Mechanical Properties of Matter PDF

Mechanical Properties of Matter SPH 3107: PHYSICS 1A Lecture  Mechanical Properties of Matter Mechanical properties of matter are the Factors that affect the strength of a material behavior of matter when acted upon by Magnitude of applied force: It is ea...

Mechanical Properties of Matter SPH 3107: PHYSICS 1A Lecture  Mechanical Properties of Matter Mechanical properties of matter are the Factors that affect the strength of a material behavior of matter when acted upon by Magnitude of applied force: It is easier external forces. for a material to withstand a small force than a large force. These mechanical properties include; Cross-sectional area of a material: A material of large diameter (large cross- 1. STRENGTH: sectional area) is able to withstand a This is the ability of a material to withstand an large force than a material of small applied force before it breaks. Materials that diameter. have this property are said to be strong. Nature of the material: Different a) A strong material is a material that can materials withstand different forces withstand a large force before breaking. before breaking e.g. a steel rod is able to b) Strong materials include; concrete, metals, withstand large forces than a piece of etc. wood. 2  Properties of matter 2. STIFFNESS: 3. DUCTILITY: This is the ability of a material to resist any This is the ability of a material to be changed force that try to change its shape and size. or molded into different shapes and sizes Stiff materials are not flexible, and they without breaking. require a large force to be bent. Ductile materials are flexible, and they can Stiff materials include; concrete, steel, iron be bent greatly before they break. etc. Ductile materials include; copper wire, How to increase the stiffness of a material: plasticine, rubber etc. By reducing the length of a material. 4. BRITTLENESS: By reducing the temperature of a material. This is the ability of a material to break suddenly without bending when a force is applied on it. Brittle materials are not flexible, and they Differentiate cannot be molded into other shapes. stiffness from Brittle materials include; chalk, glass, bricks, dry biscuits, concrete, charcoal, etc strength 3  Properties of matter 5. ELASTICITY: This is the ability of a material to regain its original shape and size when a stretching 6. PLASTICITY: force is removed. This is the ability of a material not to regain An elastic material is a material that can its original shape and size when a regain its original shape and size when a stretching force is removed. stretching force is removed. A plastic material is a material that Elastic materials include; rubber springs, cannot regain its original shape and size etc. when a stretching force is removed. The extension of an elastic material Plastic materials include; plasticine, depends on; clay, etc. 1) Nature of a material. 2) Magnitude of stretching force. 4  Hooke’s law It states that the extension of a material is directly proportional to force applied provided that the elastic limit is not exceeded. 𝐹 = 𝑘𝑒 Between O and P: The extension, 𝑒 is directly proportional to applied force (Load, 𝐿) hence Hooke’s law is obeyed in this region. In this region, the material can regain its original shape and size when the stretching force is removed 5  …. Between P and E: Beyond M: In this region, the material undergoes elastic This point represents the maximum stress a deformation until it reaches the elastic limit, 𝐸. material can withstand (i.e. the maximum load it In this region, Hooke’s law is not obeyed but the can handle). material can regain its original shape and size Addition of any extra load (force) at this point when the stretching force is removed. makes the wire to break on reaching the breaking point B. Beyond E: IMPORTANT DEFINITIONS Point, 𝐸, is the elastic limit of the material. Proportional limit: Therefore, beyond E, the material undergoes This is a point beyond which Hooke’s law is plastic deformation whereby it cannot regain its not obeyed. original shape and size when the stretching force is removed. Elastic limit: The material is permanently stretched between This is a point beyond which a material Y an M. cannot regain its original shape and size when a stretching force is removed. 6  …. Yield point: This is a point beyond which a material is Tensile Stress: permanently stretched and there is a permanent This is the ratio of force applied to the cross- increase in length when the stretching force is sectional area of a material. removed. 𝐹𝑜𝑟𝑐𝑒 Elastic deformation: 𝑆𝑡𝑟𝑒𝑠𝑠 = This is a temporary deformation which occurs 𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 before the elastic limit and the material can 𝐹 regain its original shape and size when the 𝜎= stretching force is removed. 𝐴 Plastic deformation: SI Unit is 𝑁𝑚−2 This is a permanent deformation which occurs after the elastic limit and the material cannot Distinguish between regain its original shape and size when the Pressure and Tensile stress. stretching force is removed. 7  …. Tensile Strain: Young’s Modulus: This is the ratio of extension to the original This is the ratio of tensile stress to tensile length of the material. strain of a material. ′ 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 𝑌𝑜𝑢𝑛𝑔 𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 = 𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑇𝑒𝑠𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑎𝑖𝑛 𝑆𝑡𝑟𝑎𝑖𝑛 = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝐹ൗ 𝐹𝑙1 𝑙2 − 𝑙1 =𝑒 𝐴 = 𝜖= ൗ𝑙1 𝐴𝑒 𝑙1 The SI unit of Young’s modulus is 𝑁𝑚−2 Tensile strain has no units since extension and original length have the same units. (𝑃𝑎𝑠𝑐𝑎𝑙𝑠). A metal rod of length 2 m and cross- sectional area 0.005 m² is subjected to a tensile force of 10,000 N. Calculate the Young's modulus of the rod if it elongates by 1 mm. 8  …. Tensile forces: When tensile forces act on a material, they cause the particles of the material to be pulled further apart from one another. This causes an increase in length of a material but the thickness of the material decreases. Compression forces: When compression forces act on a material, they cause the particles of the material to be pressed more closely together. This causes a decrease in length of a material but the thickness of the material increases. 9  … Shear Force: As part of a quality control check, a A shear force is the force needed to fracture the manufacturer of washing line subjects a material in direction parallel to applied force. A shear force is produced when two equal, but sample to a tensile test. The sample of opposite forces are applied on the body. Shear washing line is 12 m long and of constant forces causes a body to be twisted and circular cross section of diameter 5.0 mm. deformed. The manufacturer measures an extension of 42 mm under a stretching load of 72 N. The manufacturer also breaks the line under a load of 240 N. a) Calculate the Young modulus of the washing line. b) Calculate the breaking stress of the line. c) If the Young modulus of the line stays constant throughout what is the extension of the line just as it breaks? 10  …. The graph below is the stress-strain graph for a The graph represents stress-strain curves for two metal that obeys Hooke’s law over the region different materials X and Y. Both materials are covered by the graph. stretched until they break. a) What is the Young modulus of the metal? A wire made from this metal has a diameter of 0.15 mm and a length of 2.5 m. b) Calculate the extension of the wire under stress of 200 MPa. i) Define the term ductile. ii) Which of the materials is ductile? iii) State and explain which of the two material has a greater value of Young modulus. 11  Surface Tension Intermolecular forces Cohesive force The force between two molecules of a substance Cohesive force is the force of attraction is called intermolecular force. This between the molecules of the same intermolecular force is basically electric in substance. This cohesive force is very nature. strong in solids, weak in liquids and When the distance between two molecules is extremely weak in gases. greater, the distribution of charges is such that the mean distance between opposite charges in the molecule is slightly less than the distance Adhesive force between their like charges. So, a force of Adhesive force is the force of attraction attraction exists. between the molecules of two different When the intermolecular distance is less, there substances. E.g., due to the adhesive force, is overlapping of the electron clouds of the ink sticks to paper while writing. molecules resulting in a strong repulsive force. Mercury does not wet glass because the The intermolecular forces are of two types. cohesive force between mercury molecules They are (i) cohesive force and (ii) adhesive is greater than the adhesive force between force. mercury and glass molecules. 12  Surface tension of a liquid Surface tension is the property of the free surface If 𝐹 is the force acting on the length 𝐿 of the of a liquid at rest to behave like a stretched line AB, then surface tension is given by: membrane to acquire minimum surface area. 𝐹 𝑇= 𝐿 Imagine a line AB in Surface tension is defined as the force per the free surface of a unit length acting perpendicular on an liquid at rest. The force of surface imaginary line drawn on the liquid surface, tension is measured tending to pull the surface apart along the as the force acting line. Its unit is 𝑁𝑚−1. per unit length on either side of this It depends on temperature, impurities and imaginary line AB. solubility. The force is The surface tension of all liquids perpendicular to the decreases linearly with temperature, and line and tangential to become zero at critical temperature. the liquid surface. 13  …. Quiz. How does addition of impurities effects the Rise of Liquids in Capillary Tubes: A tube whose surface tension of a liquid? radius is very short, and uniform is called a The presence of impurities either on the capillary tube. When an open capillary is dipped surface or dissolved in it, affect surface tension in water. The water rises to some height in the of the liquid. Highly soluble substances capillary tube. increase the surface tension of water, whereas sparingly soluble substances reduce the Example: The surface tension of soap solutions is surface tension of water. 2 × 10−2 𝑁𝑚−1. How much work will be done in making soap bubble of diameter 2 𝑐𝑚 by blowing? Some Important Examples of Surface Tension Insects Walking on Water: Various insects can easily walk on the surface of the water because the force of their weight is not enough to penetrate the surface of the water Floating Needle: A needle made of steel can Quiz: Calculate the work done in blowing a soap easily be made to float on the surface of the bubble of radius 10 cm, surface tension being 0.08 water even though it is many times denser than Nm-1. What additional work will be done in further water because of the surface tension of the blowing it so that its radius is doubled? water. 14  Fluid Dynamics Fluid dynamics refers to a sub-discipline of Turbulent flow is an uneven flow of fluid fluid mechanics that revolves around fluid characterized by changes in pressure and flow in motion. speed. Laminar flow is a fluid flow type in which the fluid particles move in parallel layers, with each layer moving in the same direction. This type of flow occurs when a fluid flows in a smooth, continuous stream without mixing the layers. 15 …. 16 …. 17