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Molecular Explanation of Hooke’s Law

This article explains the molecular basis of Hooke's Law, relating stress and strain in materials. It discusses the intermolecular forces, elastic and plastic deformation, and the concept of ductility and brittleness. The stress-strain curves for ductile materials (like copper) and brittle materials (like cast iron) are presented, highlighting their different behaviors. The Young's modulus is also introduced as a measure of material stiffness.

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Molecular Explanation of Hooke’s Law

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  1. Molecular Explanation of Hooke’s Law r0 r0 When the stress is zero the mean separation of the moleculesis ro A tensile stress acts in opposition to the attractive forces between the ions and is therefore capable of increasing their separation

  2. Intermolecular force For values of r close to ro the graph can be considered to be linear, and provided that the stress is not so large as to take the intermolecular separation out of this region equal increases in tensile stress will produce equal increases in extension r=ro Intermolecular separation The energy used in stretching the wire is stored in the potential energy of the stretched individual bonds. Note that this graph also implies that Hooke’s Law applies to compresion

  3. Stress Strain Curves

  4. Stress Strain Curve For A Ductile Material Ductility is a term used to describe a material which can be deformed plastically. Hence a ductile material is one which can be drawn into wires. e.g. Copper and mild steel are ductile whereas concrete and cast Iron are brittle

  5. Stress Strain Graph For a Ductile Material point of maximum stress elastic limit (yield point) stress N/m2 breaking stress fracture limit of proportionality strain

  6. Stress Strain Graph For Cast Iron It can be seen that the concrete curve is almost a straight line. There is an abrupt end to the curve. This, and the fact that it is a very steep line, indicate that it is a brittle material. The curve for cast iron has a slight curve to it. It is also a brittle material. Both of these materials will fail with little warning once their limits are surpassed. Cast Iron breaking stress fracture stress N/m2 breaking stress concrete strain

  7. Note the position of stress and strain on the graph axes. Note that strain is a pure number Up to the elastic limit, the graph takes the form y=mx stress Nm-2 The gradient of this graph is called the modulus of elasticiy or: Young’s Modulus Young’s Modulus (E) = tensile stress tensile strain strain

  8. The Units of Young’s modulus Young’s Modulus (E) = tensile stress tensile strain tensile strain has no units So the dimensions of Young’s modulus are identical to the dimensions of stress (Nm-2) However as force units can be written as kgms-2 F = m a (N) = kg ms-2 and stress =Force/Area i.e. kgms-2m-2 So Young’s modulus is often written in the units kg m -1s-2

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