Below is the table, which I will collect my data/results in.
Once I have collected the data I will use it to draw a force-extension graph
as shown below.
If the elastic band obeys Hooke’s law then the results plotted should give us a straight line and then we can find out the elastic energy stored from the area under the graph.
If the elastic band does not obey Hooke’s law then the results plotted will not give us a straight line and so I will estimate the elastic energy stored (area under the graph) using an approximation method.
E.g. find the energy represented in one square and count the number of squares.
In this case the energy stored:
At extension of 0.1 = area A under the graph
At extension of 0.2 = area A+B under the graph
At extension of 0.3 = area A+B+C under the graph
At extension of 0.4 = area A+B+C+D under the graph
Accuracy and Sensitivity
To maximize the accuracy in the experiment I will take 3 reading for each test and then I will take an average.
I will also be using equipment, which is accurate and give me reliable results.
I will use an electric weighing machine that weighs to every gram. I would use this to measure the staple.
I will also use two one-meter rulers, which I will measure the height of the staple when fired. I will measure to every 5cm because when the staple is fired it will be to quick to get a precise height of the staple but I will repeat the same test 3 times.
I will also be using an 8cm piece of string to attach it onto the weight holder and the elastic band. So when the elastic extends I can place the staple on the elastic and when in position to measure the height of the staple I will cut the string and the staple will be fired into the air and I will measure, I will do this for each test.
I decided to use the piece of string instead of holding the elastic band with my fingers and then taking the weights of with my other hand. This is because holding the elastic band at a specific extension with my fingers could increase or decrease the extension and so would effect my results very much. Using a string between the weights and the elastic band, the extension will stay the same and I will have time to get into the right position to measure the height of the staple. This method is more accurate and will give me more reliable results.
When doing the experiment the 2 meter rulers will be stuck with some blue-tack on the wall opposite to the stand/clamp on the table. I will sit on the table behind the stand and clamp lining myself with the 2-meter rulers so when judging the height of the staple when fired is easier and I can get a more reliable and accurate results.
Safety
In this experiments the staple that is fired has sharp ends to it and so it can be dangerous. So throughout this experiment I will wear goggles and work in an area away from others.
Method
1) Set up the equipment as shown in the diagram on the first page.
2) Cut a 8cm of string
3) Attach the string to the weight holder (weight holder weighs 100g)
4) Attach the other end of the string to the elastic band.
5) Measure the extension of the elastic band and record it.
6) Get into the right position to record the height of the staple.
7) Cut the string and record the height to the nearest 5cm.
8) Repeat each test 3 times and then take an average of the height.
9) Repeat the same experiment using the next weight (200g).
Obersavation and Recording
To calculate the amount of elastic energy stored in the elastic band at different extension, I drew a graph based on the results shown below. The area under the graph is represented of the elastic energy stored at various extensions.
From my graph, each 1cm * 1cm square is represented of 0.005 J of elastic energy.
The elastic energy is an approximation. I have tried to be as accurate as possible whilst counting the squares.
I found that the distance from the floor to the ceiling was 3.32m and the distance the elastic band traveled from rest while attached to the clamp to the point where it hits the ceiling to be 2.07m.
From looking at the results we can see that the maximum height reached by the staple, the point where it hit the ceiling was when its extension was 10cm. From this I can calculate the amount of elastic energy stored in the band using my graph. I can also calculate the amount of energy transferred to the staple, ie the potential energy gained, by using the equation mgh. The distance the staple traveled being 2.07m and the mass weighed to be 2g.
Potential energy gained by the staple = mgh
= 2.0g 9.81 2.07
= 0.002 kg 9.81 2.07
= 0.041 J
I can also calculate the efficiency of the energy transferred to the staple:
Efficiency = mgh * 100
Area
= 0.041 J * 100
0.175
= 23.43%
Evaluation
In the experiment I was trying to measure the efficiency of the energy transfer for the staple fired into the air, by the elastic band.
The energy conversion in the experiment is the transfer of elastic energy stored in the elastic band to potential energy gained by the staple after it has fired into the air.
Elastic energy → Potential energy
From looking at my results the general pattern is that an increase in extension increases the height of the staple that is fired. The graph I have produced, force extension graph also show this. The graph does not follow Hooke’s law, as the line is not straight.
The values I collected for the elastic energy was 0.170 J and energy converted into potential energy in the staple after it had been fired was 0.041 J. The percentage efficiency for this energy transfer was 24.1%. This means only a small amount of elastic energy was converted to potential energy and most of the energy had been lost.
The reason for this could be due to the air resistance. I stretched the elastic at different lengths and observed how far the staple shot off as a result. At first the relationship between the extension and the distance was close, nearly the same. Then air friction could of decreased the distance traveled for a given stretch. This would mean that the staple would have gained less potential energy.
Also this experiment involves the transformation of elastic energy to potential energy between the elastic and the staple. But when the elastic band is stretched and released this involve the transformation of elastic energy to kinetic energy so some energy could have been lost due to this kinetic energy.
Another reason could be that when stretched, energy could of been lost as a form of heat. When the elastic band is stretched the rubber polymer chains become more orderly and H bonds form between these chains. This H bond formation is exothermic therefore the stretched elastic band will feel warm and heat will be lost. (Reversing this process (when unstretched), the polymer chains become disorderly, the H bonds break and as this is endothermic, heat is absorbed and the band feels cool.) This heat energy lost will have an effect on the transfer of energy between the elastic band and the staple.
To keep this experiment as accurate as possible I took 3 reading for each test and then I took an average. I used appropriate and reliable equipment and used them properly.
When taking the results I will also draw the graph at the same time so if any chance an anomalous result does occurs I can go back and repeat the same test to get the right result. I also design the experiment so I would be as accurate as possible using the equipment from the lab.
I thought that the experiment went well, the results that I got I thought was accurate and reliable. I thought that the experiment was well planned, reducing any factor that would lead to unreliable results.