Learning Objectives for Final Exam Fall, 2012 Physics 2210

Transcription

1 Learning Objectives for Final Exam Fall, 2012 Physics 2210 Operationally defined quantities (They are defined in terms of the operations you perform to, by measurement, compare an object or quantity with a standard. Don t know what they are but do how much.): Be able to fill in the chart. Quantity Symbol SI Unit How defined? These are undefined in terms of other quantities but Mass M kg by comparison with standard kilogram (kg) Length L or x or y m by comparison with standard meter (m) or z Time T s by comparison with standard second (s) Charge* Q coulomb by comparison with standard coulomb (C) * Instead of charge the fourth undefined quantity is usually defined in terms of a standard ampere; charge then becomes a defined quantity however the present ordering has somewhat greater simplicity. Where do these come from? Measurement; comparison with a standard. Mathematically derived quantities: Be able to fill in the table below except those with entry X Quantity Linear Relation Between Angular Position r =xi+yj+zk s=rθ (θ in radians) Θ Velocity v=dr/dt v=rω ω=dθ/dt Acceleration a=dv/dt a=rα α=dω/dt Momentum p=mv L=rxp L=Iω (rigid body; fixed axis of rotation) (I= r 2 dm) Force and Torque F= ma (F=dp/dt) Γ=rxF Γ=Iα (Γ=dL/dt) Work W= F dr X W= Γdθ Kinetic Energy K= ½ mv 2 X K= ½ Iω 2 Potential Energy U B/A =-W A to B Conservative forces X Total Energy E = K+U X E=K+U Power P=dW/dt X P=dW/dt Where do these definitions come from? They are mathematically derived from other definitions: both derived and not derived U B/A =-W A to B Conservative torques SI System of Units Know the following SI units kg, m, s, C, N, J, W, radian. Know how to get the SI units for all entries in the tables above. Definition of System. System (S) : Region of Space and everything in it. Internal force: Force on a body in S due to another body in S. External force: Force on a body in S due to another outside of S.

2 Newtons Laws of Motion Know Newton s Laws a. Newton s Second Law (definition of force) F = ma (later F = dp/dt). b. Get First Law from Second: If net force is zero, v = constant. c.third law: For every force F of type resulting from body A acting on body B, there exists an equal and opposite force F of same type resulting from body B acting on body A. d. Where do these come from? Definitions of force and system. Fundamental Force Laws There exist force laws that are believed to be more fundamental but the following is a reasonable introduction: Know the equation and relative strength for gravitation and know the names and relative strengths of electgromagnetism and nuclear: a. Gravitation between two point masses (very weak) F on 2 due to 1 = - Gm 1 m 2 r 12 /r 12 3 where r 12 is a vector from mass 1 to mass 2 b. Electromagnetic (unit strength) c. Nuclear (strong) d. Where do these come from? Measurements. Derived Force Laws Know and understand how to use the following derived forces a. Gravitational force on an object of mass m when near Earth s surface: F = mg b. Elastic (Spring) F = - k x c. Moving friction: f moving = μ moving N where N is the magnitude of the force pushing the two surfaces together and the frictional force acts in a direction opposite the velocity. d. Static friction: f static μ static N and f static + f sum of all other applied forces = 0 e. drag force: the velocity-dependent force opposing the motion of an object through a fluid. f. Where do these come from? Measurements or by derivation from fundamental force laws. Fundamental Theorems Know and understand the following theorems: a. Work kinetic energy theorem: The net work done by all forces on a single particle equals the change in its kinetic energy. Where does this come from? Definitions of work and kinetic energy. a. Conservation of Total Linear Momentum in a System (S): If F net external = 0, then P total = constant in time. Where does this come from? Definitions of Force and System. b. Conservation of Total Angular Momentum in a System (S): If Γ net external = 0 then L total = constant in time. Where does this come from? Definitions of Torque and System. b. Conservation of Energy

3 If the total mechanical energy in a system doesn t change then the total mechanical energy is conserved. Where does this come from? It is a tautology. Applications General Be able to apply the definitions, laws, and theorems to specific cases. For example, use potential energy in a gravitational field near the surface of the earth and kinetic energy to determine the speed of an object rolling down an inclined plane from rest at height h. Circular Motion Know and understand the relationships for uniform circular motion and know how to derive them. a. a=v 2 /R b. v=rω c. a = -ω 2 r d. a and r are perpendicular to v. e. r = R[icos(ωt) + jsin(ωt)] Elastic (inelastic) Collision A collision between two objects where kinetic energy is not (is) converted into heat Simple Harmonic Oscillator 1. Understand how to set up Newton s Second law (or torque form) for a. Mass-spring system: -kx = md 2 x/dt 2. Get the solution: x = A cos (ωt) where ω = (k/m) 1/2. Understand amplitude A, frequency f, period T=1/f, radian frequency ω = 2πf. b. Simple pendulum: -mglsinθ=id 2 θ/dt 2, where =ml 2 and ω=(g/l) 1/2. Solution θ=θ max cos(ωt). Remember for small oscillations sinθ θ in radian measure. c. Torsion pendulum: -κθ=id 2 θ/dt 2, where ω=(κ/i) 1/2. Solution θ=θ max cos(ωt). 2. Qualitatively understand damping, forced oscillations, and resonance. Wave Motion 1. Know two forms of the equation for sinusoidal wave motion: y(x,t) = A cos (kx±ωt) and y(x,t) = A cos2π(x/λ ± t/t). 2. Understand amplitude A, frequency f, period T, wavelength λ, wave number k= 2π/λ, radian frequency ω=2π/t, wave velocity v, and frequency in hertz, f=ω/2π=1/t. 3. Understand how to derive the direction of the wave from the equation by setting the phase equal to a constant and taking the derivative of x with respect to time. 4. Know how to use equations for velocity: string: v=(f/μ) 1/2 where F is string tension and μ is mass per unit length; sound in a gas: v=(γp/ρ) 1/2 where γ is the ratio of specific heats, P is pressure, and ρ is mass density. 5. Intensity is defined as I=P/A where P is power of a source and A is the area. The decibel measure of sound intensity is defined as β=10log(i/i 0 ) where I 0 is a reference intensity equal to W/m 2.

4 Important Applications of Wave Motion. Name Defining Equation Resulting Solution Interference (plane y=a 1 cos(k 1 x 1 ±ω 1 t)+a 2 cos(k 2 x 2 ±ω 2 t) Beats (plane Standing Waves (plane Doppler Effect: Take x 1 =x 2 =0; A 1 =A 2 =A, ω 1 ω 2 y=acosω 1 t+acosω 2 t A 1 =A 2 =A; v 1 =-v 2 ; k 1 =k 2 =k ; ω 1 =ω 2 =ω ; y=acos(kx-ωt)-acos(kx+ωt) Take u + when source is trying to close the space with observer and vise versa. y=2acos[(ω 1 - ω 2 )t/2]cos[(ω 1 +ω 2 )t/2] Beat frequency is absolute value(ω 1 -ω 2 ) y=2asin(kx)sin(ωt) f observed =f source (v+u observer ) /(vu source ) v is sound speed Equilibrium Understand the nature of the stability of the following type of equilibrium: stable, meta stable, neutrally stable, and unstable. Know the rules for static equilibrium, F i = 0, τ i = 0, and how to use them. Learning Objectives, Physics 2210, Chapters Definitions: You needn t memorize these; understand them and be able to use them properly. Quantity Definition Symbol SI unit Notes Density mass/volume ρ kg/m 3 Scalar Pressure Force/area P Pa=N/m 2 Scalar Heat Temperature Energy being transferred by means of a temperature difference alone Proportional to the mean kinetic energy of the random motion of molecules. Q J Scalar T K Scalar Specific Heat Q=cmΔT c J/kg K Entropy S = dq/t S J/K Heat: Specific Heat: Q=cmΔT where c is the heat capacity and ΔT is the temperature rise. Heat Transfer: Conduction dq/dt =-kaδt/δx. Gives the energy flow (heat flow) in watts where k is the conductivity, and ΔT is the temperature difference over thickness Δx Convection is the heat energy transferred by moving a volume of fluid from one position to another. Radiation is heat transferred by electromagnetic radiation. It often follows the Stefan-Boltzman law for radiated power: P=eσAT 4 where e is the emissivity, A is the radiating area at temperature T, and σ is the Stefan-Boltzmann constant 5.67x10-8 W/m 2 K 4. A perfect blackbody or radiator has e=1.

5 Thermal Behavior of Matter: Ideal Gas Law: pv=nrt n is the number of moles (=grams/gram-atom) where one mole contains 6.02x10 23 particles (Avogadro s number), R=8.314 J/K mol (ideal gas constant) Kinetic Theory of Temperature for an ideal, monotonic gas: (mv 2 /2) average =3kT/2 where k=1.38x10-23 J/K is Boltzmann s constant. Phase Changes: (Not on final) Q=Lm where m is the mass of material and L is the heat of transformation (often called latent heat) Thermal expansion: (Not on final) Linear Δx/x =αδt where α is the linear expansion coefficient. Volume ΔV/V=βΔT where β is the volume expansion coefficient. Thermodynamics First Law of Thermodynamics: ΔU=Q+W Change in internal energy = heat added plus work done on the system Work done on gas: W=- pdv Processes: Isothermal. Constant Temperture: pv=constant Constant Volume. Isobaric. Constant Pressure: Adiabatic. No heat lost of gained: pv γ =constant where γ = C p /C V. Be able to draw a representative Carnot cycle labeling and describing the four branches. Efficiency of a Carnot heat engine: e=1-t c /T h =1-Q c /Q h Second Law of Thermodynamics: Statement 1: No heat engine can have a greater efficiency than a Carnot engine. Statement 2: It is impossible to construct a heat engine that extracts energy from a reservoir and delivers an equal amount of work. Statement 3: (Not on final) The entropy of a closed system never decreases. Entropy (Not on final) Entropy is the measure of the energy available to do work. Low entropy, high availability of energy to do work. At maximum entropy of a system, no work can be done although there is much energy. Entropy is a measure of the probability for a particular macroscopic state of a system to exist. Extra Items The fundamental concepts of algebra and calculus are assumed in this course, There will be questions on the final concerning some of these.