What could be the suggestions for making minimum error in young's modulus searle's method?
Answers
Answer:
Introduction
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.
Explanation:
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.
Youngs Modulus by Searle method
Wire extension due to pulling force
Normally, we use Searle's method to measure the Young's modulus of a material. As Young's modulus is independent of the shape of the material, we can utilize any shape for its calculation. In particular, a thin circular wire fulfills our requirement. In this method, the length L of the wire is measured by a scale, diameter d of the wire is measured by a screw gauge, length l of the wire is measured by a Micrometer or Vernier scale, and F is specified external force.
Differentiate the expression for Y to get the relative error in the measured value of Y,
Δ
Y
Y
=
Δ
L
L
+
2
Δ
d
d
+
Δ
l
l
where
Δ
L
,
Δ
d
, and
Δ
l
are the errors in the measurement of
L
,
d
and
l
, respectively. Generally, accuracy of these errors measurements depends on the least count of the measuring instrument.
We use Searle's technique to degree Young's modulus of a material. As Young's modulus is impartial of the form of the material, we will make use of any form for its calculation. In particular, a skinny round cord fulfills our requirement. In this technique, the duration L of the cord is measured via way of means of a scale, diameter d of the cord is measured via way of means of a screw gauge, duration l of the cord is measured via way of means of a Micrometer or Vernier scale, and F is detailed outside force.
Searle's equipment is used for the dimension of Young's modulus. It includes same period wires which might be connected to a inflexible support. To apprehend how Searle's equipment is used to decide Young's modulus of elasticity of the cloth of a given wire, study the underneath experiment.
Young's modulus equation is E = tensile stress/tensile strain = (FL) / (A * extrade in L), in which F is the implemented force, L is the preliminary period, A is the rectangular area, and E is Young's modulus in Pascals (Pa).