ELASTICITY

1:-INTRODUCTION👉

While studying the concept of rigid body, we assumed the distance between the two points should be fixed. But real solids do not obey the concept. When external forces are applied on the body, it may get deformed. The internal forces developing inside the body try to restore its original shape. So the property of the material by virtue of which the bodies restore thier natural shape and size or oppose the deformation produced in them is called ELASTICITY.

  • When a body completely gains its natural shape and size after removal of external forces, it is called perfectly ELASTIC body. This is an ideal concept i.e. none of the material is perfectly elastic. QUARTZ may be considered as almost perfectly ELASTIC.
  • When a body doesn’t regain its natural shape and size after the removal of external forces, it is called perfectly PLASTIC body. Example:- Wax & wet clay are assumed to be perfectly PLASTIC.
  • In real practice, no body is perfectly elastic. All the bodies existing in nature lies between these two extreme limits. In a body when elastic behavior decreases, the plastic behavior increases.
  • In solids, atom or molecules are arranged in a regular pattern where each molecules experience the force due to neighbouring molecules. But solid overall remains in a state of stable equilibrium. On application of deforming force, molecules get displaced from their original position & restoring force acts between the molecules which try to bring the solid in its natural shape.

2:-STRESS👉

  • On applying external force, the shape or size of a body changes. But internal restoring forces are produced inside the body which tries to regain the original shape. The internal restoring force acting per unit area of cross-section is called STRESS.

          STRESS = internal force/area = F/A

  • In SI system, unit of stress is ( Newton/meter^2 ) & in CGS system, it is ( Dyne/cm^2 ) having dimensional formula ( ML^-1T^-2 ).
  • STRESS is of two types:-

                      (A) Normal Stress 

                      (B) Tangential Stress

(A) NORMAL STRESS:- The external forces (deforming forces) acting per unit area normal to the surface of a body is called normal stress. It is of two types.

                (1) TENSILE STRESS:- When the to parts of the body on the two sides pull each other than it is called as tensile stress. Example:- a wire stretched by equal & opposite forces.

                (2)COMPRESSIVE STRESS:- When the two parts of the body on the two sides push each other than it is called as compressive stress.

(B) TANGENTIAL STRESS:- The external ( deforming force ) acting per unit area tangential to the surface of a body is called tangential stress.

(3) STRAIN👉

When a deforming force act on the body, there is a change in dimension of the body & the body is said to be deformed. The ratio of change in dimension of the body to the original dimension is called STRAIN.

               ðŸ‘‰     Strain is of 3 types:-

  1. Longitudinal strain:- It is defined as the increase in length per unit original length when deformed by the external force.

        👉Longitudinal strain = change in                 length/initial length = ∆L/L
         Where L is original length & ∆L is             increase in length.

      2. VOLUME STRAIN:- It is defined as             the change in volume per unit                   original volume when deformed               by the external force.

        👉 Volume strain = change in                           volume/original volume = ∆V/V

          Where V is original volume & ∆V               is change in volume.

       3. SHEAR STRAIN:- When the                            external force tangential to the                surface of the body acts on it, the            body suffer a change in shape                    maintaing it’s volume constant.                The ratio of the displacement of a            layer in the direction of                                tangential force & the distance of            that layer from the fixed surface              is called SHEARING STRAIN.

                            Figure:-A

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