describe a method to determine Young's modulus of the material of a time wire
Answers
Answer:
Any solid material undergoes some elastic deformation if we apply a small external force on it. It is very important to know the extent of this deformation. Whenever, engineers design bridges or buildings and structural implants for body, it is useful to know the limits of elastic deformation for endurance.
Young's modulus is a measure of the stiffness of a solid material. It is calculated only for small amounts of elongation or compression which are reversible and do not cause permanent deformation when the external applied force is removed. For this reason, it is also called elastic modulus.
A stiff material has a high Young's modulus and changes its shape only slightly under elastic loads. A flexible material has a low Young's modulus and changes its shape considerably e.g. Young's modulus of steel is much more than rubber. So contrary to our perception, steel is considered more elastic than rubber. Young's modulus is a characteristic property of the material and is independent of the its dimensions i.e., its length, diameter etc. However, its value depends on ambient temperature and pressure.
Consider a wire of length L and diameter d. Let its length L increases by an amount l when the wire is pulled by a longitudinal external force F. Young's modulus of the material of the wire is the ratio of longitudinal stress to the longitudinal strain i.e.,
Y
=
F
/
A
l
/
L
=
4
F
L
π
d
2
l
The units of Young's modulus are the same as that of stress (note that strain is dimensionless) which is same as the units of pressure i.e., Pa or N/m2. Graphically, Young's modulus is generally determined from the slope of stress-strain curve.
Explanation: