Further Prediction Graph:
Preliminary Work:
Preliminary Method:
The same method was used for the preliminary work as was used below, in the main experiment. However, different types of balls were used, released at different heights and bounced on different surfaces, as seen in the table above. Furthermore, in order to obtain readings for the hot squash ball, the ball was simply rolled on a bench several times to generate some heat.
Justification:
To achieve the most accurate result possible, it is important to investigate a ball that bounces constantly. In doing my preliminary experiment, the golf ball proved to be the most constant when bounced. I found the golf ball to be the most constant as the other balls had irregularities and further problems affecting the accuracy of the investigation. The baseball was slightly irregular in its shape, giving several random readings. The large seam on the baseball may have also contributed to the readings it gave. The tennis and baseball were both big and the bigger the ball the bigger the chance of unequal quality of surface. For example, parts of the tennis ball may have been worn away, an unequal quality of surface causing it to bounce irregularly. The tennis ball also has a white seam, which may have been the part of the ball that made contact with the floor, resulting in another irregular reading. The squash ball was very inefficient, delivering very low bounce heights, making it very hard to judge what height the ball reached. The lower the efficiency, the lower the bounce and the more inaccurate the readings are, as the percentage error is bigger. Furthermore, the squash ball was temperature dependent meaning the air expands as the temperature increases. This causes the squash ball to increase in size, becoming denser and resulting in further inaccuracies. The table tennis ball was very light and even a slight breeze could have shifted the path of the ball, affecting the bounce heights and producing less constant results. A further problem due to the mass of the table tennis ball was the air resistance. The air resistance has a huge effect on the table tennis ball, as it is so light, much greater than any of the others. I found the golf ball to be the most constant as it had none of these problems or irregularities.
I have chosen to use the floor as the surface upon which the golf ball will bounce for several readings. Firstly, by observing my preliminary work, it is clear that the floor is much more efficient than the bench, 16% more efficient. The less efficient the surface, the lower the ball will bounce and the higher the percentage error. The higher the percentage error, the more inaccurate the readings are. Secondly, The benches have many crevices, which may have caused the ball to bounce randomly, giving inaccurate readings. Thirdly, as the bench is higher than the floor, it would have been very hard to read the bounce heights without having parallax errors, causing the readings to be inaccurate. Finally, the bench was used as apparatus in the sense that the upper stand was placed on it. If the bench were used as the surface to bounce the ball on, there would be no place for the upper stand to rest on making it very hard to position the upper rule accurately, resulting in unreliable readings.
I chose a range of values, from 40cm to 200cm in order to give readings that avoided the effects of air resistance, some that showed the effect of air resistance and readings that avoided large percentage errors. For example, I didn’t want to have any release heights below 40cm as I would have encountered large percentage errors, causing unreliable readings. However, I wanted to have a few readings below 100cm to avoid great amounts of air resistance. I also wanted readings higher than 160cm to show the effects of air resistance. This is why I chose five different release heights at 40, 80, 120, 160, and 200cm.
Apparatus:
2 Stands
2 Clamps
2 Bosses
2 Rules –1m
1 Golf Ball
Sticky Tapes
Method:
- After collecting the apparatus, one stand was placed on the floor and the other, on the bench directly above it. The bosses and clamps were attached to the stands, so that the clamps were parallel to the floor, perpendicular to the stand and pointed away from the bench.
- The first rule was obtained and attached vertically to the lower clamp at approximately a height of 50cm. Once the rule was inserted into the clamp, the clamp was tightened. The height of the boss was then adjusted so that the base of the rule was in contact with the surface of the floor. The rule needed to be perpendicular to the floor and rotated so that the face of the rule with the … (markings) on, were clearly visible, in order for myself to carry out the experiment and measure the heights. The second rule was placed in the upper clamp and adjusted as the first rule was, although the base of the second rule in contact with the top of the first rule, not the floor.
- Now the apparatus was set up, the golf ball was taken in my right hand and held beside the lower rule at a height of 40cm, my initial release height. By kneeling, I put myself in a position where my eye level was parallel to this height. The ball was held with the tips of my forefinger and thumb and my palm was positioned above the golf ball. The base of the ball was in line with the 40cm mark and held approximately 2cm away from the rule, ensuring the base of the ball remained in line with the 40cm mark.
- The ball was then released by quickly moving my forefinger and thumb away from each other, allowing the ball to drop vertically along side the rule. After the golf ball had bounced off the floor, I swiftly repositioned myself so that my eye level was parallel to the highest height the ball reached. I saw the reading from the rule that the base of the ball reached and noted the result down.
- A small piece of sticky tape was placed at the height I believed the base of the ball to have reached and I repeated the release of the ball at a height of 40cm, taking the same precautions as previously. However, after releasing the ball I positioned myself so that my eye level was parallel to the height of the sticky tape and saw if the ball bounced higher, lower or the same. The height was recorded and the sticky tape adjusted if the reading had changed.
- The release of the ball at a height of 40cm was repeated a second time giving three bounce height readings for a release height of 40cm.
- The ball was released at four more different heights of 80cm, 120cm, 160cm and 200cm. Each release height was repeated twice to give three readings and the same rules and precautions were taken for all five of the release heights.
- The average of the bounce heights were calculated to give one average bounce height for each of the five release heights. Using this average bounce height, an average efficiency was calculated for each of the five release heights.
- A graph was finally drawn with a trend line, displaying my results of this investigation, i.e. the efficiency of the bounce of a golf ball at different release heights.
Diagram:
Variables: -
Bounce Heights
Temperature
Release Heights
Type Of Golf Ball
The surface upon which the ball bounces
The independent variable is the release height and the dependant variable is the bounce height. The temperature could have caused the results to be unreliable as it may have changed the size of certain apparatus if the temperature dramatically increased or decreased. However, the experiment was done in one day where the temperature was thought to have remained constant at 22°C. The type of ball had to remain the same as different balls have different masses, which may affect the bounce heights. In order to recognise my golf ball, a named label was stuck on it to ensure the using of the same ball. If the ball were bounced on a bench, as seen in the preliminary experiment, the ball was less efficient. Usually, the harder the surface, the higher the ball bounces and the more efficient it is. This is because a harder surface absorbs less kinetic energy from the ball. Therefore, it gives most the energy back resulting in a higher, more efficient bounce. However, although the bench is just as hard, if not harder, than the floor, the bench is a piece of wood suspended in the air. Therefore, there is a lot of air below the bench, so when the bench is struck by the ball it vibrates more than the floor, and the air below it vibrates. This means a huge amount of sound energy is emitted and lost in the atmosphere. Whereas the floor doesn’t lose nearly as much sound energy, producing a more efficient bounce. It is clear by looking at the preliminary experiment, the surfaces upon which the ball can bounce, result in very different bounce heights and efficiency. This is why the surface that was chosen, the floor, was kept constant throughout the experiment.
Obtaining Evidence:
Analysing:
By observing my graph and table, it is clear that as the release height increases, so too does the bounce heights. This is clear as by looking at the graph one can see there is a positive correlation, thus the bounce heights increasing with the release heights. However, if the release heights were to be in direct proportion to the bounce heights, as I firstly predicted, the trend on the graph would be a linear one. Although the trend on the graph showing release heights vs. bounce heights is a curve, it passes through the origin and is a very slight curve. This shows that the bounce heights are roughly proportional to the release heights. The trend is a slight curve because as the release heights are increased, the golf ball travels in the air for a longer period of time, allowing the air resistance to act on the ball for a longer time. Furthermore, some energy is lost through heat and sound. Therefore, it would be impossible for the ball to have bounced to the height of which it was released. For example, one may have expected the average bounce height to be 200cm at a release height of 200cm, making it 100% efficient. However, the energy lost through sound and heat meant that it might have bounced to a height of 175cm. This can be said as the average bounce height for the golf ball was 33cm, when released at 40cm. When the golf ball was released at 40cm, the air resistance couldn’t have affected the ball greatly as it would have had very little time to act on the ball. Therefore, most of the loss in energy and height, was due to the sound and heat being emitted, not the air resistance. This is why one can say approximately that 5 out of the 7cm lost in that bounce was the loss in heat and sound energy. Because the release height was 200cm rather than 40cm, the gravitational potential energy will be five times as much. Therefore, the loss in heat and sound energy will be five times as great too. With this in mind, the loss in height when the ball reached its’ bounce height will be five times less than when it was released at 40cm. Therefore, this would give a bounce height of 175cm. However, if one looks at the table or graph, one can see that the bounce height was 150cm, 25cm less than would may have been expected. This loss in height must have been due to the air resistance that was able to act on the golf ball for longer, reducing the amount of kinetic energy the ball acquired on its decent, resulting in a lower bounce height.
A more accurate way of proving the increasing effect of air resistance as the release heights increase, is to take the average bounce height of the golf ball when released at 40cm and 80cm, and multiply the value by the amount of times the release heights of 40 and 80 go into the release height of 200cm. This is more accurate as it doesn’t involve estimation. In doing this, one should get 33×5=165 and 66×2.5=165. Both multiplications give a answer of a bounce height of 165cm if the golf was released at 200cm. This would be a sensible prediction of the bounce height when the golf ball was released at a height of 200cm. However, the resulting value was significantly lower, 150cm. Therefore, something other then the loss of sound and heat energy must have caused the ball to lose kinetic energy and bounce lower than expected. This must have been the increase in air resistance, which had an effect of at least 15cm. This therefore proves that as one increases the release height, air resistance has a greater effect causing the ball to bounce at a lower height.
The graph showing efficiency vs. release heights seems to have a very steep negative correlation and trend line. This makes it seem that the efficiency is radically declining as the release heights increase. However, if one looks at the same graph on a larger scale, it is clear that the efficiency is steadily decreasing as predicted.
My final prediction agreed with the outcome of the experiment to an extent. The bounce heights did increase as the release heights increased, the graph of bounce heights vs. release heights did slightly curve and the efficiency did gradually decrease. However, the trend didn’t curve as much as I predicted as I thought the ball would have been closer to reaching its’ terminal velocity than it was. Although, my prediction was correct and stated that the bounce heights would increase less as the release heights increased due to air resistance, the trend was much less of curve than predicted. This could have been because the release heights didn’t extend high enough, only to 200cm, and wasn’t sufficient to show the extreme effects of air resistance on the ball. If a table tennis ball was used, at 200cm, the effects of air resistance would be extremely clear as the mass of a table tennis ball is much less that of a golf ball and the air resistance would have a greater effect at the same height. Therefore, the table tennis ball would have been very close to reaching its terminal velocity. Through this, one can say my prediction was also wrong as I miss judged the height of which the golf ball needed to be released to greatly see the effects of air resistance.
It is clear, through looking at the graph of efficiency vs. release heights, the efficiency of the golf ball decreases as the release heights increase. As explained earlier, this gradual decrease is due to the air resistance. However, this decrease may have been due to other variables that were not monitored closely enough. Although the temperature was measured, it may have caused unreliable readings. The temperature can have great effects on experiments causing unreliable results. This is because as the temperature increases or decreases, it causes objects and apparatus to increase or decrease in size. The main apparatus in this experiment was the golf ball itself. If the temperature were to have increased, the molecules inside the golf ball would have spread apart as temperature causes the forces between the molecules to weaken enabling the molecules to break apart from each other and move freely. This then results in the golf ball increasing in size as the molecules are no longer held so tightly together causing the ball to expand and become less dense. For example, if one heats a liquid, the attractions between the molecules are weakened and they move freely. As a result of this, the liquid turns into a gas. The gas then has a larger volume, but the same mass, making the gas less dense then it was as the liquid. This is the same with the golf ball, in the sense that the ball has a larger volume, the same mass and a lower density. Now the golf ball’s properties have changed, the amount of energy the ball has at all the transformations, is different. When the golf ball is held at the release height, it will have the same amount of gravitational potential energy, as the values for height, mass and gravity remain the same. However, after the gravitational potential energy is converted into kinetic energy, the ball will acquire a lot less kinetic energy when just prior to hitting the floor. This is because the ball has the same mass and the same strength of force, air resistance, is pushing up on the ball. However, the air resistance has a larger area to act on as the ball has expanded. This causes the air resistance to have a much greater effect, reducing the ball’s velocity, thus reducing the amount of kinetic energy. When the ball now hits the floor with less energy, sound and heat energy are lost, the kinetic energy is transformed into strain potential energy. As the ball is compressed, the molecules aren’t as tightly and closely packed together so the molecules don’t spring back to their original position as promptly and forcefully as they would do if the golf ball hadn’t expanded due to the temperature rise. This results in the kinetic energy on the ascent being less and the ball reaching a lower bounce height. This also results in the efficiency being much less then expected. This could explain why the efficiency was a long way off the trend line for the value of the release height at 200cm. However, the temperature was measured at 22°C at the start of the experiment and was unlikely to have changed dramatically throughout the day.
I consider my results to be reliable as each release height was repeated twice to give three bounce heights for each of the five release heights. Although the method was limited in the sense that the golf ball couldn’t have been released at a height where it would have reached its’ terminal velocity and only five different heights were measured, the maximum 200cm, with the results I acquired and the reliability of them, certain basic conclusions can be drawn. The bounce heights increased roughly proportional to the release heights. However, the bounce heights increased less each time the release height increased, producing a slight curve on the graph. The efficiency gradually decreased when looked at from a scale of 0-100%. As the release heights increased, the air resistance had a greater effect on the golf ball. However, it would not be fair to conclude that the bounce heights remain the same once the ball has reached terminal velocity, as a height big enough to suffice the ball reaching its’ terminal velocity, was not feasible. Therefore, several conclusions can be drawn to a large extent although some would not be reasonable to make. Furthermore, the conclusions made above agree with my final prediction stated earlier to a large extent.
Evaluating:
Although my results were sufficient enough to draw reasonable conclusions, there were some problems that I encountered. When the golf ball was dropped at the release heights, it was quite difficult for me to release the ball accurately, i.e. without moving, but at the same time read the bounce height accurately, i.e. getting into a parallax position. This was difficult as I would have to swiftly move from dropping the ball, to reading the bounce heights. This problem could have easily been solved by allowing two people to work with one apparatus, so that one person could drop the ball and the other could read the bounce heights.
I chose five different release heights to get a broad range of results. However, it may have been better to have had an even broader range as the biggest height wasn’t enough to see the dramatic effects of air resistance. If I would have extended my heights to 300cm, I believe I would have obtained the results I wanted. The consistency of the data collected was of high quality as all three readings for each of the five release heights were within 3cm of each other. This makes my results and conclusions very reliable.
Although there were no anomalous results there were a few on the graph showing efficiency vs. release heights, that weren’t on or very near the trend line. The efficiency of the golf ball at a release height of 40cm, 150cm and 200cm seemed to be higher or lower then they should have been. Although I chose to have the minimum release height at 40cm to avoid large percentage errors, a small percentage error may have occurred at this height as it is still quite a low reading. Reasons why the other two results weren’t as expected, could be irregularities on the surface the ball bounced, the floor. Although the floor was chosen over the bench for this exact reason, there may have still been some bumps in the area the ball bounced, causing random results. As explained before, temperature changes may have caused these irregular readings. However, both these reasons seem unlikely as the data was consistent and it is doubtful that the temperature would have changed enough in the time the experiment took, to affect the results. An explanation for all the irregularities is that they’re not irregular. If the trend were a curve, then the trend line would pass through nearly all of the readings, leaving no irregularities. However, I believe the trend to be a linear one rather than curved. The efficiency decreases as the release heights increase because of the air resistance acting longer on the golf ball. However, if the trend were to be a curve, it would mean the air resistance acting on the ball is not only acting on the ball for longer as the release heights increase, but also acting disproportionately. I don’t believe this to be true, so the trend remains linear and the reason behind the irregularities may be inaccuracies in the reading of the bounce heights or releasing of the ball.
The releasing of the ball was done manually and although done with precaution, it was likely that upon releasing, my hand may have moved, especially as I had to quickly move into a position to read the bounce heights. Even the slightest of movements affects the energy the ball obtains and the bounce heights. A better way of carrying this out would have been to collect another boss and clamp, and attach it to the stand at the appropriate release height. Then place the ball in the clamp and tighten enough to stop the ball from falling. The same precautions would apply, such as placing the clamp so that the base of the ball is at the given height. When ready, one would loosen the claws of the clamp, releasing the ball to fall to the ground. This way, the apparatus holding the ball will be sure to remain still, unlike one’s hand, and the ball will be sure to have dropped rather than pushed to the floor. This may have been causes of other irregularities or random data. When one held the ball and released it, it is possible that the ball wasn’t dropped, rather pushed, giving it more kinetic energy and resulting in a higher bounce height. Using a clamp prevents both these inaccuracies from happening.
Although a piece of sticky tape was placed at the bounce height to improve the accuracy of the next reading, an electronic device with a type of sensor could have been placed alongside the two rules. When the ball were to reach its highest point the device could flash where the bounce height was to prevent parallax errors from occurring.
After looking at all these improvements, the method used for the experiment was clearly not the most accurate. However, the conclusions drawn earlier can still remain reliable conclusions as although the accuracy would be improved, the basic outcome and results of the experiment would remain the same. Furthermore, some apparatus mentioned in improving the experiment above, was not available in the laboratory and could not have been used, such as the electronic device that could have been used to measure the bounce heights. Having said that, there are certain factors that one needs to recognise when looking at the conclusions. Air resistance, anomalies, irregularities and random nature of the bounce, percentage errors with small distances, temperature changes, are all problems that affect the results and hence the conclusions.
Other variables such as different type of golf ball, different surface and different temperatures are all variables that when changed, affect the efficiency of the bounce of a golf ball or any ball very much. If one were to use the same surface, ball and release heights, but rather than a temperature of 22°C, a temperature of 0-5°C. The molecules inside the ball would begin to freeze or at least become very stiff. As a result of this, there would be very little strain potential energy as the molecules would compress very slightly if at all. The bounce heights would be a lot smaller and the efficiency a lot less than it would be if the temperature were as it was in the experiment above. If one changed only the surface, from the hard laboratory floor to a soft carpet floor, the bounce heights and efficiency would be virtually nothing. This is because carpet is soft and would absorb most of the energy the ball had, not much energy would be given back to the ball, the strain potential energy would be very small and the ball would have virtually no kinetic energy on the ascent.
For further work, one could have a larger range, reaching 300 or 400cm. This would show the effects of air resistance a lot clearer than at 200cm. Different types of golf balls could be used to show which is most efficient. The surface upon which the ball bounces could be different lengths and thickness of grass on a golf course, such as, on the putting green, in the sand or in the rough. To further extend the experiment, it could be done in a vacuum to rid the problem of air resistance. I would strongly predict that the efficiency would be very near to 100% as little sound or heat energy would be lost, if any. Air resistance would be none existent, so the release height wouldn’t effect the efficiency unless the release height was sufficient for the golf ball to reach its’ terminal velocity, in which case the efficiency would keep decreasing as the bounce height would remain the same.