Tips & Formulas Elasticity | Concordia University Wisconsin

University:
Concordia University Wisconsin
Course:
PHYS 1514 | General Physics I
Academic year:

2023
Views:

297

Pages:

3
Author:

Marilyn James

MECHANICAL PROPERTIES OF MATTER ELASTICITY 1. STRESS = F Internal restoring force = Res Area of cross section A There are three types of stress : (i) Longitudinal Stress (a) Tensile Stress : (b) Compressive stress : (ii) Volume Stress : F A (iii) Tangential Stress or Shear Stress : L D F C change in size of the body original size of the body 2. Strain = (i) Longitudinal strain = (ii) Volume strain = (iii) Shear strain = change in length of the body L = initial length of the body L change in volume of the body V = original volume of the body V tan  A B l l displacement of upper face or = = L L distance between two faces B L D F C F 3. Relation Between angle of twist and Angle of shear AA' = r  and Arc AA' =  So r=     where = angle of twist, 4. r l = angle of shear Stress – Strain Graph Breaking strength B Elastic Region Elastic Limit Y E Plastic Region 0 Strain Stress 5. Hooke's Law within elastic limit : stress  strain 6. Young's Modulus of Elasticity Y= C Pr op o L i m r t io n it P longitudinal stress Fl = longitudinal strain Al If L is the length of wire, r is radius and  is the increase in length of the wire by suspending a weight Mg at  Mg / r  its one end then Young's modulus of elasticity of the material of wire Y = l / L   = 2 MgL r 2 l MgL gL2  2 AY 2Y 7. Increment of length due to own weight l  8. Bulk modulus of elasticity K = 9. Bulk modulus of an ideal gas is process dependence F/A P volume stress =  V    V  volume strain      V   V  For isothermal process PV = constant  PdV + VdP = 0  P=  dP So bulk modulus = P dV / V For adiabatic process PV = constant  PV  1 dV  V  dP  0   PdV  VdP  0  P   dP dV / V So bulk modulus = P For any polytropic process PVn = constant  nPVn–1dV+VndP=0  PdV+VdP=0  nP = So bulk modulus = nP 1 1  Bulk modulus K 10. Compressibility 11. Modulus of Rigidity  C shearing stress (Ftangential ) / A =  shearing strain  dP dV / V MECHANICAL PROPERTIES OF MATTER lateralstrain longitudinalstrain 12. Poisson's Ratio = 13. Work done in stretching a wire 14. W= 1 × stress × strain × volume 2 W= 1 F Δl 1 × × × A × l × F × Δl 2 A l 2 Rod is rigidly fixed between walls Thermal tension = YA 15. A ? ////////////// Thermal stress = Y ? ////////////// Thermal Strain =  Effect of Temperature on elasticity When temperature is increased then due to weakness of inter molecular force the elastic properties in general decreases i.e. elastic constant decreases. Plasticity increases with temperature. For example, at ordinary room temperature, carbon is elastic but at high temperature, carbon becomes plastic. Lead is not much elastic at room temperature but when cooled in liquid nitrogen exhibit highly elastic behaviour. For a special kind of steel, elastic constants do not vary appreciably temperature. This steel is called 'INVAR steel'. 16. Effect of Impurity on elasticity Y is slightly increase by impurity. The inter molecular attraction force inside wire effectively increase by impurity due to this external force can be easily opposed.