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The elasticity of copper investigation

Extracts from this document...

Introduction

The elasticity of copper investigation

Aim

The aim of this experiment is to investigate how the extension of a length of wire is affected by the force. I will then find stress and strain after finding these variables, for which I can finally complete my objective which is to find the young’s modulus for the material, in this case copper wire.

Hypothesis

I predict that when a wire is subjected to a stretching force, in this case wire being pulled by the force of weight, then the wire likely to be stretched. This does depend on the material as the more flexible the material is the more possibility there is of stretching. I think that the copper wire will have a young’s modulus of about 130 GPa, as the secondary source has worked this out

The stretching force which extends material by equal steps is called Hooke’s law. image00.png

Equation:

Stretching force, F = spring constant, k * extension, Δx

(N)                                (N 1/m)                 (m)

So the lower the gradient the more flexible the spring will be, vice verser.

This formula can be used to calculate the spring constant, which means that we can work out the force needed to extend the copper wire by 1 metre. So we can predict the amount of extension of the copper wire when adding Newton’s.  

Δx = stretched length – original length

k, can also be referred to as stiffness

The point before X is the limit of proportionality (F α x) it is where the strain is proportional to stress. Point X is called the elastic limit

...read more.

Middle

‘The ultimate tensile stress is the measure of strength.’

This is when the material is likely to break so can no longer stretch, but will not be testing this in my experiment.

Strain: the extension per unit length produced when an object is stretched or squashed. This has no unit because it is a ratio.

Strain, ε = Extension, Δx (m)

    Original length, L (m)

For e.g. if there were two wires different lengths, everything else same, the longer wire would be under more strain.

‘It stretches by the same fraction of its original length.’

Young’s modulus: this is the ratio of stress to strain in a material when it is stretched, provided Hooke’s law is obeyed.

Young’s modulus, E = Stress, σ (Pa)

                           Strain, ε

image02.png

Method

  1. Gather all apparatus in one place safely, then setup the apparatus up like diagram shows.image04.pngimage03.png
  1. Measure the length of wire on the metre rulers, ensuring the wire is taught and straight along the rulers. Measure the diameter along the wire, at least in three different places (as the wire may not be the same everywhere). Place the sellotape pointer on the wire, any where as long as it is against the rule and take own these results.
  1. The wire may have to be long to see a significant change in extension; however the temperature may affect the length. I suggest that a preliminary experiment take place to work this out.  
...read more.

Conclusion

R-squared value: An indicator from 0 to 1 that reveals how closely the estimated values for the trend line correspond to your actual data. A trend line is most reliable when its R-squared value is at 1 or near 1. It is also known as the coefficient of determination.

Evaluation

The uncertainty of the extension is 0.01cm  

(0.01/1.7)*100 = 1.7%

The uncertainty of the length of wire is 0.001m

(0.001/1.760)*100 = 0.05%

The uncertainty of the diameter of the wire is 0.01mm

(0.01/0.31)*100 = 3.1%

To ensure I had a safe experiment I wore safety goggles, also setup the experiment in the centre of the table.

I made sure that the clamp stand was firmly placed on the floor so that it wouldn’t wobble and affect the results taken down.

I tried to keep my eye level in line with the marker measurements to rule out parallax error.

I took many results down to have accurate results and averaged them.

The reason for the line of best fit not going through the origin there may have been due to systematic error. This may because there was friction on the pulley, to remedy this problem grease could be used. Also the ruler was not long enough for the whole wire to be measured so the 2 rulers may be disjointed, so to remedy this problem I would need a longer ruler. Also the taught wire may not be horizontal to the pulley when tied to the clamp so the wire is longer than it can be measured, to solve this problem I used a wooden block, but it wasn’t enough.

The main two measurements that contributed to young’s modulus were the diameter and the extensions as they were used to calculate the stress and strain.  

...read more.

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