Methods
You will need
- A spherical wooden ball of diameter 2cm
- A 45cm plastic V shaped ramp
- 2 50cm rulers accurate to 1cm
- A wooden block with a G-clamp
- A stand and clamp
- A light gate connected to a computer
- A stop-clock
- A hard work surface.
Set up the experiment as shown in the diagram. The plastic ramp is supported by the stand and clamp and can be used to change the speed of the ball. The wooden block is also clamped to the bench with a G clamp. The two rulers should be placed between the bottom of the ramp and the wooden block, providing a small channel to guide the ball to the block.
Method A
This method requires the use of the stop-clock to measure the time it takes for the ball to travel from a suitable point to the block and then the time taken for it to travel back again. Press the start button of the stop-clock when it passes a suitable point, then when the ball hits the block press the reset button. The stop-clock may appear to have stopped but in fact it is still running. Then press the stop button when the ball has bounced back to the point where you started timing. The stop-clock should now say the amount of time taken for the ball to reach the wooden block. Record this time and then press the reset button, the stop clock should now say a new time, this is the cumulative time of the experiment. By subtracting this second time from the first you can calculate the time taken for the ball to rebound.
These two times are the time taken for the ball to travel from the suitable point to the block, and the time taken for the ball to travel from the block to the suitable point. They should be then recorded in a table.
Method B
This method uses a light gate connected to a computer, which gives readings of how long the ball took to pass through the light beam. The readings on the computer should come in pairs, the first reading being the time taken for the ball to pass through the light beam on its approach, and the second reading when its rebounding. Sometimes the ball may bounce out of the channel made by the rulers when it hits the block, if this happens then only one reading appears on the computer as it has only passed the light gate once. This reading should be ignored and the ball dropped again, until its bounces off the block and passes back through the light gate.
Preliminary Experiment
The reason for my preliminary experiment was that I wanted to find a suitable material as the ball, a suitable angle for the slope, where abouts I should position my light gate so that it would record the speed of the ball as soon as it rebounds and also a suitable point to start timing from in Method A. In theory the closer the light gate is to the block the more accurate the readings should be as the speeds are recorded just before the ball hits the block and just after. However if the light gate is too close to the block (less than the diameter of the ball) then there is only one reading as it only breaks the beam once.
The bigger the angle of the slope, the faster the approach speed of the ball is, and the more likely that the ball will bounce out when it hits the block. But if the gradient of the slope is too small then I will not be able to get a big enough variation in speeds. I intend on finding a slope angle that provides a good balance.
For my preliminary experiment I chose Method B as I feel that this will probably be the more accurate of the two as there is less scope for human error. Here are my results from dropping the ball at 6cm and 34cm.
From trying various different angles for the slope, I found that about 30° was a perfect angle. At this angle I was able to vary the velocity of the ball quite a lot, and also most of the balls stayed in the channel the vast majority of the time. Rather than use a protractor, which may be inaccurate I used trigonometry to ensure that the angle was exactly 30°.
When dropped from 34cm the large and small metal ball failed to rebound off the block at all and all the metal balls didn’t rebound off the block when dropped from 6cm. I found that when using the small wooden ball, it tended to bounce out of the channel a lot more than the other balls as it has the smallest mass and is also quite small (diameter of 1.5cm). It required a lot of retakes for the ball to bounce straight off the block and to get 2 readings. The marble consistently stayed in the channel and also rebounded off the block back through the light gate. However from looking at my results there is a very small difference between the speeds that it rebounded at both heights. I found that when the marble was dropped from similar heights the results that the light gate recorded were almost identical. This means that when doing
Method A it would be very hard to get accurate results as the rebound speed varies very slightly. The ball that I found to be the most consistent in staying in the channel as well as giving a varied rebound speed was the large wooden ball. It is this ball that I will do my experiment with.
The closer the light gate is to the block then the more immediate the readings are, as they are taken just before it hits and just after. Because of this I’m going to position the light gate 2.5cm from the block. This is close enough to ensure reliable results, and far away enough so that I get two readings, as the ball diameter is 2cm.
The suitable point from the block I found to be about 25cm. Anything less than this was difficult to collect results for, as when the ball was dropped from 40cm I had to press both buttons on the stop-clock very quickly in succession as it was going so fast. This means that the closer the point is to the block the more inaccurate it is, but when it’s far away then the ball is unable to rebound back up to the point. When I made the point 40cm away from the block, I found it very easy to use the stop clock at all speeds but was unable to get results below 10cm, as the ball did not rebound far enough. I found that a good balance at which I could get reliable results with the stop-clock as well as use all heights was 25cm away from the block.
For my experiment I’m going to take my results from the computer to 3 decimal places and 2 decimal places when using the stop-clock. But when calculating the speed for Method A, I will use 3 decimal places so that both methods are to the same degree of accuracy.
Observation
Results
Method A
To find the velocity I just substituted time into the equation S = Distance / Time
Where the distance is 0.25m.
Repeat 1
Repeat 2
Method B
Repeat 1
Repeat 2
Analysis
In order to show the relationships between the approach speed and the rebound speed of both methods, I have constructed a few graphs.
We can see from the graphs that the more accurate of the two methods is definitely Method B. On this graph there are no anomalous results, which proves that the data is fairly reliable. The gradients of both graphs are also quite close to each other, in theory they should be the same, but some minor anomalies skew the line.
A graph has a straight line if both axes are proportional to each other. In this case the approach speed and rebound speed. Since they are straight lines this proves my prediction that Va Vr. This also means that they both lose almost the same amount of energy to the block. In theory they should both lose the same amount of energy to the block, as they are the same experiment only with different speed measuring devices.
In order to find the amount of energy lost to the block I need to do the following calculations,
If KE of the rebound / KE of the Approach = Proportion of Energy Retained
then
Gradient = Va / Vr Therefore
Gradient² = (Va / Vr)² = KE Approach / KE rebound
So (1 / Gradient)² = (KE rebound / KE approach)²
So as (KE rebound / KE approach)² = Energy Lost
And (1 / Gradient)² = (KE rebound / KE approach)²
Then this means that (1 / Gradient)² = Energy Lost
And so 1 – (1 / Gradient)² x 100 is the percentage energy loss
Gradient of Method A = 0.854 so 1 – (1 / 0.854)² = - 0.371 (3 d.p)
So the calculated energy loss to the block from Method A is 37.1%
Gradient of Method B = 1.072 so 1 – (1 / 1.072)² = 0.130 (3 d.p)
So the calculated energy loss to the block from Method B is 13.0%
Evaluation
I think that my results that I have obtained are reasonably accurate and precise, especially the results for the method B. The reason for this is that the majority of the points are on the line of best fit for method B although there is more variation for method A as this method is less accurate. The reason that method A is more inaccurate than method B is that there is far more scope for human error. For this method I had to press the button on the stopwatch at exactly the right time for the result to be correct. Any deviance from the correct time would have caused the result to be slightly inaccurate. I have a few anomalous results for method A for when the approach speed is high. This is because the faster the ball is going the harder it is to be accurate with the stopclock, and so the results do not fit on the line as well. For example if the stop clock button was pressed slightly after the ball passed it, then the distance between the point and the block would be too small, and then if is was pressed equally late after it had come back and passed the point again then the distance between the block and point would be too big. This means that if my reflexes were equally slow both times then the approach speed and rebound speed for that result would be way out. This explains the anomalous results when the ball was travelling fast, as the timings would be far less accurate and so would skew the graph and subsequently the gradient.
The percentage of energy losses to the block for the two methods are quite different to each other, this is due to the experiments themselves being more or less accurate then each other. As a whole I think that the percentage of energy lost in method B is more accurate than method A as the points fit on the line of best fit much better and so the gradient of the line is more accurate.
The reason that I only collected data for heights of 28, 32, 36 and 40cm in method B and not 30, 34, 38cm is that the ball continually bounced out when it hit the block at these heights. When dropping the ball at anything above 24cm I found that it required numerous repeats to ensure that I got 2 results, as the ball refused to stay in the track. However after about 4 tries for each height I finally got a reliable result.
If I were to repeat the investigation I would take more results for each height, and also drop the ball from more heights. For example I would take 3 readings for each height as well as increase the heights by 1cm instead of 2cm. For method A I would also use a more accurate stopclock, one with 3 decimal places instead of 2. As well as have somebody with amazing reflexes using it, so that the results are even more reliable than if I were to do it.
With these more accurate results it would also mean that my conclusion is more reliable.
Bibliography
http://learntech.uwe.ac.uk/radiography/RScience/sciencestudypack/energy1.htm