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# The acceleration of a ball down various inclines

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SARANG PALERI        EXPERIMENTAL RESEARCH PROJECT        10G

SCIENCE EXPERIMENTAL RESEARCH PROJECT

THE ACCELERATION OF A SPHERE OVER DIFFERENT INCLINES

PREPARED BY SARANG PALERI

CONTENTS

1. Abstract
2. Introduction
3. Aim
4. Hypothesis
5. Materials
6. Method
7. Results
8. Discussion
9. Conclusion

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ABSTRACT

In this experiment, I constructed a project to test the change in velocity of a spherical object down a slope, and how that is affected by different inclines. I will record the time a ball takes to get to the bottom of a plank, measuring the times it takes to get to different intervals. The inclines I will be using to roll the ball down are at 2°, 4°, 6°, 8° and 10°. The control will be at 90°, as the only force acting on it is gravity. I will roll the ball down the plank 5 times at each angle, ruling out some random errors. The ball will be a Wilson Championship Heavy Duty 70g tennis ball. The plank can be any length, but it is preferable to use pine wood, as it is soft and is not undulating. The measurements are made with multiple stopwatches, to record times at each interval. The independent variable is change in incline angle, and the dependant variable is velocity down the plank. The acceleration of the ball is determined by further analysing these results.

INTRODUCTION

My Semester 2 Science Assessment Task requires me to research and investigate an experiment of my own interests and analyse certain scientific principles concerned with this task. The experiment I conducted tests the change of velocity of a spherical object down a slope, and how that is affected by different inclines. The reason I chose this experiment was because I found motion, and how forces induce it, to be very interesting. Possibly being able to mathematically link different rates of acceleration, and maybe being able to calculate the forces exerted on an object during decline is certainly a very enticing prospect, considering this is more useful than many skills I have acquired in my lifetime.

This experiment is technical, as it contains various scientific principles that are used in careers in engineering. Jobs like physics engineers overseeing crash tests to see any flaws in collisions tests, and to interpret results, are available to people with this type of knowledge. This experiment only increases my fascination with this type of science. This experiment also improves certain personal skills, such as the ability to collate, analyse, interpret and conclude. This is another reason I chose this experiment.

Sir Isaac Newton was renowned for many things, among them his studies of refraction and decomposition of white light, calculus, and his Three Laws of Physics, but amid these fine achievements, he was the first to fully explain what gravity is. His inspiration was a falling apple, and he wondered why the apple went towards the ground, and not in any direction. Then he came up with an incredible insight: if this mysterious force that can pull apples from trees can reach to the tallest apple tree, then its range could probably go even further than the atmosphere, maybe to the moon and beyond. His understanding of his force is phenomenal, considering he had no basis of evidence that this force existed, yet his idea developed incredibly. He even went on to create a Law of Universal Gravitation, which suggests that every particle of matter in the universe attracts every other particle of matter with a force proportional to the masses of both entities. Gravity is very important in relation to this experiment.

The force at work in this experiment is gravity, but friction also contributes, as no friction will result in the ball sliding rather than rolling down the incline. Gravity is a force which is measured with the rate of acceleration it at which objects fall. It is a force created by the presence of mass, and the more mass an object has, the more pulling force it has on everything else to the centre of the mass, which is the centre of gravity. On Earth, the rate at which objects fall is 9.8 metres per second squared, or 9.8m/s2, or 9.8 metres every second. During the experiment, I expect the acceleration rate will be much less, considering the ball is travelling down a gradient to reach the centre of gravity, rather than receiving a direct route to it.

The experiment is influenced by the force of gravity, and this experiment will illustrate the effect that gravity has on an accelerating ball rolling down an incline.

AIM

The aim of this experiment is to measure the acceleration down an incline, and how that varies with changes in incline.

HYPOTHESIS

I believe that the rate of acceleration will increase with increases in incline; the control will make the ball accelerate the fastest and the 2° inclined plank will make the ball decline the slowest.

MATERIALS

The materials I will be using are:

• 2.5 metre pinewood plank
• Wooden support (plain plank of wood, measured carefully)
• Metronome
• Results table
• Wilson Championship Heavy Duty 56g tennis ball
• Video camera (optional)
• 4 stopwatches

METHOD

Before beginning the experiment, steps need to be taken to rule out random errors. Firstly, you need to polish the pine wood plank, to minimise friction. Also, the experiment must be conducted indoors, so no wind can affect the experiment. If you need to, using a hair brush gently strip the tennis ball of excess hair. After this, the experiment may start, although there are 2 ways to complete it, a being the first way, b being the second:

1. Using trigonometry, figure out the height of the wooden support which will be placed under the plank. If starting off with the 10° plank, the support will be 34.73cm long (It would make more sense to start off at the 10° plank, as you will only need to shorten the wooden support every time you change the incline, rather than buying 5 different supports.

2.        Set up wooden support and place the pine wood plank on top, the end of the plank lying on the support.

3a.         With helpers timing when the ball go over the intervals, hold the ball touching the inclined end, waiting for everyone to be ready.

3b.        Position a camera so it has the entire plank from a side-on view in focus. Also turn on the metronome

4a.        When the helpers are ready, let go of the ball, and let the helpers time when the ball gets to each interval.

4b.        When ready, roll the ball down the ramp exactly when the metronome beeps.

5b.        View the video on the computer, figuring out a scale ratio to the real plank and measuring how far it travelled.

1. After receiving the times, plot results in the results table.
1. Repeat experiment until completing the incline 10 times.

RESULTS

 Distance after 0.5 sec (cm) Distance after 1 sec (cm) Distance after 1.5 sec (cm) Distance after 2 sec (cm) Distance after 2.5 sec (cm) Distance after 3 sec (cm) Distance after 3.5 sec (cm) 2° -Result 12° -Result 22° -Result 32° -Result 42° -Result 52° -Result 62° -Result 72° -Result 82° -Result 92° -Result 10 4.34.24.34.64.44.54.34.64.34.5 16.817.117.217.017.217.217.217.317.017.0 40.139.538.638.738.438.039.038.338.939.4 68.768.970.469.366.367.969.068.669.068.9 109.1106.5107.2107.0105.5106.1107.0107.5107.4107.9 153.1153.4153.0153.8153.7154.3152.8153.5154.0154.2 210.6210.7210.4209.7209.9210.8210.0210.3209.1210.4 2° -Average 4.4 17.1 38.9 68.7 107.1 153.6 210.2 2° -Distance travelled per 0.5 sec 4.4 12.7 21.8 28.9 38.4 46.5 56.6 2° -Difference in distance travelled per 0.5 sec 8.3 9.1 7.1 9.5 8.1 10.1 2° - Average of above 8.7 4° -Result 14° -Result 24° -Result 34° -Result 44° -Result 54° -Result 64° -Result 74° -Result 84° -Result 94° -Result 10 8.49.18.99.28.68.38.58.38.28.5 34.533.932.433.533.735.834.233.232.933.8 76.577.477.178.276.577.677.777.177.276.4 136.9136.9136.5135.1136.5136.2136.8135.9136.4135.7 211.0213.9213.7213.6213.1212.7214.1213.8214.7212.9 4° -Average 8.6 33.8 77.2 136.3 213.4 4° -Distance travelled per 0.5 sec 8.6 25.2 43.4 59.1 77.1 4° -Difference in distance travelled per 0.5 sec 16.6 18.2 15.7 18.0 4° -Average of above 17.125 6° -Result 16° -Result 26° -Result 36° -Result 46° -Result 56° -Result 66° -Result 76° -Result 86° -Result 96° -Result 10 11.211.811.911.312.712.912.412.212.011.2 50.851.651.251.050.451.650.951.251.051.3 114.7115.8114.9115.2115.1115.6115.4114.3114.9115.1 206.0205.1204.8205.2205.6204.7204.6205.9205.8205.9 6° -Average 12.0 51.1 115.1 205.4 6° -Distance travelled per 0.5 sec 12 39.1 64 90.3 6° -Difference in distance travelled per 0.5 sec 27.1 24.9 26.3 6° -Average of above 26.1 8° -Result 18° -Result 28° -Result 38° -Result 48° -Result 58° -Result 68° -Result 78° -Result 88° -Result 98° -Result 10 17.417.718.116.516.916.318.017.616.917.4 67.167.967.466.767.868.568.468.068.267.4 153.6154.8154.2154.4154.3154.4153.5153.3154.7153.1 8° -Average 17.3 67.7 154.0 8° -Distance travelled per 0.5 sec 17.3 50.4 86.3 8° -Difference in distance travelled per 0.5 sec 33.1 35.9 8° -Average of above 34.5 10° -Result 110° -Result 210° -Result 310° -Result 410° -Result 510° -Result 610° -Result 710° -Result 810° -Result 910° -Result 10 21.220.721.921.421.621.721.621.520.921.3 86.686.986.286.985.786.386.585.985.286.0 191.7191.7192.6192.7192.1193.0191.4192.3192.6191.5 10° -Average 21.4 86.2 192.2 10° -Distance travelled per 0.5 sec 21.4 64.8 106 10° -Difference in distance travelled per 0.5 sec 43.4 41.2 10° -Average of above 42.3

DISCUSSION

As can be seen from these results, my hypothesis stating that the ball would accelerate more rapidly on steeper inclines was correct. As the inclines got steeper, the ball would accelerate more quickly down the incline. The acceleration of the inclines also were mathematically connected, as the ‘Average of difference in distance travelled per 0.5 sec’ statistic increased by approximately 8.7 cm per 2° incline every 0.5 sec. Seeing as acceleration is measured is measured in d/t2,the difference in acceleration between inclines is 8.7cm/0.5s2, meaning the acceleration is 8.7/0.25. To convert this to cm/s2, the latter equation must be multiplied by 4, meaning the difference in distance travelled between 2° inclines is 34.8m/s2. This experiment has proved that there is a mathematical correlation between acceleration on different inclines.

The correlation between the distances due to the 34.8m/s2 equation is evident, with the distance travelled by the ball on the 2° incline in the first 0.5 second interval being approximately half that on the 4° incline. Similarly, the distance travelled in the first 0.5 second interval on the 6° incline is 3 times that of the 2° incline. This suggests that the acceleration of the ball is proportional to the angle. The acceleration of the ball is created by gravity, so gravity’s force is affected by the angle. The acceleration between each angle is the gravitational constant being manipulated by the angle of the incline. Generally, the gravitational constant (g) perpendicular the Earth’s surface is 9.81 m/s2. Because it is perpendicular, it is at 90° to the Earth. Because of the incline I made the ball roll down, it was rolling on a 2° incline at first. Its acceleration was 34.8cm/s2, so g is 28. 2 times larger than g on a 2° incline. Although they are not exactly proportionally, as g should be 45 times larger than g at a 2° incline, there still may be a correlation between each other, using transcendental numbers or functions such as sine, cosine or tangent.

There were difficulties measuring the steeper inclines, as it took longer and longer to get the measurements considering how quickly the ball got to a fast velocity. This probably made the results more inaccurate, therefore it was necessary to measure each incline 10 times rather than 5, to receive consistency in my results and to minimise random errors as much as possible. Also, I used a technique which assisted the accuracy of my results, by videotaping the ball’s decline down the ramp, slowing the video down and measuring how far down it got by using ratios. I used a metronome on a mobile phone set at 120 beats per minute because you could hear it in the video and stop it at the appropriate time and measure how far the ball had rolled. Other problems with the experiment were the amount of time it took to retrieve the results, as there were 50 videos to take and to interpret. Also, the ball rolled off the plank many times, so I needed to align it very exactly so it did not fall off. I could not guide the ball with an indentation into the wood because that would cause friction to the ball, slowing the ball down.

The variables that I reduced to minimise random errors were mainly wind and friction. The ball’s friction on the wood was minimised by removing excess hairs, and the wood’s friction on the ball was removed by lightly polishing the wood with sandpaper. There may have been some measuring errors, but hopefully that was removed with the repetition of each experiment.

Ways I could expand on the experiment are maybe to investigate the effect of mass on particular inclines, or maybe in freefall. This will test Galileo’s theory of all similarly shaped objects will accelerate at the same rate towards Earth. His theory suggests that mass does not affect the acceleration towards Earth, only the top speed it can reach while accelerating.

CONCLUSION

There is a mathematical correlation between acceleration and the incline angle, and the acceleration is brought about by gravity. The gravity is affected by the incline angle, lessening the acceleration it exerts on a spherical body. The change in incline angle resulted in a proportional change in distance travelled by the ball.

BIBLIOGRAPHY

• Rickard, G., Phillips, G., Ellis, J., Jeffrey, F., Robinson, P. (2006) Science Dimensions 4, Essential Learning, Pearson Education Australia, Melbourne.
• www.newton.cam.ac.uk/newtlife.html

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## Here's what a star student thought of this essay

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### Response to the question

The author has produced a good report about an experiment to compare the acceleration down a ramp of a ball at different angles of incline. They have come to a conclusion and compared this with their hypothesis. However, I would ...

### Response to the question

The author has produced a good report about an experiment to compare the acceleration down a ramp of a ball at different angles of incline. They have come to a conclusion and compared this with their hypothesis. However, I would have developed the experiment by using the results to calculate the vertical acceleration due to gravity, comparing this to the true value of 9.81, and using this information to calculate the friction force, for example.

### Level of analysis

They have used their results to come to a conclusion Ã¢â‚¬â€œ that the acceleration is proportional to the angle Ã¢â‚¬â€œ although mathematical analysis shows that this is incorrect. In fact, the acceleration is proportional to the sine of the angle (a = 9.81sinÃŽÂ¸). Further analysis of results would have made this error clear Ã¢â‚¬â€œ for example calculating a predicted acceleration based on the assumption that the acceleration was directly proportional to the angle and comparing this with the experimental results. However, as this is a physics experiment rather than a maths one, this may not have had a significant effect on the marks. They have drawn one graph, however, this has only been used to illustrate the fact that there is a relationship between the angle and the acceleration. When we did a similar experiment in college, we were advised to plot a graph of distance against time squared, and use this to calculate the acceleration (2 x the gradient), rather than just stating that there appears to be some correlation. This would also have enabled the author to come to the correct conclusion.

### Quality of writing

The authorÃ¢â‚¬â„¢s spelling and grammar is good throughout. However, they have occasionally conflated gravity with acceleration - Ã¢â‚¬ËœÃ¢â‚¬â„¢ The gravity is affected by the incline angleÃ¢â‚¬Â Ã¢â‚¬â€œ which may suggest to the marker that they didnÃ¢â‚¬â„¢t understand the difference between the two (gravity is a constant force exerted by massive objects, causing other objects to accelerate). This is an easy mistake to accidentally make, but one which could cause the loss of several marks. They have also not stuck with scientific conventions throughout Ã¢â‚¬â€œ one major example being standard units. The graph used centimetres and centiseconds, which is confusing for the reader. Also, I find it much easier to do calculations when using standard units, making me less likely to make mistakes, which would certainly lose marks. Another lack of convention, although probably not too significant, is the authorÃ¢â‚¬â„¢s habit of directly addressing the reader - Ã¢â‚¬Å“you need to polish the pine wood plankÃ¢â‚¬Â Ã¢â‚¬â€œ this sounds unprofessional, and I would have rephrased it as: Ã¢â‚¬Ëœthe pine wood plank is firstly polishedÃ¢â‚¬â„¢. The report is well presented, with clear headings, tables, graphs, and a fairy chronological layout. This makes it much easier to read and mark. However, I would not have included some sections, such as the introductory paragraph about why they have chosen this topic. This is highly unlikely to be a necessary part of a scientific report, other than in some kind of covering letter, so I would never include it unless it is specified in the mark scheme. The author has also included other unnecessary words such as Ã¢â‚¬Å“the rate at which objects fall is 9.8 metres per second squared, or 9.8m/s2, or 9.8 metres every secondÃ¢â‚¬Â. This really is unnecessary! Overall, they have shown a good understanding of how to correctly present a report, but made a few noticeable errors, which may lead to confusion.

Reviewed by dragonkeeper13 29/03/2012

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