To use rubber bands to produce an accurate and reliable spring balance to weigh fish caught by an Angler. We have to consider how reliable and sensitive the gauge will be.
The Anglers Problem
Aim
To use rubber bands to produce an accurate and reliable spring balance to weigh fish
caught by an Angler. We have to consider how reliable and sensitive the gauge will be.
Prediction
I predict that the greater the weight applied to the band, the further it will stretch. This is due to extension being proportional to load, and so if the load increases so does the extension and so does the stretching distance.
I believe that the best device would produce results to form a graph similar to the one below (line of best fit shown in red).
I predict that the two bands in series will be the most sensitive device, due to its length. It will also be more stretchy (blue line). However its elastic limit will not be that high. The 2 bands in parallel will not be as sensitive but it will have a high elastic limit (green line). I believe that the 2 parallel connected to the one band will be a good device. It will be sensitive (due to its length) and it could cope with a heavy load due to the thickness of the top half. The two bands in parallel connected to the two bands in parallel will be both sensitive and strong. This would make the best device.
Hypothesis
Hookes Law states that if you apply force (f) to a spring, the spring will stretch by some length (x). Doubled force means double the stretch. This is known as a mathematically direct relationship. Line of best fit for a force vs. stretch graph would be a straight line ascending steadily, as the weight increases. This is because the amount the spring stretches is directly proportional to the stretching force.
This direct relationship can be represented by the formula: y = mx+b, where m is the slope and b is the y-intercept. So y is the force and m is the spring constant (size of force that stretches spring by 1cm) and b is 0.
So using Hookes Law we can write F= KX (force=spring constant x extension). To find the value of K I will add weights so the band stretches by 1 cm. Using elastic band I will try and replicate the properties of a spring, as this would make the best suited device.
Higher values represent stronger, less stretchy bands, and lower values represent weaker easier to stretch bands.
The only limitation to Hookes Law comes if you stretch the band beyond its elastic limit or, in other words, when you stretch the band so far it permanently deforms.
If the F=KX relationship applies to results gained from a certain formation with the bands, then this is the best device to weight the fish, as it show that the spring is both accurate and sensitive, and that the amount the band stretches is proportional to its stretching force. So if the extension doubles when you double the force, and the band goes back to its original length afterwards, then this is the best formation for the Angler.
For a regular rubber band doubling the weight would more than double the extension. This is due to its elasticity and is why I have to use different formations.
If the bands are in series they will stretch a lot and be very sensitive, due to its length.
If the bands are in parallel they wont stretch as much, but will cope with more weight. I will use this to create a formation that will use the positive aspects of both, without the negative aspects thus creating the best device.
Rubber bands are polymers. For such a versatile material, it has a very simple structure. A molecule of polyethylene is nothing more than a long chain of carbon atoms, with two hydrogen atoms attached to each carbon atom. Sometimes it's a little more complicated. Sometimes some of the carbons, instead of having hydrogens attached to ...
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If the bands are in parallel they wont stretch as much, but will cope with more weight. I will use this to create a formation that will use the positive aspects of both, without the negative aspects thus creating the best device.
Rubber bands are polymers. For such a versatile material, it has a very simple structure. A molecule of polyethylene is nothing more than a long chain of carbon atoms, with two hydrogen atoms attached to each carbon atom. Sometimes it's a little more complicated. Sometimes some of the carbons, instead of having hydrogens attached to them, will have long chains of polyethylene attached to them. This is called branched, or low-density polyethylene. When there is no branching, it is called linear polyethylene. Linear polyethylene is much stronger than branched polyethylene, but branched polyethylene is cheaper and easier to make and so our elastic bands are probably made with this material and so will not be as strong.
A rubber band has some very interesting thermodynamic properties based on its structure.
You can easily perform the following experiments. Obtain a rubber band and quickly stretch the rubber band and then press it against your lips. You will feel a slight warming effect. You can also carry out the reverse process. First, stretch a rubber band and hold it in position for a few seconds. Then quickly release the tension and press the rubber band against your lips. This time you will feel a slight cooling effect. A thermodynamic analysis of these two experiments can tell us something about the molecular structure of rubber.
Rubber molecules in their normal state are in a state of disorder (high entropy). Under tension, the molecules line up and the arrangement becomes much more ordered (low entropy). When the tension is removed, the stretched rubber band spontaneously snaps back to its original shape. The cooling effect means that it is an endothermic process, so the entropy of the rubber band increases when it goes from the stretched state to the natural state. This means that the rubber band will eventually wear out in the end (after the Angler has used it quite a few time).
Plan
To conduct this experiment I will need elastic bands (of the same type), a metre ruler, 2 clamp stands, and weights.
I will use 4 different formations of bands. These formations are as follow: 2 bands in parallel, 2 bands in series, 2 bands in parallel connected to two bands in parallel, and 2 bands in parallel connected to one band and one band.
I will suspend the elastic band from the clamp stand. A second clamp stand will hold the metre ruler in place, starting from the top of the band. I will then add weights, starting with the lightest and ending with the heaviest. I will measure the initial length of the band, and the length of the band after the weight has been added. I will use these measurements to calculate the extension of the band (Extension=New length-Original length). Before adding more weights I will check that the bands original length is the same as it was previously, as we do not want it to stretch.
Before deciding on the range of experimentation I carried out a preliminary investigation to find the elastic limits of the band. To do this I added weights to the band until it no longer returned to its original length or until it snapped. The band often snapped when weights over 12 kg were applied to it. The band deformed at weights over 3kg (obviously this depended on the type of formation). This gave me a suitable rage of weights to work with. I will use 10 different weights: 200g, 400g, 600g, 800g, 1kg, 1.2kg, 1.4 kg, 1.6kg, 1.8kg and 2kg. I will increase the weights by 200g each time to see how sensitive the bands are. To see how a small change in weight the device detects. A good angler would catch fish weighing from 250g to about 2 kg, which is why I will use these specific weights. By using a weight of 2kg I will not exceed the proportional or elastic limit of the band. I hope to carry out the experiment 3 times and take an average to increase the reliability of m results.
To ensure that this experiment is a fair test I will measure the original length and the extended length accurately to the nearest cm, using a ruler which measures to the nearest cm. I will make sure I use the same type of bands (ie. Same thickness, length etc.). I will add the same sequence of weights to each formation of bands.
I will wear safety goggles whilst conducting the experiment just in case the band snaps.
Results:
One band
Weight applied to band (N)
Initial length of band (cm)
Length of band after weights applied (cm)
Extension of band (cm)
2
6.0
3.0
4.50
4
6.0
8.0
9.50
6
6.0
26.0
7.5
8
6.0
34.5
26.0
0
6.0
40.0
31.5
2
6.0
44.0
35.5
4
6.0
48.0
39.5
6
6.0
50.5
42.0
8
6.0
53.5
45.0
20
6.0
56.5
48.0
Two bands in series
Weight applied to band (N)
Initial length of band (cm)
Length of band after weights applied (cm)
Extension of band (cm)
2
6.0
22.5
6.50
4
6.0
32.0
6.0
6
6.0
46.0
30.0
8
6.0
61.0
45.0
0
6.0
69.5
53.5
2
6.0
75.5
59.5
4
6.0
81.0
65.0
6
6.0
85.0
69.0
8
6.0
88.5
72.5
20
6.0
92.0
76.0
Two bands in parallel connected to two bands in parallel
Weight applied to band (N)
Initial length of band (cm)
Length of band after weights applied (cm)
Extension of band (cm)
2
6.0
9.0
3.00
4
6.0
22.0
6.00
6
6.0
26.5
0.5
8
6.0
32.5
6.5
0
6.0
40.0
24.0
2
6.0
46.5
30.5
4
6.0
55.5
39.5
6
6.0
60.0
44.0
8
6.0
68.0
52.0
20
6.0
76.0
60.0
Two bands in parallel connected to one band
Weight applied to band (N)
Initial length of band (cm)
Length of band after weights applied (cm)
Extension of band (cm)
2
6.0
20.5
4.50
4
6.0
26.0
0.0
6
6.0
32.5
6.5
8
6.0
40.0
24.0
0
6.0
47.5
31.5
2
6.0
57.5
41.5
4
6.0
65.0
49.0
6
6.0
71.0
55.0
8
6.0
77.0
61.0
20
6.0
81.5
65.5
Two bands in parallel
Weight applied to band (N)
Initial length of band (cm)
Length of band after weights applied (cm)
Extension of band (cm)
2
8.00
0.0
2.00
4
8.00
1.5
3.50
6
8.00
3.5
5.50
8
8.00
6.0
8.00
0
8.00
9.5
1.5
2
8.00
21.0
3.0
4
8.00
24.0
6.0
6
8.00
26.0
8.0
8
8.00
29.0
21.0
20
8.00
31.5
23.5
Conclusion:
According to my findings the best device for the Angler would be the two bands in parallel two bands in parallel. This is evident when looking at my graph. The gradient of the line is quite steep which showed the devices sensitivity and it also shows that the band was quite stretchy. Hookes Law does apply to this as the amount the spring stretches is directly proportional to the stretching force. By taking two values from my results you can see that doubling the force, doubles the extension. At 2N the bands extension is 3cm, and at 4N the bands extension is 6cm. This was not always the case. The band did not lose it elasticity. Rearranging the F=KX formulae to K=F divided by X I can work out the spring constant, by taking points off my graph. E.g. 10/25= 0.4. This applies, more or less, to my results. (0.4x37N=16.8).
The two bands series was very sensitive and lost its elasticity at around 8N. The two band parallel was not as sensitive but was very reliable and the amount of force was proportional to its stretching force. E.g. 4N-3.5cm and 8N-8cm). Creating a device with these two one mixed would be a good one, which is why two band parallel-two band parallel was so good.
The one band, as expected was not a good device as its elastic limit was low and it was not as sensitive in detecting small weights, like the others. It would not make a reliable device. This is due to its high entropy.
The two band parallel connected to the one band was a good device. It was sensitive to weight change, but Hookes Law did not really apply to it in the way that I had hope.
My line of best fit was good without any anomalous results.
There are reasons why some devices were better than others. Materials expand or contract when they heated. This property of the material called its entropy. The entropy of a material is a measure of the orderliness of the molecules that make up the material. When the molecules are arranged in an ordered fashion, the entropy of the material is low. When the molecules are in a disordered arrangement, the entropy is high. When a material is heated, its entropy increases because the orderliness of its molecules decreases. This occurs because as a material is heated, its molecules move about more energetically. In materials made up of small, compact molecules, the molecules move about more, and they push their neighbouring molecules away. Rubber, on the other hand, contains very large, threadlike molecules. When rubber is heated, the sections of the molecules move about more vigorously. In order for one part of the molecule to move more vigorously as it is heated, it must pull its neighbouring parts closer. Heating the stretched rubber band causes segments of the molecules to move more vigorously, which can be represented by wiggling the middle of the string back and forth. As the middle of the string moves, the ends of the string get closer together. In a similar fashion, the molecules of rubber become shorter as the rubber is heated, causing the stretched rubber band to contract.
When weights were applied to a band it causes them to stretch heat which results in the molecules becoming ordered. When it goes back to its normal state the molecules are disordered. This is why some bands elastic limits were low. This is why we had to come up with devices to account for this. Bands like two in series and one band entropy was too high and the two bands in parallels' were too low. Accounting for this we had to come up with a device whose entropy was not too high or low.
Evaluation:
My experiment was quite good considering the conditions offered to us. There are not really any anomalous results but we did not achieve the doubling effect. There are a number of factors which could have affected our experiment.
No rubber bands are identical. We could have used slightly different elastic bands for each experiment.
If the bands had been heated previously, then the structure of the molecules in the rubber would be disordered and therefore the band would not perform as well as it could have.
I believe that we did measure and calculate the extension accurately.
We exceeded the elastic limits of the bands for a couple of the devices, but this just showed they were not suitable devices for an Angler.
We did, however, produce a device that the F=KX relationship applied to.
My prediction on the whole was correct and my experiment gave results which I was happy with. I would have liked to have repeated the experiment 2 more times and take an average to increase reliability of my results; however there was not enough time.
The doubling effect (described in Hooke's law) was discovered by scientists with better facilities, techniques, and more time than we have, which is another reason why I did not get the doubling effect.
Given more time we could have improved our results by conducting the experiment more times, and trying different techniques.
I would have liked to conduct a Simple Harmonic Motion experiment which requires measurements of time over an oscillation of the band being acted on by different forces. This would allow me to see if my spring constant was accurate. My method of experimentation for simple harmonic motion would be to suspend the band as in the first experiment and place on the required weight. I would then stretch the band a further 15mm and then release the band and take a time measurement for an oscillation in the band. Only one test would be needed to find the spring constant but I would take 5 tests each with a different weight. There is a formula I could use to work out the spring constant with these results, and I could compare it with that of my Hookes Law experiment.