explain the graph developed using readings from Searles apparatus
Answers
Searle’s method uses two wires of the same material, one of which will be loaded with various weights.
E =
To calculate Young’s modulus we need to know:
The cross-section area of the wire (A). This is measured by using a micrometer to determine the radius of the wire, and then using the formula area of circle = πr2. The radius must be measured in metres, and is typically 2 x 10-4 m. This gives an area of 1.26 x 10-7 m2.
The length of the wire (l, measured in metres).
The force and the extension.
The weight of a 1 kg mass is 9.81 N.
We plot a graph of the extension (m, horizontal axis) against the weight (N, vertical axis).
The gradient of this graph (change in vertical measure / change in horizontal measure) is the ratio F/x. If we multiply this ratio by l and divide by A we have the Young modulus for the wire.
Measuring the extension:
The ‘business end’ of the apparatus is a device which holds the two wires parallel, and allows the extension of the loaded wire to be measured.
You need to label this diagram to show:
Constant mass attached to stress the reference wire.
Variable mass attached to stress the test wire.
Flexible connectors.
Level reference from one wire to the other.
Thumbscrew with scale to level the reference.
Clamps for wires.
Reference wire.
Test wire.
Advantages of this apparatus:
Thermal expansion of the test wire is correct by thermal expansion of the reference wire.
Long, thin wires allow maximum extension for minimum force.
Problems:
Difficulty measuring the cross-section area.
Extensions very small.
Mass, not weight, is measured.
Need high, secure mounting point unless apparatus adapted.
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1 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.
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 given by, after this 1st pic
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.
