Exam #3 format same as Exam #2 “Study Hints” have been posted to Bb (these are “hints”, not a “Study Guide”) Reminder: HW #9 due tonight, 11:59 p.m. Reminder: Recitation Quiz #10 tomorrow Today: States/Phases of Matter, Deformation of Solids, Density, Pressure Today’s material WILL NOT be on the exam

Course Evaluation 5 bonus points (as detailed in syllabus) Window: Wed Nov 17 – Wed Dec 8 Go to Department of Physics homepage: www.as.uky.edu/physics Look for the link to the Online Course Evaluation under the “Courses” tab on the left-hand side of the webpage.

Four States (Phases) of Matter Solid Liquid Gas Plasma Plasma: When gas heated to high temperature, electrons surrounding atomic nuclei are “freed”. Resulting system is collection of equal numbers of negatively-charged electrons and positive-charged ions. Found in stars. Far more abundant than solid, liquid, and gaseous phases. Compare mass of Sun (2e30 kg) to mass of Earth (6e24 kg)! MS = 2 x 1030 kg ME = 6 x 1024 kg

What is the Universe Made Of ? Dark Matter: affects the motion of stars in galaxies, in ways that cannot be accounted for with the gravitational force of normal, visible matter. Dark energy responsible for the acceleration of the universe. May account for 70% of all matter in the universe. Related to matter via Einstein’s relation E = mc^2, which will study in PHY 213. Open research questions. We don’t know (yet) what they are !! E = mc2 PHY 213

NaCl: sodium chloride (table salt) Types of Solids Crystalline Solids: Amorphous Solids: Glassy Form of SiO2 NaCl: sodium chloride (table salt) Na Cl Atoms have an ordered Local ordering to the atoms, structure but no long-range order

Why Are Solids Stiff, and Tend to Maintain Their Shape ? Atoms in solids held together by electrical forces (PHY 213), and vibrate about these positions. A vibrating atom can be viewed as being bound in its equilibrium position by “springs”. If an external force is applied to such an object, the “springs” are compressed, and solid is slightly deformed. When external force is removed, springs “spring back”, and solid returns to its original shape and size. Solids are said to have “elasticity”.

F Deformation of Solids Elastic Behavior : It is possible to change the shape / size of a solid by applying an external force. When the external force is removed, the object tends to return to its original shape / size. Elastic Properties of Solids : Stress : Force per unit area causing a deformation. Strain : Measure of the amount of deformation. stress = elastic modulus  strain analogous to the spring constant in F = –k · Δx “stiffness” of a material

Elasticity in Length Under application of an external force, bar will attain an equilibrium : (1) Length > L0 (2) External force balanced by internal forces  Bar is said to be “stressed”. Tensile Stress : Tensile Strain : Ratio of the magnitude of the external force F to the cross-sectional area A Ratio of change in length ΔL to original length L0 ΔL tensile strain = dimensionless tensile stress F SI : N/m2 = Pascal L0 = A

stress = elastic modulus  strain Young’s Modulus Recall, we just said that : stress = elastic modulus  strain Plugging in our definitions for the tensile stress and strain : Linear relationship between stress and strain Young’s Modulus [SI: Pascals] A material with a large Young’s Modulus is difficult to stretch or compress !

Elastic Limit If the stress is sufficiently large (e.g., from very large force), it is possible to exceed the “elastic limit”. At this point, the linear relationship between the stress and strain breaks down. Ultimate Strength : Greatest stress the material can withstand w/o breaking Breaking Point : Just beyond Ultimate Strength

Shear Modulus: Elasticity of Shape face F Object subjected to a force parallel to one of its faces, while opposite face held fixed by a second (equal but opposite) force. Called shear stress. –F opposite face Volume does not change !! shear stress shear strain shear modulus SI: Pascals

Bulk Modulus: Volume Elasticity If a solid is under uniform pressure, it undergoes a change in volume, but not in shape. Such as when a solid is immersed in a fluid Material with large bulk modulus difficult to compress [ Note: Compression ΔV < 0 results from positive pressure ΔP > 0 ] volume stress, “pressure” bulk modulus

Just a Note … Table 9.1 in your textbooks lists typical values of Young’s Modulus, Shear Modulus, and Bulk Modulus for various materials. You don’t need to memorize these. Will be provided if/when needed.

Example For safety in climbing, a mountaineer uses a nylon rope that is 50 m long, and 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. What is its Young’s Modulus ?

Density vs. lead wood If a lead brick and a piece of wood have the same volume, which one is more massive (i.e., heavier) ? A measure of the difference between the lead and wood is given by the “density” of an object : For an object having uniform composition of its mass : SI: kg/m3

Densities Substance Density [kg/m3] Water (@ 4 deg Celsius) 1.000 x 103 Ice 0.917 x 103 Aluminum 2.70 x 103 Lead 11.3 x 103 Gold 19.3 x 103 Mercury 13.6 x 103 Air 1.29 Ethyl Alcohol 0.806 x 103 ice expands !!

Pressure Fluids (liquids, gases) cannot sustain shearing stresses. The only stress that a fluid can exert on a submerged object is one that tends to compress it. Force exerted by fluid on object ALWAYS PERPENDICULAR to the object’s surfaces. If F is the magnitude of a force exerted perpendicular to a surface of area A, the pressure P is : F : Newtons A : m2 P : Pascals

Atmospheric Pressure At sea level, standard atmospheric pressure is : 14.7 psi [pounds/inch2] 1.01 x 105 Pascals The “gauge pressure” means the pressure above that of atmospheric pressure. [Gauge reads 0 if tire is not pumped up.] So the “absolute pressure” of a car tire inflated to 30 psi of “gauge pressure” = 30 + 14.7 = 44.7 psi.

Example The four tires on a car are all inflated to a gauge pressure of 2.0 x 105 Pascals (~29 psi). Each tire has an area of 0.024 m2 in contact with the ground. What is the automobile’s weight (in Newtons) ?

Next Lecture Class 9.6: Buoyant Forces and Archimedes’ Principle