights may be represented higher.
Almost every result followed a trend so it is likely that the results as a set were recorded to a satisfactory level of accuracy. However, where there were slightly anomalous results (for example the first drop at 272 centimetres) it is likely that this was due to an abnormality on impact with the floor, such as the ball landing on a slight indentation in the floor or even on a small amount of dirt which might have softened the impact, rather than an error in judgement of the bounce height of the ball. Ideally, and for perfectly accurate results to possibly two decimal places, electronic equipment would still have been used, but I think the correct pattern was still shown using only the human eye. My prediction is likely to be correct in that all the results supported it, though I only had time to vary the concentration over a limited range of values, so I am not sure how true it is outside this range, although the pattern of results suggested that terminal velocity would soon have been reached had more recordings taken place.
