How I will conduct my experiment
I will set up a clamp stand with my springs on it, attach weights of 1N,2N,3N,4N,5N,6N and 7N to a single spring and then to two springs in parallel. When I attach weights to the two springs in series however I shall only go up to 4N as anymore force than this may exceed the limit of elasticity of the springs in series, causing the springs to have plastic properties and not behave as a spring thus making any further readings inaccurate. I will then measure the extension of the springs using a meter-stick and take a repeat set of results to ensure the reliability of my findings. In order to attach the weights to the springs I will use copper wire. The mean of my 1st and my repeat set of results will be calculated for the single spring, the two springs in parallel and the two springs in series. I will then plot graphs for each set of springs onto the same axes and compare them. As force is proportional to extension all three lines of best fit should be relatively straight lines. The line of best fit for the two springs in parallel should have a higher gradient than the single spring as its spring constant should be higher and the line of best fit for the springs in series should have a lower gradient than the line of best fit for the single spring as it should have a lower spring constant.
Apparatus
To obtain these results I will use the following apparatus:
Clamp Stand- to hang the springs from and to ensure that the springs are well balanced and do not topple off the bench as this would cause a risk to the safety and to the accuracy of the experiment.
5 identical springs- must be identical to ensure a fair test
Copper wire- to attach the weights to the springs; this is particularly important for the two springs together in parallel as I will need to ensure that the weight lies in between the two springs and that the weight is distributed evenly over the two springs otherwise I could end up with one spring extending more than the other and this would result in inaccurate findings.
Meter stick- to measure the extension of the spring; I will measure the extension by marking on the clamp stand where the spring reaches to when it has no force acting upon it and then measure from this to where the spring reaches when it has a force acting upon it.
Set of weights on a hook, each weighing 100g, which is equal to a force of 1N. When I want to apply a force of 7N on the spring, I shall put 7 of the 100g weights onto the hook.
Accuracy and Reliability
To ensure this is a fair test I will keep all of my apparatus the same. I will ensure that the springs are identical; this is very important as if the springs are not identical they will have different properties and therefore different spring constants. This would affect the extension of the springs and cause my results to be inaccurate. I will also try not to exceed the limit of elasticity of the springs, as this would make any readings incorrect. I shall also take a repeat set of readings from each different set of springs to ensure the reliability of my findings.
Obtaining
How I obtained my results
I obtained my results by measuring the extension of the springs after each 1N of force was added. I measured this distance in mm using a meter stick. I chose millimeters to be relevant precision as the starting length of the springs was only quite small. I used copper wire to attach the hook with the weights on to the bottom of the spring; this ensured that the weights were balanced properly. After I had added each extra weight to the springs, I gently lowered them down to prevent them from losing balance. I took a repeat set of results for each set of springs to ensure the reliability of my findings. I took readings of the extension of springs in parallel and a single spring when forces of 1,2,3,4,5,6 and 7 Newtons are applied to them but I only went up to 4N when applying force to two springs in series as they will have a lower limit of elasticity. If I were to exceed this limit any readings I took after the limit was exceeded would be inaccurate.
Tables of Results
Single Spring
Two Springs in Series
Two springs in Parallel
Observations
The two springs in series extended a lot more than the single spring and the two springs in parallel extended a lot less than the single spring. Also the extension of the two springs in series seems to increase more rapidly than the extension of the springs in parallel.
Analysing
I plotted the results of my experiment onto a graph then drew lines of best fit for the average extension of the single spring, the two springs in series and the two springs in parallel on the same axes so that they could be compared. I calculated the average of my results by dividing the sum of the first reading and the repeat reading by two.
All three of my lines of best fit are straight lines, which shows that as I predicted, extension is always proportional to force. My graph also shows that the two extension of the two springs together in series is roughly twice that of the single spring and the extension of the two springs together in parallel is half that of the single spring. Also the line of best fit for the extension of the springs in parallel is much steeper than the line of best fit for the extension of the single spring, and the line of best fit for the extension of the springs in series is not as steep as the line of best fit for the extension of the single spring.
I calculated the spring constants for the single spring, the two springs in parallel and the two springs in series by finding the gradients of their lines of best fit. I found the gradient of my lines of best fit by dividing the highest value reached on the force axis by the highest value reached on the extension axis. I have drawn the lines from which I calculated the gradients of my lines of best fit onto my graph. By doing this I found the spring constant of the two springs in parallel to be 5.71 x10-2 (3s.f.), the spring constant of the single spring to be 2.30 x10-2 (3s.f) and the spring constant of the two springs in series to be 1.14 x10-2 (3s.f). As I had predicted earlier, the spring constant of the single spring (2.30 x10-2) 2x the spring constant of the two springs in series (1.14 x10-2). However the spring constant of the single spring is not quite half of the spring constant of the springs in parallel, yet it may be near enough to half of the spring constant of the singles together in parallel to say that my prediction about that was correct. My readings for the extension of the two springs in parallel may not be very reliable as the points are not all very close to the line of best fit as the points around my other two lines of best fit are. As it was very difficult to keep the weights balanced when measuring the extension of the two springs together in parallel the readings I obtained could have been inaccurate. These results suggest that when springs are put together in series or parallel, they do have the properties of a new, different spring and two springs put together in series have a lower spring constant as they act like a spring of a longer length.
Evaluating
Overall, I think the way in which I conducted my experiment was effective and efficient. All three of my lines of best fit were straight lines, which indicates that the two variables are proportional, as I had expected. I think I made sure that my experiment was a fair test, as I used identical springs, identical weights and added 1N extra weight for each reading when measuring all three arrangements of springs, I also ensured that none of the springs exceeded their limit of elasticity . I think that my readings of the extension of the single spring and the two springs in series were reliable as all of my points lie almost directly on their lines of best fit and I do not have any anomalous results for the extension of the single spring or for the extension of the two springs together in series. However I do have an anomalous result for the extension of the two springs together in parallel. This set of results is generally not as close to its line of best as the other two sets of results are. This is because it is very difficult to keep the weight balanced when measuring the extension of the two springs in parallel because of the method I used. To make the readings of the extension of the two springs in parallel more accurate I could use a different method of securing the weight onto the springs. A paperclip could be bent in an appropriate way to balance the weights more evenly than the copper wire and therefore make my readings more accurate. Perhaps I should have taken a third set of readings to make the average of my results more reliable.
Some further work I could do to prove my theory about springs in series and parallel would be measuring the extension of three or more springs in series or parallel. Or I could even investigate the limit of elasticity of springs in series and in parallel. If three springs in series extend three times as much as one single spring, and three springs in parallel extend a third as much as a single spring then this would support my findings in this investigation.