1. Chapter 9
Solids and Fluids

2. States of matter
Solid
Liquid
Gas
Plasma

3. 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

4. Solids
Crystalline solid: atoms have an ordered structure (e.g., diamond, salt)
Amorphous solid: atoms are arranged almost randomly (e.g., glass)

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. stress = modulus * strain
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

12. 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
Thomas Young
(1773 – 1829)

13. 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

14. 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

15. Hydraulic stress The stress is fluid pressure P = F/A
Strain is a dimensionless ratio ΔV/V
The modulus is called the bulk modulus

16. Density and pressure Density SI unit of density: kg/m3 Pressure
Blaise Pascal
( )
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

17. Atmospheric pressure Atmospheric pressure:
P0 = 1.00 atm = 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

18. 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

19. 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

20. Measuring pressure
Mercury barometer
Open-tube manometer

21. 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.

22. 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

23. Archimedes’ principle
of Syracuse
( 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

24. 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

25. 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?

26. 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

27. Equation of continuity Equation of continuity
For a steady flow of an ideal fluid through a tube with varying cross-section
Equation of continuity

28. Bernoulli’s equation For a steady flow of an ideal fluid:
Daniel Bernoulli
( )
Bernoulli’s equation
For a steady flow of an ideal fluid:
Kinetic energy
Gravitational potential energy
Internal (“pressure”) energy

29. Bernoulli’s equation
Total energy

30. 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.

31. 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

32. 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

33. 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)

34. 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

35. 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

36. Contact angle
If cohesive forces are greater than adhesive forces, Φ > 90°
If adhesive forces are greater than cohesive forces, Φ < 90°

37. 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

38. 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

39. 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

40. Questions?

41. Answers to the even-numbered problems
Chapter 9
Problem 14:
1.9 × 104 N

42. Answers to the even-numbered problems
Chapter 9
Problem 22:
10.5 m;
no, some alcohol and water evaporate

43. Answers to the even-numbered problems
Chapter 9
Problem 26:
0.611 kg