Phy 2053 Announcements Elastic Properties of Solids

„ Stress - force per unit area „ Good luck on Exam 2! causing the deformation „ Exam 2 grades – grades should be „ Strain - measure of the available by Monday, April 6 on UF e- amount of deformation „ The elastic modulus is the Learning web site. constant of proportionality between stress and strain „ Exam 2 solutions will be posted early „ Three types of moduli:

next week „ Young’s modulus, shear modulus, bulk modulus „ HW Assignment 9 next Wednesday, April 8

Young’s Modulus: Young’s Modulus: Elasticity in Length, Stress = F/A FLΔ Hooke’s Law redux Strain = ΔL/L0 = Y A ALo

F ΔL AY L0 Stress = Y ⇒ F = ΔL A L L Stress = Y x Strain or = Y 0 0 Strain ΔL

Stress (F/A) has units of N/m2 1 N/m2 = 1 Pascal (Pa) k F

Example #9-11 Shear Modulus

Determine the elongation of the F „ shear stress = rod shown below if it is under a A tension of 5.8 × 103 N. Δx shear strain = h FxΔ = S Ah

„ S is the shear Δx F modulus „ A material having a h Y = 7 x 1010 Pa Y = 11 x 1010 Pa large shear modulus Al Al is difficult to bend -F

1 Bulk Modulus Notes on Moduli ΔV Δ=−PB „ Solids have Young’s, Bulk, and V Shear moduli „ A material with a large bulk modulus is difficult to compress „ Liquids and gases have only bulk moduli, they will not undergo a „ The negative sign is included since an increase in pressure shearing or tensile stress

will produce a decrease in „ The liquid or gas would flow instead volume

„ B is always positive „ The compressibility is the reciprocal of the bulk modulus

Pressure

„ The force exerted by a fluid on a submerged object at any point if perpendicular to the surface of the object F N P ≡ in Pa = A m2

Density Pressure F N „ The density of a substance of P ≡ in Pa = uniform composition is defined as A m2 its mass per unit volume: m ρ ≡ V 3 3 „ Units are kg/m (SI) or g/cm (cgs) 3 3 „ 1 g/cm = 1000 kg/m

2 Pressure and Depth Pressure and Depth equation

„ Examine the darker „ region, assumed to „ Po is normal be a fluid atmospheric „ It has a cross- pressure sectional area A 1.013 x 105 Pa „ Extends to a depth h below the surface

„ The pressure does Three external forces A act on the region not depend upon the shape of the container

Liquid in a U- tube Liquid in a U- tube Patm Patm Patm Patm

h1 = h2 h1 h1

h2 h2

P = Patm + ρgh1 P = Patm + ρgh2 P = Patm + ρgh1 P = Patm + ρgh2

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