Michael Ofori

Introduction

The aim of this investigation that I am about to carry out is to undertake a stress-strain analysis (Young Modulus) of a wire found on an ancient mummified Persian princess who according to one translation is a daughter of the King Xerxes which was about 2,600 years ago.

After I have found the young modulus of the wire, I would then by comparison of the young modulus of other materials wires, conclude whether the wire found on the mummy is made from a modern alloy.

Background Information (Theory)

Stress is defined as an internal force produced by application of an external load. It is the relationship between the applied force and the area over which it acts.

Stress(σ)= applied force per unit area = =

The definition and symbol for stress is also used for tensile stress (when a sample is pulled) and for compressive stress (when a sample is squashed). The SI of stress is the pascal (Pa) or Nm-2. The stress needed to break a material is called the compressive or tensile stress and is a measure of the strength of the material that does not depend on the size of the sample.

If a force is applied over a surface area, there would be stress applied to the body. The shape of the body changes as a result of the applying stress. To measure this change, the size or shape of the body after the force is applied is compared with the size or shape of the body before. This is called strain. Strain is the amount of deformation a material experiences per unit of original length in response to stress.

Change in length x

Original Length L

The same definition and symbols are also used for tensile and compressive stress. As strain is a ratio of two lengths, it has no units and is therefore dimensionless.

When stress is applied to a material, strain is produced in the material. The strain is proportional to the stress provided the stress does not exceed a limit known simply as the limit of proportionality. Within this limit, the value of stress/strain is constant for a given material and is known as the young modulus which is the stiffness of the material.

The Young Modulus E = = =

The unit of E is the same as the unit of stress because strain has no units. Therefore E is given in pascals or newtons per metre squared (Nm-2).

Equipments I will need (Apparatus)

- A “G” clamp
- A 1.5m long wire found on the mummy.
- Safety glasses.
- 1kg weights of up to 8kg.
- A pulley.
- A 100cm ruler.
- A micrometer- For measuring the diameter of the wire
- Choc Block- To
- Screw Driver
- Paper sticker- To know the initial point of wire before extension.
- A 100g weight hanger- To hang weights on.

Method

- Using the “G”clamp provided, fix one end of the 1.5metre long wire on clamp making sure it is tightened and secure.
- Using the right length of table in conjunction to the 1.5 metre long wire, fix the pulley provided securely on the table making sure it is tight and firm. Make sure you check that the fixed “G” clamp on the other side of the table is straight towards the pulley.
- Extend wire from the “G” clamp over the pulley making sure that it is at least 10 cm below the pulley to use for hanging the weights on.
- Using the screw driver and the choc block, unwind the screws in the choc black and put wire straight through it until it is at least 6cm past the choc bloc. Put about 3cm of the wire back through the choc block and using the screw driver, tighten the screws securely. The end part of the wire below the pulley should look like a sort of round loop you can put the weight hanger on to hang freely in the air.
- Put the 100g weight hanger onto the loop and make sure it hangs freely in the air.
- At this point in time, the wire would a bit kinky and not that straight enough for experimenting on. Add 500g of weight onto the weight hanger in order to stretch the wire a bit so that the wire would be straight enough for experimentation. The 500g weight is going to be assumed to be the start point for the investigation
- Using the micrometer, measure the diameter of the wire provided at 6 different lengths and workout the mean diameter of the wire.
- Using the paper stickers provided, stick paper preferably 10cm near the pulley and stick a ruler on the table straight under the wire.
- Record the initial length of where the sticker on the wire using the ruler below it.
- Add 1kg of weights onto the weight hanger.
- Take the reading of the final position of the sticker using the ruler under the wire.
- Repeat steps 9-11until you have 8 readings overall.
- When all measurements have been taken, insert results into a well structured table containing units, headings etc.
- Work out the strain value for each of the results by using the formula (x/L) where “x” is the change in length of the wire after weights had been added on and “L” the initial length of the wire before the weights were added on.
- After working out the strain value, Use the formula (πr2) or (πD2/4) to calculate the cross-sectional area (A) of the wire in m2 using the mean diameter of the wire.
- Calculate the stress value for each result using the formula (F/A) where “F” is the weight force (m×g) and “g”which is going to be taken as is 9.81. The letter “A” is the cross-sectional area πr2 with units in m2.
- Plot a correlation graph of stress against strain and workout the young’s modulus by using the gradient to calculate it’s value (stress÷strain).
- After the young’s modulus is calculated, undertake a comparison analysis with the young’s modulus of other materials to conclude whether it is made from a modern alloy.

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*** A well documented report of a classic practical procedure which needs a greater degree of consideration given to how the writer could increase the reliability of the data. To improve Include a clearly labelled diagram of the apparatus involved. Give a clear description of how the independent and dependent variables were measured. As an example there seems to be no mention of the control of temperature or the measures taken to avoid exceeding the elastic limit of the wire. It would have helped to replicate the measurements and perhaps to take measurements whilst unloading the wire to ensure the elastic limit has not been exceeded. A graph with appropriate error bars should be included. The consideration of error needs could be given more consideration as there is no discussion on exceeding the elastic limit or the effect of changes in temperature.