Mechanical Properties Of Solids And Fluids Flashcards
Elasticity
Property of a body to regain its original state on the removal of deforming force
Slope of stress strain graph gives
Modulus of elasticity
Stress
Restoring force/ area
Strain
Change in dimension/ original dimension
Young’s modulus (Y)
Y= tensile stress/ longitudinal strain
Y = Fℓ/ A∆ℓ
- F: force
- A: area
- ℓ: length
Tensile stress
Restoring force per unit area
Bulk modulus (B)
B = volume stress/ volume strain
B = F V/ A ∆V
B = PV/ ∆V
- F: force
- A: area
- V: volume
- P: pressure
Properties of modulus of elasticity
- independent of the dimensions of the body
- depends on the nature of the material and temp
- as temp↑, modulus of elasticity ↓
- steel is more elastic than rubber
- metals are more elastic than their alloys
Young’s modulus is applicable for
Solids only
Bulk modulus is applicable for
Solids, liquids, and gases
Fractional change in density
∆ ρ / ρ = P/B
- ρ: density
- P: pressure
- B: bulk modulus
Compressibility (k)
k = 1/B
-B: bulk modulus
Shear modulus (G)
G = shearing stress/ shearing strain
G = FL / A ∆x
- A: area
- ∆x: change in shape
Shear modulus is applicable for
Solids only
Breaking stress
Breaking load/ area
It’s a constant for a given material
Work done in stretching a wire
W = ½ F∆L
L: extension
This work is stored as elastic potential energy
Elastic potential energy stored in a stretched wire
U = ½F∆L
Energy density of a wire (u)
u = elastic potential energy/ volume
u= ½(F∆L/ AL)
u = ½ stress × strain
Area under stress strain graph gives
energy density
Poisson’s ratio (μ)
- μ= lateral strain/ longitudinal strain
- μ = (-∆D/D) / ∆L/L
Poisson’s ratio when there’s no lateral strain
μ = 0
Poisson’s ratio when there’s no volume change
μ = ½
Force acting on a body immersed in liquid
- weight, W = mg = Vρg
- upthrust = Vσg
ρ: density of object
σ: density of liquid
Weight for floating body
Wₐₚₚₐᵣₐₙₜ = Wₐ꜀ₜᵤₐₗ - upthrust =0
