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• Level: GCSE
• Subject: Maths
• Word count: 4059

# Study how balls bounce, specifically focusing on how drop height affects the rebound height. I also aim to find out if any pattern or generalisation can be taken from this.

Extracts from this document...

Introduction

## Aim

The aim of my investigation is to study how balls bounce. I am specifically focusing on how drop height affects the rebound height. I also aim to find out if any pattern or generalisation can be taken from this.

## Variables

There are many variables that can affect this experiment; one of the most important ones is drop height. Depending on how high the drop height is, theoretically, the higher the rebound height is. This is because there is more energy being put into the ball so there should be more energy coming out. If the ball is made of elastomers then it could be because the elastomers are being stretched more and more as the ball is being dropped from higher and higher. Elastomers are chains of polymers that have a high stretch ability. They consist of long polymer chain coiled together and mixed up randomly. There are very few links between the coils. The elastomers in a ball stretch when they hit the ground, this is because they under a tensile force. This energy is then used to propel the ball up or rebound. All elastomers stretch when put under this kind of force. They will though reach a point where they can not stretch any more than they are already doing, so the graph will plateau and the ball will not bounce any higher no matter how high or hard it is dropped.

The mass of the ball is also an important factor. The higher the mass of the ball, the higher the gravitational potential energy will be at the specified drop height. As the ball falls it still has some potential energy so it is accelerating constantly, it will do this until it reaches a terminal velocity.

Middle

Where the question marks are it was either impossible to measure or I was unable find the correct value.

## Accuracy and Values

I have a lot of variable that I am keeping constant:

• There are 9 values for drop height each going up in intervals of 25cm:

100, 125, 150, 175, 200, 225, 250, 275, 300. I will be measuring it in centimetres (cm). I believe that this gives the experiment a wide range of results so it is a better representation of the relationship between drop height and rebound height. I am measuring using a metre rule; it is accurate to the nearest 1cm. So I am therefore going to be measuring the rebound heights to the nearest centimetre. For each value I do I am going to repeat the experiment 3 times so that I can make an average, this will give me a clearer view of the relationship between drop height and rebound height.

• I had to find which ball I was going to use. I chose to use the tennis ball because I found that this was most visible when looking to see where the ball had rebounded to on the metre rule. It was important to measure the drop height from the bottom of the ball and also the rebound height from here to make sure that the experiment is fair. If it is not measured from here it is hard reading where the ball has got to. Because the ball covers the numbers on the rule.
• I decided to drop the ball on a concrete floor because it is far better than a normal floor because it is harder so therefore makes the ball bounce better because less energy is lost through the floor absorbing it.
• The temperature of the room was around 20ºc, I didn’t actually measure this but this is what I estimate would be around. This could be a fault in my method.

Preliminary experiment

I had to find the things that I was going to keep constant in my experiment this included doing some initial experiments to find what would be best and give the best results. The things I investigated were:

• Which ball was I going to use?
• Where was the best height to start from?
• Where was a good height to stop at?
• What was a sensible interval between the drop heights?
• How accurate was I going to be?
• What floor was I going to drop the ball on?

I did have a couple of problem that I had to sort out; one of these was where to read the ball from. You have to be on the exact same level as the ball, if you look at it from above you underestimate the actual rebound height. If it is looked at from below the rebound height is always overestimated. Therefore due to this fact I had to conduct a preliminary experiment before each of the drop heights to see what sort of height the ball was going to rebound to; and then adjust my eye level to this height. This eliminated or at least reduced the chance of parallax errors. I also found that the ball had to be dropped from directly above the metre rule because otherwise it was very hard to see exactly where the ball had rebounded to on the rule. You needed two people to conduct the experiment, one to drop the ball, the other to see where the ball rebounded to on the metre rule.

Initially I had to find which ball I was going to use. I chose to use the tennis ball because I found that this was most visible when looking to see where the ball had rebounded to on the metre rule. It was important to measure the drop height from the bottom of the ball and also the rebound height from here to make sure that the experiment is fair. If it is not measured from the bottom, reading where the ball has got to is quite hard, because the ball covers the numbers. When deciding what was going to be the minimum drop height I had to take into consideration the size of the error percentage. The larger the minimum drop height was, the lower the error percentage would be. I decided on an error percentage of 1%, this means my results are very accurate. Another problem that was encountered was that the rule was not always vertical; a solution to this problem was to use a spirit level.

## Equipment

Here is a brief list of the equipment I used:

• Meter Rule
• Tennis Ball
• Spirit Level (in the preliminary)

Conclusion

When the ball was dropped, it was a human hand that dropped it and therefore there are many factors that can affect the ball. When it is dropped by a person a slight spin could be put on the ball all of which would change its aerodynamics and therefore affect the speed at which the ball fell. Also people have grease on their hands, which if it rubbed off on the ball could also affect the way the ball fell. If some sort of machine could have be used which would have dropped the ball so that no spin at all was put onto the ball it would be far more accurate.The air pressure and temperature weren’t under my control so this could have had, however small, an affect on the way the ball bounced. If the ball was placed in neutral laboratory conditions this would show the true relationship between drop height and rebound height. It would not be affected by any adverse conditions that could change the results.The surface that I dropped the ball on wasn’t 100% perfect there were a lot of dents and deformities in it and I didn’t actually check to see if it was completely level. If I was going to do the experiment again I would make sure that the surface was completely level and that it was clear of cracks and deformities that could affect the way the ball bounces.

I think that it would be very interesting investigating how the variables stated in my variables section affect the relationship between the drop height and rebound height.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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