The Modulus of Elasticity for a material
It is useful to have a property of a
material that is independent of the size of the sample and can be use to compare its elastic
properties with another - this is called the Modulus of Elasticity for the material. The modulus of
elasticity is defined as:
Modulus of elasticity = Stress/ Strain
There are
three types of moduli
(a) the Young Modulus - tensile and compression longitudinal
stress
(b) the shear modulus - a shearing stress
(c) the bulk modulus - volume changes of
the specimen
The Young Modulus
This is defined as the ratio of
longitudinal stress to longitudinal strain. This is the modulus we need if we want to investigate the
change of length of a object - more accurately any linear dimension (width, length or height).
(Figure 1)
Longitudinal stress =
Force(F)/Cross sectional area (A) = F/A
Longitudinal strain = Extension(e)/Original length (L
o)
= e/L
o Therefore:
Young Modulus (E) = [F/A]/[e/Lo] = FLo/eA
The
values for the Young modulus for some common materials are given in the following table.
| Material |
Young modulus(Gpa) |
|
Material |
Young modulus(Gpa) |
| Diamond |
1200 |
| Bone |
18 |
| Mild steel |
210 |
|
Concrete |
16.5 |
Copper |
120 |
| Beech wood |
15 |
| Cast iron |
110 |
|
Oak |
11-12 |
Bronze |
96-120 |
| Pine |
11-14 |
| Slate |
210 |
|
Sandstone |
6.3 |
Aluminium |
70 |
| Plastic |
2.0 |
| Granite |
40-70 |
|
Nylon |
2.0 |
Lead |
18 |
| Rubber |
0.02 |
| Titanium |
116 |
|
|
|
Example problem
A steel wire 10 m long and with a cross-sectional area of 0.01 cm2 is hung from a support and a mass of 5 kg is hung from its end.
Calculate the new length of the wire. The Young modulus for steel = 210 GPa.
Extension (e) = 50x10/[2.1x1011x1.10-6] = 2.38 mm
Therefore new length = 10.0024 m
Fishing line extension
Fishing line behaves in an odd way - the initial
extension is not static - it increases as the creep continues! Fishing lines are designed to not only
support a static load they must cope with the sharp shock of the rod being flipped back or the fish
jerking the line.
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