# Draw stress and strain graphs for the metal copper and the alloy constantan. Calculate the figures of young's modulus for copper and constantan. Discuss the physics involved.

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Introduction

AS Physics Data Analysis coursework

This coursework assignment requires me analyse and evaluate data on copper and constantan given to me. It entails investigating the young’s modulus of the metal and alloy. Thus I will use many methods during to complete my investigation.

Aims:

- To draw stress and strain graphs for the metal copper and the alloy constantan
- To calculate the figures of young’s modulus for copper and constantan
- To discuss the physics involved

Plan:

In this investigation I have received results for extension of copper and constantan for certain forces applied to it, for which I will analyse and calculate the young’s modulus. The results I have been given are forces applied to copper and constantan, three sets of results for the metal and alloy and this can be used by averaging data to give more accurate results thus these results given to me will be used to create graphs, calculate young’s modulus and analyse data for both metals so I can complete my investigation.

I will need to draw a force and extension graph for both copper and constantan, the extension shown will be the averaged value for each metal. I will also calculate the stress and strain values and plot this on a graph for both copper and constantan, I will plot these on the same graph and analyse the graph, hence I can find any patterns from the data and this will require me to draw my graphs accurately so I can correctly analyse the results to make judgements and conclusions.

I will use Microsoft Excel spreadsheet program to make tables of data, with the data I have been given. I will be using formulas to calculate average extension, stress, strain and young’s modulus for copper and constantan.

Middle

1.000E-03

1.000E-03

2.000E-03

1.33E-03

3.720E+07

6.35E-04

5.86E+10

6

3.000E-03

2.000E-03

3.000E-03

2.67E-03

5.580E+07

1.27E-03

4.39E+10

8

4.000E-03

3.000E-03

3.000E-03

3.33E-03

7.440E+07

1.59E-03

4.69E+10

10

5.000E-03

4.000E-03

4.000E-03

4.33E-03

9.301E+07

2.06E-03

4.51E+10

12

6.000E-03

5.000E-03

5.000E-03

5.33E-03

1.116E+08

2.54E-03

4.39E+10

14

7.000E-03

5.000E-03

5.000E-03

5.67E-03

1.302E+08

2.70E-03

4.83E+10

16

9.000E-03

6.000E-03

6.000E-03

7.00E-03

1.488E+08

3.33E-03

4.46E+10

18

1.100E-02

7.000E-03

1.000E-02

9.33E-03

1.674E+08

4.44E-03

3.77E+10

20

1.600E-02

1.000E-02

1.200E-02

1.27E-02

1.860E+08

6.03E-03

3.08E+10

22

2.200E-02

1.500E-02

4.500E-02

2.73E-02

2.046E+08

1.30E-02

1.57E+10

24

9.600E-02

3.200E-02

1.400E-01

8.93E-02

2.232E+08

4.25E-02

5.25E+09

26

BROKE

4.300E-02

BROKE

4.300E-02

2.418E+08

2.05E-02

1.18E+10

28

BROKE

BROKE

BROKE

BROKE

BROKE

BROKE

BROKE

Table 1

CONSTANTAN | |||||||

Force (N) | Extension (m) | Extension (m) | Extension (m) | Average Extension (m) | Stress (Pa) F/A | Strain (Ratio) E/L | Young's Modulus |

0 | 0 | 0 | 0 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |

2 | 0 | 0 | 0 | 0.00E+00 | 2.08E+07 | 0.00E+00 | 0.00E+00 |

4 | 2.00E-03 | 1.00E-03 | 1.00E-03 | 1.33E-03 | 4.16E+07 | 6.35E-04 | 6.55E+10 |

6 | 3.00E-03 | 1.00E-03 | 1.00E-03 | 1.67E-03 | 6.24E+07 | 7.94E-04 | 7.86E+10 |

8 | 4.00E-03 | 2.00E-03 | 2.00E-03 | 2.67E-03 | 8.32E+07 | 1.27E-03 | 6.55E+10 |

10 | 4.00E-03 | 3.00E-03 | 3.00E-03 | 3.33E-03 | 1.04E+08 | 1.59E-03 | 6.55E+10 |

12 | 5.00E-03 | 3.00E-03 | 4.00E-03 | 4.00E-03 | 1.25E+08 | 1.90E-03 | 6.55E+10 |

14 | 5.00E-03 | 4.00E-03 | 5.00E-03 | 4.67E-03 | 1.46E+08 | 2.22E-03 | 6.55E+10 |

16 | 6.00E-03 | 4.00E-03 | 5.00E-03 | 5.00E-03 | 1.66E+08 | 2.38E-03 | 6.98E+10 |

18 | 8.00E-03 | 4.00E-03 | 5.00E-03 | 5.67E-03 | 1.87E+08 | 2.70E-03 | 6.93E+10 |

20 | 8.00E-03 | 4.00E-03 | 6.00E-03 | 6.00E-03 | 2.08E+08 | 2.86E-03 | 7.28E+10 |

22 | 8.00E-03 | 5. |

Conclusion

I have concluded that my prediction was correct as this was shown by my calculations and can be seen in the graphs I have drawn that constantan has a higher young’s modulus than copper.

I will now evaluate the accuracy of the data given to me and calculations I have made myself. I have set the my percentage error to be 5%, so if the percentage error is above 5% then I believe this is not accurate enough for an A-level experiment.

Percentage error in measurements % error= (Error in measure/measurement) x 100 | Area of wire Smallest measurements: 0.005x10-3m (Micrometer) and 0.35x10-3m (smallest recorded measurement). (0.005x10-3/0.35x10-3) x100 = 1.43% error The error percentage maximum I set was 5%, I have worked out the error percentage of area of wire to be 1.43%, and therefore this is acceptable. |

Original Length Length of wire taken as 2.1m The error in measure of metre rule is 5mm (5x10-3m) (0.005/2.1) x100 = 0.238095238% = 0.24% error This error is acceptable as it is well below the 5% error maximum I set, so this was seen to be literally an error free measurement. | Force Mass= 100g each, but 2N intervals in force, so 200g mass for each interval. The mass error is between 99-101g, so +/- 1g. As two were used then 1x2= +/-2g error. (2/200) x100 = 1% error As my error maximum was set to 5%, a 1% error for force is acceptable. |

Bibliography

- http://www.york.ac.uk/depts/chem/course/studhand/solids.html- found out composition of copper and constantan. (7/10)

- http://www.azom.com/details.asp?ArticleID=60- information on copper alloys (5/10)

- AS physics text book: very useful, chapter 4-5 are very useful and contained lots of information on the physics theory of my investigation (9/10)

- AS-physics CD-ROM: provided guides on how to set out coursework and information on the experiment hat this coursework was based on. (8/10)

- AS Physics teacher: Miss Bottomly: Very helpful. Introduced coursework, hence this would not have been possible without teachers help. (10/10)

By, Kamlesh Vadukul (Heathland school) AS-Level Physics

Word count: 5153

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

This is a well structured and well written report.

1. The sources of information need to be indicated within the work itself.

2. The running commentary should be removed.

3. The conclusions show good practice.

4. The evaluation should suggest further research opportunities.

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Marked by teacher Luke Smithen 13/08/2013