PROPERTIES OF MATTER · Part 12

EXAMPLE . A wire of length m with the area of cross- section – m is used to suspend a load of N. Calculate i) the stress developed in the wire ii) the strain and iii) the energy stored. Given: Y= × N m − . Solution (i) stress = F N m (ii)  strain stress Y (no unit) (iii) Since volume = × – m , Energy stress strain volume ( ) × × ( ) ( . ) − = J . . Applications of elasticity The mechanical properties of materials play a very vital role in everyday life. The elastic behaviour is one such property which especially decides the structural design of the columns and beams of a building. As far as the structural engineering is concerned, the amount of stress that the design could withstand is a primary safety factor. A bridge has to be designed in such a way that it should have the capacity to withstand the load of the flowing traffic, the force of winds, and even its own weight. The elastic behaviour or in other words, the bending of beams is a major concern over the stability of the buildings or bridges. For an example, to reduce the bending of a beam for a given load, one should use the material with a higher value of Young’s modulus of elasticity. It is obvious from Table . that the Young’s modulus of steel is greater than aluminium or copper. Iron comes next to steel. This is the reason why steel is mostly preferred in the design of heavy duty machines and iron rods in the construction of buildings. . . Elastic energy When a body is stretched, work is done against the restoring force (internal force). This work done is stored in the body in the form of elastic energy. Consider a wire whose un-stretch length is L and