# Bouncing balls

Aim: The aim of my coursework is to investigate factors that affect the bounce height of a ball. Before I start my investigation I have brainstormed some ideas that will affect the height the ball will bounce to:* Temperature of the molecules inside the ball* Material of the ball* Mass of the ball* Drop height* Surface dropped onto* Whether it is dropped in a vacuumAfter looking at the factors that affect the reaction of the ball I have decided to investigate the drop height and type of ball. I made this decision because it was an investigation that I would be able carry out in the period of time I was allowed and I had the equipment and area available to me, to carry out the investigation. The only other one I could have possibly investigated would have been an Increase in temperature however I decided not to investigate this any further.

I did not use a vacuum, as it would be an un-performable investigation to make within a school laboratory. That is why I decided on the variables I did.Hypothesis: I predict that as I increase the drop height of the balls the higher the bounce height will be. I am predicting this because as the ball is held higher it gains more gravitational potential energy therefore has more energy to convert to kinetic, or the energy released by the object, and will bounce higher. If my results follow the rules of law of conservation of energy to bouncing balls then the ball will bounce higher when dropped from a higher height.Background information: It doesn’t take much effort to lift a ball off the ground. However, work is being done to the ball as it is being lifted, giving it energy.

This energy is potential energy. When the ball is dropped, the ball begins to move. The potential energy begins to be converted into kinetic energy – the energy of motion. Energy is defined as the ability to do work and work. Energy is measured in Joules. To help understand this concept, scientists have classified energy into two types or states. Potential energy is the energy acquired as work is being done to an object and kinetic energy is the energy released by the object as it is doing work.The amount of work put into an object, its potential energy, must always be equal to the amount of work the object can do, its kinetic energy.

For example; the higher the ball is lifted off the ground, the higher it will bounce after hitting the ground. Experience tells us that the ball can never bounce back to its original height. The falling ball loses some of its energy to air friction, to internal forces within the ball, and to friction between the ball and the ground on impact. After impact, the ball and the spot directly under the ball are slightly warmer, as some of the energy is lost as heat.The gravitational potential energy of an object, like a tennis ball, is related to its mass and the height to which the ball is lifted and can be expressed by the formula:G.P.

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E (gravitational potential energy) = Weight X Height = MGHYou can see from the formula that the greater the weight and the higher the position of the ball, the greater the potential energy. The kinetic energy of the falling ball is related to the mass of ball (m) and its velocity (v). This mathematical relationship is expressed as:Kinetic energy = 1/2 mvï¿½According to the equation, the heavier the ball and the faster it is moving, the greater the impact on the ground. Neglecting friction for the ball we’re using, the potential energy before you drop the ball will be equal to the kinetic energy just before it hits the ground. However due to the air resistance (friction) the ball looses energy as it falls and will never bounce to its original height. It also release energy upon impact and the ball will compress slightly, changing the forces internally and externally. This lose of energy means that ball has less energy when bouncing back up and again loses energy when moving upwards, despite gaining G.

P.E., due to friction.Different types of material will compress differently therefore will bounce and react differently on impact with a hard surface. A ball made from a soft material will compress a lot on impact and the hard surface will absorb all the energy causing the ball to bounce up only a little. A harder ball will not compress and will bounce up higher because less energy is lost on impact.

If the material of the ball is fury (e.g. a tennis ball) then its surface area is likely to be larger therefore giving it a larger area to release energy on impact.Another factor that will affect the bounce height will be the internal materials. The more pressure a ball has inside it, the less its surface dents during a bounce and the more of its original energy it stores in the compressed air. Air stores and returns energy relatively efficiently during a rapid bounce, so the pressurized ball bounces high. But an under inflated ball dents deeply and its skin flexes inefficiently. Much of the ball’s original energy is wasted in heating the bending skin and it doesn’t bounce very high.

In general, the higher the internal pressure in the ball, the better it will bounce.As further evidence to support my prediction below is a preliminary investigation showing how increasing the drop height increases the bounce height. The table below shows the results that were collected from the investigation, which involved: changing the drop height of a single tennis ball on to a hard surface and measuring the bounce height.In the experiment as the drop height increases so did the energy in which the ball had. This meant it had more energy to convert to kinetic so on impact kept more energy to bounce higher.These results helped me to make my prediction and change necessary factors in order to get the best results possible for the investigation. My results also gave me a basic outline of the processes involved in the investigation and what I am likely to encounter or see when I come to do the experiment.

I found that the time in which we had to conduct the experiment was insufficient so next time round I would have to use all the time available to ensure I get the best results possible. My preliminary results show a definite trend, as I increase the drop height of all the different balls, the bounce height increases. My graph shows that there is a line of best fit and there is a pattern, a positive correlation is present.

The balance we used only showed weights to 1 decimal place making it harder to get the most accurate results possible for the masses of each ball type. Next time round I would use a more precise balance, even if it were only to 2 decimal places. Working too quickly can cause inaccuracy so I will need to use the time wisely in order to get the best results to support or undermine my hypothesis. I will also need to make sure the surface is the same each time. Measure the bounce height from the bottom of the ball. This will make sure I measure the height correctly and evenly each time I drop the ball.Apparatus* 2 Meter rulers* Hard surface (e.

g. tiled floor)* Tennis ball* Ping pong ball* Bouncy ball* Heavy rubber ball and a light rubber ball* Rounder ball* Plastic mesh ball* Weighing balanceThe diagram below shows how the experiment will be set upType of ballTennisPing pongBouncyRubber (heavyRubber (light)RounderPlastic meshMass (g)57.52.622.

1166.974.377.345.9Method: I plan on using all the safety procedures and fair testing I can to get the best and most accurate results I possibly can. I will set up 2-meter ruler on a hard surface and drop each ball. I will drop each ball (Tennis ball, Ping pong ball, Bouncy ball, Heavy rubber ball and a light rubber ball, Rounder ball and a Plastic mesh ball) 5 times from each individual height to ensure I get the best and most accurate results possible. I will drop the balls at intervals of 10cm starting at 100cm down to 10cm.

I will measure the drop height and bounce height from the bottom of the ball. I will then work out the average bounce height for each ball from each height and plot them on a graph. This will allow me to see if there is any trend or pattern. It will also provide sufficient evidence to support or undermine my hypothesis.

Fair testing: There will only be two variables in my experiment, which are going to be the height the ball is dropped and the type of ball being used. Therefore I will need to make sure that all the other possible variables are kept the same. The temperature must be consistent otherwise the particles will have more or less energy and the bounce height will be affected largely.

The surface the ball is to be dropped on must remain constant. This will make sure that the surface has the same compressibility each time to make the experiment fair and accurate. I will not be using a vacuum with any of my experiments so this will make it a fair test.Range and number of tests: I will take measurements of each of the drop heights of the balls from 10.

cm to 100cm at intervals of 10.cm. I will repeat this 5 times. I will do this in order to get the most accurate results and so I can get an average bounce height.

Risk assessment: there are several dangerous factors to this seemingly harmless experiment. You should always take care when doing any experiment. Do not throw or miss-use the balls otherwise an injury may be obtained. Always place un-used equipment in a safe place so others do not trip of fall over it.

ResultsHeight dropped from (cm)Tennis BallPing Pong BallBouncy BallHeavy Rubber BallLight Rubber BallRounder BallPlastic Mesh Ball100cm5570825068274253718249672940567183506928405570834867254157698349663037Average55.270.282.649.267.427.84090cm5165744758303751657645623137526475486329365266764660283851657548632737Average51.46575.

246.861.2293780cm4660664155283247606140572534486064405626354859613856273347606539582934Average47.259.863.439.

656.42733.670cm4155583852262941545834502330405459355322324055603453243042545936522528Average40.854.458.835.4522429.

860cm3444513042232634455229442328364651294323273547523345222737454833452226Average35.245.450.

830.843.822.

626.850cm3039402738212232394329372221314043273618203139422638202130404226392123Average30.839.

4422737.620.421.440cm253132213014242634342231152326333521321222633332232171927333220301519Average2632.833.221.23112.421.

430cm172424824131319252217251114192622172612162025231824111617252418251115Average18.4252315.624.811.614.820cm141716141710101417161316911151816121691114181513168101417161117911Average14.217.

415.812.616.4910.610cm89989669888965910879769108710678978967Average8.69.

287.69.26.26.2I have carried out a scientific investigation that is designed to prove whether or not the bounce height of a ball is affected by the drop height or the material from which the ball is made. To do this I followed my plan that I made before hand.AnalysisOverall my graph does show a positive correlation in all the cases.

This meant as I increase the drop height of each ball the bounce height also increases. The lines of best fit indicate that all my results were very accurate and fit the line very well, being close to it. There were no anomalies because all the results fitted the patterns well.My results can tell me various things about how the bounce height of a ball is affected, particularly how drop height and material affect it.

Repeating each height meant I could get even more accurate results and has very reliable evidence when proving or undermining my hypothesis. The averages were calculated scientifically and accurately thus making them reliable.When the drop height was 100cm the majority of the balls bounced back up to at least half the original drop height. There were three exceptions to this. The heavy rubber ball, the rounder ball and the plastic mesh ball did not bounce higher than 50cm. This will be because there mass is so high that the majority of the gravitational potential energy is lost upon impact and through resistance such as air and friction. Another possibility is that they do not compress very well so upon impact none of the energy is absorbed but instead lost and little is retained for the bounce.The rest of the balls, the bouncy ball and ping-pong ball in particular, bounced back up to as much as over 3/4 of the original drop height.

The ping-pong ball has the lowest mass closely followed by the bouncy ball. This means there will be less resistance but also less gravitational energy because the mass is less. However the bouncy ball is highly compressible and will retain vast amounts of energy upon impact. The ping-pong ball is hollow, reducing its mass and also making the pressure inside a lot higher, therefore the less its surface dents during a bounce and the more of its original energy it stores in the compressed air. Air stores and returns energy relatively efficiently during a rapid bounce, so the pressurized ball bounces higher.At 90cm the tennis ball hardly changed in terms of bounce height, it bounced up 0.

8cm less than the previous bounce height at 100cm. With all of the other types of ball there was a noticeable change. The rounder ball actually bounces nearly 2cm higher. This however, I believe to be an anomaly. According to the laws of gravity and kinetic energy a ball should not have has much energy when its lower therefore should not bounce as high. Having said this, all the results at that particular height were similar giving an average above what I would of expected. The bouncy ball once again bounced the highest.

It looses a fraction of its energy during flight and upon impact but still retains enough energy to bounce back up to 2/3 of its original drop height. Most of the balls bounce up between 3cm and 6cm lower than when dropped at 100cm.When the balls were dropped from 80cm they all decreased in height. This means that they did not have or retain, as much energy therefore could not bounce as high. They have less gravitational energy because they are closer to the ground. As the ball falls the gravitational energy is converted to kinetic energy so the ball accelerates as it falls. When a ball is higher it will fall, and accelerate faster and hit the ground harder, bouncing up higher.Having even less gravitational energy when being dropped from 70cm once again all the balls decreased in bounce height.

I noticed a significant drop in the tennis ball. It decreased 7cm whereas the other balls only decreased by 4cm or 5cm. The tennis ball is highly compress-able and has little internal pressure. As the ball drops the gravitational energy is converted to kinetic energy. However upon impact this energy is converted to elastic potential energy. This means that the ball is compressed like a spring, and it is this reaction force that pushes the ball back up into the air. The tennis ball being furry has a larger surface, which will cause more friction and resistance.

Also as the ball hits the floor it loses energy through thermal energy. Therefore the tennis ball will lose more heat energy because of its larger surface area.At 60cm, there was an unusual change. It was not an anomaly because the results were continually similar.

The bouncy ball and light rubber ball had the largest decreases in bounce height. These two balls have always bounced highest due to there light, compress-able, and pressurized structure. Now however they lost nearly 8cm in both cases from the bounce height. All the remaining balls lost between 3cm and 5cm.

This means that the balls reaction changes in-between 60cm and 70cm drop height. They both react differently at this drop height.They may lose more energy through friction or resistance or it may just be because the have less gravitational potential energy to start with. At this height the bouncy ball only has GPE (gravitational potential) of around 0.1326 joules.

[I calculated this by multiplying the weight of the ball (mass (Kg) X gravitational force (10n)) by the drop height, which was 60cm. This gave me (0.0221Kg X 10N) X 0.6m.

]. Compared to previous height this is a difference of about 0.0221joules. The ball looses its own mass in joules every time it decreases in height by 10cm. Therefore it has less energy to store and use to bounce back up.Decreasing the height by another 10cm, the balls all varied in the amount of height they lost when compared with the previous height.

Assuming my statement is correct, the balls loose their own mass in joules every time the height is decreased by 10cm, each ball should have half the amount of GPE as at 100cm. Technically this means the should bounce half as high. 5 out of the 7 balls did show this. They bounce nearly half as high at 50cm as when they did at 100cm. The rounder ball however did not show this.

When dropped from 100cm it bounced 27.8cm but then at 50cm it bounced 20.4cm. It has retained nearly 3/4 of its bounce height despite the vast decrease in height.When dropped from 40cm, the balls lost on average 6cm from their bounce heights.

This applies to all except the plastic mesh ball that did not differ. It retained its bounce of 21.4cm despite the change of GPE. This could have been cause by an increase of temperature.

The increase in thermal energy causes the internal gases to expand therefore increasing the pressure of the ball. This makes the ball bounce higher because the more pressure a ball has inside it, the less its surface dents during a bounce and the more of its original energy it stores in the compressed air, so the pressurized ball bounces higher. All the other balls seemed to follow the normal laws of conservation and Newton’s three laws of motion.At the next drop height, 30cm, there were considerable changes in the bounce height with differences as big as 10cm.

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