PHY 101 1nd Edition Lecture 24 Outline of Last Lecture I. 8. 5 Torque and Angular Accelerationa. Moment of InertiaII. 8.6 Rotational Kinetic EnergyIII. 8.7 Angular MomentumOutline of Current Lecture IV. 9.1 States of Mattera. Solidsb. Liquidsc. Gasesd. Plasmae. Strange UniverseV. 9.2 Elastic Moduli of Solidsa. Elastic Properties: Stress, Strain & Elastic Modulusb. Young’s Modulusc. Shear Modulusd. Bulk ModulusCurrent LectureChapter 9: Solids & Fluids9.1 States of Matter- Matter: a collection of interacting particles (atoms. Molecules, charged particles, etc.)- Fundamental states of mattero Solido Liquido Gaso Plasma- Solidso Have a definite volume & shapeo Useful models for solids – spring & ballo Solids exist in 2 distinct forms Crystalline solid – ex. DiamondThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. Amorphous solid – ex. A silicono Crystalline solids: atoms have a ordered structure Ex. Quartz, salt, diamondso Amorphous solids: atoms are arranged almost randomly Ex. Glass- Liquids:o Has definite volume, not shape Takes the shape of its containero For the same material. Liquids exist at a higher temp. Ex. Water vs. iceo The molecules “wander” through the liquid in a random fashiono The intermolecular forces are not strong enough to keep the molecules in a fixed position- Gaseso No definite volume or shape Can be easily compressedo Ex. Air, H2 and He gaso Molecules in constant random motiono The molecules exert only weak forces on each other; collide occasionallyo Average distance between molecules is very large compared to the size of the molecules- Plasmao Most abundant form of matter in the universe (stars)o When gas is heated to a very high temp: Many of the electrons are freed from the nucleus Resulted in a collection of electrically charged ions & electronso A star is a massive, luminous sphere of plasma held together by its own gravity- Strange Universeo All of the aforementioned forms of matter are referred to as “normal matter”o Normal matter About 5% of universal contento Dark matter About 25% of total matter Cannot be seen opticallyo Dark energy Responsible for acceleration of the expansion of the universe; may be as much as 70% of all mattero Unfortunately, we still don’t know precisely what dark matter & dark energy are9.2 Elastic Moduli of Solids- All solids are deformable- Both size and shape can be changed by applying force- If the applied force is small or when the forces are removed, the object tends to retain its original shapeo Elastic behavior- A solid may undergo a plastic deformation if the external stress is beyond certain critical valueo Objects cannot restore their original shape if they are deformed plasticallyElastic Properties: Stress, Strain, & Elastic Modulus- Suppose some forces are applied to two cylindrical wires- Will the amount of deformation be the same?o Force alone is not a good measure- Stress: force per unit areao F/Ao SI Unit: Pascal (Pa)  1Pa = 1 N ·m2- With an applied stress F/A, objects (ex. Rods) made of the same materials will have identical strain ΔL/Lo F/A ≈ ΔL/Lo The elastic modulus is the constant of proportionality between stress and strain Stress = elastic modulus x straino Strain: fractional deformation  dimensionless- The elastic modulus measure the stiffness of the material- A material with a large elastic modulus is hard & difficult to deform- There are 3 kinds of deformationso Tensileo Shearo Bulk- Correspondingly, we haveo Tensile modulus (Young’s modulus) – Yo Shear modulus – so Bulk modulus – B- ** depends on the material, NOT on the shape or sizeYoung’s/ Tensile Modulus: Elasticity in Length- Consider a long bar of length Lo clamped at one end. A force F is applied at the other end, the bar will deform (elongate)- How large is the deformation (elongation) ΔL?o F/A ≈ ΔL/L  F/A = Y(ΔL/Lo)- F/A is called the tensile stress- ΔL/L is the tensile strain- Y: young’s modulus  SI Unit: Pascal (Pa)- Young’s modulus applies to a stress of either tension or compression- A solid deforms elastically only within certain maximum stress – elastic limit- Beyond the elastic limit:o it will not return to its original lengtho it will eventually break when the stress is beyond the breaking pointShear Modulus: Elasticity of Shape- one force is parallel to one of the object’s face, the opposite face is fixed- shear stress: F/A- shear strain: Δx/h = ratio of the horizontal displacement and the height of the objecto F/A ≈ Δx/h  F/A = S(Δx/h)o Δx: relative shift between the top & bottom surfaceso S: shear modulus  Unit: Pascale (Pa)o No volume change for this type of deformationo In shear stress, the force is parallel to the cross-sectional areao In tensile stress, the force is perpendicular to the cross-sectional areaBulk Modulus: Volume Elasticity- Bulk modulus characterizes the response of an object to uniform (isotropic) squeezing. Forces are perpendicular to and act on, all surfaces- The object undergoes a change in volume without a change in shapeo F/A ≈ - Δv/v  F/A = -B(Δv/v)- Volume stress: F/A = ΔP (also known as pressure) & Δv/v is volume strain- B: bulk modulus  Unit: Pascale (Pa)- A material with a large bulk modulus is difficult to compress- The compressibility k is the reciprocal of the bulk moduluso K = 1/B- Solid’s have Young’s, Bulk and Shear moduli- Liquids have only Bulk moduli, they DO NOT undergo a shearing or tensile