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# Investigation of the rebounce height of the tennis ball

Updated: Oct 24, 2019

Introduction

An object's gravitational energy is proportional to its position in height. When the tennis ball is lifted from the ground, it gains potential energy and right before it is released, the energy gets fully transformed into kinetic energy and once the tennis ball bounces off the ground, some of that energy gets absorbed into sound and heat.

The energy lost is in fact a constant fraction of the initial energy before the drop of which we can call Ef , meaning by the first bounce the height will be hxEf , the second hxEfxEf , the third hxEfxEfxEf and so on. This proves that no work is 100% efficient and that everything has some wasted energy in the process.

From the experiment, once the tennis ball was dropped, potential energy transformed into kinetic and once the ball bounced on the concrete surface the energy again transformed into elastic potential energy once the ball was squashed and then back to kinetic energy to a certain height lower than the initial meaning some energy was lost to heat and sound of the tennis ball.

I decided to investigate the relationship between the drop of the height and the rebounce height of the ball on a concrete surface, because I have been interested in the energy transformation as well as loss of systems in a non-isolated area. Since starting IB one of the first things we learn is the conservation of energy and how no energy is ever lost but only transformed, which made me want to investigate how it does transform and what effect it has. I chose this simple experiment to learn more of this law.

Research question

The rebounce height of the ball depending on the height of which it is released from.

Hypothesis

My hypothesis is that if the ball is dropped from a higher height, the rebounce height will also increase and if dropped from a lower height, the rebounce height will decrease as well but that the ball will never bounce back to the exact same height considering full elastic collision is not possible in the real world and energy will be lost once the tennis ball hits the ground. The lost energy will in this case transform into thermal, sound, air resistance and compression energy making the bounce of the ball to decrease as the height also decreases. Thus as the law of conservation of energy states that energy cannot be created or destroyed, the ball will transform energy making some go to waste; the total amount of energy will remain the same.

Method

Graph 1 shows the average rebounce height on the selected heights from 20-100 cm and fortunately has a best fit line pretty close to the values with small uncertainties, which is favoured. Again, the drop height shows that as the height from which the ball is dropped from increases the rebounce height as well and vice versa, considering as the conservation of energy explains that as more potential energy is gained, the greater the height. This is noticeable in the graph, considering the line only goes up and never down, thus giving a linear relationship.

Evaluation

Based on the data collected and the analysis section, I can state that my results support the theory and the hypothesis; my prediction was right and the ball did in fact bounce back higher as it was dropped from a higher height and the bounce was shorter as the ball was dropped from a lower height. This concludes that the height from which the ball is dropped from is in fact proportional to the rebounce height of the tennis ball.

Also, the ball didn't rebounce back to its initial height, meaning the tennis ball followed the conservation of energy theory and energy was lost to sound and heat once it reached the concrete floor.

Looking at the the tables, table 1 shows an accuracy and consistency with all the trials being around the same value. Table 2 also seems accurate and supports the hypothesis considering it shows that renounce height is in fact proportional to the height it is dropped from. Graph 1 also shows accuracy, however it does not have a y-intercept in the origin which is where my data became inaccurate. The lack of the origin intercept is because the rebound height was measured from the middle of the ball instead of from the bottom, which is something to improve for the next time.

Bibliography:

1. Physics for the IB Diploma; Second edition (John Allum and Christopher Talbot)

2. https://www.britannica.com/science/conservation-of-energy

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