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4) The Young Modulus
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Whats the Young modulus a measure of?
The 'stiffness' of a material
What is Young's modulus?
- when you apply a load to stetch a material, it experiences a tensile stress and tensile strain
- up to the limit of proportionality, the stress and strain of a material are proportional to each other
- so below this limit, for a particular material, stress divided by strain is a constant, which is called the Young modulus
Whats the symbol for the Young modulus?
E
Diagram of the equation for the Young modulus
What are the units of the Young modulus?
The units of the Young modulus are the same as stress as strain has no units
Nm^-2 or pascals
Experiment to find the Young modulus of a material:
1) Select a test wire as long and thin as possible (the longer and thinner the wire, the more it extends for the same force- this reduces the uncertainty in your measurements.
2) Find cross-sectional area of the wire. Use a micrometer to measure the diameter of the wire in several places and take a mean. Then use formula for area of circle.
3) Clamp wire to bench so you can hang weights of one end. Start with smallest weight necessary to straighten wire (dont include this weight in your final calculations)
4) Measure distance between fixed end of wire and marker (unstretched length)
5) Increase the weight in steps (e.g. 100g intervals, recording the marker reading each time). Increasing the weight causes the wire to stetch and the marker to move. Calculate the extension by finding the difference between the reading and the unstretched length
6) Use your results from this experiment to calculate the stress and strain of the wire and plot a stress-strain curve
Diagram of the equipment used for the Yong modulus experiment:
How do you work of the Young modulus from a graph?
The gradient of a stress-strain graph gives the Young modulus
(only works up to the limit of proportionality
How do you find the strain energy (or energy stored per unit unit volume) from a graph?
The area under a stress-strain graph gives the strain energy per unit volume
How else can you calculate the energy per unit volume, as long as Hooke's law is obeyed?
Diagram of why steel can be useful:
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