Physics (101) Properties of Matter Lecture Notes PDF

Physics Department Faculty of Science Mansoura University Elasticity: Elasticity: is that property of a body by which it experiences a change in size or shape whenever a deforming force acts on the body. Elasticity: Elongation...

Physics Department Faculty of Science Mansoura University Elasticity: Elasticity: is that property of a body by which it experiences a change in size or shape whenever a deforming force acts on the body. Elasticity: Elongation Contraction Solid Solid Material Material Original Original Compressi Pulling size ng length Molecules Attractive Molecules Repulsive pushed closer molecular away from molecular together from forces pull all their forces causes their the molecules equilibrium the atoms to equilibrium back position return position Applied Change in Compressiv Reduction force is length of e force is in size removed the material removed Elasticity: Elastic materials: The material that restores its original shape after removing stress (load) from it. Plastic materials: The material that fails to restore its original dimensions after removing the applied stress, it's said to plastic. Hooke’s Law — Stress and Strain:  Stress: the force (F) per unit area (A) Stress = F/A  Its units are dyne/cm2 or N/m2.  Strain: the change in material dimensions relative to the original dimensions. It’s dimensionless. ΔL, is directly proportional to the magnitude of the applied force F. Hooke’s Law — Stress and Strain: ΔL is inversely proportional to the cross-sectional area A of the wire ΔL is directly proportional to the original length of the wire Lo. So, we can write Hooke’s Law — Stress and Strain: Strain Stress Y : This constant, called Young’s modulus (Elastic modulus) and depends on the type of material. Its unit (N/m2). Example 2.1: Example 2.1: Stress-Strain Curve : Materials can be essentially classified into two groups according to their stress-strain curves, ductile materials and brittle materials. 1. Ductile materials curve: OA: the material obeys Hooke’s law which means that it retains or recovers its original shape whenever it is freed from stress. AB: The material in this region doesn’t obey Hooke’s law. Point A is called the proportional limit because beyond this point, stress and strain terminate their linear relationship. If we removed the stress on the rod in AB, the material would still can recover its original shape. Point B is therefore known as the elastic point (elastic limit). Stress-Strain Curve : BC: Point B is also known as the upper-yield point, as beyond it the material surrenders to stress and begins to deform. The stress decreases until point C, which is known as the lower-yield point, but the material continues to elongate. CD: The material tries to resist this change and tends to harden. This is known as strain hardening. The material growing longer and thinner, until point D, which represents the material’s maximum strength (ultimate strength). DE: Now, only the neck experiences any further deformation. The neck Necking and Fracture in ductal materials. grows thinner and weaker until point E, where it breaks;. Point E is called the fracture or rupture point. Stress-Strain Curve : 2. Brittle materials curve: Brittle materials share the same relationship except they don’t exhibit a yielding phenomenon. These materials skip the plasticity region and undergo a fracture directly after the elasticity region. It survives until the elastic limit, after which it fractures when subjected to excess stress. Elastomers: materials that can be stretched to cause large strains. Example 2.2 Compressing a steel column. A 445,000-N load is placed on top of a steel column 3.05 m long and 10.2 cm in diameter. By how much is the column compressed? Y= 21×1010 N/m2. Example 2.2: Example 2.3: Hooke’s Law for a Spring: Hooke’s Law for a Spring: Elasticity of Shape – Shear: Elasticity of Shape – Shear: we find experimentally that & Note that F/A has the dimensions of a stress and it is now defined as the shearing stress: 𝑆 , called the shear modulus (torsion modulus and the modulus of rigidity). The larger the value of S, the greater the resistance to shear. Note that the shear modulus is smaller than Young’s modulus Y ????. Example 2.5: Example 2.5: Elasticity of Volume: Elasticity of Volume: Constant of proportionality B, called the bulk modulus. The minus sign in the equation because an increase in the stress (F/A) causes a decrease in the volume, leaving ∆V negative. Compressibility: The reciprocal of the bulk modulus B, called the compressibility k, is a measure of how easy it is to compress the substance. The bulk modulus B is used for solids, while the compressibility k is usually used for liquids ‫ فى حالة غمر جسم فى سائل فإن اإلجهاد الواقع على الجسم يساوى ضغط السائل على الجسم وبالتالى‬ No shear modulus and no Young’s modulus are given for liquids??? Example 2.6: For Consideration ???? Change in length (longitudinal strain) Change in width (lateral strain) Ratio???