Energy absorbed by a bouncing ball.

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Luke Hawkins                                                                02/05/2007

13 Hackpen

Physics Coursework

Energy Absorbed by a Bouncing Ball

Aim

My aim is to find out whether there is a relationship between the energy absorbed by a bouncing ball and its initial height that it was dropped from.

I hope to be able to answer the following question:

‘Does the initial height of the ball determine how much energy is absorbed in each bounce?’

Introduction

When plane designers are designing a plane they have to carry out in depth research into each feature of the plane, the materials to be made from and whether it would withstand the immense pressures in the air. A very important area that they have to look at carefully is the wheels of the plane. The wheels will have to be made out of a material that is really strong so that they can withstand the friction and weight of the plane when landing and taking off. When the wheels touch the ground when landing they must be able to absorb lots of energy for the plane to begin to slow down.

One way in which I am going to model measuring the energy absorbed by a plane wheel is by using a ball and dropping it from various heights to measure the energy absorbed. Although I will not be able to carry out the experiment at great heights, like in a plane, I hope to be able to model the idea in the classroom. I will do this by using different balls at various heights each representing a different material. I will be using a ball to represent the wheel as this is the nearest representation that I could thin of that I could use to carry out my experiments.

Theory

When a ball is dropped from a height, its potential energy, PE, is converted into kinetic energy, KE. When the ball collides with a surface, some of its energy is used to deform the ball and is eventually converted into heat energy. The ball therefore rebounds with less kinetic energy and so will rise to a lower height than its starting position.

The initial potential energy equals mgh (mass x gravity x height). Therefore, if no energy is lost as the ball falls through the air, the kinetic energy, ½ mv²1 (1/2 mass x velocity²), will be equal to the loss of potential energy (mgh1).

The potential energy at a maximum height after the first bounce equals (mgh2). Therefore, the initial kinetic energy after the bounce equals (1/2mv²2), which equals the potential energy, equal to mgh2.

Therefore, the equation that is used to calculate the fraction of energy absorbed by a bouncing ball can be worked out by using this equation:

Fraction of energy = PE before collision – PE after collision

                                KE before collision

                      = h¹ - h²

                        h¹

* taken from ‘Practical Physics at A-Level’ by Trevor Cross

Measurements of h¹ and h² will enable the fraction of energy absorbed to be worked out.

But in order to use this equation I need to know how to work out the potential energy of the ball in the first place. This can be worked out by using the following equation:

PE = Mass x Gravity x Height

PE = mgh                        * where g = 9.8

The Experiment

This is a diagram showing how I am going to take my experimental results. This is just one method that I could choose from to get my results but I have chosen to use this method as it is simple to perform, easily available for me to carry out and because I think that this will get me the necessary reliable results that I require.

There are a number of different methods in which I can carry out this experiment, but I have chosen to use the following method because it was easily available for me to carry out in the school science laboratories.

Other methods that I could have chosen to collect my results are as follows:

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  • Measuring the surface area of contact when the ball is dropped.

By measuring the surface area of contact of the ball when it falls, you should be able to notice a difference in size indicating how much energy was absorbed by the ball when it bounced. When the ball hits the ground the ball will deform slightly as it collides with the hard surface. Therefore, the bigger the surface area of contact, the greater the energy the ball has absorbed because the ball has squashed more.

The problem with this experiment is that it is very difficult to measure ...

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