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Youngs Modulus of Elasticity of Nicrome Wire

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Introduction

YOUNGS MODULUS OF ELASTICITY OF NICROME WIRE

PLANNING:

Aim:

This experiment is to ascertain the Youngs’ Modulus of Nicrome wire.

Youngs’ Modulus is defined as stress divided by strain, by the equation:

(Force/Area)/(Extension/Original Length)

Or:

(Force * Length) * (Extension * Cross-sectional Area)

The Youngs’ Modulus For Nicrome wire will be determined in this experiment by the following set-up.

Method

        The wire is uncoiled from the roller carefully to make sure that there are no chinks in the wire. This would cause the wire to become weak at one point and would fracture before the wire could take its’ full strain. At one end of the wire, the wire is wrapped around a wooden block with another block laid on top. Then a g-clamp will tighten these blocks together trapping the wire, to prevent the wire from slipping.

        At the other end, there is roller pulley that simply allows weights to be added in the direction of the wire, using the weight hook and weights, attached by a strong knot.

        A small piece of coloured cellotape will be attached to near both ends of the wire. As weights are added, there is a possibility that the wire may just slip rather than becoming taught and stretching.

...read more.

Middle

Original Diameter of the wire = 0.175mm = 1.75 x 10-4 meters.

Area = 0.0000000962m3 = 6.92 x 10-8m3

image00.png

These results may be unduly accurate and this will be taken into account in the conclusion. As the Young’s Modulus concerns the region where Hookes Law is obeyed, then this will be the region where the extension increases in small equal amounts. In this case it is 1-9 Newton’s here. As this only caused small extensions of 1mm per each weight added, this is where the biggest errors will occur.

Ruler to half millimetre accuracy

0.5mm in 8mm = 0.5 / 8 * 100 = 6.25%

CONCLUSION

What is Young’s Modulus Of Elasticity for Nicrome Wire?

Young’s Modulus For Elasticity is defined as Stress Over Strain.

So (Force * Length) * (Extension * Cross-sectional Area)

...read more.

Conclusion

        This shows that this area is obeying Hook’s Law because using the y=mx+c equation, this would say c ≈ 0 (approximately equal to 0). So y=mx  where ‘t’is the stress, ‘x’ is the strain, and ‘m’ is the constant; being Young’s Modulus.

Conclusion:

        My results are accurate, because the graph was a very straight line, as all the points could be plotted to a good degree of accuracy to the original plot from the y=mx equation;

Stress = (5.52 x 1011 ) x Strain

:-> Where 5.52 x 1011 Gpa is my result for Young’s Modulus for Nichrome Wire

Stress (Pa)

Strain

Stress=(5.52 x 10^11) x Strain

Error From Original

10393792.2

2.8*10^-4

1.8829 x10^-5

6.72%

20787584.4

5.6*10^-4

3.7689 x 10^-5

6.72%

31181379.61

8.40*10^-4

5.6488x10^-5

6.72%

41575168.81

1.12*10^-3

7.5317 x 10^-5

6.72%

51968961.01

1.4*10^-3

9.4147x10^-5

6.72%

62362753.21

1.68*10^-3

1.1268 x 10^-4

6.72%

72756545.41

1.96*10^-3

1.3181 x 10^-4

6.72%

83150337.62

2.24*10^-3

1.5063 x 10^-4

6.72%

        Dividing the result of multiplying the stress by my Young’s Modulus by the original, and multiplying by 100 calculated the error from original column.         

        For every multiplication I got a a result of 6.72%, which is close to my approximate error range of 6%.

My results compared to my prediction:

        My results, did not entirely agree with my prediction. From preliminary experiments the Young’s Modulus would be in the region of 180 GPa. Also, from sources the modulus of elasticity for nickel is  

...read more.

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