Chapter 9 Solids and Fluids Elasticity Archimedes Principle Bernoulli s Equation States of Matter Solid Liquid Gas Plasmas Solids Stress and Strain Stress Measure of force felt by material Force Stress Area SI units are Pascals 1 Pa 1 N m2 same as pressure Solids Stress and Strain Strain Measure of deformation L Strain L A F L dimensionless L Young s Modulus Tension F F A Y L L tensile stress A L tensile strain L Measure of stiffness Tensile refers to tension Example 9 1 King Kong a 8 0x104 kg monkey swings from a 320 m cable from the Empire State building If the 3 0 cm diameter cable is made of steel Y 1 8x1011 Pa by how much will the cable stretch 1 97 m Shear Modulus F A S xh Sheer Stress Sheer Strain Bulk Modulus F P A B V V V V B Y 3 Change in Pressure Volume Strain Pascals as units for Pressure F P A 1 Pa 1 N m2 Example 9 2 A large solid steel Y 1 8x1011 Pa block L 5 m W 4 m H 3 m is submerged in the Mariana Trench where the pressure is 7 5x107 Pa a By what percentage does the length change 0 041 b What are the changes in the length width and height 2 08 mm 1 67 mm 1 25 mm c By what percentage does the volume change 0 125 Solids and Liquids Solids have Young s Bulk and Shear moduli Liquids have only bulk moduli Ultimate Strength Maximum F A before fracture or crumbling Different for compression and tension Densities M V Density and Specific Gravity Densities depend on temperature pressure Specific gravity ratio of density to density of H2O at 4 C Example 9 3 The specific gravity of gold is 19 3 What is the mass in kg and weight in lbs of 1 cubic meter of gold 19 300 kg 42549 lbs Pressure Pascal s Principle F P Pressure applied to any A part of an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container Each face feels same force Transmitting force Hydraulic press F1 F2 P A1 A2 An applied force F1 can be amplified A2 F2 F1 A1 Examples hydraulic brakes forklifts car lifts etc Pressure and Depth w is weight w Mg Vg Ahg Sum forces to zero PA P0A w 0 Factor A P P0 gh Example 9 5 skip Find the pressure at 10 000 m of water DATA Atmospheric pressure 1 015x105 Pa 9 82x107 Pa Example 9 6 Assume the ultimate strength of legos is 4 0x104 Pa If the density of legos is 150 kg m3 what is the maximum possible height for a lego tower 27 2 m Example 9 7 Estimate the mass of the Earth s atmosphere given that atmospheric pressure is 1 015x105 Pa Data Rearth 6 36x106 m 5 26x1018 kg Archimedes Principle Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object Example 9 8 A helicopter lowers a probe into Lake Michigan which is suspended on a cable The probe has a mass of 500 kg and its average density is 1400 kg m3 What is the tension in the cable 1401 N Example 9 9a A wooden ball of mass M and volume V floats on a swimming pool The density of the wood is wood H20 The buoyant force acting on the ball is a Mg upward b H20gV upward c H20 wood gV upward Example 9 9b A steel ball of mass M and volume V rests on the bottom of a swimming pool The density of the steel is steel H20 The buoyant force acting on the ball is a Mg upward b H20gV upward c steel H20 gV upward Example 9 10 A small swimming pool has an area of 10 square meters A wooden 4000 kg statue of density 500 kg m3 is then floated on top of the pool How far does the water rise Data Density of water 1000 kg m3 40 cm Floating Coke Demo SKIP The can will a Float b Sink Paint Thinner Demo SKIP When I pour in the paint thinner the cylinder will a Rise b Fall Equation of Continuity What goes in must come out mass density M A x Av t Mass that passes a point in pipe during time t Eq of Continuity 1A1v1 2A2v2 Example 9 11 Water flows through a 4 0 cm diameter pipe at 5 cm s The pipe then narrows downstream and has a diameter of of 2 0 cm What is the velocity of the water through the smaller pipe 20 cm s Laminar or Streamline Flow Fluid elements move along smooth paths Friction in laminar flow is called viscosity Turbulence Fluid elements move along irregular paths Sets in for high velocity gradients small pipes Ideal Fluids Laminar Flow No turbulence Non viscous No friction between fluid layers Incompressible Density is same everywhere Bernoulli s Equation 1 2 P v gy constant 2 Sum of P KE V and PE V is constant How can we derive this Bernoulli s Equation derivation Consider a volume V of mass M of incompressible fluid 1 1 KE Mv22 Mv12 2 2 1 1 2 Vv2 Vv12 2 2 PE Mgy2 Mgy1 Vgy2 Vgy1 W F1 x1 F2 x2 P1A1 x1 P2A2 x2 P1 V P2 V 1 2 1 2 P1 gh1 v1 P2 gh2 v2 2 2 Example 9 12 A very large pipe carries water with a very slow velocity and empties into a small pipe with a high velocity If P2 is 7000 Pa lower than P1 what is the velocity of the water in the small pipe 3 74 m s Venturi Meter Applications of Bernoulli s Equation Venturi meter Curve balls Airplanes Beach Ball Straws Demos Example 9 13a nsider an ideal incompressible fluid oose or 2 a b c Example 9 13b Consider an ideal incompressible fluid choose or Mass that passes 1 in one second mass that passes 2 in one second a b c Example 9 13c nsider an ideal incompressible fluid oose or v2 a b c Example 9 13d nsider an ideal incompressible fluid oose or P1 P2 a b c Example 9 14 Water drains out of the bottom of a cooler at 3 m s what is the depth of the water above the valve 45 9 cm a b Three Vocabulary Words Viscosity Diffusion Osmosis Viscosity v F A d Friction between the layers Pressure drop required to force water through pipes Poiselle s Law At high enough v d turbulence sets in Diffusion Molecules move from region of high concentration to region of low concentration Fick s Law Mass C2 C1 Diffusion rate DA time L D diffusion coefficient Osmosis Movement of water through a boundary while denying passage to specific molecules e g salts
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