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Copper Young's modulus

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Introduction

Title:

Measuring Young’s modulus of copper

Aim:

To study the stress/strain behavior of copper wire and estimate the Young’s modulus of copper

Apparatus:        

Copper wire s.w.g.32        about 4 m

G-clamp        ×1

Wooden block        ×2

Metre rule        ×4

Pulley on clamp        ×1

Micrometer screw gauge        ×1

Hanger (0.01 kg)         ×1

Slotted mass (0.05 kg)         ×8

Slotted mass (0.1 kg)        ×6

Slotted mass (0.2 kg)        ×4

Slotted mass (0.5 kg)        ×1

White label sticker        ×1

Safety goggles        ×1

Rubber tile        ×1

Theory:

When a force F is applied to the end of a wire with cross-sectional area A along its length, the tensile stress = image00.png

If the extension of the wire is Δl, and its original length is lo, the tensile strain = image01.png

Under elastic conditions, a modulus of elasticity of a wire, called the Young modulus E, is defined as the ratio of the tensile stress applied to a body to the tensile strain produced. image10.png where E is expressed in N m-2 or Pascal (Pa).

E is a constant when Δl is small according to the Hooke’s Law which stated that the stress applied to any solid is proportional to the strain it produces for small strain.

Therefore, when a material has a larger the value of E

...read more.

Middle

0.255

0.250

0.225

0.230

0.225

0.255

0.225

0.255

Average diameter of the wire = (0.240±0.005) mm

Percentage error in d =image18.png

Readings for the graph:

Load m/kg

0.10

0.20

0.30

0.40

0.50

0.60

0.65

Extension Δl/mm

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Load m/kg

0.70

0.75

0.8

0.85

0.90

0.95

1.00

Extension Δl/mm

3.5

4.0

5.0

6.0

6.5

7.5

Broke

image19.png

Data analysis:

Young’s modulus, image10.png

where F is the tension in the wire and A is the cross-section area

Sinceimage20.pngandimage21.png

image02.png

From the graph, the slope of the best fit line through the points of the straight line portion of the graph,image03.pngimage04.png

image05.png

...read more.

Conclusion

Improvement of the Experiment:

  1. Fixed the metre ruler by another G-clamp so that measurement of the extension can be more accurate.
  2. In order to measure extremely small extension with high precision, “optical lever” (a mirror mounted on a small pivot) can be used instead of just using a simple meter stick.image14.png
  3. Repeat the experiment several time and take average of the extension values so that more accurate result can be obtained
  4. The experiment can be repeated as below so that the small extension of the wire can be measured accurately by vernier scale; moreover, there will be no extra fractional fore due to the presence of pulley.

image15.png

  1. Repeat the experiment by using copper wire with different s.w.g and take an average of the Young’s modulus obtained so that we can estimate the value of Young’s modulus of copper more accurately.

Precautions:

  1. Wear safety goggle during the experiment so as to protect our eyes when the wire breaks eventually
  2. The load should not be too high off the floor, and there should be a suitable soft landing platform, such as runner tile right below the load.
  3. The unstretched length should be at least 3m for the wire to extend.  

--------------------------------------------------END-----------------------------------------------

...read more.

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