An experiment to investigate and determine how rubber behaves when tension forces are applied to it.

Physics AT1

An experiment to investigate and determine how rubber behaves when tension forces are applied to it

By Jess McFarlane 11WM

Aim

The initial aim of my experiment is to investigate how rubber behaves when tension forces are applied to it. I also intend to figure out why this happens so that the data that I am provided with will help me to analyse what I plan to write about during this set coursework. For the actual experiment I will be using a rubber band, as this is an easier and less complex way of carrying out the investigation.

Introduction

When a sample of material in the form of rubber, such as in this case, is pulled so as to apply a tension force, the sample would become longer in size. And the difference between the new length of the sample and its existing length, when there was no tension applied to it, this is called the extension of the particular sample. Tension is a force that is applied to an object of material that is able to change in size, for example, these types of materials could be used, rope, springs, rods, wires and in this particular case rubber.

Tension is the name given to a force, which acts through a stretched sample or object e.g. when a pulling force is applied at each end of the rope, it is said to be under tension.

Extension occurs in this experiment as well. A definition of extension is when an object such as rubber is stretched and the extension is the difference in the original length and the new length. The diagram below shows this more clearly.

I wish to include extension in my experiment, as I think that it will help me to analyse my data better. This is because the extension is proportional to the tension, in some materials and for all applied tensions up to the stage when the actual sample breaks and also the extension is proportional to the tension for when all tensions applied up to a certain stage and when the sample of material starts behaving in a more complex. Also some materials behave in ways that their extension is not proportional o the tension. I wish to see whether extension will have an effect on the proportionality on the tension and extension.

Hooke’s Law states that, “for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load.” Elastic behaviour, according to Hooke’s Law, is when there are displacements in the molecules of the rubber sample being used, are moved from their normal positions, which means they are proportional to the force that causes the displacement. The deforming force may be applied to a solid by stretching, compressing, squeezing, bending, or twisting. So a rubber band exhibits elastic behaviour according to Hooke's law because the small increase in its length when stretched by an applied force doubles each time the force is doubled.

The formula for Hooke’s Law is: F = kx

Where F = the applied force, k = the constant and x = the change in length

But Hooke’s Law cannot be applied throughout the experiment because as the rubber band would reach a certain point in its deformation and extension, the limit of proportionality would be reached and Hooke’s Law would no longer be accurate. This is the point is the rubber band’s elastic limit and if the force were to be removed from the rubber band, it would no longer return to its original shape.

All rubber like materials are polymers, which are high molecular weight compounds consisting of long chains of one or more types of molecules. The process called vulcanisation or in simpler terms curing, produces chemical links between the loosely coiled polymeric chains and therefore elasticity occurs because the chains can be stretched and the cross links cause them to spring back when the stress is released. This is why rubber acts in such a way that when a tension force is applied to it and then is released, the rubber band reforms into its original shape.

Prediction

In the experiment it is quite hard for me to say how the results will turn out and I am not sure if the tension will be proportional to the extension as my background knowledge on the situation is minimal. I do predict though that the extension will be proportional to the tension up to a point where all tensions are applied and the rubber band will suddenly snap. This is because the physical properties of a rubber band are those of which will eventually snap as the tension increases and if the load weighing it down is too much.

The rubber band increases in length a certain way until it will suddenly give way. This is because the tension exerted on the rubber band cannot be too great and that the extension of the sample will only go a certain way before it can be extended any longer than it’s original length. The three diagrams below show the way in which an elastic band works and how it’s properties do not allow the extension to be a great length and the tension to kept to a minimal.

A regular rubber band that has no tension applied to it

The rubber band that has tension applied at each end, with an extension

A rubber band where the tension was too great and it snaps

This is a preview of the whole essay

A regular rubber band that has no tension applied to it

The rubber band that has tension applied at each end, with an extension

A rubber band where the tension was too great and it snaps

The tension exerted on the sample of rubber, must be linked to the length it has been stretched. As the tension was to increase, it would do so by a certain length, hence the extension would increase by a certain length. Tension is measured in newtons (N), which is force being exerted on something and the extension is measured in metres (m) or centimetres (cm); the most likely scenario for this experiment would be in cm and there would be force being pulled on the rubber band, which would measured in kilograms (kg) or grams (g), which again grams would be the most likely option for the set scenario.

This allows me then to construct a formula to measure the proportionality of the extension and tension. This formula would be as follows:

Tension (N) = Extension (cm) x Weight added to the rubber band (g)

I predict that the formula that I have come up with will provide me with the information I need to find out whether the tension and extension are proportional and then I can lead on to explain why in my analysis.

I have also worked out that 1N = 1kg and this is what I am going to base my knowledge on. I feel that I will have to use the extension somewhere in my experiment but I am unable to comply where as of yet. I need to carry out the experiment first before I can comment on this, as I am not entirely sure what to comment on at this actual time and moment.

I predict that after 10 N of force has been applied to the rubber band it will reach its elastic limit and then it will stop following Hooke's law, where the amount the rubber band is stretched out of shape past its original size. It will not apply Hooke’s law after a certain amount of force has been applied to it and the rubber bad will eventually be extended too much and it will suddenly break. This means that the greater the weight applied to the band, the further the band will stretch. This is because extension is proportional to load and so if load increases so does extension and so stretching distance. I also predict that the results will produce a straight-line graph and if I were to continue the experiment to further study the elastic limit I predict the graph would flatten out after 11 Newton's were the rubber band would be stretched out of shape, or Hooke's law would come into play.

Safety

First I have to make sure that I am not sitting down while doing the experiment because if something were to happen, I would have less time to move. This is not a major concern but can easily occur and so it is rather safe than sorry. For the safety of the others the experiment will be conducted in an open space away from the people, there will be ample space between each experiment.

Fair Test

To make the experiment a fair test I will have to make sure that the clamp is absolutely straight because if it is crooked I won't get the same length of each elastic band. I will also have to make sure that the rubber band is the same if I need to conduct the experiment at a later date as if it was a different rubber band, this would change the structure of my data and ruin all my observations. Plus if I was to redo the experiment or add data to what I would have already colleted from lesson time, I would have to make sure that the same conventional method was used otherwise my recordings may come out different to what they were originally. To make it a fair test I am going to repeat each level of force added 3 times.

Graphs

From the measurements made I would expect to calculate the final tension force exerted on the rubber band, as my aim predicts. And then maybe from these results I would construct a graph to show the relationship between the tension and extension. The graph would show the tension along the y-axis and the extension along the x-axis. I would then use the graph to explain and analyse the data that I will have collected.

I would also create another graph to show load vs. tension. This would show the relationship in how the load would affect the tension and so this would be useful as I could again use it in my analysis to help me explain my predictions.

The two graphs that intend to construct are illustrated and labelled below:

Apparatus

Working surface so that I can conduct my experiment on this and make sure that it is stable otherwise this could affect my end results as the rubber band may behave differently and is easily able to stretch and then compress again.
A stand so that I can fit my g-clamp to this.
A g-clamp to hold a suitable sized nail for the rubber band to fit around.
A large nail for the rubber band to rest upon.
A rubber band to test the tension forces exerted and record any results.
A hook and set of light weights so that I can use these as my means of tension on the rubber band.

Method

I did in fact have first intentions of fixing a stiff object the desk and wrap one end of the rubber band round it so that this would reduce any experimental error and would always be fixed in the same place. I was then going to use my finger and pull on the elastic bands, certain lengths until it would suddenly break but I then realised that this would be the wrong way to conduct the experiment as I would not know the exact tension being exerted on the rubber band as I my hand would exert different tensions every time I were to pull the rubber band. I did in fact pull the rubber band by hand just to see how it reacted when a tension force was applied to it and I found out that up until a certain point of pulling the rubber band becomes more “stiff” and harder to pull until it suddenly breaks.

Instead what I am going to do is use a set of apparatus that I explained above and set them up in a way shown below.

I will use the apparatus shown above in such a way that the tension force acting on the rubber will be the weights that I will place on the other end of the suspended rubber band. This way I can keep the experiment more of a fair test and this should eliminate any experimental error as the rubber band will always be situated in a fixed position, over the nail and the weights that I will be using will be kept at a constant increases until the rubber sample suddenly breaks. This way it makes it easier for me to record my results and I also know that there will be minimal difference on the tension given out each time as the weights are near exactly the same.

I will set up the apparatus as shown but firstly conduct a preliminary test to see the expected outcome for the real teat. I am going measure the length of the rubber band and then conduct the experiment, as I will explain below.

First of all I will set up the apparatus as shown on the before page. The very second thing I will immediately have to do is measure the rubber band in cm. This will act as the constant throughout the experiment as I do not intend it to change but to make sure if there was any change in the rubber bands length after the weights have been put on, I will take the weights off every time I add one on and then measure the rubber band again. This will be done to eliminate any possible experimental error that may be caused because the sample elongates slightly. This is slightly different to my preliminary test due to the fact that I can compare once the two sets of results have been recorded, for the purpose of the analysis and evaluation.

With the rubber band suspended over the nail I will place the hook (this is the object that will hold the weights) on the free end of the rubber band and as this already weighs 10g I will have to measure the extension. I will then continue to add 10g weights to the hook, connected to the rubber band until there is a sudden break in the sample or if I think that the sample is on the verge of breaking. The only problem with that is though, my own human instinct may not be correct and so this maybe another thing to do in the preliminary test and once I think the rubber band has enough weight suspended on it, I will stop but then record more data to see how much it would really take. This would be done only in the preliminary test and I can then judge whether I should commit myself to doing the same thing again.

I will also have to construct a suitable table for me to fill my results into. The following template is what it should look like.

The table on the previous page resembles in no way in which I predict the results to come out as, it is just of what a template of the table should look like for the preliminary and final results to be recorded.

Results

The original length of my rubber band was 9.1 cm

These I could say were a set of preliminary results as intended mainly to test how far the rubber band would stretch. These results were collected from the first test I did, where I increased by 10g each time until reaching 100g where I increased by 100g because I wanted to test how far the rubber band would stretch. I reached a point of 1100g where I thought the rubber band could take as much weight as possible and stopped.

I would have carried on adding weights but I also observed the results, which I took were changing. It was evident to me that after a certain point from where the rubber band was being stretched by too much weight, the extension was not following a certain pattern as it was before. I was led to believe that from my introduction that the rubber band was no longer following Hooke’s Law. This means that if I am to say this that means that the results at the beginning of the experiment did not apply Hooke’s Law and that only up until a certain point did they start to and up to a certain point in my results where they finished. I cannot tell from my table of results but hopefully my graph will help me explain this theory a little more fully.

This is the second set of results

This was how far I got up to due to lack of time and I thought it would be a sufficient amount of data to use for my analysis, conclusion and evaluation.

Analysis

I chose to record the sets of data like this as it is set out in a simple way and can easily be evaluated. As we were limited to just only above one hour to conduct our experiment but we were given two separate occasions on what to do so, I could only come up with the data provided above, but I do think that it will be sufficient enough to use. I also made a change in the way I set my data table out form my template in the method. I originally wanted to have a column of data where it showed the length of the rubber band every time I was to add a weight and then take it off and finally measure the rubber band. This was to unpractical in the final experiment as I would not have had time to do this but I do not think it would’ve made a whole lot of difference to my results.

The tables of results obviously show that as the weight or force acting on the rubber band were to increase then so did the extension. But by just looking at the results it is hard to analyse whether there is any relation between the tension and force acting on it, to whether there they are in proportion, also to see whether the tension and extension are in proportion. This is why I have constructed two graphs, extension vs. load for both sets of data

The first graph shows that there is a quite sudden increase in the load towards the extension but then levels off to curve upwards again and then round off. This is the same for the other graph as well and they do show at one particular point in on the graph is where the extension and tension are proportional and Hooke’s Law is applied. I think that this maybe able to be worked out using Hooke’s Law formula but I do not intend to do so at the risk of being severely incorrect.

Evaluation

I personally think that the experiment was a complete success as nothing major happened and everything went to as according to plan. The results I produced related well to my predictions and conclusions. There was also no safety aspect to be concerned with throughout the whole experiment. So I can say that it is possible for an experiment to commence and run smoothly without any major faults.

My results from the experiment were reasonably accurate, however there are some readings which are not consistent, which could be due to measuring errors. These errors may be due to difficulty to see accurately or maybe because of the way my experiment was set up. But I do not think this would be the main reason, as I will explain below.

The control in the experiment was the length of the rubber band as this was meant to be kept constant but I have noticed from the graphs constructed and from the first set of results compared to the second set, there are differences between the two. In this first set of data I can say that the experiment ran rather smoothly and nothing went wrong with I had planned to do but comparing the data I collected from the second experiment I have noticed a slight change in the pattern of results.

For example in the fist experiment at 100g the extension of the rubber band was 0.8cm and in the second experiment the extension was 0.75cm. There is minimal difference between the two as I would expect but as the load becomes heavier the equivalent loads in each experiment lead to a different extension, which I think is abnormal. Take for example 500g in the first experiment, there was an extension of 14.45cm but in the second experiment there was an extension of 15.75cm. This is now a considerable difference.

I can take this difference to what I explained earlier on in the experiment. From research I have found out that a rubber band can be stretched to a certain point until released where it would return to its original shape and length. Now this may cause a considerable problem within my second set of data. This is because in the first experiment I must have applied such a tension force on the rubber band that it must have had such as extension that after a certain point of added load, the rubber band reached a limit to which it would not extend any more without being deformed. This I think is the point of elasticity and this is where Hooke’s Law is no longer applied to the rubber band.

Therefore I have come up with a better way in which I could personally conduct this experiment. I would firstly have to measure the rubber band and record its original length. I would then set up the apparatus as I explained in my method, every time I would add a 10g weight, I would measure the new length, and work out the extension as usual but instead of adding another weight, I would take the load off and measure the rubber band to test whether its original length would have changed. I would continue to do so until I would record a new length for the rubber band after such a tension force to be applied that it would have changed the structure of the rubber band. This way I can then work out where the point of elasticity is and repeat my experiment as many times without fear of any experimental error caused by this one thing.

There were aspects to my particular experiment that could have had an effect on my overall data and observations. This was the fact that half way through the experiment my ruler became dislodged from its original position and I had to reposition it in such a way that it would not collapse again. However this was different to my original way but did prove to be easier to work with although it could have caused some experimental error. I did position the ruler in such a way that every time I were to take down a set of results I had to 0.55cm to the data recorded. This may have caused some experimental error within my data but most likely would have been minimal.

In my hypothesis I talked about how I thought that the extension would be proportional to the tension. Well I can in fact, say that the extension is proportional to the load. The tension is the force applied to the rubber band and is measured in N/Kg, therefore presuming that the tension is in fact the load and that it is applied to the rubber band, I can say that my theory is correct. But then again it some circumstances with a rubber band this cannot be said, as the extension is only proportional to the tension when Hooke’s Law is applied and so it can only be true for some part of the data acquired. So therefore, by saying that if Hooke’s Law can only be applied to a rubber band in some circumstances, then in only these circumstances can the extension be proportional to the load.

If I was to apply the formula of Hooke’s Law as well, it could only be done with a certain amount of data. This would hence backup my evaluation of my prediction, as I would only be able to use the formula where the extension is proportional to the tension.

It is a bit hard for me to say though whether I was correct in saying that after 10N or the equivalent of 1kg of load was added to the rubber band that it did in fact deform and its properties changed. I can though assume this happened as my results did change but it is impossible to fully prove this prediction as I did not optimise my method fully due to a lack of time.

Conclusion

I can finally conclude the experiment by saying that it ran rather accordingly to plan. I thought that the data I collected was relevant to what I predicted and then evaluated and that the final practical was performed efficiently, without me needing to change many things. I learnt a lot about Hooke's law and elastic limits as a result of this investigation and I feel it was worthwhile and helpful to me, as I now understand about elastic limits better.

I can also conclude that rubber behaves in different ways when a force such as tension is applied to it. Rubber bands follow certain characteristics that other materials that apply Hooke’s Law don’t. This although is a little crude as only in certain ways does a rubber band apply Hooke’s Law and I have tried to fully explain this above. The set of data I collected to follow a certain pattern, which could be followed but again only in some circumstances.

I was in fact actually surprised by results in one way because after 1.1kg or 11N/kg was added to the rubber band it did not break and so I did not fully find out how much tension it could actually take. I do not think this would have made any difference to my results though.