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I will determine the extension of a piece of copper wire when various loads are placed upon it at the end. Using the results I will thus calculate Young`s modulus.

Extracts from this document...

Introduction

2003 practice assessed practical (physics)

Hooke`s law and measurement young modulus of copper

Section A)

Outline plan: I will determine the extension of a piece of copper wire when various loads are placed upon it at the end. Using the results I will thus calculate Young`s modulus.

Background

Youngmodulus (E) is a quantity that describes the resistance of a wire to stretching. The quantity is a property of the specific material such as steel or copper. It gives the force per unit cross section of the wire required to produce a fractional change in length.

The force per unit area applied to the wire is called the STRESS (or tensile stress), and the fractional change in length is called the STRAIN (or tensile strain). Young's Modulus is the ratio of the stress to the strain, that is:
Young's Modulus = stress/strain for the material

I predict that a graph of extension against load will be a straight line through the origin, provided the elastic limit has not been reached, the gradient will give us L/ A* E from which e can be calculated.

Labelled diagram

Consideration of safety:

  1. Goggles must be worn at all times when a spring(s) are under tension in the room. This is because if the wire snaps etc. it could potentially hit you, and if in the eyes cause blindness, so its inperitive that they are worn at all times.
...read more.

Middle

0.19

2/90

0.19

0.185

0.195

Average

0.195

0.185

0.1925

Calculation of Average wire diameter

= (0.195 + 0.185 + 0.1925) / 3

= 0.1908mm

Thus the average cross sectional area of the wire is

Force = mass * 9.81 ms

Table of readings

                                                Final length, attempt;

Mass/g

Mass/Kg

Force/N

Orig.L/M

1/M

2/M

3/M

Mean

Extension/M

100

0.1

0.981

2.3

2.30

2.30

2.30

2.3

150

0.15

1.4715

2.3

2.301

2.30

2.301

2.3007

0.3007

200

0.2

1.962

2.3

2.3015

2.3015

2.3015

0.3015

250

0.25

2.4525

2.3

2.302

2.302

2.302

0.302

300

0.3

2.943

2.3

2.3025

2.3025

2.3025

0.3025

350

0.35

3.4335

2.3

2.303

2.304

2.303

2.3035

0.3035

400

0.4

3.924

2.3

2.304

2.304

2.304

0.304

450

0.45

4.4145

2.3

2.305

2.305

2.306

2.3055

0.3055

500

0.5

4.905

2.3

2.305

2.305

2.305

0.305

550

0.55

5.3955

2.3

2.307

2.308

2.307

2.3075

0.3075

600

0.6

5.886

2.3

2.309

2.309

2.309

0.309

Unfortunately errors can easily occur in this experiment, the first way of minimizing the percentage error in the experiment is to identify the sources that could cause such a problem; these being.

When measuring the extension there are 3 main sources of uncertainty.

  • Meter rule
  • Parallax error
  • Zero error

I plan to minimize these by;

  • Careful choice of meter rule, as man are bent and warped
  • Fixing a head and eye position against something so that the parallax error is minimized as I will be looking at the ruler from exactly the same angle.
  • Record results from 0.0 M
  • If there is a zero error, take it away from the results.

When measuring the weight of the mass the following sources could effect the results;

  • Zero error on the scales
  • Not allowing for the weight of the cradle
  • Simply using the weight that is imprinted on the mass instead of weighting it.
...read more.

Conclusion

The equipment was packed away and the experiment was completed within the hour.I observed a changing in mass or load on the wire and no change in any of the identified variables.

C Analyzing Evidence and Drawing Conclusions.

Force/N

Area/M

Sress/Nm  (Pa)

Length/M

Extension/M

Strain

Youngs modulus

0.988

0.000000113

8743362.832

2.3

0

0

0

1.47

0.000000113

13008849.56

2.3

0.3007

0.130739

99502341.14

1.96

0.000000113

17345132.74

2.3

0.3015

0.131087

132317762.2

2.45

0.000000113

21681415.93

2.3

0.302

0.131304

165123366.3

2.94

0.000000113

26017699.12

2.3

0.3025

0.131522

197820522.2

3.43

0.000000113

30353982.3

2.3

0.3035

0.131957

230030178.9

3.92

0.000000113

34690265.49

2.3

0.304

0.132174

262459245.5

4.14

0.000000113

36637168.14

2.3

0.3055

0.132826

275828107.1

4.91

0.000000113

43451327.43

2.3

0.305

0.132609

327665747.9

5.4

0.000000113

47787610.62

2.3

0.3075

0.133696

357435786.7

5.89

0.000000113

52123893.81

2.3

0.309

0.134348

387977203.1

The stress was simple to calculate as it simply meant dividing the force by the area, as so;

The strain is a simple ratio it involves dividing theextension by the length;

Thus the young’s modulus can be found for every plotted point separately on the graph; this is done by dividing the stress by the strain. As I predicted earlier the material obeys hookes law and froms a straight line through the origin until the elastic limit is reached. As well as we can calculate the extension from the gradient of the graph because its equal to L / E*A.

When a material obeys Hooke’s law, then its force, extension graph is a straight line through the origin (see graph). This is only the case up to the proportional limit. The graph being a graph of force against extension, the area is the energy stored in the wire. As the equation of the graph is F=kx, the equation of the area is image00.png.

From the graph we can say that as the load increases on the wire the extension also increases proportionally, up to a certain point known as the elastic limit, this is because it is obeying kooks law as described above, and for this material whilst under low load the strain is proportional to the stress..

...read more.

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