Title Med-RM_Phy_SP-2_Ch-9-Mechanical Properties of Solids.pdf ✅

40 Mechanical Properties of Solids NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 or, x L AY F  The work done by the elastic force in a further extension dx is dxx L AY FdxdW  The total work by the elastic force in an extension 0 to L is     L L L AY xdx L AY W 0 2 )( 2 This work is stored into the wire as its “elastic potential energy” (U). Hence 2 )( 2 L L AY WU  LFL L LAY          2 1 2 1 )(extension force) stretching maximum( 2 1 U  ...(i) (strain) (stress) 2 1 volume unit per work)(orenergy Potential  ...(ii) 1 2 Potential energy (or work) per unit volume = (strain) 2 Y  ...(iii)  2 1 stress Potential energy (or work) per unit volume = 2 Y ...(iv) Elastic Hysteresis As a natural consequence of the elastic after-effect, the strain in the body tends to lag behind the stress applied to the body so that during a rapidly changing stress, the strain is greater for the same value of stress. This lag of strain behind the stress when body is unloaded is called elastic hysteresis. A C Stress Strain Fig.: Vulcanised rubber B O Hence, some amount of energy is absorbed by the material in the cycle which appears as heat. The magnitude of the energy absorbed per unit volume is proportional to the area bounded by the loop. Factors Affecting Elasticity (i) Effect of Temperature : Almost for all materials, the modulus of elasticity decreases with the rise in temperature, but the elasticity of invar remains unchanged with the change in temperature. (ii) Effect of Impurities : The addition of impurities affects the elastic properties depending on whether impurities are themselves more or less elastic. When carbon is added to iron, and potassium to gold, their elasticities are strengthened. (iii) Effect of Annealing : By annealing (i.e., heating and the cooling gradually) large crystal grains are formed, and hence the elasticity of the material decreases. (iv) Effect of Hammering and Rolling : By hammering and rolling, crystal grains break up into smaller units, and hence the elasticity of the material increases.