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Young's Modulus of Nylon

Extracts from this document...

Introduction

Young’s Modulus Investigation                         J. Lee

Young’s Modulus Investigation

AS Physics Coursework

J. Lee


Introduction

This investigation aims to find the value of Young’s Modulus for a specific material, in this case nylon fishing line.

Young’s Modulus (E) is a measure of a material’s stiffness, determined by the formula:

image00.png

The standard unit of measure for Young’s Modulus is the pascal (Pa). 1 pascal is the same measure as 1 Nm-2 (Nm being Newton Metre).

A material always retains the same Young’s Modulus value regardless of how much it is stretched or strained, and this should be revealed in this investigation by gathering a definite value of the modulus for nylon.

Hypothesis

Through research that I conducted before starting the investigation, I have determined that the correct Young’s Modulus value of Nylon lies in the range 1-7GPa (the large range being due to different make-ups of Nylon with it being a compound). I should therefore be looking at achieving a final result within or very close to this range.

Since stress is proportionate to strain in the Young’s Modulus formula, and the modulus value remains the same, I would expect the value of stress and strain to proportionally increase with each other.

Experiment Plan

In order to carry out this investigation into the value of Young’s Modulus of nylon, I will conduct an experiment to gather the values of stress and strain when increasing force is added to the material, and will take readings as weight increases until the breaking point of the nylon is reached.

In order to calculate stress and strain, I will need to record each of the following variables throughout the experiment:

Force applied to the material [F] (Newtons/N)
Area of a cross-section of the material [A] (Metres-squared/m
2)

...read more.

Middle

3.92x108

0.542

0.125

0.231

1.70 x109

12.753

3.00x10-8

4.25x108

0.542

0.129

0.238

1.79 x109

13.734

BREAKING POINT

Error and Uncertainty

See first experiment results for explanation.

Area: Uncertainty of +/- 0.001mm. Diameter of 0.195mm, so uncertainty percentage is 0.5%.

Original Length: Uncertainty of +/- 0.001m. Length was 0.542m, so uncertainty is 0.18%.

Extension: Uncertainty of +/- 0.001m. Ranges from a length of 0.009m with 11% uncertainty, to a length of 0.129m with 0.78% uncertainty.

Table of Results – Third Experiment

STRESS

STRAIN

YOUNG’S MODULUS (Pa)
STRESS/STRAIN

Force (N)

Area (m2)

STRESS

Lo (m)

Extension (m)

STRAIN

0

2.84x10-8

-

0.459

-

-

-

0.981

2.84x10-8

3.45x107

0.459

0.013

0.028

1.22x109

Region of Elasticity

1.962

2.84x10-8

6.91x107

0.459

0.02

0.044

1.59 x109

2.943

2.84x10-8

1.04x108

0.459

0.026

0.057

1.83 x109

3.924

2.84x10-8

1.38 x108

0.459

0.032

0.070

1.98 x109

4.905

2.84x10-8

1.73 x108

0.459

0.041

0.089

1.93 x109

5.886

2.84x10-8

2.07 x108

0.459

0.048

0.105

1.98 x109

6.867

2.84x10-8

2.42 x108

0.459

0.054

0.118

2.06 x109

7.849

2.84x10-8

2.76 x108

0.459

0.058

0.126

2.19 x109

8.829

2.84x10-8

3.11 x108

0.459

0.062

0.135

2.30 x109

9.810

2.84x10-8

3.45 x108

0.459

0.069

0.150

2.30 x109

10.721

2.84x10-8

3.78 x108

0.459

0.072

0.157

2.41 x109

11.772

2.84x10-8

4.15 x108

0.459

0.076

0.166

2.50 x109

12.753

2.84x10-8

4.49 x108

0.459

0.082

0.179

2.51 x109

13.734

2.84x10-8

4.84 x108

0.459

0.085

0.185

2.61 x109

14.715

2.84x10-8

5.18 x108

0.459

0.096

0.209

2.48 x109

15.696

2.84x10-8

5.53 x108

0.459

0.106

0.231

2.39 x109

16.667

2.84x10-8

5.87 x108

0.459

0.114

0.248

2.36 x109

17.658

BREAKING POINT

Error and Uncertainty

See first experiment results for explanation.

Area: Uncertainty of +/- 0.001mm. Diameter of 0.19mm, so uncertainty percentage is 0.53%.

Original Length: Uncertainty of +/- 0.001m. Length was 0.459m, so uncertainty is 0.22%.

Extension: Uncertainty of +/- 0.001m. Ranges from a length of 0.013m with 7.7% uncertainty, to a length of 0.129m with 0.88% uncertainty.

Average values for Young’s Modulus (GPa)

Calculated from Region of Elasticity only

First Experiment

1.42

Second Experiment

1.50

Third Experiment

1.66

Overall Average Value

1.53

Breaking point of the nylon (force in Newtons/N)

First Experiment

13.734

Second Experiment

13.734

Third Experiment

17.658

Mode Breaking Force

13.734

Mean Breaking Force

15.042

Graphs of Results from Experiments 1 – 3

To analyse my data and begin interpreting my findings from the experiments, I decided to plot of stress against strain values for each one.

The graph of each experiment can be found on the next three pages.

...read more.

Conclusion

Experimental Technique
Using a manual wooden ruler, accurate only to 1mm, left large room for error when taking readings in the experiments. The layout of my apparatus in general also created reliability problems, as I had to make sure I was perfectly level with the bottom of the nylon thread to take an accurate reading, and with the amount of readings being taken it is likely that there was a mistake made during this process at some point.
Some parts of the experiment however used better technique, for example the micrometer which was accurate to 0.001mm provided very accurate results of the reading for diameter which means my cross-section area values are of good reliability.

Suggestions for Improvement and Further Work

Since my values for Young’s Modulus proved to be questionable, I would suggest that further investigation needs to be carried out in order to achieve a more conclusive result.

It would be a good idea to repeat the investigation of the elastic region two more times so that greater accuracy can be achieved by calculating an average final value from the three experiments.

The experiments all seemed very vulnerable to sources of human error and so in future investigations I believe the set-up and technique needs to be adjusted to reduce the reliance on human measurements and contact with the nylon.

Upon obtaining a more reliable conclusion for the nylon investigation, I would also suggest expanding the investigation to new types of material so that the behaviours and values of different types of material can be analysed. A good proposal for this would be to see how polymers, such as nylon, react differently to metals or brittle materials when stress is applied.

...read more.

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