Using 10% as a figure for this loss:
A ball with a mass of 10g is dropped from 1m
10g = 0.01kg = weight of 0.1N
0.01N x 1m = 0.1 joules of G.P.E
- 10% = 0.1 x90
100
- x 9
10
- x 9 = 0.09J
The ball after point B now has 0.09J of E.P.E
This can be converted to 0.09J of kinetic then G.P. energy
The ball still has a mass of 10g or a weight of 0.1N
So it can reach a height of 0.09 m
0.1
0.09 = 0.9 = 0.9m
- 1
Working with the same ball from 2m
0.1N x 2m = 0.2J of G.P.E
0.2 x 90
100
0.2 x 9
10
- x 9 = 0.18J after point B
0.18 = 1.8 = 1.8
- 1
The ball dropped from 1m would bounce to 0.9m where as the ball dropped from 2m would bounce 1.8m. The ball dropped from a higher height bounces higher.
Preliminary practical
To test this prediction I will need to drop a tennis ball from varied heights and record the height it bounces to.
It was decided, after watching the ball to see how accurately the bounce height could be measured, that the ball should be dropped at 20cm intervals from 2m to 20cm to obtain enough results.
Therefore two metre sticks will be needed, these will be taped together to keep them at a constant height.
Results:
Problems:
It was difficult to hold the metre sticks steady- this can be resolved by taping them to the wall.
Doing a preliminary practical will help me in my plan because I will know exactly what apparatus I will need, which heights I will be dropping the ball from and how we will measure this. It will make my plan clearer and easier to follow.
Plan
Apparatus:
- 2 metre sticks
- A Tennis ball
- Masking tape
The range of measurements was decided during the preliminary practical; 2m-0.2m every 0.2m.
Method:
Starting at 2m the ball will be held with the bottom of it in line with the height mark on the ruler of the height that is being recorded.
The ball will be dropped and a second person will watch it, they will see the height that the ball bounces to.
This measurement will be recorded.
This will be repeated three times at each height.
This will then be repeated for 1.8m, 1.6m, 1.4m, 1.2m, 1m, 0.8m, 0.6m, 0.4m, and 0.2m.
Controlling variables:
We will ensure that this is a fair test by using the same ball and floor for each drop, the same person will drop the ball and the same person will take the measurement for each drop. The ball will be dropped not pushed. Repeating each height three times and calculating the average will make the results accurate.
(No safety precautions are needed for this practical.)
Results:
I result was repeated because it was drastically different to the other two results for that height.
results
line of best fit
Conclusion
These results tell us that the higher the height a ball is dropped from the higher it bounces. For example at 2 metres the ball bounces to 1.3 metres but at 1 metre it bounces only to 0.61 metres. This is consistent throughout the height range. This is what I predicted would happen. This is because the amount of energy the ball starts with is relative to that it ends with because of the conversions which happen: chemical potential-gravitational potential-kinetic-elastic potential and sound-kinetic-gravitational potential.
The ball weighs 56g or 0.56N. Therefore at 2m its G.P.E is 0.56 x 2 = 1.12 J
At the height of the bounce its G.P.E is 0.56 x 1.3 = 0.728 J
At 1m its G.P.E is 0.56 x 1 = 0.56 J
At the height of the bounce its G.P.E is 0.56 x 0.61 = 0.3416 J
Because the ball starts off with more energy, though it looses a percentage of its energy to the surroundings in the bounce, it ends up with more energy.
To prove that as I predicted it is a percentage of the original energy that is lost in the bounce I must calculate the efficiency of the bounce:
The calculation for this is Energy after bounce x 100
Energy before bounce
The height the ball is at represents the amount of G.P.E it has.
So efficiency = Height at top of bounce x weight of ball x 100
Height at top of drop x weight of ball
(This can be cancelled down to Height at top of bounce x 100)
Height at top of drop
So the simplified calculation for this is y x 100
x
This can be shown in an efficiency table:
The average efficiency is 62.8% (total efficiencies added together and divided by 10)
This efficiency can be shown in a Sankey diagram:
The trend on this graph shows that, in general, the higher the drop the lower the efficiency. This is because we started with the highest height this meant that the ball was hotter the lower we went. Therefore it had more energy and was able to bounce higher, as it converted this heat to kinetic energy and then to G.P.E.
This trend also proves that the amount of energy lost in the bounce is relative to the amount of energy the ball begins with- as I predicted, if it was not then the efficiency would be greater the higher the drop.
Evaluation
This experiment was not particularly accurate because the measurements in columns i, ii, and iii are not as close as they should be to each other. On the graphs the lines of best fit are not as close to the results lines as they could be. This is because the only way of measuring the results to this experiment are by eye and this is not an accurate measuring device.
The measurements for 0.2m were particularly inaccurate- the difference in efficiency for example is much more pronounced than the differences between other results, this is probably because when dealing with such small distances it is even harder to see the height which the ball has reached.
On the efficiency graph the results for 0.4 and 2 are out of the trend, as the results on this graph are based on the measurements taken this means that the 0.4 and 2 results are not as accurate as they should be. There is no explanation why these particular results are inaccurate other than they were not measured well.
I believe that though the measurements are not accurate the range of my results gives me grounds enough to draw an accurate conclusion because the range is large enough to show any huge errors- such as that of the 0.2m results.
Other useful data on this hypothesis would be results for different makes of ball, or on different surfaces recording the bounce heights for different drop heights. The trends could be compared to prove that the hypothesis is correct under all circumstances.
In order to gain more accurate data this experiment should be repeated with the use of a digital camera so that the footage could be slowed down and exact bounce heights could be determined. However this experiment was entirely suitable to prove my prediction, as I have.
Safety:
For safety the person who is undertaking the exercise should be careful that they do not miss their footing, sensible shoes and clothing should be worn and too much exercise should not be done.
Results
