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# To plan an experiment to measure the extension in a piece of copper wire, taking accuracy to be of the utmost importance. The aim is to determine the Young's Modulus of the copper wire.

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Introduction

AS Physics Assessed Practical (Skill P) – Elasticity of a Copper wire

By Priyesh Patel 12O

Investigation into the elasticity of a copper wire

Planning

Aim:

To plan an experiment to measure the extension in a piece of copper wire, taking accuracy to be of the utmost importance. The aim is to determine the Young’s Modulus of the copper wire.

Introduction:

I am required to investigate how the extension e of a length of copper wire changes as the stretching force F is increased. In doing this, making sure I play careful attention to safety. Accuracy is the main issue in this experiment, so it has to be taken into account, in the equipment used, this means that the percentage error has to be at its lowest possible value.

There many things that I can look at which are related to this investigation, such as the Young’s modulus of a wire:

Stiffness is a measure of the resistance to deformation such as stretching or bending. The Young modulus is a measure of the resistance to simple stretching or compression. It is the ratio of the applied force per unit area (stress) to the fractional elastic deformation (strain). Its SI units are MN/m2 (meganewtons per sq m) or, equivalently, MPa (megapascals).

The properties of materials can be looked at also:

• Elasticity. This is the ability of a material to return to its original shape and size after distorting forces (i.e. tension, where this investigation is concerned) have been removed. Materials, which have this ability, are elastic: those, which do, not, are plastic. Elasticity is a result of intermolecular forces- if an object is stretched or compressed, its molecules move further apart or closer together respectively. This results in a force of attraction (in the first case) or repulsion (in the second), so the molecules return to their average separation when the distorting force is removed. This always happens while the strength of the force is below a certain level (different for each material), but all elastic materials finally become elastic if it exceeds this level (elastic limit and yield point).
• Hooke’s law. States that, when a distorting force is applied to an object, the strain is proportional to the stress. As the strength of the force increases, though, the limit of proportionality is reached, after which Hooke’s law is no longer true.

Piece of wire under extension

Strain is stated as change in length per unit length.

 Strain = e l

Where e = change in length; l = original length

Stress is stated as force applied per unit area.

 Stress = F A

Where F = force applied; A = cross-sectional area.

• Elastic limit. The point, just after the limit of proportionality, beyond which an object ceases to be elastic, in the sense that it does not return to its original shape and size when the distorting force is removed. It does return to a similar shape and will continue to return to this new form if forces are applied, i.e. it stays elastic in this sense. The yield stress of a material is the value of the stress at its elastic limit.
• Yield point. The point, just after the elastic limit, at which a distorting force causes a major change in a material. In a ductile material, like copper, the internal structure changes- bonds between molecular layers break and layers flow over each other. This change is called plastic deformation. (The material becomes plastic). It continues, as the force increases, and the material will eventually break.

Below is a stress/strain graph for a ductile material, like copper.

• The tension force acts on the wire when it is under stress and strain, it is equal and opposite which, when applied to the ends of an object, such as a wire, increase the length. The intermolecular force resists them.

Middle

 Diameter of wire, (d) mm 0.19 Load, Kg 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Force, (f) N 0.98 1.96 2.94 3.92 4.90 5.88 6.86 7.84 8.82 9.80 10.78 Initial length of wire, (l) m 2.32 Extension, (e) m 0.01 0.02 0.02 0.03 Break Diameter of wire, (d) mm 0.28 Load, Kg 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Force, (f) N 0.98 1.96 2.94 3.92 4.90 5.88 6.86 7.84 8.82 9.80 10.78 Initial length of wire, (l) m 2.32 Extension, (e) m 0.01 0.02 0.03 0.04 0.04 0.05 0.05 0.06 0.06 0.06 0.07 Diameter of wire, (d) mm 0.32 Load, Kg 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Force, (f) N 0.98 1.96 2.94 3.92 4.90 5.88 6.86 7.84 8.82 9.80 10.78 Initial length of wire, (l) m 2.32 Extension, (e) m 0.01 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.05 0.06 0.06 Diameter of wire, (d)

Conclusion

As the wire is stretched, the diameter of the copper wire decreases, we get plastic deformation before it snaps, for example if we look at a copper rod as a large scale to the thin wire you can see from the below that the copper rod ‘necked’ before it broke.

This happens because metals like copper, (above) are ductile- they can have large plastic deformations without fracturing. It happens because atoms move, as the plastic deformation in the crystal structure move, to place of lower stress. The copper becomes thinner when atoms move away from the stressed part. The stress then increases because the cross-sectional area is now decreased. This increases the ductile flow and so the metal yields and gets thinner and thinner. Once plastic deformation starts, atoms will continue to flow without any increase in stress. This stretching under a constant load is called creep. The thinning of a wire/rod is called necking.

There is also the problem that the kg masses may not weigh the given value, there is a small chance that this would be inaccurate, the only way to find out is by weighing the mass using a electronic scale, which is accurate to 0.001g.

Bibliography

 “Physics For You” By Keith Johnson “Dictionary of Science” By C. Stockley Simmone Hewett C. Oxlade Sue Holt J. Weitheim John Miller “Physics 1” By David SangKeith GibbsRobert Hutchings “Science Desk Reference” By Patricia barnes-Svarney www.s-cool.co.ukwww.allmeasures.com Encarta 2002

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