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Important Points on Elasticity for JEE Main 2015


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Important Points on Elasticity for JEE Main 2015

  1. 1. Elasticity Important points 1. Deformation The change in the size and/or shape of a body is called deformation and the external force producing the deformation is called the deforming force. 2. Types of Bodies a. Elastic Bodies: They regain their original size and shape, when the deforming forces are removed. E.g. Metals like steel, copper b. Plastic Bodies: They do not regain their original size and shape. When the deforming forces are removed they retain the deformed shape. E.g. plasticine, wax, butter c. Rigid bodies cannot be deformed. 3. Stress Internal Restoring Force (F) per unit area of cross-section. 2 1 1 2 2 t F stress SI unit (N/m ) A Stress L MT F Mg For a wire,tensilestress ; A r volume stress dP change in pressure Tangential Force F Shearing stress Area A 4. Strain e dv Tensile strain . Bulk (volume) strain L V Shearing strain( ) Lateral displacement of a layer Perpendicular distance of the layer from the fixed layer Strain has no units and dimensions.
  2. 2. 5. Hooke’s Law Stress Constant within elastic limit Strain This constant is called the modulus of elasticity. 6. Longitudinal stress Young's modulus Y Longitudinal strain 2 2 F / A Mg/ r MgL e/L e/L r e 7. volume stress Vdp Bulk Modulus(K) volume strain dv 8. shearing stress Ft Rigidity Modulus( ) shearing strain A Where Ft is the component of the force, tangential to the area. SI unit of y, k and n is N/m2 9. D Lateral strain D Poisson'sratio( ) Longitudinal strain L L It has no units and dimensions. Its limiting values are -1 to 0.5. 10. Work done in stretching a wire or strain energy stored in the wire is given by 2 1 2 1 1 1 YA W load extension F 2 2 2 L 1 W Average force extension (F F ) 2   
  3. 3. 11. Work done (or strain energy) per unit volume 2 2 1 stress strain 2 1 (stress) 1 (strain) Y 2 Y 2 12. 1 2 P.E. stored in a spring Kx 2 13. Useful Points i. Thermal Stress: If there is a fall in temperature (θ), then a wire fixed between two rigid supports tries to contract and tensile stress is developed. It is called thermal stress. If α is the coefficient of linear expansion, then Thermal stress= Y α θ ii. Y is determined by using Searle’s method. The graph of extension against load (or mass) is straight line. Form this graph we get the proportional limit, elastic limit, yield point and breaking point. We can also find the ductile and brittle metals. iii. For rubber, the stress-strain graph is not linear. A large strain is produced for a small stress. Rubber is an elastomer.