Lecture 26: Elasticity - Young's Modulus
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1. Elasticity of Materials:
A relationship between stress, strain and Young's Modulus is introduced by analogy with springs. The properties of various metals are compared, and the stress vs. strain curve is described.
2. Measuring Stress vs. Strain:
An apparatus for measuring very small elongations of a wire under stress is described. A set of measurements are made to construct the stress vs. strain curve for a copper wire. From these, both Young's modulus and the ultimate tensile strength can be calculated.
3. Spring Constant of a Wire:
At low stress values, where the stress vs. strain curve is linear, one can generate simple harmonic oscillations in the vertical direction by hanging an object from a wire.
4. Speed of Sound in Materials:
The speed of sound in a material depends on the stiffness (Young's modulus) and density of the material. The speed of sound and length of a rod determine the roundtrip time of a pressure disturbance introduced at one end. From this follows the fundamental frequency at which a rod resonates.
5. Demo with a 2 kg Block and Two Strings:
A 2 kg block is suspended from one string, and an identical string is suspended from the block. Professor Lewin pulls on the lower string. Which string will break first, the upper one or the lower one? The lower string will break first if the force is impulsive (a quick jerk) because it will elongate faster than the upper string. If we pull slowly the upper string will break first as its tension will then always exceed that of the lower string.
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