Aim To see how the efficiency of a bouncing ball varies with the height it is dropped from.

Efficiency of a Bouncing Ball

Aim

To see how the efficiency of a bouncing ball varies with the height it is dropped from.

Background Information

Energy is needed with everything, (light, sound, heat…ect). Energy is defined as the ability to do work- to make something happen. The easiest way to detect energy is when it is changed form one form to another. To then measure how much energy is present, we can measure how much work done whilst the transformation is occurring.

An object can store energy as a result of its position it is in, such us when a ball is held at height, it stores energy. This stored energy is also referred to as Potential Energy (PE), it is called potential energy because the ball has potential to drop, converting the PE into kinetic energy, if it is let go. The higher the ball is dropped from the ground, the more kinetic energy it will need to fall back down. The kinetic energy is converted from the Gravitational Potential Energy the ball has when it is elevated. Gravitational Potential Energy is the energy stored in an object as the result of it vertical position. The ball falls to the ground due to force of gravity by converting the gravitational potential energy (GPE) into kinetic energy needed for the ball to move. The higher the ball is elevated the GPE it has. As the ball falls down, its GPE falls as it is converted into kinetic energy, the amount of kinetic energy stored increases as more of the gravitational energy is converted. The more kinetic energy the ball has stored, the faster the ball is going to go.

When a ball hits the ground, there is obviously friction, which transforms some of the kinetic energy into thermal energy and often sound energy as well. The rest of the kinetic energy that has not been used for thermal or sound energy will be transformed into elastic potential energy when the ball comes into contact with the ground. When a ball hits a surface, all the kinetic energy it has stored is immediately transformed. The floor, the ball or both become slightly dented out of shape as a result of the velocity and force they have collided with. As the ball and the floor try to regain their original shape, thy repel each other and immediately transform the elastic potential energy they have stored into kinetic energy. This energy, now stored in the ball sends it into the air. The more kinetic energy there was in the ball to begin with, the more energy there will now be left to convert back into kinetic energy. The ball will rise, or bounce higher. That is why I predict that as I increase the height of which the ball is dropped at, the height of the bounce of the ball will also increase. The reason I predict this is because I know that as you increase the height ball dropped, the more gravitational potential energy stored within it. So as this happens, the amount of potential energy converted into kinetic energy has also increased. As the ball bounces back after touching the floor, there is a greater amount of kinetic energy being converted back into potential energy, so as this happens the height of the bounce will also be higher.

If a ball were completely 100% efficient, then no energy would be lost during the bouncing process. For this to happen, no energy can be lost with sound or thermal energy due to friction. If a ball lost none of this energy whilst being dropped and hitting the floor, it would bounce to the same height as it was dropped from. There are no balls that are 100% efficient however some balls are more efficient than other.

Some factors that can affect the bounce height of a ball, not including the dropping height are:

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Some factors that can affect the bounce height of a ball, not including the dropping height are:

Pressure inside of the ball
Material of the ball
Material of the floor
Surface area of the ball
The force at which the ball is dropped by
Accuracy of measurement

I chose to control the height that the ball was dropped from this is because I thought it would be the easiest factor for me to control. Also, I felt that the other factors would be relatively easy for me to keep constant. If I used the same ball each time the surface would always stay the same, as would the pressure inside of the ball and the material of the ball. If I did my experiment in the same place and on the same surface for each height, the material of the floor could be kept constant. The person dropping the ball would be the same and not exert any force onto the ball. This way, all my factors I am not measuring will remain as constant as I can make them.

The Preliminary Experiment

I have chosen to use a bouncy ball to investigate. I chose a bouncy ball for my investigation because after quickly testing each balls bounce height, the bouncy ball was more suitable for the experiment I was going to do. I need to carry out some preliminary experiments so that can effectively plan for my investigation. If I carry out the preliminary experiments, I can then alter my method to exclude any thing that when wrong, or didn’t worked very well.

For my preliminary experiment, the bouncy ball was dropped from three different heights of 0.2m, 0.6m and 1m. Each reading was repeated two times and then an average bounce was found for each height.

Conclusion

There were no anomalous results. I would say that my results are probably quite accurate because we made extra care to make the trial experiment fair, and my results turned out how I expected they would. The main reason I did this preliminary experiment was to give me some idea of how my main experiment was going to turn out and so I could be prepared. I now know that the person reading the measurement on the ruler must always be the same person and must view the ruler from the same place all the time (head on ) , otherwise the results would not be as accurate.

Now that I have completed my preliminary experiments, and I know what to expect, I can start my main experiment.

Prediction

The reason I believe that if a ball is dropped at a higher height, the height of the bounce will also be higher. So there should be a direct proportional graph. This is because as you know as you increase the height of a ball; the amount of gravitational energy stored within will increase. I know this because the formula for working the potential energy is:

POTENTIAL ENERGY= MASS % GRAVITATIONAL FIELD STRENGTH % HEIGHT

You can see from this formula that the potential energy will increase if the height increases. Also as the height increases the kinetic energy will also increase, this is because at a higher height, the velocity of the ball will also increase, and we know by the formula that as the velocity is increased so does the amount of kinetic energy:

KINETIC ENERGY = ½ % MASS % VELOCITY

When the ball is falling down there is a greater amount of potential energy being converted into kinetic energy, then when the ball hits the ground it has no potential energy, the kinetic energy of the ball is being used to dent the ball. Then when the ball has dented so much that is cannot dent anymore, this means is has no kinetic energy but still has some energy stored as elastic potential energy this is used to dent the ball. However some energy has been turned into heat and sound, meaning the elastic potential energy will be less than its initial gravitational potential energy.

When the ball is returned to its original shape, that energy that has been stored as elastic potential energy is converted back into kinetic energy, heat and sound energy, this is when the ball starts to bounce. As there was a greater amount of gravitational energy due to the height, the amount of elastic potential energy stored in the ball would also be greater. So when the greater amount of elastic potential energy stored in the ball would also be greater. So when the greater amount of elastic potential energy is converted back into kinetic energy, heat and sound will also be greater, so the height of the bounce will also be higher. But because some if its initial energy is converted into heat and sound energy, it will finish up with less gravitational potential energy then what it started of with, so the height of the bounce of a ball will be less then the starting height.

Apparatus

1 meter ruler
Bouncy Ball ( 14.1g)
Lab Jack
Wooden Blocks x3
Video Camera

Diagram

Method

Weigh the ball on the weighing scales
Place the wooden blocks on the floor
Place the camera of the wooden blocks
Hold the ruler vertical
Drop the ball and record the results
Look back on the camera using slow motion and record the exact results.
Repeat the experiment two times in each height
The heights are: 1m, 0.8m, 0.6, 0.4m, 0.2m.

The same ball was used for each experiment. For each height, an average was found and the results recorded.

Accuracy and Reliability within my results:

I will try to do as much as I can with my experiments to reduce the chance of human experimental error and to make my results reliable and accurate.

I will go through all the factors that affect the bounce height of a ball, and change only the drop height. I will try to keep all the other factors constant if I can.

Surface area of the ball – I will keep this constant by using the same bouncy ball for each experiment. The surface area won’t vary from experiment to experiment.

Pressure inside of the ball – If the same ball is being used for each experiment, the pressure inside the ball will also remain constant.

Material of the ball – Because the ball is not changed then this factor will remain constant. This is the same for factor four. The material of the floor will not change because the experiment is being carried out in the same place each time.

5. Force at which the ball is dropped – this will not change, as the same person will be dropping the ball each time. This means that if a person exerts a force on the ball without realising, they probably do it with all the experiments. Using the same person means that although the results will be slightly inaccurate due to human error, the percentage error will always be roughly the same. Although the person will try their best not to exert any force and hold the ball in their hands lightly.

Accuracy of Measurement - this will be the easiest thing to keep constant. This is because we have a video camera so we can video record it then slow the recording down and get the results.

Safety Precautions

I will make sure that no one is walking underneath where the ball is going to be dropped so that no-one gets hit by the ball. After I have dropped my balls I will pick them up so no-one slips or slides on them and may cause injury to them. I will tie my hair up so it doesn’t get in my way whilst taking measurements. Finally I will not mess around whilst the experiment is taking place.

When I get my set of results, I can use them to approve or disapprove my hypothesis relating GPE with drop height and bounce height with drop height. I can also exclude any anomalies I have. I can then draw a graph and the line on the graph will show if my results are correct and what they mean. If all my points line up quite close to the line of best fit, they are probably reliable and correct.

Obtaining Evidence

My results came out much like I expected. The experiment went to plan and I didn’t find there were any difficulties which prevented me from getting good results.

I drew a graph to show these results:

Conclusion

As you can see my prediction is slightly wrong. I predicted there would be a straight line through the origin. Instead there is a slight curve, showing that when I was using the lower drop heights, more of the kinetic energy that was stored was used in the bounce. As the drop height increased, more and more of the kinetic energy in the ball is lost during the fall and collision with the ground and so the difference between the bounce heights gets smaller. The average bounce height increases less and less the higher the drop height becomes.

I think this is because I over looked an energy-wasting factor. When a ball is dropped from a higher drop height there is more friction due to air resistance. Meaning the ball will lose a lot of energy this way.

In order to prove my hypothesis correct that drop height is directly proportional to the amount of gravitational potential energy stored in the ball I am going to make some calculations using the formula for GPE.

The GPE formula is:

GPE = HEIGHT x MASS x GRAVITATIONAL FIELD STRENGTH

Using the formula, I can work out how much GPE the ball has at the start of each investigation and after the ball had bounced.

To conclude with my graphs I need to find the efficiency of the ball to complete my aim, I will do this by: GP after bounce X 100

GP before bounce

Evaluation

Overall, I believe my results were as accurate and as reliable as I could have made it. I was pleased I did not achieve any anomalies, meaning that I got good results and also that I performed the investigation with great care. The camera that we had really helped to attain those vital recordings that we needed to get. I think though the ball should have been dropped by a mechanical device so there would be no force exerted onto the ball. I had enough evidence to explain why my graph was a curve instead of a straight line. However all my results did follow a pattern, I did not have any unexplainable results because I took enough test and averages to be wrong!

If I could do this experiment again I might investigate with a different ball. Such as a ping pong ball. This would be interesting as the ball is much lighter and made out of different material as a bouncy ball. Also the ball is much smaller. I think there would be less air resistance as the ball is smaller and lighter.

I really enjoyed this investigation!