GCSE SCIENCE COURSEWORK:
HOOKE'S LAW
INTRODUCTION
As it is known, different materials have different properties. They act differently under different circumstances. There are a number of properties of matter which can be explained in terms of molecular behaviour. Among these properties is elasticity.
Intermolecular forces: these are electromagnetic forces between molecules. The strength and direction of these forces differ in accordance to the separation of the molecules.
Materials are often subjected to different forces. Forces can be distorting, that is they can alter the shape of a body. Two distorting forces I shall look at are tension and compression.
Tension/tensile stress, more generally referred to as stretch, happens when external forces (larger red arrows) act on a body so that different parts of that body are pulled to go in different directions. In most materials, the intermolecular force (smaller aqua arrows) of attraction shows resistance to these external forces, so that once the external forces have abated, the body resumes its original shape/length.
Compression/compressive stress, more generally referred to as squashing, happens when external forces act on a body of material so that different parts of that body are pushed in towards the centre of the body. In most materials, the intermolecular force of repulsion acts against these external forces, so that when the distorting force is removed, the molecules return to their original arrangement and spacing.
Materials that do this are known to have the property of elasticity. In short, elasticity is the ability of a material to return to its original shape and size after distorting forces (i.e. tension and/or compression) have been removed. Materials which have this ability are elastic; those which do not have this ability are considered plastic.
This always happens when the distorting force is below a certain size (which is different for each material). This point where the body will no longer return to its original shape/size (due to the distorting force becoming too large) is known as the elastic limit (which differs from material to material). As long as the distorting force is below this size, the body that is under the external forces will always return to its original shape.
As the body is put under more and more stress (distorting force), the body strains (deforms, extends) more and more. Right up to the elastic limit, the body will continue straining, in accordance to the size of the stress. This is where Hooke's Law comes in.
Hooke's Law states that, when a distorting force is applied to an object, the strain is proportional to the stress. For example, if the load/stress is doubled, then the extension/strain would also double. However, there is a limit of proportionality (which is often also the elastic limit), only up to which Hooke's Law is true.
Since the strain is proportional to the stress for different materials where Hooke's Law is true, then there should be a fixed ratio of stress to strain for a given elastic material. This ratio is known as its Young's Modulus. Young's Modulus can be calculated from the stress and the strain of an object under tensile/compressive stress.
e = change in length/extension of object, in cm
p = original length of object, in cm
a = cross-sectional area of object, in cm2
f = size of force applied, in newtons
For example, ...
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Since the strain is proportional to the stress for different materials where Hooke's Law is true, then there should be a fixed ratio of stress to strain for a given elastic material. This ratio is known as its Young's Modulus. Young's Modulus can be calculated from the stress and the strain of an object under tensile/compressive stress.
e = change in length/extension of object, in cm
p = original length of object, in cm
a = cross-sectional area of object, in cm2
f = size of force applied, in newtons
For example, the Young's Modulus of Mild Steel = 2 x 1011 N m-2
Copper = 11 x 1010 N m-2
Hooke's Law and Young's Modulus apply to most elastic materials, with the exceptions.
A special shape which material can be bent into to in order to optimize use of the elasticity of a material is a spring. Springs are used by us everywhere: in seats, mattresses, cars, toys, and all other sorts of necessary objects and items we encounter in our daily lives. They are normally made from metal, though they can come from plastics, rubber or even glass.
When compressive stress is applied to a spring, the spring noticeably 'shortens', though the actual length of the body material shortens very little. It is due to this special shape of springs that let it do this. The same occurs when tensile stress is applied. When a spring is being extended or pulled on, it may seem the spring is changing length dramatically, but in actual fact the spring's body material relatively doesn't change shape at all, but rather the shape of the body is more spaced out.
AIM
My objective in this experiment is to find out how a spring varies in length with added load. I also want to witness Hooke's Law in action, and I want to observe the behaviour of the spring/s even after the load added causes the stress in the spring to exceed the elastic limit.
PLAN
My experiment is fairly straight forward to set up and carry out. In my experiment the data that I intend to assemble is the extension of the spring each time new/extra load is added to it. It is necessary that I use the most appropriate equipment for my experiment, hence I have chosen to use a retort stand which will hold up the spring and its weights up, a second retort stand from which a meter rule will be suspended. The metre rule will be right up against the spring, so as to ensure an accurate reading. There is no evidence that I can take before hand, other than the material of the spring.
This entire experiment has to be as accurate, fair, precise and reliable as can practically be, but it is only possible to make it so to a certain extent. For instance, I cannot be absolutely sure that that all Newton weights weigh exactly 1000 grams, nor is it practical to find a ruler that is absolutely accurate. Hence I am forced to settle for the metre rule, which is accurate to about 1 millimetre, and I will be aware that the Newton weights will be within an accuracy of about ± 20 grams. These factors will not really be in my control; however I can reasonably account for them when I construct a graph from my table by using error bars for each point plotted. Another measure I am taking is that I shall not be the only one to take readings from the metre rule; I shall have two other peers who will also be reading off the same metre rule. From these 3 readings I shall draw up averages of level of weight applied to the spring.
To be practical and observing at the same time, I must choose an appropriate extent and range, as well as appropriate integers, for the data that I intend to collect. I will be going to take the first measurement as the length of the spring when there is no mass attached to it. The last measurement shall be right up to when the spring can no longer hold on to the weights. I have a rough idea of the spring that I shall use, and I am assuming now that the spring shouldn't be able to hold much more than 13 kg. I shall be adding the weights one at a time (one Newton/kilogram at a time), and I shall be taking measurements at each of these intervals. The measurements that I shall take of the length of the spring will be in millimetres.
So basically, once I have set up the entire apparatus, I shall start off taking the measurement of the spring when it is free of load, then let my peers take theirs. Then I shall add a Newton weight one at a time, taking measurements with my helpers each time I add one. Of course we'll be wearing our goggles, because I don't want to take any risks.
) Collect equipment.
2) Prepare apparatus as shown in diagram.
3) Record the length of the spring when it is load-free, to cm, in the prepared table for results.
4) Add a weight/mass of 1 kg or 1 N, and then take the new length of the spring. Record in the prepared table for results.
5) Continue adding on weights/masses of 1 kg, recording the length of the spring each time in the prepared table for results.
This should be carried on until the weights can no longer be attached to the hanging spring.
APPARATUS
The apparatus that I shall need set up for my experiment consist of the following items:
. Retort Stands (x 2)
2. Boss and Clamps (x 2)
3. Metre Rule
4. Spring (length: 50 mm)
5. Newton Weights (x 15 approximately)
Other items I shall need are three pairs of goggles.
SAFETY
I must consider my safety when working in the laboratory. It is common when this type of experiment is carried out that when a weight or anything for that matter is suspended from something as unstable as a hanging spring, the item in being suspended is prone to fall. And many a time the item that falls lands on someone's foot. That is why I have planned to prepare my apparatus on a table top where, if the masses should fall, they will only drop a short height onto the surface of the table.
Another safety issue that I feel safer to take into account is the elasticity and elastic potential energy in the spring. If the spring is holding some weight, and the weight should slip off the spring, the spring may 'spring' off the retort stand, and has some chance of getting into someone's eyes. This I shall not let happen, which is why I shall be wearing goggles, and have those who are working near/with me to wear them also. Another measure I shall take to counteract this risk is clamp the top-end hook of the spring to the retort stand, so that it doesn't just suspend through the hook, but by the clamp also.
PREDICTION
I predict that at around 8 kilograms/newtons, the spring, the stress shall exceed the springs region of elasticity, and the spring will probably break at around 12 kilograms. I say this because I have a rough idea of how the spring shall be (its size, weight, etc.). Naturally, I assume that the up to around 8 kilograms, the spring will obey Hooke's Law (which is general theory anyway), and that the strain shall be proportional to the stress, and when I double the weight, the extension should double also.
IMPLEMENTATION
Load (N)
Actual Length (mm)
Extension (mm)
Reading 1
Reading 2
Reading 3
Average
0
50
50
49
50
-
83
82
83
83
33
2
18
17
19
18
68
3
46
46
47
46
96
4
77
77
77
77
27
5
207
206
207
207
57
6
234
234
235
234
84
7
265
264
264
264
214
8
295
296
295
295
245
9
327
325
327
326
276
0
356
356
355
356
306
1
390
389
390
390
340
2
421
421
420
421
371
3
456
454
455
455
405
4
501
503
504
503
453
5
556
553
553
554
504
6
611
610
611
611
561
The table on the previous page contains the results from my experiment that I carried out. The whole experiment took approximately 30 minutes, which is in a sense quite quick, especially because I completely planned my experiment. Everything went well and no one was hurt, luckily. The measurements were recorded appropriately and fairly. Other than that, there isn't much else to comment on.
At the end, when the spring couldn't suspend any more mass, I measured the spring again, when it was load free. Its length had changed, its new length is 84 mm.
ANALYSIS
From the table of results above, I have managed to construct the following graphs.......
In GRAPH 1, I only included values where Hooke's Law was true, or where the spring hadn't yet deformed. Here my results weren't too inaccurate, as can be seen from my line of best fit. They all fell well within the X error bars. In the second I included all my results, and when the spring deformed is pretty obvious. This I can tell from my graph, where it shows a distinctive drop in the steepness of the slope near the end of the graph. I have indicated where the spring deforms by the point where two dotted red lines meet up and that also shows under which weight or load the spring reached its elastic limit.
I managed to do the line of best fit accurately using the computer, and my line of best fit was really close or on all the points of the graph. I know that the graph shows proportionality by the way that the line of best fit is straight and on all the X error bars.
CONCLUSION
Some of my predictions turned out right, the spring obeyed Hooke's Law up to a certain point, and the strain was proportional to the stress up to that point also. I can see this from the line of best fit which I included GRAPH 1. However my prediction of the spring reaching its elastic limit at around 8 N, was pretty much well off target. So I now know that the spring's elastic limit is at around 13 N in load. After 16 kilos, the spring couldn't really hold anymore, though it hadn't broken or anything. If I were able to continue adding more and more load to the spring, I may have been able to get a more extended graph and I would've been able to see things such as the springs yield point and where the spring would break. Unfortunately that was not possible here, and therefore I only worked out spring's elastic limit, or the limit of proportionality. So I also know that the spring, or even the spring's material, obeys Hooke's Law. And of course, the spring was really and truly deformed, coming
EVALUATION
Personally, I think that I carried out this experiment successfully, and my method of carrying it out and my method of recording were appropriate, safe, accurate to a reasonable extent, and efficient too. I didn't come across any weird data or anomalies, and my data presented clear-to-see evidence. It also had a lot of integrity, considering how I recorded and obtained my data. However, there is an important mistake that had not come to my mind, and that is I hadn't made any record of the material of the spring. I think if I had taken note of the material of the spring, I would have been able to make some comments upon the elasticity of that material. Personally, had it been beneficial to me, I would've carried out this entire experiment again, but this time with a spring of slightly longer length (maybe 7 cm) and better capability of holding onto load. This would help me find out how the spring behaves after the load has exceeded its elastic limit. I think the data and the evidence is reliable enough to support my conclusion, and luckily there was no inconsistence to worry about or account for.
Emad Rahman - 11NGO - Sapphire House - Science - Mr DeJonge
GCSE Coursework - Hooke's Law - 08/05/2007
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