For example, when small weights are suspended from a spring, doubling the weight doubles the extension (Hooke’s law) and the system is termed linear. If too much weight is added, such a simple law does not govern the extension.
Safety Precautions
In order to safely perform my experiment I need to make sure that I stand at all times, in case the weights accidentally fall or the elastic band snaps and the weights fall on my foot. This is not a particularly dangerous experiment and therefore there are no other precautions I need to take in order to be safe. Safety goggles could also be worn if I am worried about fragments of elastic band hitting me in the eye, but seeing as the bands are not particularly brittle this is not a problem.
Measurements
I have thought at length about the number of measurements I will take of the extended elastic band length and have decided to take six measurements from each elastic band after I add each newton weight, unless the elastic limit has been reached. I will test three elastic bands. There is not a time limit on the experiment and so setting a time measurement is not a problem. I will measure the extension in centimetres/millimetres.
Prediction
I expect that my experiment will show that;
· The extension of the band will not be proportional to the force applied, as Hooke’s law does not apply to elastic bands as it does to springs,
Graph of weight against extension for some different materials
· The length of the band will affect the experiment and create a difference in the results, because a longer band will be able to hold more weight, it will not however change the shape of the graph, just the size of the curve.
· There will be a point where the line within the line graph ceases to follow its original path, this point will be called the elastic limit and all materials stretched beyond it will be plastically deformed, from my research I have learned that plastic deformation is,
The irreversible deformation of a material stressed to beyond its elastic limit.
This research proves there is an elastic limit and that materials stretched beyond it will never return to their original state.
· The elasticity limit of the bands will affect the results of my experiment unless avoided.
Solids return to their original shape when stretched or deformed to a certain extent.
The above research shows that after the elastic limit has been exceeded the material will not return to its original form.
OBTAINING
Results Tables
ANALYSING
After studying my research, it is clear to me that the results I have collected follow no specific pattern, and the extension of the band after each weight is added is random. Below I have taken some results from my table to better illustrate my opinion.
As you can see there is no connection between the extension before or after each weight is added to the elastic band. To show this is the same with the other bands I checked the results from the other two tables and found that my prediction was correct I have inserted some of the sections from the tables I studied in greater detail below.
As you can see there was absolutely no link between the weight I added to the band and the length the band stretched. The results I gathered also supported the rest of the predictions I gave, if the elastic band was longer, there was less strain on the band because there were more molecules in the band to divide the weight up between them and they only had to hold a small part each. If the band was smaller, the strain would be shared over less particles and this would mean each molecule had to hold more. I did not reach the elastic limit of any of my bands but if I had I am confident that it would have made my results unreliable, by stretching the band too much and causing plastic deformation,
‘The irreversible deformation of a material stressed to beyond its elastic limit’.
I plotted a graph on the results I obtained. The graph turned out just as I had expected, and looked similar to the shape of the graph on the elasticity of elastic bands I researched. This graph can be seen in my prediction and the graph form my experiment is on the next page.
EVALUATION
The experiment went just as I had planned, I had no need to alter for any reason, any of my method. The procedure was carried out in a calm, sensible and safe manner. I consider the results I collected to be accurate and I checked, but I did not find any anomalous results present in any of my tables or graphs. My data is accurate because I took great care in reading all my measurements, and controlling all the variable factors that could have made my results unreliable. The investigation I performed gave me all the information I needed to perform the experiment with ease, and the research I examined gave me any interesting, extra details I needed to know. If I was asked to improve my investigation to make my results much more reliable, I would only make two changes. Firstly I would measure the results in millimetres, not centimetres so that my results, although already accurate, could be more precise than they are now. I think to discover even more evidence to support my conclusion, I would have to perform my experiment again, only with elastic bands of different width. If I wanted to go even further in my inquiry, I could complete my experiment once more and use bands of different weight in combination with the other two factors I had previously examined, length and width.
Research
Sources-The Oxbridge Reference Collection,
-My preliminary experiment,
-Key Science four, book two,
-The World of physics,
-Encarta 95.
Hooke, Robert (1635-1703)
Chemist and physicist, born in Freshwater, Isle of Wight, S England, UK. He studied at Oxford, became curator of experiments to the Royal Society (1662), and in 1677 was appointed its secretary. He formulated the law governing elasticity (Hooke’s law), and invented the balance spring for watches. The Gregorian telescope and microscope are materially his inventions, with which he made important observations, many of which were published in his Micrographia (1665)
Hooke’s law
In physics, a law expressing the proportionality of strain to the stress causing it; stated by Robert Hooke. It is valid for small stresses only. When applied to springs, a small extension x of the spring exerts a proportional restoring force, F=-kx, where k is a constant, a measure of the springs stiffness.
Strain
The fractional change in the dimensions of some object subjected to stress, expressed as a number. For force acting along the axis of a rod, linear strain is the change in length divided by the original length. Volume strain is the fractional discharge in volume for an object pressured on all sides. Shear strain measures the effectiveness of a twisting force.
Stress
A force per unit area which acts on an object attempting to deform it. A force F applied along the axis of a bar of cross section A produces a linear stress of F/A, units per Pa (pascal). Such a force is involved in attempts to pull apart layers of atoms (tensile stress) or to push them together (compressive stress). A twisting force causes shear stress, which tries to slide layers of atoms over one another.
Elasticity
In solids, the property that a stressed material will return to its original size and shape when the stress is removed. It usually corresponds to a direct proportionality between stress and strain. In a metal bar, for example, up to a strain of about 1%, doubling the tension along the bar’s length causes double the extension.
Plastic Deformation
The irreversible deformation of a material stressed to beyond its elastic limit (Yield point). Further increases in stress cause disproportionately large deformations until a fracture point is reached. Ductile materials are those which undergo large plastic deformations (eg most metals); brittle materials undergo small plastic deformations.
Non-linear Physics
The study of systems in which the response to a stimulus is not directly proportional to the size of the stimulus. For example, when small weights are suspended from a spring, doubling the weight doubles the extension (Hooke’s law) and the system is termed linear. If too much weight is added, the extension is not governed by such a simple law: the system is non-linear. A pendulum undergoing large swings is a non-linear system. High intensity light, such as laser light, induces non-linear responses when interacting with atoms.
Molecules
The ratio of stress to stress to strain and the elastic limit of a material are determined by the molecular structure of the material. The distance between molecules in a stress-free material depends on a balance between the molecular forces of attraction and repulsion. When external force applied, creating stress molecular distances change and the material becomes deformed. If the molecules are tightly banded to each other, even for a large amount of stress there will be little strain. However if molecules are loosely banded, a small amount of stress will cause a big strain. Below elastic limit, when force is removed, the molecules return to their original position, this means that elastic materials return to their original shape.
Key Science Four Book Two
The experiments shown in this book show that the steel spring and the rubber band behave elastically, regaining their initial length after they have been stretched and the weights have been unloaded. Here is a graph showing this experiment’s results when it has previously been carried out with elastic bands, metal springs and a polythene strip.
Graph of extension against weight for different materials
This diagram shows us how we would set up the above experiment.
Investigating Stretching
Hooke’s law for springs states that the extension of a spring is proportional to the weight it supports. By applying this law you can weigh an object or force as shown in the diagram below.
Using Hooke’s law to find an unknown weight
Although Hooke’s law only refers to springs, other materials are said to obey the law too if the extension is proportional to the stretching force. This may be written as an equation;
FORCE= CONSTANT x EXTENSION
My Preliminary Experiment
I decided that to better understand the experiment I was about to conduct, I should perform a similar experiment with springs, to test Hooke’s law and see if his theory was accurate. I had already predicted my theory about the proportionality of stress to strain in elastic bands not being linear, based upon my research in the Key Science four book, I just needed to test one of Hooke’s other discoveries in his study of elasticity to see if his observations were reliable.
These were my results;
A graph of these results can be seen on the next page.
The World of Physics
This book goes even further that those I had previously researched as it goes on to describe what actually happens in the molecules of an object as it is stretched.
The tension we feel in a stretched spring is due to all the forces of attraction between the molecules in the spring.
The molecules of a solid are limited to vibrations about a fixed position. They are closely packed and usually in a regular pattern, making them high density objects. Solids return to their original shape when stretched or deformed to a certain extent.