The Young’s Modulus


The Young Modulus is stress / strain

Apply a load to stretch a material - material experiences a stress and a strain.
Up to the limit of proportionality, stress and strain are proportional.
Below this limit, stress/strain is a constant. Constant is Young Modulus (E).
Young Modulus = E = Stress/Strain.
Young Modulus - a measurement of stiffness.
Units for Young Modulus are the same as stress (Nm^-2 or pascals).
It’s used by engineers to make sure their materials can withstand sufficient forces.

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To find the Young Modulus, you need a very long wi

Test wire should be thin and as long as possible. Longer and thinner wire - more extension for the same force, reduces uncertainty.
Find CSA. Use micrometer to measure diameter of wire at three points along the wire, work out an average. Assume the cross section is circular, use: area = πr^2.
Clamp the wire to a bench, hang weights off one end of it. Start with the smallest weight necessary to straighten the wire (not included in calculations).
Measure distance between fixed end of wire and marker.
Increase weight - wire stretches, marker moves.
Increase weight in steps, recording marker reading each time - extension = difference between reading and unstretched length. Use mass meter or digital scales to accurately find weight you add with each step.
Use results to calculate stress + strain and plot stress-strain graph.
Use this experiment to find fracture stress, add weights to wire to roughly find force required to break wire. Repeat with identical wire but add weights in small increments, helps you find breaking force more accurately.

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Plot a stress-strain graph of your results to find

Plot stress-strain graph (stress in y axis, strain in x axis)
Gradient of graph = E (Young Modulus)
Area under graph = elastic strain energy per unit volume.

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