|Aim||The aim of this experiment is to determine the Young’s modulus of elasticity of the material of a given wire.|
|Apparatus Required||A wire of uniform cross-section|
A meter scale or ruler
A micrometer screw gauge or Vernier caliper
A load hanger
A set of weights
A clamp stand
A spirit level
A stopwatch or timer
|Theory||Young’s modulus of elasticity is a measure of a material’s stiffness or resistance to deformation under stress. It is defined as the ratio of stress to strain within the elastic limit of a material. Mathematically, it is given by:|
Y = stress / strain = FL / AΔL
where Y is the Young’s modulus of elasticity, F is the applied force, L is the length of the wire, A is the cross-sectional area of the wire, and ΔL is the change in length of the wire due to the applied force.
In this experiment, we will apply a gradually increasing load to the wire and measure the corresponding increase in length of the wire. We will then plot a graph of force against extension and use the slope of the graph to determine the Young’s modulus of elasticity of the wire.
|Prosedure||Set up the clamp stand and attach the wire to it using the load hanger.|
Ensure that the wire is vertical and straight by using the spirit level.
Measure the initial length (L) and diameter (d) of the wire using the meter scale and micrometer screw gauge or Vernier caliper, respectively.
Apply a known load to the wire using the set of weights and measure the corresponding increase in length (ΔL) of the wire.
Record the data in a table and calculate the stress and strain using the following equations:
Stress (σ) = F / A Strain (ε) = ΔL / L
Repeat steps 4-5 for different loads.
Using the data obtained, plot a graph of force against extension (ΔL).
Draw the best-fit straight line through the graph.
Measure the slope of the graph. The slope of the graph represents the value of the Young’s modulus of elasticity (Y) of the wire.
|Observation and Result||The result of the experiment is the Young’s modulus of elasticity of the material of the given wire. We will obtain a graph that represents the relationship between force and extension (ΔL) of the wire.|
Observation: During the experiment, we observe that as the load applied to the wire increases, the extension of the wire also increases. By plotting the values of force and extension on a graph, we observe a linear relationship between these variables. The slope of this line can be used to determine the value of the Young’s modulus of elasticity of the wire.
We also observe that the wire exhibits elastic behavior up to a certain point, after which it undergoes plastic deformation. The elastic limit is the maximum stress or force that a material can withstand without undergoing permanent deformation. In this experiment, we must ensure that we do not exceed the elastic limit of the wire, as this would result in permanent deformation and inaccurate results.
This experiment demonstrates the concept of Young’s modulus of elasticity and the behavior of materials under stress. It also highlights the importance of ensuring that we operate within the elastic limit of a material when measuring its mechanical properties.