y = mx + b
where m is the slope and b is the y-intercept.
More specifically:
y = mx + b F = Force in Newtons
k = Spring constant
Zero x = Extension in Meters
F = kx
Here, k is called the spring constant. It is measured in units of N/m.
Hooke’s law applies to both stretchable and compressible springs (and of course elastic bands!).
There is only one limitation to Hooke’s law, and that’s if you stretch the spring beyond it elastic limit. Or in other words, when you stretch or compress the spring so far that it permanently deforms (or in our case, snaps).
To sum it all up, Robert Hooke found that extension is proportional to the downward force acting on the spring.
My method of experimentation will be to use a clamp stand and a boss clamp to suspend an elastic band from. We will then use a meter rule to measure the length of the elastic band as the weights are being put on. We will then add weights, one at a time, and measure the new length of the elastic band. To find the extension, all we have to do is take the old length away from the new length. We did this experiment twice. The first time we found the elastic limit for the elastic band, and so the second time we knew not to go that far when putting the weights on. The first time we found that at 2400g it snapped. So the second time we chose to go up to 2000g. The reason we chose 2000g instead of, say, 2200g is that the limit of proportionality is slightly less than the elastic limit of the elastic band, therefore, using 2000 I can make sure that I do not exceed the proportional or elastic limit of the band. We will carry out the experiment 3 times, the first and second being us measuring the length as the weights are put on, and the third us measuring the length as the weights are being taken off to see if there is a difference in the length when it is taken off and when it is being put on. We will also take an average. However, I will not use the third experiment in my average.
As far as safety precautions go, we will wear safety goggles, just in case the elastic band does snap, which will be highly unlikely, due to the first experiment we did to find out the elastic limit. But, we will also use something to hold the clamp in place, so it doesn’t fall over.
Experiment diagram
The weights we had were 10N each, so I have started off with 10N and finished with 200N.
Results table
Measurements are in cm.
These are recorded on a graph on the next page.
On my graph, it shows a positive correlation. That means that as the force increases, then so does the extension of the elastic band, as we would’ve thought to happen. If we were unloading the band then it would still go up as a positive correlation, unless it doesn’t obey Hooke’s law. If it doesn’t obey Hooke’s law then it would be more of a curve then a straight line. The experiment we did obeys Hooke’s law as you can see from the graph. There is nothing out of place and so nothing really seems wrong. If our elastic band had snapped then at the top it would go up but not across, that would show that it has snapped and/or has become inelastic. But if it goes across and not up then that would be a spring, but that’s not what we are looking at.
Evaluation
The results I obtained were reasonably reliable and quite accurate, as the graph shows, because the points are close to the line of best fit. However, the results were not quite as accurate as I would have hoped, because different elastic bands were used for the first and second experiment, and, no two elastic bands are alike. In terms of reliability to the Hooke’s law theory, the experiment was conducted twice and then an average taken, the results being quite close together. However, it appeared that as the extension increased the difference between the two results decreased slightly. The reason could be that the elastic band was nearing its limit of proportionality. This shows that my results for this experiment support Hooke’s Law, which proves the prediction to be correct.
The first experiment to find the elastic limit for the elastic band helped with the safety precautions. There was very little danger that the elastic band would snap if the elastic limit was not reached.
In conclusion the results supported each other as well as the laws they were based on. If the experiment were to be repeated, then I would make some changes in the way it was carried it out to reduce experimental error.
- In both tests it would have been preferable to hold the ruler in place by using a boss clamp instead of holding it. This would ensure more accurate results by removing human error.
- I would have used a pointer on the elastic band that would also help me gather the information more accurately, this would help by pointing to the measurement instead of us having to bend down and look.
By undertaking the experiment again I could ensure that the results were accurate which would mean that the averages were more reliable.
