An Investigation into the relationship between the forces applied to a length of wire and its extension. Aim: – To investigate the relationship between the extension [e] of a length of copper wire and the force [f] applied to the wire, to do this I intend to use Hooks law the linear modulus is known as stress/strain, also known as Young’s modulus [E]. I hypothesise tat as we increase the amount of force applied to the wire, so its extension will increase. As this was what I found in previous experiments involving Hooks law. Diagram: –
I will use Young’s modulus as it links the two factors that we wish to investigate in that to find a value for Youngs modulus you need to find two values, stress and strain E = Stress where; – stress = Force [f] also;- Strain = extension [e] Strain Cross sectional area [a] original length [l] As we can see from above stress is calculated using force and cross sectional area there for involving force as we require, this will be my input variable and will be the value subject to change. Strain involves extension and original length therefore also bringing in extension, as I required this would be the variable that I will measure.
The other variables involved, original length and cross sectional area will have to be maintained as constants as these are active variables I young’s modulus. This is a specific form of Hooke’s law of elasticity. The units of Young’s modulus in the English system are pounds per square inch, and in the metric system newtons per square metre (N/m2). The value of Young’s modulus for aluminum is about 1. 0 107 psi, or 7. 0 1010 N/m2. The value for steel is about three times greater, which means that it takes three times as much force to stretch a steel bar the same amount as a similarly shaped aluminum bar.
Young’s modulus is meaningful only in the range in which the stress is proportional to the strain, and the material returns to its original dimensions when the external force is removed. As stresses increase, Young’s modulus may no longer remain constant but decrease, or the material may either flow, undergoing permanent deformation, or finally break. _ To a greater or lesser extent, most solid materials exhibit elastic behaviour, but there is a limit to the magnitude of the force and the accompanying deformation within which elastic recovery is possible for any given material.
This limit, called the elastic limit, is the maximum stress or force per unit area within a solid material that can arise before the onset of permanent deformation. Stresses beyond the elastic limit cause a material to yield or flow. For such materials the elastic limit marks the end of elastic behaviour and the beginning of plastic behaviour. For most brittle materials, stresses beyond the elastic limit result in fracture with almost no plastic deformation. _
I hypothesize that as i incears the load applied, and therefore the force[f] the extewnsion of the wire [e] will also increase. i predict that the relationship between the two will be proportional. I have decided upon this outcome due to my background reaserch into the matter. I found that when streching metals a modulus applies called youngs modulus, this tells us that when streching a wire we get a graph of stress against strain where stress is equall to load/crossectional area therefore incorporating load and strain is equal to extension/original length.
Advanced Physics by tom duncan states that tensile strain is directly proportional to tensile stress during elastic deformation. This statment is known as hookes law The outcome graph looks like this:- we can see a proportional relationship between the two variables at the beggining of the graph due to the constant gradient, a6t piont b we can see the graident is constantly changing. here youngs modulus no longer applies because the material has passed its elastic limit.
i think that me graph of oad/extension will be very simular provided the other factors involved remain constant, these are cross sectional area and original length. To do this i intend to take multiple readings of the crosssectional area of the wire throughout the experiment to find an avrage as i know that the wire will become thinner as i strech it, as i descoverd in my preliminary tests. Also i i will keep a constant original length this is fairly straiht forward an easy to achive.
i have decided upon a lenght of 2. 5m for the wire because a longer wire is easier to strech as i found in my preliminary investigation and i have also decided to use a thin wire of 0. 5 mm in diameter as this will also make the wire easier to strech, by doing this i can cary out the experiment using lighter loads and therefore make it safer, it also of high importance to wear saftey gogles while carying out the experiment to protect the eyes when the wire breaks.
The extension will be of a small figure and there fore the measuring equipment will have to be able to measure small amounts e. g. a millimetre quite accurately. I have decided after carrying out some preliminary work that it would be best suited if I were to increase the load applied to the wire and therefore the force [f] in amounts of 100g, as we tried the experiment using 50g weights but it proved difficult to suspend so many from the wire but the 100g weights were still accurate enough.
We will continue to add the weights to the wire until breaking point which we found to be around 1700g which required 17 100g weights to be applied, and around 17 results taken of which this would be repeated multiple times. I also found that the extension varied from 0. 25 mm to 3cm and therefore needed an measuring device that was accurate to a 1/4 of a millimetre but could measure up to 3 centimeters for this I found vernieer callipers to be the best suited.
These allowed an exterrmly accurate measurement as small as 0.25mm and allowed us to measue lenghts as large as 10cm this was far larger than the required amount. To carry out the experiment i would use the apparatus in a way shwn in the above diagram (fig 1). this method was the best for me to use as it was implamentable as we had all the required equipment to hand, Although i did find some other methods in my research that would provide a more accurate set of results. i found it to be more accurate because the experiment was suspended from the celing and the wire was entrly vertical.
Unfortunatly this method was unimplamentable due to lack of equipment, i found the main reason why my method was less accurate was because the force was applied by the weight to the wire in a vertical irection but the majoraty of the wire ran horizontaly along the desk therefore the force as not properly tranfered through all the wire this was shown in my perliminary results because we set up another pointer near the weight and measued extension here it showed that the extension was far greater near the weight than near the clamp where we were measuring it. i also found that other factors infuencing my results were ‘necking and creeping’.