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# Copper Young's modulus

Extracts from this document...

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 =

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

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.  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

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 =

 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

Data analysis:

Young’s modulus,

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

Sinceand

From the graph, the slope of the best fit line through the points of the straight line portion of the graph,

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.
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.

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-----------------------------------------------

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