Esticity Definition Esticity: A wire is cmped t one end nd oded t its free end. It is found tht the ength of the wire chnges. The force is known s deforming force, the chnges known s deformtion. If fter remo of the deforming force the body regins its origin ength the body is sid to be perfecty estic. If fter the remo of the deforming force the body retins its chnged form competey the body is sid to be perfecty pstic. Hooke s w: For sm deformtion the deformtion produced is proportion to the deforming force. Stress: The tot extern force ppied per unit re is known s stress. Stress F/A Unit: Newton /m 2, Dimension: [ M 1 T 2 ] Since pressure is so defined s the force per unit re hence stress & pressure he sme unit & dimension. Stress cn be definedd into three (1) (2) (3) Norm Stress Tensie Stress Shering or Tngenti Stress Norm Stress Force / Are of the surfce to which the force is ppied Tensie (ongitudin) Stress: When equ forces re ppied simutneousy ong the free directions of body resuting oume chnge the force per unit surfce re is known s tensie stress. Shering Stress or Tngenti stress: Force per unit re of the surfce to whichh the force is pre producing chnge in shpe. Shering Stress Force / re of the surfce to which the force is pre Strin: The rtio of the chnge in dimensionn (such s ength, oume...) to the origin dimension is known s strin. Strin Strin Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 1
Esticity Definition Since it is the rtio of two sme physic quntities it hs no unit nd dimension. Depending upon the shpe of the body nd the nture of the force ppied we he three different types of strin. (1) iner Strin (2) oume Strin (3) Shering Strin iner Strin: The rtio of chnge in ength to the origin ength (i)ongitudin Strin (ii) ter Strin & D Origin ength nd dimeters & d Chnge in ength nd dimeter / iner strin produced ong the direction of ppied force nd is known s ongitudin strin. d / D The iner strin produced ong the direction perpendicur to the force ppied is known s ter strin. Hooke s w: Within the estic imit the strin produced is proportion to the stress ppied nd the rtio of stress to strin is constnt known s moduus of esticity or coefficient of esticity. It is found tht up to certin ue of stress; strin ries inery with stress, boe tht prticur ue of stress the iner retionship ceses to hod good nd is known s estic imit. Since strin hs no unit nd dimension hence moduus of esticity hs sme unit nd dimension s stress Newton / m 2, [ M 1 T 2 ] Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 2
Esticity Definition Young s Moduus (Y): et us consider wire cmped t one end nd oded t its free end. The ength of the wire increses (the dimeter or bredth of the wire decreses). Gien: Origin ength of the wire A Are of cross section of the wire F the force ppied the chnge in ength of the wire in the direction of force ppied F/ /A Norm Stress, / ongitudin strin. Appying Hook s w, within the estic imit the ongitudin strin is proportion to the norm stress & the rtio of norm stress to the ongitudin strin is constnt knownn s Young s moduus of esticity (Y). Norm Stress F/A Y ongitudin Strin / Y F A F. A. If 1 m, A 1 m 2, 1 m then Y F Hence Young s moduus of mteri cn be defined s force required to stretch wire of tht mteri hing unit ength ( 1m) & unit re of cross section (A1 m 2 ) by unity ( 1m ) (2) Buk Moduus (k): et us consider cube ABCDEFGH hing oume. et Equ force per unit re P ( Stress) is ppied simutneousy t the center of the sides fces ong perpendicur to the surfce s shown. Then P is known s tensie stress. The oume of the cube wi increse. et chnge in oume of the cube oume strin Appying Hook s w within the estic imit the oume strin is proportion to the tensie stress nd the rtio of tensie stress to oume strin is constnt known s buk moduus of esticity. Buk Moduus k p p Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 3
Esticity Definition Physic significnce: Gien K I ron > K Copper k Iron P 1 P2 > P > P 1 > k 2 Copper Substnce hing greter buk moduus of esticity is difficut to be compressed, mong soid iquid nd gs, iquid is most difficut to be compressed nd hence iquid possesses high ue of k, where s gs cn be esiy compressed nd possesses ow ue of k Gs possesses two ues of buk moduus of esticity. The oume of gs cn be chnged by chnging pressure but for the sme chnge in pressure the chnge in oume is different under condition (i) Isotherm Condition (T constnt) (ii) Adibtic condition (ΔQ 0) Hence gs possessess two ue of k (i) Isotherm buk moduus of esticity (E i ) (ii) Adibtic buk moduus of esticity (E ) et P Pressure of the gs oume of the gs t pressure P. et the pressure be chnged to (P+ ) the oume decreses to Tensie stress oume Strin k E (1) (i) Isotherm buk moduus of esticity E i E i (2) Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 4
Esticity Definition We know tht under isotherm condition pressure & oume of gs re reted by P Constnt Differentiting P + 0 P (3) Putting eqution (3) in (2) E i P (4) (ii) Adibtic buk moduus of esticity (E ): We know tht under dibtic condition pressure & oume of gs re reted by γ P C γ C Constnt p Differentiting: Rtioof twospecifichetsof gs(constnt) Pγ γ 1 + [ γp + ] γp γp E γp E γ 1 E γp γ Ei P Qγ > 1 > E i γ 0 0 (5) Rigidity Moduus (n): et us consider rectngur bock ABCDEFGH, who s ower surfce ABCD is rigidy cmped. A force f is ppied pre to the surfce EFGH which is pre to the cmped Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 5
surfce. chnge. Esticity Definition The shpe chnges to ABCEDE F G H. The size i.e. the ength, bredth, oume etc does not The body is sid to be shered. The ppied force f per unit re of the surfce to which the force is pre is known s shering stress or tngenti stress F/ Where re of the surfce EFGH EAE HDH FBF GCG θ Shering strin or nge of sher Appying Hook s w within estic imit rtio of shering stress to shering strin is constnt known s rigidity moduus. Rigidity Moduus ( η) et EE retie dispcement between two yers which re seprted by distnce tnθ shering strin θ η E, AE f f θ,sinceθ is sm,tnθ θ Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 6
Esticity Definition Poissons Rtio (σ): A wire is cmped t one end nd oded t its free end. The ength of the wire increses nd the bredth or the dimeter of the wire decreses. Thus eery ongitudin strin is ccompnied by ter strin (uness preented). & D origin ength nd dimeter of the wire. & d chnge in ength nd dimeter of the wire. ongitudin strin ter strin d D Within estic imit the rtio of ter strin to ongitudin strin is constnt nd is known s Poisson s rtio. d ter strin Poissons Rtio ( σ) D on ngitudin strin The negtie sign indictes tht the two strins re just opposite in nture i.e. when one is extension other is contrction. Sefstudy.in High Schoo Tutori Css Notes Gener Physics Pge 7