9 Solids & Fluids elasticity of solids pressure and pascal’s principle buoyancy and archimedes’ principle Homework: 1, 3, 5, 37, 39, 56, 69, 70.

Solid Deformation stress = force/area = pressure strain = fractional change in length Solid Moduli ~ stress/strain ~ stiffness

Solid Deformation Length Change: stress = F/A, strain = DL/Lo, Young’s Modulus, Y = stress/strain. Volume Change: stress = F/A = p, strain = -DV/Vo, Bulk Modulus, B = -Dp/(DV/Vo)

Pressure, p p = force/area Unit: pascal, Pa 1 Pa = 1N/m2. Example: 100N applied to 0.25m2. Pressure = 100/0.25 = 400N/m2.

Density r = mass/volume SI Unit: kg/m3 common unit: g/cm3 1,000 kg/m3 = 1 g/cm3

Gauge Pressure is Differential Pressure

Depth and Fluid Pressure P = Po + rgd P is the pressure at depth d. Po is the pressure at the fluid surface r is the fluid density Example: increase in pressure at a depth of 1m in water = (1,000)(9.8)(1.0) Pa

Barometer

Pascal’s Principle Example: A2/A1 = 100 F2/F1 = 100

Buoyancy and Archimedes’ Principle

L=0.5m cube of steel in water Vo = L3 = (0.5m)3 = 0.125 m3 FB = (fl.density)(Vo)(g) = (1,000kg/m3 )(0.125 m3 )(9.8N/kg) = 1225N Compare FB to W of object: W = mg = (ob.density)(ob.volume)(g) = (7,800)(0.125)(9.8) = 9555N What is its weight when under water? W’ = W – FB = 8330N

1kg object is weighed in water W’ = 9.2N. What is its density? FB = W – W’ = 9.8N – 9.2N = 0.6N FB = (fl.den.)(ob.vol.)(g) = 0.6N FB = (1000)(ob.vol.)(g) = 0.6N (ob.vol.) = 6.12x10-5cubic meter (ob.den.) = mass/vol. = 1kg/(6.12x10-5) 16,333 kg/m3. = 16.333 g/cm3. This is not pure gold.

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Example: Object mass 0.150kg density 2g/cm3 is weighed in water.

Example: calculate speed water exits the hole in terms of the given parameters.