Method: We are going to set up a retort stand and clamp on the edge of a desk with a G – clamp to hold the stand in place. Then we will place a ruler in the retort clamp and attach a spring to the end of the clamp. We will measure the spring with the ruler to gain a starting point. Then we will attach a 1 Newton weight (hanger) to the spring, and measure the extension of the spring on the ruler. Once we subtract the starting point we will have a measurement for the extension of the spring. We will then add 1N weights to the hanger to measure forces from 2N to 10N and we will record the length of the spring at each stage in mm. We will then repeat the experiment to obtain a second set of readings from which we will calculate the average.
Then we will attach two springs on top of each other (in series) to the retort clamp. We will again measure the extension using 1N – 10N weights. We will repeat this process with two springs next to each other (in parallel). Finally we will then repeat these two experiments again and calculate the average of the results.
Equipment:
Safety: When we are using the springs we must be careful that the springs don’t suddenly break and spring back into our faces. This means that we will need to wear goggles.
Results: Here are the results from the investigation. The table shows the extension of the spring at all weights for all three experiments, and the graph has been plotted from the averages. The final column is a constant (F/e):
In the tables, the extension = total extension – distance to zero. This gives the extension of the spring.
k = F/e, the force in Newtons/mm spring extension.
For example, 2/41 = 0.04878 N/mm
Conclusion: The graph shows all the results for each experiment with lines of best fit. The results from all the springs show that the extension increased in equal steps, with the parallel springs about half the step length of the single spring, and the series springs about double the step length of the single spring.
From my results I can draw the definite conclusion that the spring extension is proportional to the stretching force. This is also shown by the value of k in the final column of the results table, which is a constant. The value of k = F/e, so for k to stay equal, doubling the force must double the extension.
My results show that my other predictions were correct. The parallel springs shared the load of the force, so the step length was only half that of the single spring, and the spring constant therefore doubled. With the series springs, the load acted on each of the springs separately, so the step length was double that of the single spring, and the spring constant halved. It had the effect of putting two single springs one under the other.
Evaluation: In my investigation, I definitely collected enough results to support a firm conclusion. I think my group worked well together, and the results we collected were accurate. However we did have a few anomalous results, for which there could have been a few reasons.
Firstly, when an extra weight was put onto the hanger, the spring initially over stretches and then pulls back, having the effect of making the spring bounce up and down, and it never really comes to rest. Our results could have been affected by this as it made it slightly difficult to take the readings.
Secondly, we did use different people to take the measurements, so the people could have used slightly different techniques, which could have affected our results.
Lastly, the springs we used were not brand new, and had been slightly overstretched. This has no effect on the stretching of the spring, and Hooke’s law still applies. However, it did make it difficult to pick out a second spring exactly the same length for the experiment with two springs in parallel and series. Again this could have an effect on our results.
Although I think our experiment was carried out well and reliably, I think there was still potential for improvement. If I were to repeat the experiment I would make a few changes. I would make sure the springs were new springs, or not stretched past their yield point to make our results even more accurate . I would also make sure the same person did the measuring each time and their technique used was repeatable.
To further improve my results and extend the experiment, I could make a few other changes. I could take measurement at every 0.5 Newtons, which would increase the number of readings. I could also use three springs in parallel and series to see what effect this has. Lastly, I could extend the springs to beyond their yield point and see what effect this had on the results.