Elasticity
December 8, 2016
Categorised in: 12th Physics
(1) Stress = $F/A$
(2) i. Tensile strain: $E/A$ = ${Mg}/{πr^2}$
ii. Volume = ${A dP}/{A}$ = $dP$
iii. Shearing: $F/A$ (tangential)
(3) Strain: ${\text"Change in dimension"}/{\text"Original dimension"}$
(4) i. Longitudinal: $l/L$
ii. Volume: – ${dv}/{V}$
iii. Shearing: tanθ
(5) Elastic constants:
i. Young’s Modulus: $Y = {FL}/{Al}$
ii. Bulk Modulus: $k = V {dP}/{dV}$
iii. Modulus of Rigidity: $η = F/{A tanθ}$ = ${F}/{Aθ}$
(6) Lateral Strain: $d/D$
(7) Poisson’s Ratio: ${\text"lateral strain"}/{\text"longitudinal strain"}$ = ${dl}/{DL}$
(8) $W = 1/2 \text"load x extension"$ = $1/2 Fl$
(9)
Strain Energy/ Unit volume = $U = 1/2 F/A l/L$ i.e. 1/2 (stress) (strain)
$U = 1/2 Y (strain)^2$ = $1/2 {(stress)^2}/{Y}$
(10) Apparant weight = $V g [ρ_b – {a ρ_l}/{100}]$
${\text"Apparant weight"}/{\text"Original weight"}$ = ${ρ_b – {ρ_l}/{100}}/{ρ_b}$ = ${V_g}/{V ρ_b g}$
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