The Mechanics of Gravitational Potential Energy in Falling Balls

Introduction

Originally Gravitational potential energy (mph) is stored in a ball before its released. as the ball falls and the speed increases The potential energy of the moving ball is changed to kinetic energy (1/2mv2) then it looses all the potential energy as soon as is touches the floor. If there is no energy loss the energy (I. e. P. E and K. E) remains the same The ball deforms and slows down as it touches the ground. Here the balls kinetic energy is causing the ball to deform.

When the ball is deformed some of the energy is stored as potential energy and another name for this energy is elastic potential energy and this in some cases this energy is changed into heat and sound and some is converted to heat and sound. As soon as the ball losses all its speed and reaches its highest deformation only then it looses its kinetic energy and it stops moving. And when some of its energy Is changed to heat and sound its kinetic energy decreases than its original gravitational potential energy.

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Here all the energy (elastic PE + heat + sound) remains the same.

And then when the ball turns back into its original shape the elastic potential energy is then changed to kinetic energy. As soon as the ball leaves the ground it will begin to slow down as it rises and its kinetic energy is changed back to gravitational potential energy. Since some of its original energy has been changed to heat and sound it will finish up with less gravitational energy than it began with i.

e. the rebound height is less than the starting height. Additional Information A solid expands when it's heated. Inside, the molecules energize and bounce around the solid with enough energy have more energy and bounce around the solid.

The hotter the solid becomes, the more they vibrate. This causes the solid to expand slightly when heated. Solids cannot be compressed because the molecules are already packed very close together. When the solid hits the ground the atoms push each other away forcing the ball to bounce higher. So this is another factor in consideration. My aim is to investigate how the temperature has an effect on the height of the bounce of a squash ball.

Equipment:

• Meter rule - to make sure the drop height is 1m and to measure the bounce height
• Squash ball - to be able to conduct the experiment
• Beaker - to create the water bath
• Water - to create the water bath i??
• Tongs - to keep the ball below the water bath surface i??
• Thermometer - to ensure the water is at the right temperature i??
• Timer - to ensure the ball stays in the water bath for the right amount of time i??
• Kettle - to get the water bath to the higher temperatures i??
• Ice - to get the water bath to the lower temperatures

Method

1. I will be using the temperature choice of 0 C to 70 C and I will be going up in 10  C. I will only be going up to 70 C because I know that after that temperature the rubber of the squash ball will become damaged. I went down to 0 C as it is the lowest temperature because after that point the water will reach freezing point. This temperature also shows a low bounce height and if the temperature goes any lower it would be very difficult to read the bounce height. I will be repeating each temperature 5 times to make sure correct results and to be able to get a fair average. Also I will be able to see any anomalies and not take them into account for my average. I will use a water bath in which I will put the squash ball. I will let the squash ball remain in the water bath for 3 minutes as I know from my initial work that it takes 3 minutes for the squash ball to reach thermal equilibrium. I will let go of the ball from a height of one meter as I have found from my initial work that this is a good height to provide me good results that gives a good variety of results and is suitable for all the other temperature's bounce heights. Also, I will be taking the bounce height measurements from the bottom of the ball each time. I will record all the results in a table with an average column so that my results can be compared.
2. Next I will put the results onto a graph to see if there are any patterns and how the results relate to the line of best fit. To ensure the test is fair For each beaker I will be using the same amount of water to make the test fair, and I will make sure that the water in the water bath remains at the right temperature when the squash ball is in it to make sure that the squash ball will reach thermal equilibrium. I will also be making sure that the squash ball is left in the water bath for 3 minutes to make sure that the ball reaches thermal equilibrium. I will be using the same squash ball during the experiment so that there is nothing affecting the results except the temperature. I will be taking the measurement of the bounce height from the base of the ball each time so that the results are in proportion to each other and can be compared. Prediction Before the ball is dropped I know that, energy is stored as GPE (gravitational potential energy). As the ball falls its speed increases and the GPE is converted to KE (kinetic energy), so half way through the fall half of the ball's energy id GPE and half is KE.
3. Just before the ball hits the floor all its energy is KE and none of it is GPE. Once the ball hits the floor, all the KE is converted to EPE (elastic potential energy) and some is lost as heat and sound energy which makes its energy less than its initial GPE. When the ball bounces back off the floor the EPE is converted back to KE, heat and sound. The ball will start to slow down as it rises and its KE is converted back to GPE but because some of its initial energy has been converted to heat and sound it will finish with less GPE than it started with. So I think that the hotter the ball is, the higher the height of the bounce will be. I think this because I know from my that when the gas that is inside the ball is heated up, the volume of the gas will slowly expand and the molecules will start to move faster which will often make them hit the sides more harder. This causes the rubber to expand and contain more elastic energy. We could understand from this that the bounce height would be bigger because the more stretched the rubber is, the better it changes elastic potential energy into kinetic energy when the ball touches the floor and makes the ball bounce higher.
4. Then, the hotter the ball is, the firmer it is and the quicker it will gets its shape back, so then it loses very few energy and then has more energy to use to bounce higher. On the other hand, I think that the lower the temperature of the ball, the lower the bounce height because I know from my background scientific knowledge that the molecules are moving slower and therefore won't hit the rubber as often or as hard as at hotter temperatures. This would mean that the rubber wouldn't be as good at storing elastic potential energy and converting it into kinetic energy when the ball hits the surface. The bounce height for all the temperatures will be much less than the original dropping height because energy is lost converting elastic potential energy into kinetic energy. Risk assessment To make sure that the investigation is safe I ensure that there is no one around our working area so nobody could get hit by the ball. I will also make sure that when the ball falls on the floor at any point I will pick it up straight away so that nobody can fall over it.
5. I will also make sure that if the beaker of water will be in the middle of the table so that it doesn't get knocked off spilling the water and creating a safety hazard of a slippery floor and broken glass. I will also make sure that if there are any spillages, I will clear them up straight away to prevent anyone slipping. Initial work I did some initial work to see what the best height is to drop the ball from is and how long I need the ball to heat up in the water bath for it to reach thermal equilibrium.

To investigate the length of time the squash ball needs to be kept in the water bath to reach thermal equilibrium I put the ball in the water bath at 30i?? C. I left the ball in the water for 1, 2, 3, 4 and 5 minutes. After each length of time I dropped the ball from a metre height and recorded the bounce height. When the bounce height no longer changed, the first length of time that gave this height is the length of time the ball takes to reach thermal equilibrium.

I repeated each length of time three times to make sure I got accurate results and was able to get an average which I could look at to see at which point thermal equilibrium was reached. I can see from this that thermal equilibrium was reached at 3 minutes because this was the point that 28cm at a bounce height was reached and because the height didn't increase more than 28cm it means that thermal equilibrium was reached.