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Chapter 9 Solids and Fluids. States of matter Solid Liquid Gas Plasma. Solids Have definite volume and shape Molecules: 1) are held in specific locations by electrical forces 2) vibrate about equilibrium positions 3) can be modeled as springs connecting molecules. Solids
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Chapter 9 Solids and Fluids
States of matter • Solid • Liquid • Gas • Plasma
Solids • Have definite volume and shape • Molecules: • 1) are held in specific locations by electrical forces • 2) vibrate about equilibrium positions • 3) can be modeled as springs connecting molecules
Solids • Crystalline solid: atoms have an ordered structure (e.g., diamond, salt) • Amorphous solid: atoms are arranged almost randomly (e.g., glass)
Fluids • Fluids – substances that can flow (gases, liquids) • Fluids conform with the boundaries of any container in which they are placed • Fluids lack orderly long-range arrangement of atoms and molecules they consist of • Fluids can be compressible and incompressible
Liquids • Have a definite volume, but no definite shape • Exists at a higher temperature than solids • The molecules “wander” through the liquid in a random fashion • The intermolecular forces are not strong enough to keep the molecules in a fixed position
Gases • Have neither definite volume nor definite shape • Molecules are in constant random motion • The molecules exert only weak forces on each other • Average distance between molecules is large compared to the size of the molecules
Plasmas • Matter heated to a very high temperature • Many of the electrons are freed from the nucleus • Result is a collection of free, electrically charged ions • Plasmas exist inside stars
Indeterminate structures • Indeterminate systems cannot be solved by a simple application of the equilibrium conditions • In reality, physical objects are • not absolutely rigid bodies • Concept of elasticity is employed
Elasticity • All real “rigid” bodies can change their dimensions as a result of pulling, pushing, twisting, or compression • This is due to the behavior of a microscopic structure of the materials they are made of • Atomic lattices can be approximated as sphere/spring repetitive arrangements
Stress and strain • All deformations result from a stress – deforming force per unit area • Deformations are described by a strain – unit deformation • Coefficient of proportionality between stress and strain is called a modulus of elasticity • stress = modulus * strain
Thomas Young (1773 – 1829) • Tension and compression • Strain is a dimensionless ratio – fractional change in length of the specimen ΔL/Li • The modulus for tensile and compressive strength is called the Young’s modulus
Tension and compression • Strain is a dimensionless ratio – fractional change in length of the specimen ΔL/Li • The modulus for tensile and compressive strength is called the Young’s modulus
Shearing • For the stress, force vector lies in the plane of the area • Strain is a dimensionless ratio Δx/h • The modulus for this case is called the shear modulus
Hydraulic stress • The stress is fluid pressure P = F/A • Strain is a dimensionless ratio ΔV/V • The modulus is called the bulk modulus
Blaise Pascal (1623 - 1662) • Density and pressure • Density • SI unit of density: kg/m3 • Pressure • SI unit of pressure: N/m2 = Pa (pascal) • Pressure is a scalar – at a given point in a fluid the measured force is the same in all directions • For a uniform force on a flat area
Atmospheric pressure • Atmospheric pressure: • P0 = 1.00 atm = 1.013 x 105 Pa • Specific gravity of a substance is the ratio of its density to the density of water at 4° C (1000 kg/m3) • Specific gravity is a unitless ratio
Fluids at rest • For a fluid at rest (static equilibrium) the pressure is called hydrostatic • For a horizontal-base cylindrical water sample in a container
Fluids at rest • The hydrostatic pressure at a point in a fluid depends on the depth of that point but not on any horizontal dimension of the fluid or its container • Difference between an absolute pressure and an atmospheric pressure is called the gauge pressure
Measuring pressure • Mercury barometer • Open-tube manometer
Chapter 9 Problem 19 A collapsible plastic bag contains a glucose solution. If the average gauge pressure in the vein is 1.33 × 103 Pa, what must be the minimum height h of the bag in order to infuse glucose into the vein? Assume that the specific gravity of the solution is 1.02.
Pascal’s principle • Pascal’s principle: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container • Hydraulic lever • With a hydraulic lever, a given force applied over a given distance can be transformed to a greater force applied over a smaller distance
Archimedes of Syracuse (287-212 BCE) • Archimedes’ principle • Buoyant force: • For imaginary void in a fluid • p at the bottom > p at the top • Archimedes’ principle: when a body is submerged in a fluid, a buoyant force from the surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight of the fluid that has been displaced by the body
Archimedes’ principle • Sinking: • Floating: • Apparent weight: • If the object is floating at the surface of a fluid, the magnitude of the buoyant force (equal to the weight of the fluid displaced by the body) is equal to the magnitude of the gravitational force on the body
Chapter 9 Problem 34 A light spring of force constant k = 160 N/m rests vertically on the bottom of a large beaker of water. A 5.00-kg block of wood (density = 650 kg/m3) is connected to the spring, and the block–spring system is allowed to come to static equilibrium. What is the elongation ΔL of the spring?
Motion of ideal fluids • Flow of an ideal fluid: • Steady (laminar) – the velocity of the moving fluid at any fixed point does not change with time (either in magnitude or direction) • Incompressible – density is constant and uniform • Nonviscous – the fluid experiences no drag force • Irrotational – in this flow the test body will not rotate about its center of mass
Equation of continuity • For a steady flow of an ideal fluid through a tube with varying cross-section Equation of continuity
Daniel Bernoulli (1700 - 1782) • Bernoulli’s equation • For a steady flow of an ideal fluid: • Kinetic energy • Gravitational potential energy • Internal (“pressure”) energy
Bernoulli’s equation • Total energy
Chapter 9 Problem 43 A hypodermic syringe contains a medicine having the density of water. The barrel of the syringe has a cross-sectional area A = 2.50 × 10-5 m2, and the needle has a cross-sectional area a = 1.00 × 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F of magnitude 2.00 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle’s tip.
Surface tension • Net force on molecule A is zero, because it is pulled equally in all directions • Net force on B is not zero, because no molecules above to act on it • It is pulled toward the center of the fluid
Surface tension • The net effect of this pull on all the surface molecules is to make the surface of the liquid contract • Makes the surface area of the liquid as small as possible – surface tension
Surface tension • Surface tension: the ratio of the magnitude of the surface tension force to the length along which the force acts: • SI units are N/m • Surface tension of liquids decreases with increasing temperature • Surface tension can be decreased by adding ingredients called surfactants to a liquid (e.g., a detergent)
Liquid surfaces • Cohesive forces are forces between like molecules, adhesive forces are forces between unlike molecules • The shape of the surface depends upon the relative strength of the cohesive and adhesive forces • If adhesive forces are greater than cohesive forces, the liquid clings to the walls of the container and “wets” the surface
Liquid surfaces • Cohesive forces are forces between like molecules, adhesive forces are forces between unlike molecules • The shape of the surface depends upon the relative strength of the cohesive and adhesive forces • If cohesive forces are greater than adhesive forces, the liquid curves downward and does not “wet” the surface
Contact angle • If cohesive forces are greater than adhesive forces, Φ > 90° • If adhesive forces are greater than cohesive forces, Φ < 90°
Capillary action • Capillary action is the result of surface tension and adhesive forces • The liquid rises in the tube when adhesive forces are greater than cohesive forces
Capillary action • Capillary action is the result of surface tension and adhesive forces • The level of the fluid in the tube is below the surface of the surrounding fluid if cohesive forces are greater than adhesive forces
Viscous fluid flow • Viscosity: friction between the layers of a fluid • Layers in a viscous fluid have different velocities • The velocity is greatest at the center • Cohesive forces between the fluid and the walls slow down the fluid on the outside
Answers to the even-numbered problems Chapter 9 Problem 14: 1.9 × 104 N
Answers to the even-numbered problems Chapter 9 Problem 22: 10.5 m; no, some alcohol and water evaporate
Answers to the even-numbered problems Chapter 9 Problem 26: 0.611 kg