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# Young Modulus of Copper

Extracts from this document...

Introduction

Physics TAS

Young Modulus of Copper

Objectives

-Determine the Young modulus of copper by simple experiment

-Study the relationship of strain and stress between elastic and plastic deformations of copper

-Verify a wire will not return to its original length after certain extensions

Preview Questions

1.Hooke's Law states that the elastic force is directly proportional to the extension (or compression) of the elastic body. A wire obeys Hooke's Law only if it is within its elastic limit.

2.Elastic deformation means a stretched wire will return to its natural length. If the wire is stretched beyond its elastic limit, it will not return to the original length and will make permanent extensions. This is called plastic deformation.

3.A longer wire will extend more than a shorter wire of the same cross-sectional area under the same applied force.

4.As in Q.3 , force constant can be easily affected by geometric factors such as length and cross sectional area. But the stiffness of materials depends on their Young modulus only, which is not affected by geometric factors. So force constant is not a good quantity to compare the stiffness of materials.

Apparatus

Copper wire ..................1 roll                         slotted mass with hanger

100g hangers ....................1

100g slotted mass .........~15

G-clamp ....................1                          white label sticker.................1

clamp-on pulley ..........1                     micrometer screw gauge...........1

metre rule ................2                               newspaper.............several

Theory

The following quantities is important for the experiment's concerns:

Stress is defined as  σ=Force / Cross-sectional area ( F/A )

Strain

Middle

D4

Mean

Value

(in ±0.005mm)

0.370

0.365

0.670

0.370

0.3688

Natural length of the wire=1.15m

Experiment 1:

 Load(kg) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Extension(10^-3 m) 0 0.5 0.5 1 1 1.5 1.5 2
 Load(kg) 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Extension(10^-3 m) 2.5 2.5 3 3 3.5 4 5.5 12
 Load(kg) 1.7 1.8 1.9 2 2.1 2.2 2.3 Broken Extension(10^-3 m) 19 34 46 60 77 98 125 /

Maximum load for elastic deformation=1.3 kg

Load for breaking the wire=2.3 kg

Experiment 2 :

 Load(kg) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Extension(10^-3) 0 0.5 0.8 1 1.2 1.5 1.5 2
 Load(kg) 0.9 1 1.1 1.2 Elastic limit exceeded Extension(10^-3) 2.5 2.5 3 3.5 / / /

Calculations & Graphs

Maximum possible error of  metre rule = 0.1 cm=0.01m

Maximum possible error of

micrometer screw gauge      =0.005mm=5x10^-6 m

Cross-sectional area of the wire = 1.068x10^-7 m^2

Percentage error = 2x6.

Conclusion

Discussion

1.Near the breaking point, the shape of the wire is very narrow.

2.During elastic deformation, the hanger falls and loses gravitational potential energy. This energy change to elastic potential energy. If the wire is unloaded, the energy will be restored to GPE and the wire will return to is original length.

3.During plastic deformation, the loss of gravitational potential energy becomes the work done to increase the length of the wire (increase the separations of the particles in the wire). This energy would not be restored even the wire is unloaded.

4.Double of the amount of the load is required to break the wires.

Conclusion

To obtain the Young modulus of the copper wire by this experiment is convenient. A few apparatus and steps are needed, and it only involves easy calculations. But by comparing to the actual value(124G Pa), the result we get (38.9 G Pa) has a great difference from it.

This may due to the experiment is done in several assumptions and estimations. We assumed g=10ms^-2 and the wire is made of pure copper. We neglected environmental factors and assumed the wire was stretched evenly in every parts.

In short, although the experiment is not accurate enough, it provides a good chance for students to practice what they have learned. It is quite shocked that a very thin and long wire can withstand more than 2 kg load.

The End

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