Hypothesis
From the theory I expect to find that I will get a constant extension with every 100g added to the spring. The graph that is shown in the theory states that the yield point comes after the elastic limit. I predict that it will come very close to it, 1N or 2N away. I also expect the extension up to the elastic limit will be equal distance away from each other. I predict that my graph will look like this:
This graph is what the graph is like in the theory, so I suspect it will be the same in the experiment. I expect to see the results entered go in a straight line. I think that the elastic limit will be around 14N. At the point where there is a black cube, is where the graph starts to curve. This is where I predict the elastic limit will be.
Variables
For the experiment, the stretching force will be the independent variable. One 100g weight will be added each time. The dependant variable is the extension of the spring. The length is taken every time a weight is added. The control variables are the point where the spring is measured from and the mass of the weight being added each time. To make it a fair test, the same equipment is used. The same spring is very important. A different spring could have different qualities e.g. coil size. The spring must be as close as possible to the ruler so that an accurate reading can be made. Also the spring and ruler should be fastened securely to the clamps so that there is no chance of them moving and causing inaccurate results.
Method
The apparatus is set up as it is shown in the diagram. The goggles are worn to protect the eyes as the spring could break or shoot back up and hit someone. The scale reading is noted of the bottom of the spring. Then, a hanger is attached to the bottom of the spring. The new scale reading is taken and noted of the bottom of the spring. The total extension can now be worked out. Each time, a 100g weight is added. This increases the stretching force by 1N each time. After each time a weight is added, the hanger and weights are removed so that the spring can be tested to see if it retracts to its normal state and all the extension goes. By doing this, the elastic limit point can be seen.
First of all, the test was done only up to 5N stretching force so that my method of recording results can be tested to see if they are accurate. It was done 3 times to make sure the accuracy was at its best. The method was then used to test the spring to destruction. These procedures could not have been carried out the other way round because when it is tested to destruction, the spring passes its elastic limit. The spring would then be unfit to use for testing. For safety, the person doing the experiment should be wearing goggles and there should be nothing below the spring, as when it is tested to destruction, the weights will fall of the bottom of the spring. To achieve maximum accuracy, the spring is placed as close to the ruler as possible and a setsquare is used to read off the extension. This is placed at a right angle to the ruler so that the extension can be measured with very high accuracy. This is shown below:
My readings should be, at most, 1mm out. This is a 0.1% chance in every meter of being wrong which will give very accurate results. A fair test was achieved by making sure the hanger was still when the reading was taken. Also, the ruler and spring were made very secure in the clamps so that they wouldn’t slip.
Results
Equation
From the graph I can calculate the force constant by using the equation:
This can be worked out by using delta values of the extension and of the mass. The equation now looks like this:
ΔF = Δe = Therefore, K = .
The extension for 1N can be measured like this:
Δe= ΔF= Therefore, 1N = 4.46cm
Discussion
From the graphs on the 3 tests with 5 weights only I can see that they were very accurate. The results were within 0.1 cm of each other for each weight. This showed the accuracy while doing the experiment. From the graph with the testing to destruction, I have found using the formula that the force constant is . The elastic limit was 14N. This is what I expected it to be. After the elastic limit, the graph shows that the line curves more. This is also what I predicted. The 4 graphs helped to show consistent accuracy during the experiments, as there was not much difference between the results for the other tests. The graphs produced tied in with the graph shown in the theory. This shows that my results are accurate. From my graphs, there are no anomalous results. This shows the accuracy and reliability of my results. The method for this experiment is very good. However, it was difficult to keep the weights and spring still when taking results that meant it took longer and was difficult to record results. The accuracy of the experiment could be improved if the weights were kept still as the bottom would not bounce up and down. The investigation could be extended to see what different variables affect the results e.g. coil size, spring length. I have confidence in my results because the graph is the same as in the theory. Also I took careful measures to make sure that the results were as accurate as I could do possible.
Conclusion
I have found that the force constant for the spring is . I have also found that the elastic limit is at 14N and that the extension for 1N is 4.46cm.
