Why a sphere bounces better than a cube
When a sphere bounces, the force is concentrated in a single point on the sphere, a surface small area, this results in high pressure. And because there is more pressure, there is more compression, and so, more expansion. While, in a cube, the force will be evenly distributed across a large surface area, resulting in low pressure. And because the force is evenly distributed, there is less compression, and so less expansion. This is why a cube (or any other flat-faced object) does not bounce as well as a sphere. And for this reason, I will be using a ball in my experiment.
No Parallax
When measuring an object with a ruler, and looking at the scale at anything but a head-on, 0 degree angle. Our vision of the scale is altered based on the angle at which we look. To ensure that we are looking at the scale at a 0 degree angle, place a mirror behind, and parallel to, the ruler. When you look directly at the ruler, you will be able to see yourself head-on. And you will know that you are at a 0 degree angle to the ruler.
Preliminary Work:
For my preliminary work, I will be investigating the properties of different types of balls.
Apparatus:
- Tennis Ball (Hollow + Soft)
- Squash Ball (Solid + Soft)
- Rubber Ball (Solid + Hard)
- Stress Ball (Spongy + Soft)
- Cricket Ball (Hollow + Hard)
- Tape Measure
- Electronic Weighing Scales
- Ruler
- Clamp stand + clamp.
Method:
- Measure the circumference (at the widest point) and weight of each ball.
- Drop each ball from the height of one metre and measure the height to which it bounces.
Conclusion From Preliminary Work
From the preliminary work I found that the rubber ball bounced the highest and the squash ball bounced the lowest. I think that the tennis ball would be the best to use for this experiment, because it bounced a reasonable height, but it didn’t so high that there was difficultly measuring its’ bounce. We also found that it was difficult to accurately measure how high the ball bounced based on visual observations alone.
Variables: (Controlled)
- Height from which the ball is dropped.
- Surface the ball is bounces against.
- Material from which the ball is made.
- Pressure inside the ball.
- Size of the ball.
- Weight of the ball.
- Temperature of the ball.
Variables: (Uncontrolled)
- Gravitational force.
- Room Temperature.
- Air Pressure.
- We chose to vary Height from which the ball is dropped. and keep all other variables constant.
Apparatus:
- Ultrasound (sonar) measuring device - a device that uses sound waves to measure distance.
- Computer + “LOGIT” device.
- 2 Metre Ruler + Mirror (for no parallax and visual reference).
- Clamp Stand + Clamp.
- Surface
Method:
Range: For this experiment, I decided to increase the height from which the ball dropped by intervals of 100mm, starting at a height of 200mm and going up to a height of 1000mm.
- Set up the equipment as shown in the diagram. Turn on the Ultrasound measuring device, and load the program dealing with the device on the computer.
- Drop the tennis ball from the height of 20cm.
- To find the height bounced, take the closest recorded distance from the scanner (by the ball) away from the total height of the scanner.
- Repeat steps 2 and 3 twice more.
- Repeat steps 2-4, dropping the ball from an extra 10cm in height every time, until you reach the height of 1 metre.
Fair Test and Accuracy Points:
- Use the same ball for each experiment, different balls may have slightly different properties (weight, circumference, density) that could seriously impact the experiment and taint the results.
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Keep all the variables other than the one I am measuring constant.
- Use an appropriate scale on measuring equipment. Or results you acquire may be imprecise. Or the equipment may not have the required range of measurements on it.
- Use the same equipment to measure the height each time, different pieces of equipment may have different ranges, or be more or less sensitive.
- Repeat the experiment at least three times, and average the results. This is to ensure that I acquire accurate results, and am able to identify and discount anomalous ones.
- I will use an ultrasound measuring device, linked to a LOGIT data modem, linking it to a computer. To accurately and precisely measure and record the height of the balls’ bounce.
Diagram:
Hypothesis:
I predict “that the greater the height from which I drop the ball, the higher it will bounce, this is because, the higher the ball is, the more gravitational potential energy it possesses. And therefore as it falls, there will be more potential energy converted into kinetic energy. More kinetic energy will be converted into elastic potential energy on impact. And Because there is more elastic potential energy, the ball will have greater kinetic energy with which to bounce.” And that “The percentage of the energy lost by the ball between the point from where it is dropped, and the point to which it bounces, will remain constant- this is because there will always be a constant ratio of energy : friction. For example, if the ratio was 2:1, then, for every 100 Jules of gravitational potential energy the ball possessed, in between being dropped, and the highest point of its’ bounce. The ball would lose 50 Jules of its total energy due to friction. This would occur, because, as the height increases, the amount of G.P.E increases, but so does the distance to travel (and therefore the friction). Friction is caused by the ball colliding with particles and molecules in the air, this causes the movement of these particles- the result of this is thermal energy. The ball loses energy, when moving (in the form of heat) due to friction. And upon impacting with the ground, in the form of sound.
Results:
Note: A grey cell denotes ANOMALOUS result.
Analysis of Results:
From the results of my experiment, I have found that the greater the height from which the ball is dropped, the higher the ball bounces. By calculating the percentage of the original height bounced, I have also found, that the ball bounces approximately 50% of the height from which it is dropped (Between 46% and 56%). This is reinforced by the evidence that the ball loses roughly 50% (between 44% and 54%) of its energy between being dropped, and reaching its highest point of bounce. This means, that from whatever height the ball is dropped (in the earths’ atmosphere), there is sufficient friction (or air resistance) to approximately halve the amount of energy it possesses.
Analysing the graphs (attached), the gradient of “A graph to show the height of a balls’ bounce against the height from which it was dropped” 0.5115 cm[vertical]/cm[horizontal]. This means that, for every centimetre in height the ball was dropped, it would bounce 0.5115 centimetres in height. From the second graph “ A graph to show the initial amount of gravitational potential energy and the final amount of gravitational potential energy, against the height from which the ball was dropped“, I found, by calculating the gradient. That for every centimetre in height the ball was raised, it had 551.8 Joules (551.8 J/cm) of Gravitational potential energy before being dropped. And 278.66 Joules (278.66 J/cm) of Gravitational potential energy at its’ highest point after bouncing.
Conclusion:
From my results, I draw the conclusion that “The height to which a ball bounces when dropped, is 50.5% of the height from which the ball is dropped”. 48.85% of the energy is lost to two things; firstly, when the ball is both falling and bouncing, it is colliding with particles in the air, this air resistance, or friction, causes energy to be lost, in the form of heat and sound. Also, when the ball bounces, it is now moving against the force of gravity. The result of this, is that the balls’ kinetic energy is being transformed back into gravitational potential energy. In terms of the percentage of energy lost, height is irrelevant, because, the greater the height you drop the ball from, the further it has to travel (and therefore the more friction it must overcome), and so, even though you have more gravitational potential energy, you also have more friction. So the height bounced is always approximately 51.15% of the height from which the ball is dropped.
In terms of height bounced, I conclude that “The height to which a ball bounces when dropped is directly proportional to height from which it is dropped”. This is because, the greater the height from which you drop the ball, the more Gravitational potential energy the ball possesses. When the ball is dropped, this is transformed into Kinetic energy, which in turn, on impact with the ground, is transformed into elastic potential energy, and that becomes the kinetic energy of a ball bouncing. This energy transfer links the gravitational potential energy at the start (before the ball is dropped), to the Kinetic energy at the end (when the ball is bouncing vertically). And so the more gravitational potential energy you have, the more will be transferred to kinetic energy as it falls, to elastic energy as it impacts, and then to kinetic energy again, when it is rising.
Finally, “The height from which the ball is dropped is directly proportional to the amount of friction the ball will have to overcome as it falls”. This is because, the higher the ball is, the further it must travel to the ground, meaning that there will be more air in its path. This will mean that it will collide with more particles as it falls, resulting in increased “air resistance” (or friction). However, “The percentage of energy lost due to friction is always roughly 50%”, this is because, even though there is more friction, there is also more energy with which to overcome this friction- more energy is lost due to the increased friction, but the percentage of energy remaining is approximately constant.
Evaluation:
I believe that the procedure executed was accurate, and efficient. I obtained useful and conclusive results, that I was able to present in the form of graphs and charts. And easily identify trends within them. The anomalous results I found, were all within the limits of tolerance. This is because I used a sensitive measuring device (the ultrasound sensor linked into a computer). This gave me the accurate results. The few anomalies I found, were, most likely, the result of my own error in measuring the height from which I dropped them (using a centimetre ruler, I could have been half a centimetre off, even with no-parallax). And a misjudgement, however small, would have altered the amount of G.P.E the ball had.
I could have used (instead of my own eyesight) a computer-controlled robotic device, that would take the ball to the height required, and drop it from that height. This would have meant that, by allowing the computer the measure the height (in something as precise as millimetres), I could have made sure that I had the exact height required by inputting the parameters. This would have improved the accuracy of my experiment.
In this experiment, the ultrasound scanner I used, would not measure accurately detect an object less than 200mm(20cm) from it, and this prevented me from obtaining the bounce heights when I dropped the ball from 200 and 100 millimetres. If I repeated this experiment, I would use a scanner that had a faster rate of measurement, and no “dead zone” in which no measurements could be obtained (e.g. the 200mm or less, height “dead zone” I encountered) .
The evidence obtained is sufficient to support a firm conclusion. I used accurate measuring equipment and repeated each step of the experiment three times. This allowed me to identify any anomalous results (no matter how small). To acquire further evidence to support my conclusion, and to get a better line of best fit on my graphs, I could narrow the range of my investigation, and increase the number of readings taken. This time dropping the ball at 10cm intervals as opposed to 20cm ones. For additional work, I could alter the mass of the ball, and investigate the effect that has on the height of its bounce. I could also, investigate the effect that the density of the ball has on the height of its bounce. To alter the density of the ball, I would alter the balls’ temperature.