# Investigating the young modulus of a wire

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Introduction

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.

Middle

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

Test | Distance (mm) |

1 | 0.554 |

2 | 0.555 |

3 | 0.558 |

4 | 0.556 |

5 | 0.558 |

6 | 0.558 |

Total | 3.392 mm |

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

Start Point “L” (cm) | Weights Added “m” (kg) | End Point (cm) | Extension “x” (cm) | Stress = (mg/A) Nm-2. | Strain = (x/L) |

67.1 | 1 | 67.4 | 0.3 | 40359068.81 | 0.00447 |

67.1 | 2 | 67.6 | 0.5 | 80758137.62 | 0.00741 |

67.1 | 3 | 68.0 | 0.9 | 121137206.4 | 0.01331 |

67.1 | 4 | 68.3 | 1.2 | 1615162752 | 0.01764 |

67.1 | 5 | 68.6 | 1.5 | 198380566.8 | 0.02196 |

67.1 | 6 | 69.0 | 1.9 | 242274412.9 | 0.02769 |

67.1 | 7 | 69.2 | 2.1 | 282653481.7 | 0.03043 |

67.1 | 8 | 69.6 | 2.5 | 323032550.5 | 0.03612 |

I will now draw a graph

Conclusion

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

- http://www.tecquip.com/TQ%20PRODUCT%20AREAS/TASK/MF4/mf4.htm
- http://hyperphysics.phy-astr.gsu.edu/HBASE/Tables/rstiv.html
- http://www.matter.org.uk/schools/Content/YoungModulus/
- http://www.matter.org.uk/schools/Content/YoungModulus/experiment_2.html
- AS physics by Heinemann Education Publishers, isbn: 0435628925

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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## Here's what a teacher thought of this essay

*** 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.

Marked by teacher Stevie Fleming 15/10/2013