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## PHYS 101 SPRING 2014

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**PHYS 101 SPRING 2014**Review of CH 8, 9, 10, 11, 13 and 14**Ch 8:Rotational Equilibrium and**Rotational Dynamics • Torque, t, is the tendency of a force to rotate an object about some axis • t = r Fsinq • t is the torque • Symbol is the Greek tau • r is the length of the position vector • F is the tangential force • SI unit is Newton . meter (N.m) Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics Only the tangential component of force causes a torque: Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics • The net torque is the sum of all the torques produced by all the forces • Remember to account for the direction of the tendency for rotation • Counterclockwise torques are positive • Clockwise torques are negative Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics • First Condition of Equilibrium • The net external force must be zero • This is a statement of translational equilibrium • The Second Condition of Equilibrium states • The net external torque must be zero • This is a statement of rotational equilibrium Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics • When a rigid object is subject to a net torque (Στ ≠ 0), it undergoes an angular acceleration Where I is the moment of inertia: Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics Section 9.2**Ch 8:Rotational Equilibrium and**Rotational Dynamics • Conservation of Mechanical Energy • Remember, this is for conservative forces, no dissipative forces such as friction can be present • Potential energies of any other conservative forces could be added**Ch 8:Rotational Equilibrium and**Rotational Dynamics • Work-Energy Theorem • In the case where there are dissipative forces such as friction, use the generalized Work-Energy Theorem instead of Conservation of Energy • Wnc = DE = DKEt + DKEr + DPE**Ch 8:Rotational Equilibrium and**Rotational Dynamics • Angular Momentum L and Conservation of L • Angular momentum is defined as : L = I ω • Since • If St = 0 then DL=0 in other words ff the sum of all torques on an object is zero then angular momentum is conserved: • Li = Lf Ii ωi=If ωf**Ch 9: Density**• The density of a substance of uniform composition is defined as its mass per unit volume: • SI unit: kg/m3 (SI) • Often see g/cm3 (cgs) • 1 g/cm3 = 1000 kg/m3 Section 9.2**Ch 9: Pressure**• The average pressure P is the force divided by the area Section 9.2**Ch 9: Young’s Modulus**• stress = elastic modulus x strain • In the case of stretching a bar we have tensile stress F/A and tensile strain DL/L0 and the elastic modulus is called Young’s modulus Section 9.3**CH 9: Shear Modulus**• In the case of applying a shear stress F/A on an object we have shear strain Dx/h and the elastic modulus is called the shear modulus Section 9.3**CH 9: Bulk Modulus**• In the case of applying a volume stress DP on an object we have volume strain DV/V and the elastic modulus is called the bulk modulus Section 9.3**Ch 9: Pressure and Depth equation**• Po is normal atmospheric pressure • 1.013 x 105 Pa = 14.7 lb/in.2 • The pressure does not depend upon the shape of the container • One atmosphere (1 atm) = 1.013 x 105 Pa Section 9.4**Ch 9: Pascal’s Principle**• A change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container. Section 9.4**Ch 9: 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 Section 9.6**Ch 9: Buoyant Force, cont.**• The magnitude of the buoyant force always equals the weight of the displaced fluid Section 9.6**Ch9: Archimedes’ Principle:Totally Submerged Object**• The upward buoyant force is B=ρfluidVobjg • The downward gravitational force is w=mg=ρobjVobjg • The net force is B-w=(ρfluid-ρobj)Vobjg Section 9.6**Ch 9: Archimedes’ Principle:Floating Object**• The object is in static equilibrium • The upward buoyant force is balanced by the downward force of gravity • Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level Section 9.6**Ch 9: Equation of Continuity**• For a steady flow the conservation of mass leads to: r1A1v1 = r2A2v2 For an incompressible fluid: A1v1 = A2v2 • The product of the cross-sectional area of a pipe and the fluid speed is a constant • The product Av is called the flow rate, Av=DV/Dt Section 9.7**Ch 9: Bernoulli’s Equation**• States that the sum of the pressure, kinetic energy per unit volume, and the potential energy per unit volume has the same value at all points along a streamline Section 9.7**Ch 9: Applications of Bernoulli’s Principle: Measuring**Speed • Shows fluid flowing through a horizontal constricted pipe • Speed changes as diameter changes • Can be used to measure the speed of the fluid flow • Swiftly moving fluids exert less pressure than do slowly moving fluids Section 9.7**Ch 9: Application – Airplane Wing**• The air speed above the wing is greater than the speed below • The air pressure above the wing is less than the air pressure below • There is a net upward force • Called lift • Other factors are also involved**Ch 10: Linear Thermal Expansion**• For small changes in temperature • α, the coefficient of linear expansion, depends on the material Section 10.3**Ch 10: Area Thermal Expansion**• Two dimensions expand according to Section 10.3**Ch 10: Volume Thermal Expansion**• Three dimensions expand Section 10.3**CH 10: Ideal Gas**• If a gas is placed in a container the pressure, volume, temperature and amount of gas are related to each other by an equation of state • An ideal gas is one that is dilute enough, and far away enough from condensing, that the interactions between molecules can be ignored. • Most gases at room temperature and pressure behave approximately as an ideal gas Section 10.4**Ch 10: Moles**• One mole is the amount of the substance that contains as many particles as there are atoms in 12 g of carbon-12 • Molar mass is the mass of 1 mole of a substance. Section 10.4**Therefore, n moles of gas will contain**molecules. Avogadro’s Number NA The number of elementary entities (atoms or molecules) in a mole is given by Avogadro’s number:**Ch 10: Ideal Gas Law**• PV = n R T • R is the Universal Gas Constant • n is the number of moles • R = 8.31 J / mol.K • R = 0.0821 L. atm / mol.K • Is the equation of state for an ideal gas • Temperatures used in the ideal gas law must be in kelvins Section 10.4**Ch 10: Ideal Gas Law, Alternative Version**• P V = N kB T • kB is Boltzmann’s Constant • kB = R / NA = 1.38 x 10-23 J/ K • N is the total number of molecules • n = N / NA • n is the number of moles • N is the number of molecules Section 10.4**Ch 10: Pressure of an Ideal Gas**• The pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of a molecule Section 10.5**Ch 10: Molecular Interpretation of Temperature**• Temperature is a direct measure of the average molecular kinetic energy of the gas Section 10.5**Ch 10: Speed of the Molecules**• Expressed as the root-mean-square (rms) speed • At a given temperature, lighter molecules move faster, on average, than heavier ones • Lighter molecules can more easily reach escape speed from the earth Section 10.5**CH 11: Energy Transfer**• When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler increases • The energy exchange ceases when the objects reach thermal equilibrium • The concept of energy was broadened from just mechanical to include internal • Made Conservation of Energy a universal law of nature Introduction**Ch 11: Units of Heat**• Calorie • A calorie is the amount of energy necessary to raise the temperature of 1 g of water from 14.5° C to 15.5° C . • A Calorie (food calorie) is 1000 cal • 1 cal = 4.186 J • This is called the Mechanical Equivalent of Heat Section 11.1**CH 11: Heat Capacity**• The heat capacity of an object is the amount of heat added to it divided by its rise in temperature: Q is positive if ΔT is positive; that is, if heat is added to a system. Q is negative if ΔT is negative; that is, if heat is removed from a system. Section 11.2**Ch 11: Specific Heat**• The heat capacity of an object depends on its mass. A quantity which is a property only of the material is the specific heat: Section 11.2**Ch 11: Calorimetry**• You can start with SQk = 0 • Qk is the energy of the kth object where Qk = mk ckDTk • Use Tf – Ti • You don’t have to determine before using the equation which materials will gain or lose heat Section 11.3**Ch 11: Phase Changes**• A phase change occurs when the physical characteristics of the substance change from one form to another • Common phases changes are • Solid to liquid – melting (fusion) • Liquid to Solid – freezing (fusion) • Gas to Liquid – condensation (vaporization) • Liquid to gas – boiling (vaporization) • Phases changes involve a change in the internal energy, but no change in temperature Section 11.4**Ch 11: Latent Heat**• The energy Q needed to change the phase of a given pure substance is • Q = ±m L • L is the called the latent heat of the substance • Latent means hidden • L depends on the substance and the nature of the phase change • Choose a positive sign if you are adding energy to the system and a negative sign if energy is being removed from the system Section 11.4 Section 11.4**Ch 11: Latent Heat, cont.**• SI unit of latent heat are J / kg • Latent heat of fusion, Lf, is used for melting or freezing • Latent heat of vaporization, Lv, is used for boiling or condensing • Table 11.2 gives the latent heats for various substances Section 11.4**Ch 11: Graph of Ice to Steam**Section 11.4**Ch 11: Methods of Heat Transfer**• Methods of Heat Transfer include • Conduction • Convection • Radiation Section 11.5**Ch 11: Conduction**• The transfer can be viewed on an atomic scale • It is an exchange of energy between microscopic particles by collisions • Less energetic particles gain energy during collisions with more energetic particles • Rate of conduction depends upon the characteristics of the substance Section 11.5**Ch 11: Conduction, equation**• The slab of material allows energy Q to transfer from the region of higher temperature to the region of lower temperature • A is the cross-sectional area Section 11.5**Ch 11: Multiple Materials, cont.**• The rate through the multiple materials will be • TH and TC are the temperatures at the outer extremities of the compound material Section 11.5**Ch 11: Radiation**• Radiation does not require physical contact • All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules • Rate of radiation is given by Stefan’s Law Section 11.5