Investigating the young modulus of a wire

Safety

There are quite a few precautions that I would need to take during the process of experimentation. The first quite obvious form danger is when putting the weights on the weight hanger. The wire might snap and hit me in the face or body. I will make sure that I wear safety goggles as well as protective clothing to protect me from injuring myself in case the wire snaps and hits me. Also when putting the weights on the weight hanger, I will make sure that my feet are well away from beneath the hanger in case the weights fall accidentally and hit me in the legs.

Variables

In order to make this experiment a fair test, I will ensure that the weights added to the weight hanger is kept at constant weight intervals. Also to ensure more accurate data when recording measurements of the diameter of the wire using the micrometer, I will make sure I take six readings of this measurement and find the mean of the six results in order to gain more a precise and reliable data.

Another important factor of accuracy I would need to take note of when taking measurements is the para1lax error. This is an error that can be introduced when data is not read from an instrument directly from its front. In order to prevent this error, I will mark a line on the table where there the initial position of the paper sticker on the wire is and after I add the weights, I will read and record the data directly from the marked line I had initially drawn. Great care is going to be taken when the data is being read. This will ensure that I have less inaccuracy in my data results.

Sensitivity

For my sensitivity, I will use a larger range of weights for my experiment in order to gain a larger range of extension values as well as a more accurate and reliable data. Also I will make sure that when I am taking recording my data, I use appropriate significant figures for all my recordings.

Results

Below are the results I recorded from conducting the practical investigation:

From micrometer measurements

Mean = sum of data divided by the sample size

Therefore mean = 0.554 + 0.555 + 0.558+  0.556 + 0.558 + 0.558

                                                                       6

Mean = 0.556 mm

Diameter of wire = 5.56 × 10-4 m

Cross-sectional Area = πr2

Radius = Diameter = 5.56 × 10-4 m = 2.78 × 10-4 m

                      2                   2

Therefore Area (πr2) = π × (2.78 × 10-4) 2

Area “A”= 2.427 × 10-7 m2.

From main experiment

I will now draw a graph of stress against strain of which I can work out the young’s modulus using the gradient of the graph.

Please turn over to see graph

Calculations

From the graph drawn,

Interpreting And Evaluations

From the look of the graph drawn, there were some anomalous results plotted in the graph which were not on or near my line of best fit. This on my opinion might be due because of poor data recordings.

To compare and contrast the young’s modulus of the wire investigated with the young’s modulus of contemporary wires available today in order to conclude whether it is made from a modern alloy, I have copied a table from a datasheet book containing the young’s modulus of the different types of modern wires available today.

Looking at the table above and comparing it with my calculated young’s modulus value of 8.57 × 109 Nm-2, I will conclude that my calculated value compared with that of the published data values is near in similarity to that of lead meta which has a young’s modulus value of 1.57 x 1010. This concludes that the wire found on the mummy is of a fake one because lead wire is a modern wire which was not available in 2,600 years ago.

The reason why there is some variation between the datasheet value and my calculated value in my opinion is because of the fact that there were some limitations that were encountered during experimentation. These were:

• The imperfections of the thinness and thickness of the wire at different lengths when measuring the diameter of the wire using the micrometer.
• How kinky the wire was which was although weights were initially added on before experimentation.
• The number of significant figures I could measure data up to using the ruler.

During the process of measuring the thickness of the wire using the micrometer, the wire was a bit thick on one end and very thin on another end. This might have been caused by an external force being applied onto the wire accidentally and ultimately bending it which in my opinion affected the calculation of the cross sectional area of the wire (πr2) and also the young’s modulus of the wire.

Another important factor contributing to the variation between my value of young’s modulus with published data values is the crookedness of the wire. This is so because although I initially put about 500g of weights on the weight hanger to make the wire was a little straighter before experimenting, there was still some little kinks in the wire at visual contact. This in my opinion contributed to some degree of error associated with my young’s modulus because the wire was not fully stretched enough to find it find it’s tensile strain.

Also another factor contributing to some variations in the young’s modulus was the weights themselves of which I used for the investigation. Although they had on them the correctly written weight number, when I place them on the weight scale to measure their weight number initially before using them, they were at about ±1g inaccurate and this ultimately meant that the forces calculated for the stress analysis was fundamentally flawed which also affected the calculation of the young’s modulus.

The other factor was the number of significant figures that the 100cm ruler I used was able to measured up to. I had to use my naked eye to manually measure the extension of the wire after the weights had been added on in order to work out the strain in later steps. The ruler could only measure up to 0.1cm accuracy and this caused problems together with making sure you did not have any para1lax errors included when measuring and recording data.

In suggesting other ways of improving the experiment next time, I could use the same experimental procedure but this time; use a less kinky wire which has a constant thickness at different lengths. Also I would imply the technique of using material testing kits which are designed to give the modulus of elasticity, yield stress, ultimate tensile stress and percentage elongation (an indication of ductility) for a material by subjecting the specimen wire to an increasing axial load whilst measuring the corresponding elongation of the specimen  wire. This will ensure that I have the highest degree of accurate and reliable results possible.

Measuring The Uncertainty

As stated earlier, my calculated value of the young’s modulus was not of the same as published data values. Due to limitations previously discussed qualitatively, I am now going to quantitatively calculate the percentage uncertainty (error) of my equipments used to see and comment on how inaccurate they are.

Percentage error =  Error in reading

                                Average value

Micrometer  

% error = 0.001mm

                0.556 mm

= 0.179 %.

This is percentage error is not significantly high as it is under 1% so therefore the micrometer measurements were quite accurate to my surprise. However, because they do not correspond to my expectations in determining the percentage error of my calculations which was due to the apparatus that I used, I will also calculate the percentage error for the 100cm ruler see which instrument carried the most percentage error which ultimately resulted in variation of my data with published data values.

Ruler

 

% error = 0.05

              1.3625

= 3.67%.

The concludes with a clear distinction from other equipments used that the ruler carries a high degree of percentage error than any other equipment used in calculating the young’s modulus. I think most of the errors here were partly down to the parallax error used to measuring and recording data.  In future experiments I will use a more accurate form of ruler to measure the extensions in the wire or even better use a material testing kit for the whole experiment to measure the wire’s young’s modulus. This will ensure and give me more accurate and reliable results.

Bibliography

5. AS physics by Heinemann Education Publishers, isbn: 0435628925