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 3.