An investigation into the behaviour of springs inparallel when a mass is applied.

I know the maximum length I can extend the spring to without permanent deformation of the spring, is 150mm, and the from the information supplied by the manufacturer I can calculate that if I attach 200g then the length of the coiled section should be 120mm.

From my preliminary experiment I found that:-

210g causes the length of 1 spring to increase to 103mm from 20mm.

210g causes the length of 6 springs in parallel to increase to 30mm from 20mm.

So therefore I chose the mass of the load to be 210g, as this mass allows 1 spring to be stretched to 103mm, which is well inside the elastic limit of the spring, and I will not need to risk extending the spring beyond its elastic limit. Also this mass allows me to measure the extension when I have 6 springs in parallel, as if I used a smaller mass the extension of 6 springs may only have been 2mm, and this gives me a 50% of getting the wrong measurement.

The limiting factors of the experiment is the fact that we are only allowed 6 springs and 600g of slotted masses, the restriction of the number of slotted masses is not a problem as I only need 210g. But the number of spring is important as I can only get 6 different readings as the maximum number of springs that I can have in parallel is 6, which limits my experimental data.  

Variables:

Independent variable: The number of springs in parallel

        

I have chosen this as my independent variable as this allows me to investigate the behaviour of springs in parallel, springs in parallel are very accurate and the extensions to do have a large range.

Dependant variable: Extension (cm)

This is the dependant variable which means that this figure relies on the independent variable.

Constant: Mass

        

This is the constant which means that this shall stay the same throughout the experiment which was pre-determined by the preliminary experiment.  

Prediction:

I predict that as the number of springs in parallel increases then the extension should decrease.

I have made my prediction based on background knowledge and my preliminary experiment.

        I knew that as the number of springs in parallel increases the extension decreases, this is why I had to carry out my preliminary experiment as I needed to find a mass that would stretch 1 spring within its elastic limit and also stretch 6 springs s that a reading could be gained.

        Also following Hooke’s law it states that the extension of a spring is α to the force being exerted on the spring.

The extension of the spring(s) should decrease as the number of springs in parallel increases because in a sense the springs are helping each other so therefore the load is being split between the springs and therefore the extension should be proportionally less.

1 spring in parallel + mass = 103mm

2 springs in parallel + mass = x

If 1 spring = 103mm

Then 2 springs sharing the load to equal ½ the extension.

Therefore x = 52mm (51.5mm)

And so on

Includes length of spring taken away

But looking at the results from the table it is impossible for the final result to happen as the spring would have to shrink to produce this result so therefore the results need to be weighted, so taking into account the above table and graph, and the preliminary experiment, I have made the following predictions:

Includes length of spring taken away

Method:

• Set apparatus up as shown in the below diagrams ensuring that the base of the stand rests level with the desk.

• Attach the boss clamps to the top and the bottom of the stand to one attach the steel rod and the other one the clamp which attaches to the rule.

• Hook the number of required springs to the rod using the ring attached to the springs, if using 2 or more springs use another steel rod, (ensuring the mass of the rod is measured), to attach the springs to each other {see second diagram}.

• Attach a pre-determined mass (from preliminary experiment) and measure length of the spring using the set square and the metre rule, measure to the nearest mm.

• To calculate the extension use the following equation:

Extension = Final length – Initial length

Note:

That the mass of the rod was measured and noted, for the part of the experiment with more than 1 spring the mass of the rod was taken away from the total slotted mass to ensure that the total force acting downwards on the spring was still 210g (2.1N). This ensured that the experiment was accurate.

The diagram below shows the experiment apparatus with one spring (in parallel)

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The diagram below shows the experiment apparatus and two springs in parallel.

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Results:

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Analysis:

Looking at the evidence collected from the experiment I can say that the data supports my predictions to the fact that as the number of springs in parallel increases the extension of the spring decreases. This is further proved in the graph showing extension against number of springs in parallel, as this clearly shows that as the number of springs increases the extension decrease, but this is not a straight line, in fact this a curved line.

But when looking at the reciprocal of the extension (1/extension) we can clearly see that the number of springs in parallel is inversely proportional to the extension. This is because the number of springs in proportional to the extension. But this is only so after the point for 1 spring in parallel, I believe that it is only directly proportional after 1 spring because 1 spring in parallel isn’t really in parallel, as the definition of objects being in parallel means that they work together. So 1 spring by itself is not working with another object therefore it is not in parallel. This is shown in the below graph:

Looking at the graph containing the value for 1 spring we can work out the equation of the line.

(0.05, 3) & (0.10, 5)

Change in y                        5-3                        2

                                                =                = 40 (Gradient)

Change in x                        0.10-0.05                40

y = m x +- c

5 = 40 x 0.10 +- c

5 – 4 = c

Therefore C = +1

Therefore the equation of the line of 1/extension is y = 40 x +1

Comparing the results that I obtained during the experiment, to my predicted results:

Looking at the results I believe that some of my predictions where reasonably accurate as but 3 (50%) of them were some way out. I believe this to be so as I thought as the number of springs increase in parallel then the springs did not ‘help’ each other as much as I anticipated that they would have. I believed that the increase in the number of springs would have caused a fall in the extension, directly proportionally.

        But when analysing the graph comparing the reciprocal of the extension against the number of springs this produced a straight line, but this straight line was of a positive nature whilst my prediction was of a negative nature. This is because the larger the extension the smaller the reciprocal so the graph would have resulted in a positive correlation line of best fit. But should we invert the reciprocal of the extension we gain a graph similar to that of my prediction.

I can therefore say that my prediction in the sense that the extension would decrease as the number of springs increased at the relationship between