# Bouncing balls.

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Introduction

Philip Ng 24/03/2003

Bouncing

(Coefficient of restitution)

Introduction

Suppose two particles of masses and are moving in a straight line with speeds and before impact and speeds and after impact, in the directions shown in figure 1. Newton’s law of impact gives

Where - is the relative speed with which approaches and - is the relative speed with which draws away from. There is often confusion over the signs in the equation, and it is convenient to restate it in the form

Strategy:

The initial phase of the activity involves making careful, qualitative observations of a single bounce.

Next, our team takes a tennis ball and measure quantitatively how high it bounces when dropped from a given height.

Finally, one should consider the same ball bouncing several times and study the progressive decrease in the heights to which it goes.

Data Collection

In order to get the coefficient of restitution of the floor, I will look for the initial height and the height after first bouncing.

In this experiment, I have made some assumption.

Assumption: 1. No Air Resistance

2. No friction

3. No external force supplied to the tennis ball

4. Initial velocity = 0 m/s

5. Ignore the spinning

6. Acceleration: g= a= 9.8m/s-2

7. The ball makes very brief contact with the table, seeming to leave I almost instantaneously

8.

Middle

0.89

0.902

0.91

0.89

1.4

0.79

0.77

0.78

0.78

0.78

0.78

0.79

0.77

1.2

0.68

0.7

0.68

0.67

0.69

0.684

0.7

0.67

1

0.57

0.57

0.565

0.56

0.57

0.572

0.57

0.56

(The table shows the coefficient of restitution of different drop height)

(The graph shows the coefficient of restitution of bouncing the tennis ball on the floor)

To find the coefficient of restitution, as I have predicted, so I useas my prediction where,. So now I vary the value of m to adjust the line to be best fit of my max, mean, and min bounce height respectively.

By using the spreadsheet,

The gradient of the lines are: Max= 0.57

Min=0.55

Mean= 0.56

We now have the two extremes, and the error bound is 0.56+0.1

So the coefficient of restitution is Max= 0.755

Min=0.742

Mean=0.748

Comparison

To find out the coefficient of restitution, it can be calculated by the following experiment.

Now, I am going to conduct the similar experiment as before. Drop the ball from a given height, and consider the time taken for the tennis ball to stop bouncing.

From my previous work page 2), it shows that,

So the second bouncing height should be

The nth bouncing height should be

The time taken from drop height to the ground:

To solve:

As I’ve got and where v is the velocity just before first bouncing

So let u be the velocity just after first bouncing,

Conclusion

Revision of progress

To improve the match between model and experiment, I will improve the quality of experiment. In my first experiment, to record the maximum height of the tennis ball after first bouncing, I will use the electronic equipment, like detector, instead of observation by eyes. However, I will use a heavier ball instead of tennis ball, as heavier ball has larger force acting by gravity, so it has larger potential energy than the tennis ball in the same height, so the proportion of energy loss is reduced because the total energy is larger. It can reduce the experimental error.

In my second experiment, I will again use the sensor to record the time instead of observation. It is more sensible and accurate.

The effect of these amendments is to record the more accurate data, the actual bounce height and time, so that I can get a more accurate result by my equations. However, it is difficult to do these amendments because it is complicated to set up and I do not have to do that, because my result is already very good enough. So there will not be a significant difference whether I use the electronic equipment or do it by myself.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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