How to Complete Assignments

Each assignment is preceded by the following row of headings:

Asst

Introductory Problem Set

lab/activity

text

outline

Class Notes

other

query

The same headings are expanded below, with some explanation:

 

Asst (the number of the asst)

Introductory Problem Set (worked problems with explanations, to be completely mastered as a rudimentary core of understanding)

lab/activity (instructions for hands-on activities and labs, to be opened, conducted using lab materials, and submitted)

text (assignment from the text, including assigned text sections and end-of-chapter problems)

outline (there might not be any information under this heading; outline is now provided for each module)

Class Notes (click on the link and view the Class Notes (video links do not work online), or run from DVD for version with working video links; take notes)

other (miscellaneous information to help organize your knowledge, as well as some problems to be submitted early in the course)

query (document to be submitted at end of assignment, will ask about various things done in assignment, including selected assigned problems, labs, activities, class notes)

Order of tasks:

• The order in which activities are listed, from left to right, is the recommended order.  The one exception is the Class Notes, which can be viewed at any time.
• If you find that a different order works better for your learning style then you may switch the order so that it works best for you.

Objectives:

• Specific objectives for each assignment are listed in the row below the assignment.  They are listed after the assignment because only in working through the assignment can you be expected to understand all the terminology used in stating the objectives.  The objectives are intended to focus what you experience.
• Learning not a linear process.  Most of the objectives in this course take time to 'sink in'.  Full understanding of an objective first stated in a given assignment gradually develops, beginning in that assignment and continuing as it is enriched and reinforced through at least a few subsequent assignments.

• ---

  Table of Assignments, Topics, Specific Objectives

  Symbols used in this course: Note that symbols might not be correctly represented by your browser.  For this reason the Greek letters will be spelled out, with ` in front of the spelling.  You should substitute the appropriate symbol when making notes. The table below might or might not represent the symbols correctly:     `alpha a `beta b `d or `Delta D `delta d `epsilon e `lambda l `omega w `rho r `theta q `mu m `pi p `phi f `psi y `gamma g `sigma s `Sigma S `tau t
  Module 1:  Preliminary Assignment - Assignment 10 Test 1 over Module 1 is assigned as part of Assignment 10
  Orientation as instructed, including Transition to Physics II , which includes Timer, error analysis I and II, fitting a straight line, hypothesis testing time intervals, Fundamental Systems
  Asst	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  Fluids ·         Density, pressure, energy relationships, continuity and Bernoulli’s Equation. ·         Buoyancy ·         Viscosity and surface tension. Thermal Energy and Thermodynamics ·         Specific heat, calorimetry, latent heat, energy conservation. ·         Kinetic theory of gases, ideal gas laws. ·         First and second laws of thermodynamics. ·         Analysis of multi-cycle heat engines.
  Suggestion:  If you want to memorize formulas, the formula at the beginning of each bulleted paragraph is probably worth the effort.   Those formulas that aren't worth the effort are enclosed in parentheses. Fluids: P = F / A (definition of pressure). Use if you know pressure and force, or force and area, or area and pressure. `rho g h + .5 `rho v^2 + P is constant (Bernoulli's Eqn). If density `rho and gravitational acceleration g are constant, as with water near Earth's surface, we see that fluid velocity v, fluid altitude h and fluid pressure P vary in such a way that if one term goes up something else has to go down to compensate. Usually one of the three quantities will be constant so that one will go up and the other will go down. For water `rho = 1000 kg / m^3; for air `rho is about 1.4 kg/m^3. A1 * v1 = A2 * v2:  For a confined fluid, A1 * v1 = A2 * v2 (continuity equation for incompressible fluids—the amount flowing past one point is equal to the amount flowing past another). Ratio of velocities inverse to ratio of areas: v2 / v1 = A1 / A2. Remember area proportional to the square of the diameter or of the radius. Thermal Energy Transfers and Materials: `dQ = m c `dT:  The specific heat c is typically given as number of Joules per kg, per Celsius degree. Thermal energy required to raise a sample is specific heat, multiplied by number of kg, multiplied by number of degrees temp change in Celsius. In equation form, `dQ = m c `dT. `dQ / `dt = k A ( `dT / `dx):  The rate of thermal energy transfer is proportional to temp gradient `dT / `dx and temp difference: `dQ / `dt = k A ( `dT / `dx). Note t is time and T is temp. `dx is typically thickness of container. `dQ / `dt is energy transfer in Joules / sec. Kinetic Theory of Gases: One particle mass m, vel. v in cylinder length L, moving parallel to axis of cylinder exerts average force F = `d(mv) / `dt = 2 m v / ( 2 L / v) = m v^2 / L on either end. If area of end is A then: pressure = F / A = m v^2 / (L * A) = m v^2 / V, where V is volume. Noting If a single mass is divided into large number of particles and they still move parallel to the axis, there is still the same momentum change in same time interval so the above expression for pressure is not changed. KE = 3/2 (nRT):  A large number of particles wouldn't keep moving in the same direction because of collisions. The energy would rapidly get divided equally among three independent directions in space. Only one direction affects a given end of the cylinder, so now pressure is 1/3 as great as in the previous model: ·         P = 2/3 KE / V or PV = 2/3 KE ·         PV = n R T so n R T = 2/3 KE so KE = 3/2 (nRT) (n is the number of moles. To find KE per particle divide by the number of moles to get the KE of 1 mole, then by Avagadro's Number to get the KE of 1 particle.) (note for General College and especially University Physics students:   the KE referred to here is the KE of a single particle at at the rms velocity) Gas Laws: PV = n R T with R = 8.31 J / (particle Kelvin) so, for example: V2 / V1 = T2 / T1:  If P and n are constant then V is proportional to T and you can use 'straight ratios' V2 / V1 = T2 / T1 to calculate desired temp or volume. V2 / V1 = P2 / P1:  If V and n are constant then P is proportional to T and you can use 'straight ratios' V2 / V1 = P2 / P1 to calculate desired pressure or volume. P2 / P1 = V1 / V2:  If T and n are constant then P is inversely proportional to V and you can use inverse ratios P2 / P1 = V1 / V2 (note that one of the ratios is 'upside down') to calculate desired temp or volume. If you know three of the four quantities P, V, n and T you can find the fourth. Thermodynamics: When a system converts thermal energy to mechanical work as it runs through a repeating cycle, energy `dQin is transferred to the system from the 'hot source', `dQout is transferred out to the 'cold sink' and the system does work `dW. `dQin = `dW + `dQout:   Energy conservation tells us that `dQin = `dW + `dQout. efficiency = `dW / `dQin:  The efficiency of such a system is efficiency = work done by system / thermal energy transfered into system, or efficiency = `dW / `dQin . If we know two of the three quantities `dQin, `dQout and `dW we can find the third and hence compute efficiency. The maximum possible efficiency of any such system is (Th – Tc) / Th, where Th and Tc are the temperatures of the hot and cold sources.  This efficiency is theoretically achievable only by a Carnot Cycle, which consists of two adiabatic processes bounded by two isothermals.
  Assignment 00 Objectives 0.01 Observe a sequence of position vs. clock time events and present the results in a table.  knowledge of Physics I and prerequisite mathematics Technically: Observe for a sequence ot (t, x) events: {(t_i,x_i) | 0 <= i <= n}  ·         x_i and t_i are the observed or actual position and clock time of an object moving along a line, relative to a fixed point on the line and an arbitrary instant of time. ·         n is the number of clock-time-and-position observations. 0.02  For an observed series of position vs. clock time events relate position vs. clock time information to displacements and time intervals between consecutive events.  knowledge of Physics I and prerequisite mathematics Technically: Relate {(t_i,x_i) | 0 <= i <= n} U {`dt_i, `dx_i | 1 <= i <= n}  ·         `dx_i = x_i – x_(i-1) is called the displacement on the ith interval ·         | `dx_i | is the distance moved by the object corresponding to the ith interval ·         `dt_i is the time increment, or time interval, or change in clock time, corresponding to the ith interval 0.03  For an observed series of position vs. clock time events relate position vs. clock time information, displacements and time intervals between consecutive events, the definition of average rate of change, and the average rate of change of position vs. clock time for each interval.  knowledge of Physics I and prerequisite mathematics Technically: Relate {(t_i,x_i) | 0 <= i <= n} U {`dt_i, `dx_i | 1 <= i <= n} U {definition of average rate} U {average rate of change of position with respect to clock time on ith interval, vAve_i, average velocity on ith interval}  ·         Average rate of change of A with respect to B on an interval is defined to be the change in A on the interval divided by the change in B on that interval. ·         The average velocity on an interval is defined to be the average rate of change of position with respect to clock time on that interval. ·         vAve_i stands for the average velocity on the ith interval. 0.04  Relate position vs. clock time information to average velocity vs. midpoint clock time and acceleration at each clock time.  knowledge of Physics I and prerequisite mathematics Technically: Relate {(t_i,x_i) | 0 <= i <= n} U {`dt_i, `dx_i | 1 <= i <= n} U {definition of average rate} U {average rate of change of position with respect to clock time on ith interval, vAve_i, average velocity on ith interval} U {t_mid_i, `dt_mid_i, approximate average rate of change of velocity between midpoints, approximate acceleration at t_i, a_Ave_i | 1 <= i <= n-1}  0.01 – 0.04 are sequenced, each being a superset of the preceding, with new quantities underlined at each step 0.05:  Apply the definitions of uncertainty and percent uncertainty to the analysis of data.  knowledge of Physics I and prerequisite mathematics Technically: 0.05  Relate uncertainty in measured quantity value of measured quantity percent uncertainty in measured quantity uncertainty in value of a given power of measured quantity  0.06.  Use the uncertainties in two measured quantities to determine the uncertainty in the product, quotient, sum or difference of those quantities. 0.06  Relate uncertainties in two measured quantities values of measured quantities percent uncertainties in measured quantities percent uncertainty in product or quotient of measured quantities uncertainty in sum or difference of measured quantities knowledge of Physics I and prerequisite mathematics 0.07.  For a given measurement performed with a given instrument estimate the precision of the instrument, the accuracy of the measurement and the uncertainty of the measurement, and provide reasonable justification for your estimates.  knowledge of Physics I and prerequisite mathematics Technically: 0.07  Relate measurement using given instrument estimated precision of instrument estimated accuracy of measurement estimated uncertainty in measurement justification of estimate  knowledge of Physics I and prerequisite mathematics 0.08  Estimate uncertainties in measured quantities as appropriate to means of measurement (ph1 background (see also ch 1), intro asst, asst 0 query, asst 1 query)  knowledge of Physics I and prerequisite mathematics

• Asst # 00	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  00		Lab Materials Form Disk Contents Disk Contents Experiments and Problem Sets		Transition to Physics II part of intro asst			query_0 blurry video uncertainties B5. rates
  Assignment #01 Objectives  01.01.  Apply your knowledge of uncertainty to the measurement of a set of dominoes and to the ordering of their volumes. Technically: 01.01.  Relate domino measurements with largest and smallest ruler order of domino volumes uncertainty in each measurement uncertainty in volume calculation uncertainty in order of volumes knowledge of Physics I and prerequisite mathematics 01.02:  Estimate uncertainties in measuring position vs. clock time for an accelerating object and use to determine uncertainties in inferred velocities and accelerations.   knowledge of Physics I and prerequisite mathematics   Technically:   01.02. Relate for n measurements of clock time t and position x for a uniformly accelerating object percent uncertainty in x_i measurements percent uncertainty in t_i measurements percent uncertainty in inferred v_Ave_i percent uncertainty in inferred a_Ave_i percent uncertainty in slope of v_Ave_i vs. t_mid knowledge of Physics I and prerequisite mathematics 01.03.  Document the accumulation of error with successive difference quotients. deterioration of difference quotients The path from here to there: systems, diagrams, etc. sufficient to lay foundation for playing the game at your level of ability, preparation, available time and dedication
  Asst #01	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  01		Measuring Dominoes Deterioration of Difference Quotients [2] Principles of Physics students do  Brief Flow Experiment [2] Collaborative Labs Series 1 [10]					query_1 measuring a pencil, rubber band, estimate flow expt uncertainties, first- and second-diff uncertainties B6. areas
  Assignment #02 Objectives Objectives are specified in the assignment where the relevant situation is first encountered, and will typically be revisited during subsequent assignments, in the completion of which mastery is expected to build. 02.01.  Identify and explain in terms of a simple example the proportionalities among dQ/dt (rate of thermal energy transfer), L (distance between points on a flow line), A_cs (cross-sectional area of flow) and `dT/`dx (temperature gradient). Technically:  Relate {dQ/dt, k, L, A_cs, dT/dx, T_1, T_2} Introductory Problem Set, class notes 02.02. Identify and explain in terms of a simple example the proportionalities among L_0 (the original length of an object), `dL (the change in its length due to thermal expansion), A_0 (original surface area), `dA (change in surface area), V_0 (original volume), `dV (chagne in volume) and `dT (the change in its temperature). Technically: Relate {`dL, L_0, `dT, T_0, T_f, alpha, A_0, `dA, V_0, `dB, beta} Introset, class notes 02.03.  Apply the definition of specific heat to determine the quantities required to calculate it, observe those quantities and determine the specific heat. Technically: 02.03 Relate c (specific heat of an object) m (mass of the object) `dQ (change in thermal energy of the object) `dT (change in temperature of the object) T_0 (initial temperature of the object) T_f (final temperature of the object) System 5a (cylinder and mass(es) (BB’s) at vel v, elastic)   02.09.  Apply the definition of thermal conductivity to the flow of thermal energy through a wall or a bar. Technically: Relate {x_0, x_1, T_0, T_1, k, A, `dL, `dT, temperature gradient} 02.10.
  Asst #02	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  02	Set 5, Probs 10-13	General College Physics and University Physics students do Flow Experiment [2] Brief Bottlecap and Tube Setups [3] Formatting Guidelines and Conventions [2] PHeT 11.9 Gas Properties	text_02		Class Notes #03		query_2 therm energy transfer, expansion (proportionalities) univ calorimetry B7. volumes
  Assignment #03 Objectives: System 1a:  03.01.  Relate, where T_1 and T_2 are the initial temperatures of equal amounts of gas and T_f the final temperature when mixed; gas pressure constant  {T_1, T_2, T_f} 03.02.  Relate, for two samples of gas in a divided container at equal pressure, where T, V, n, m are absolute temperature, volume, number of moles and mass, {T_1, V_1, T_2, V_2, n_1, n_2, m_1, m_2, T_f} 03.03.  Relate, for two samples of the same gas in a divided container {V_1, V_2, T_1, T_2, P_1, P_2, T_f} 03.04.  Relate, for a confined gas {P, V, n, T} 03.05.  Relate, for a confined gas {P_0, T_0, V_0, N_0, P_f, T_f, V_f, N_f} All of the above objectives are addressed in the Introductory Problem Set assignments and the text assignment.
  Asst #03	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  03	Set 5, Probs 14-16	Temperature vs. Clock Time Measurements [2] Are Your Labs Posted in Readable Format? [1]	text_03				query_3 calorimetry, temp scales, gas laws univ radiation B9. surface areas _ misc
  Assignment #04 Objectives 04.01.  Apply the definition of specific heat to calorimetry problems. Technically: 04.01.  Relate for an isolated collection of n objects, where the subscript i refers to the i_th object, 1 <= i <= n c_i (specific heat of the i_th object) m_i (mass of the i_th object) `dQ_i (change in thermal energy of the i_th object) `dT_i (change in temperature of the i_th object) T_0_i (initial temperature of the i_th object) T_f (final temperature of the system) text
  Asst #04	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  04		Brief Bottle Experiments [2] Experiments to View	text_04		Class Notes #04		query_4 gas laws, energy equiv of thermal energy, univ rms vel, Units of Volume Measure
  Assignment #05 Objectives System 4:  05.01.  Observe for a system consisting of a confined gas in a bottle which also contains some water and a tube leading from the water to the surrounding atmosphere how the cross-sectional area of the tube, the volume of gas in the bottle, the volume of water displaced into the tube, and the change in the water level in the tube vary as the bottle is squeezed. Technically: 05.01.  Relate for a capped-bottle system with an open tube, where A_cs is the cross-sectional area of the tube, V_bottle the volume of the gas in the bottle, `dV_tube the volume of water displaced into the tube, `dy the change in the water level in the tube. {A_cs,`dL, V_bottle, `dV_tube, `dV_tube/V_bottle , `dV_tube/V_bottle (as %), `dy } 05.02.  Observe for a system consisting of a confined gas in a bottle which also contains some water and a tube leading from the water to the surrounding atmosphere how the pressure inside the bottle, the change in the water level in the tube, the perceived force exerted when squeezing the bottle, atmospheric pressure, the absolute temperature of the gas, the initial volume of the bottle, and the change in volume vary as the bottle is squeezed. Technically: 05.02.  Relate for a capped-bottle system with an open tube, where P is the pressure inside the bottle, `dy the change in the water level in the tube, squeeze is perceived force exerted when squeezing the bottle, P_atm, T the absolute temperature of the gas, V the initial volume of the bottle, `dV the change in volume .. {P, `dy, squeeze} {P, `dy, squeeze, P_atm} {P, `dy, squeeze, P_atm,T, V, `dV} 05.03.  Relate for a cylinder floating at equilibrium in a body of water with its axis vertical: depth of bottom of cylinder pressure at bottom of cylinder cross-sectional area of cylinder vertical force exerted by pressure on cylinder volume of submerged portion of cylinder weight of water if cylinder was full of water net force on cylinder buoyant force 05.04.  Relate for cylindrical water 'plug' of length `dL and cross-sectional area A_exit (cylinder axis horizontal) corresponding to area of outflow hole at depth y: water pressure depth net force on 'plug' work on 'plug' as it exits through hole volume of 'plug' mass of 'plug' exit velocity of plug if no energy dissipated potential energy change of system from before exit to after exit of 'plug' 05.05.  Relate for any object immersed or partially immersed in a fluid buoyant force weight density of fluid density of object volume of object volume of submerged part of object volume of water displaced mass of object mass of submerged part of object mass of water displaced weight of object weight of submerged part of object weight of water displaced force exerted by gravity on object net force on object forces on object other than gravitational or buoyant 05.07.  Relate for a bottle-and-cap system with a vertical tube and a pressure tube between two states initial and final fluid level in vertical tube initial and final lengths of air column in pressure tube density of fluid volume ratio for air column in pressure tube excess pressure necessary to support excess fluid in vertical tube atmospheric pressure volume ratio of confined gas temperature ratio of confined gas All objectives are addressed in the Introset, lab exercise, text and Class Notes for this assignment.
  Asst 05	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  05	Set 5, Probs 1-3	Raising Water in a Vertical Tube [2]	text_05		Class Notes #05		query_5
  Assignment 6 Objectives 06.01.  Relate for two points A and B within a continuous fluid pressure at point A fluid speed at point A fluid density at point A vertical position of point A pressure at point B fluid speed at point B fluid density at point B vertical position of point B KE per unit volume at each point PE per unit volume at each point PE change of small mass from point A to point B KE change of small mass from point A to point B ratio of velocities if fluid is noncompressible ratio of cross-sectional areas if fluid is noncompressible
  Asst 06	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  06	Set 5, Probs 4-6	Kinetic Model Experiment [2]	text_06		Class Notes #06		query_6
  Assignment 7 Objectives 07.01.  Relate for a bottle-and-cap system with a vertical tube and a pressure tube, between two states at constant temperature initial and final fluid level in vertical tube initial and final lengths of air column in pressure tube density of fluid volume ratio for air column in pressure tube excess pressure necessary to support excess fluid in vertical tub atmospheric pressure These objectives are met in the analysis of the lab exercise for this assignment.
  Asst 07	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  07	Set 5, Probs 7-9	Measuring Atmospheric Pressure, Part 1 [2]	text_07		Class Notes #07		query_7
  Assignment 8 Objectives: System 4: 08.01.  Determine the amount of thermal energy associated with a given change in temperature for a confined gas, Technically: 08.01  Relate for a system consisting of n moles of a monotomic or diatomic gas, where `dT is the temperature change, `dQ the thermal energy required and C_p and C_v are the specific heats at constant pressure and constant volume: {n, R, mon/diam, C_p, C_v, `dT, `dQ} 08.02.  For a single particle of given mass moving at given speed perpendicular to and colliding elastically with a piston of given cross-sectional area, with collisions occurring at a given regular time interval, apply the impulse-momentum theorem to determine the average force and average pressure exerted on the piston. Technically: 08.02.  For a single particle of mass m moving at speed v perpendicular to and colliding elastically with a piston of cross-sectional area A_cs, with time `dt between collisions, where p is the momentum, `dp the change in momentum during a collision, F_ave the average force and P_ave the average pressure on the piston: Relate {m, v, p, `dp, `dt, F_ave} Relate {m, v, p, `dp, `dt, F_ave, A_cs, P_ave} 08.03.  For a single particle of given mass moving at given speed perpendicular to and colliding elastically with the ends of a cylinder of given length and cross-sectional area, apply the impulse-momentum theorem to determine the average force and average pressure exerted on the piston. Technically: 08.03.  For a single particle of mass m moving at speed v perpendicular to and colliding elastically with the ends of a cylinder of cross-sectional area A_cs and length L, with time `dt between collisions, where p is the momentum, `dp the change in momentum during a collision, F_ave the average force and P_ave the average pressure on the piston: Relate {m, v, L, p, dp, KE }   Relate {m, v, L, `dt } Relate {m, v, L, p, `dp, `dt, F_ave, KE, A_cs, P_ave} 08.04.  For a given number of particles of equal given masses moving at given speed perpendicular to and colliding elastically with the ends of a cylinder of given length and cross-sectional area, apply the impulse-momentum theorem to determine the average force and average pressure exerted on the piston, and relate the results to the corresponding absolute temperature and total internal energy of the system. Technically: 08.04.  For a large number N of particles each of mass m_particle moving at speed v in a random direction in space, colliding elastically at an end of a cylinder of cross-sectional area A_cs and length L, where F_ave is the average force and P_ave the average pressure on the end, KE_ave the average kinetic energy and v_Ave the (rms) average velocity of the particles, n the number of moles, U the total rotational and translational KE of the particles, T the absolute temperature, n the number of moles, R the gas constant, k the Boltzmann constant, N_A Avagodro's number and the gas monatomic or diatomic: Relate {m_particle, N, v, L, F_ave, A_cs, P_ave}   Relate {T, m_particle, KE_ave, v_rms, N, n, U, C_p, C_v, monatomic/diatomic, R, k, N_A} 08.05.  For a large given number of particles of equal given masses moving at given speed, colliding randomly with one another and elastically with the walls of a cylinder of given length and cross-sectional area, apply the impulse-momentum theorem to determine the average force and average pressure exerted on the walls, and relate the results to the corresponding absolute temperature and total internal energy of the system, and to the volume of the system: Technically: 08.05.  Where in addition V is the volume, T_0, V_0, P_0, N_0 the initial temperature, volume, pressure and number of particles, `dT the change in absolute temperature, `dKE the change in KE, `dP the change in pressure, `dN the change in the number of particles Relate {m, N, v, L, Fave, A_cs, P_ave, KE_ave, V, T} Relate {direction of `dT, direction of `dKE, direction of `dP, direction of `dV, direction of `dN} Relate {`dT as percent of T_0, `dP as percent of P_0, `dV as percent of V_0, `dN as percent of N_0, `dT/T_0, `dV/V_0, `dT/T_0, `dN/N_0 | percent changes are small } 08.06.  For a thermodynamic system, where `dQ_in and `dQ_out are the heat flowing into and out of the system during a cycle, `dW the work done by the system, eff the efficiency of the system, T_c and T_h the low and high temperatures between which the system operates, eff_max the maximum possible efficiency between these temperatures, eff_Carnot the efficiency of a Carnot cycle operating between these temperatures, Relate {`dQ_in, `dQ_out, `dW, eff, T_0, T_f, eff_max, eff_Carnot} 08.07.  For a 'bottle engine' consisting of n moles of a confined monatomic or diatomic gas raising water to height y_max as is operates between states 0, 1 and 2, where `dQ is the heat input to the system during a cycles, `dPE the PE change of the system, `dU the change in the internal energy of the system and eff the ratio of PE change to input heat: Relate {P_0, V_0, T_0, n, y_max, P_1, V_1, T_1, T_f, P_2, V_2, T_2, `dQ, `dPE, `dU, eff, monatomic/diatomic} 08.08.  For a confined monatomic or diatomic gas expanding adiabatically or isothermally, where `dW is the work done by the system, `dU the change in its internal energy and `dQ the heat input: Relate {P_0, V_0, T_0, P_f, V_f, T_f, adiabatic\isothermal, `dW, `dU, `dQ, monatomic/diatomic} Objectives are covered in the text assignments, class notes and Introductory Problem Sets.
  Asst #08	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  08	Set 5, Probs 16-20	Bottle Thermometer [2]	text_08		Class Notes #08,09	Calculus in Thermo	query_8
  No new objectives for Assignment 9.  Review for test #1, which is due after completing Assignments 0 - 9.
  Asst #09	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  09		PHeT 13.31 States of Matter 15.38 Reversible Reactions	text_09		Class Notes #10,11, 12		query_9
  Module 2, Assignments 10-22
  Waves ·         Relationships among wave velocity, frequency, wavelength, density of medium, tension of medium, amplitude, energy and period. ·         Superposition of waves ·         Nature of reflection at boundaries of various types and the formation of standing waves between two points. ·         Determining wavelengths of the harmonics of a standing wave given boundary conditions. ·         Determining frequencies of harmonics from wavelengths and propagation velocity. ·         Energy in standing and traveling waves
  Waves and Optics: v = f * `lambda: The frequency f tells us how many peak-to-peak cycles of a traveling wave past in a unit of time. The wavelength `lambda tells us the distance between consecutive peaks of the wave. Thus when we multiply the frequency by the wavelength we obtain the distance travel by the disturbance in a unit of time, which is the velocity at which the disturbance propagates.  T = 1 / f:  The period T is the time required for a peak-to-peak cycle, and is equal to the reciprocal of the frequency: T = 1 / f. `omega = 2 `pi f:   The angular frequency `omega is the velocity of the point moving around the reference circle which models the simple harmonic motion of a single point as the wave passes. Since there are 2 `pi radians in a circle, `omega = 2 `pi f. y = A sin( (2 `pi f) (t - x / v) ): If the disturbance at the left-hand end of a wave traveling to the right has the form y = A sin ( (2 `pi f) t), then if the wave has propagation velocity v the disturbance will require a time delay `dt = x / v to reach position x. It follows that the disturbance at position x will satisfy the equation y = A sin( (2 `pi f) (t - x / v) ). v = `sqrt ( T / `mu ): In a uniform string whose mass per unit length is `mu = m / L, under uniform tension T, application of the impulse-momentum theorem shows that a transverse disturbance will travel at velocity v = `sqrt( T / `mu ). v = `sqrt( B / `rho):  In a liquid medium the velocity with which a disturbance is propagated is given by v = `sqrt( B / `rho), where B is the bulk modulus and `rho the density of the liquid. v = `sqrt( Y / `rho):  In a solid medium the velocity with which a disturbance is propagated is given by v = `sqrt( Y / `rho), where Y is the Young's modulus and `rho the density of the solid. v = `sqrt( `gamma * p / `rho):  In an ideal gas we have propagation velocity v = `sqrt( `gamma p / `rho), where `gamma is the ratio Cp / Cv of specific heat at constant pressure to specific heat at constant volume, p is the pressure of the gas and `rho its density. Since for an ideal gas p / `rho = RT / M, where R is the gas constant, T the temperature and M the molar mass, we can also write v = `sqrt( `gamma * R T / M). `lambda = L * (2 / n), n = 1, 2, 3, ...: For a standing wave in a linear medium, where the wave is constrained to have nodes separated by distance L, then the number of node-antinode distances spanning distance L is a multiple of 2. Since 4 node-antinode distances are required to span a wavelength, the possible wavelengths are 2 L (corresponding to 2 node-antinode spans in distance L), L (corresponding to 4 node-antinode spans in distance L), 2/3 * L (corresponding to 6 node-antinode spans in distance L), 1/2 * L (corresponding to 8 node-antinode spans in distance L), etc.. The corresponding frequencies are the f = v / `lambda values v / ( 2 L), v / (L), v / (2/3 * L), etc., making up the series 1/2 * v / L, 1 * v / L, 3/2 * v / L, 4 * v / L, summarized by the formula f = (n / 2) * v / L. The same results apply for much the same reasons when antinodes occur with separation L. `lambda = L * (4 / (2n - 1) ), n = 1, 2, 3, ... For a standing wave in a linear medium, where the wave is constrained to have nodes separated from antinodes by distance L, then the number of node-antinode distances spanning distance L is 1 plus a multiple of 2--i.e., an odd number. Since 4 node-antinode distances are required to span a wavelength, the possible wavelengths are 4 L (corresponding to 1 node-antinode spans in distance L), 4/3 L (corresponding to 3 node-antinode spans in distance L), 4/5 * L (corresponding to 5 node-antinode spans in distance L), 4/7 * L (corresponding to 7 node-antinode spans in distance L), etc.. The corresponding frequencies are the f = v / `lambda values v / ( 4 L), v / (4/3 * L), v / (4/5 * L), etc., making up the series 1/4 * v / L, 3/4 * v / L, 5/4 * v / L, 7/4 * v / L, summarized by the formula f = (2n-1)/4 * v / L. f ' = f / (1 - vSource/vSound). When a source of sound emitting pulses with frequency f is moving toward an observer with velocity vSource then if the speed of sound is vSound, the frequency detected by the observer is f ' = f / (1 - vSource/vSound). This is an instance of the Doppler Effect. f ' = f (1 + vObserver / vSound ): If an observer is moving toward a source which is emitting a sound with frequency f, then if the speed of sound is vSound the frequency detected by the observer will be f ' = f (1 + vObserver / vSound ).   This is another instance of the Doppler Effect. path difference = a sin(`theta). If waves are emitted in phase from two points separated by distance a, then if the waves are detected at a distance much greater than a, and at a position P such that a line from either source to P makes an angle `theta with the perpendicular bisector of the line segment connecting the sources, the distances traveled by the two waves will differ by distance a sin(`theta). If this path difference is equal to half of a wavelength the two waves will arrive at P exactly out of phase and the net disturbance at P will be 0. We call this destructive interference. If the path difference is equal to a whole wavelength or to any multiple of a whole wavelength the two waves will arrive at P exactly in phase and the net disturbance will be double that of either of the individual disturbances. We call this constructive interference. The condition for constructive interference is that path difference = n * `lambda for n = 0, 1, 2, .... If the path difference is equal to a whole wavelength plus a half wavelength we will again have destructive interference. The condition for destructive interference is that path difference = (n + 1/2) * `lambda for n = 0, 1, 2, ... . sin(`theta1) / sin(`theta2) = n2 / n1: Snell's Law states that if `theta1 and `theta2 are the angles of incidence and refraction for a beam of electromagnetic radiation which is directed from one material into another, then the sines of those angles are inversely proportional to the indices of refraction n1 and n2 of the two materials. The index of refraction for a material is the number n such that v = c / n, where v is the propagation velocity of the electromagnetic radiation in the material and c the propagation velocity of electromagnetic radiation in a vacuum. For most materials n varies with the wavelength of the electromagnetic radiation, which leads to the phenomenon known as dispersion. Critical Angle (angle of total internal reflection):  Total internal reflection occurs whenever the angle of incidence is greater than that for which the angle of refraction is 90 degrees. If `theta1 and `theta2 are the angles of incidence and refraction and n1 and n2 the corresponding indices of refraction, then sin(`theta2) = n2 / n1 * sin(`theta1) and if sin(`theta1) = n1 / n2, then sin(`theta2) = 1 and the angle of refraction will be 90 degrees. The value of `theta1 for which sin(`theta1) = n1 / n2 is called the critical angle.   For any angle of incidence greater that the critical angle we will have total internal reflection.
  Assignment #10 Objectives: 10.01.  Solve problems and analyze real-world situations involving the wavelength, frequency, angular frequency, and mathematical representation of a traveling wave. Technically: Relate for a traveling sine wave lambda (wavelength) f (frequency) omega (angular frequency) T (period) A (amplitude) 'time delay' between two points equation of motion of point at end equation of motion of arbitrary point waveform at given instant t 10.02.  Calculate the beat frequency of a system driven by oscillations of two independent oscillators, and explain the origin of the beats. Technically: Relate for an oscillation driven by two independent oscillators f_1 (frequency of first oscillator) f_2 (frequency of second oscillator) f_beat (beat frequency) n (number of beats occurring during time interval `dt) `dt (time interval) 10.03.  Given any of the three quantities pulse velocity, string mass, string length, string tension calculate the fourth, as well as the frequency of the first harmonic. Technically: Relate for a string: pulse velocity c string mass m string length L string tension T frequency of first harmonic Information to fulfill the Objectives is contained in the Introset assignment and Class Notes.
  Asst #10	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  10	Set 6, Probs 1-10 (phy 122 only 1-8)	Experiments to View	text_10	System 7:  2 independent pendulums:  {f_1, f_2, n, f_beat}	Class Notes #12	Practice Test	query_10 wavelength, freq, etc; per wave mth; all introset
  Assignment #11 Objectives 11.01.  Analyze the characteristics of standing waves, including frequency, wavelength, amplitude, propagation velocity and waveforms. Technically: Relate for longitudinal or transverse standing waves in a given object of given length boundary conditions positions of nodes and antinodes for fundamental oscillation lambda_1 (wavelength of fundamental oscillation) positions of nodes and antinodes for first n harmonics (n <= 4) pattern of positions of nodes and antinodes for subsequent harmonics positions of nodes and antinodes for nth harmonic lambda_n (wavelength of nth harmonic) c (propagation velocity) f_n (frequency of nth harmonic) A_max (amplitude of oscillation at antinode) A(x) (amplitude at position x) y(x, t) (position relative to equilibrium of point at position x along the object, at clock time t) sketch of y(x) for given t graph of y(t) for given x
  Asst #11	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  11	Set 6, Probs 11-13	Measuring Atmospheric Pressure, Part 2  [2] Experiments to View	text_11		Class Notes #13		query_11 harmonics univ eqn of wave
  Assignment #12 Objectives 12.02.  Apply the relationships among tension, mass, length and propagation velocity to solve problems relating to waves on a string. Technically: Relate for a traverse standing wave in string or chain under uniform tension T (tension) c (propagation velocity) m (total mass) L (length) 12.03.  Apply the principle of superposition to analyze waveforms of traveling waves and write their mathematical representations. Technically, Relate the following: waveform y_1(x), given mathematically or graphically waveform y_2(x), given mathematically or graphically superposed waveform y_1(x) + y_2(x), constructed graphically superposed waveform y_1(x) + y_2(x), represented mathematically equation y_1(t, x) of traveling or harmonic wave equation y_2(t, x)  of traveling or harmonic wave equation of superposed wave 12.04.  Apply the principle of superposition to analyze waveforms of standing harmonic waves and write their mathematical representations Technically, Relate the following: traveling sine wave y_1(t, x) traveling in positive direction, traveling sine wave y_2(t, x) traveling in opposite direction, both with common propagation speed c, frequency f and amplitude A evolution of waveform of superposed wave between two specified points boundary conditions number of harmonic matching selection of points evolution of cycle of given harmonic 12.05.  Relate traveling wave incident on fixed or free boundary reflected wave Objectives are to be achieved by continuing to work on previously assigned tasks.
  Asst #12	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  12	Set 6, Problems 1-8		text_12				query_12
  Assignment #13 Objectives 13.01.  Calculate energy and power for a wave. Technically:  Relate for a wave traveling through a medium amplitude frequency mass per unit length energy per unit length propagation velocity power For example fine the power given the amplitude, frequency, velocity of propagation and mass per unit length. Objectives are addressed in the Introset, text and Class Notes.
  Asst #13	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  13	Set 6, Probs 11-16	Initial Activities with Waves and Optics.  [2]	text_13		Class Notes #14		query_13 harmonics, energy in wave etc.x
  Assignment #14 Objectives 14.01.  Analyze the Doppler Effect for sources and/or observers moving relative to the medium. Technically:  Relate for a wave created by a source moving with velocity v_s and observed by an observer moving with velocity v_o  through a medium in which propagation velocity of the wave is c c v_o v_s f f ‘ Objectives are addressed in the Introset assignment and in the Class Notes.
  Asst #14	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  14	Set 6, Probs 17-21	PHeT 16.34 Waves on a String	text_14		Class Notes #15		query_14
  Assignment #15 Objectives 15.01.  Analyze the implications of resonant frequencies in an aluminum rod. Technically:  Relate for an aluminum rod which is supported at its middle and free at both ends length frequency of fundamental harmonic of longitudinal wave wavelength propagation velocity of sound in aluminum small change in position of support change in beat frequency as proportion of original beat frequency 15.02.  Calculate energy, power and intensity of sound waves. Relate for a sound wave pressure amplitude intensity area power of source threshold intensity decibel level Objectives are addressed in the text and lab assignments.
  Asst #15	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  15	Set 6, Problems 17-21	Experiments to View	text_15		Class Notes #16		query_15
  Assignment #16 Objectives
  Asst #16	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  16	Set 6, Problems 9-10	PHeT 16.43 Wave Interference, 17.34 Sound	text_16				query_16
  Objectives: 17.01.  Analyze straight lines representing rays of light refracted by lenses and mirrors. Relate for two broken-line paths, each defined by three points in the coordinate plane, and apply to image formation by thin lenses. coordinates of the three defining points for each path x and y intercepts of the paths point(s) of intersection of the paths triangles formed by paths with one another and with the coordinate axes sets of similar triangles and relative dimensions 17.02.  Calculate the relatationships among image and object distances, focal lengths, magnifications for thin lenses. Relate for a thin converging or diverging lens image distance object distance focal distance magnification nature of image diagrams of principle rays 17.03.  Calculate the path difference from two given points to a third given point. Relate for a given point (x_0, 0) on the x axis of the coordinate plane, two points (0, y_1) and (0, y_2) on the y axis and a wavelength length of path 1 from (x_0, 0) to (0, y_1) length of path 2 from (x_0, 0) to (0, y_2) difference in path lengths difference in path lengths as a multiple of wavelength 17.04.  For points (0, -a/2) and (0, a/2) on the coordinate plane and a wavelength lambda < a using a sketch depict the path difference corresponding to a distant observer, along paths making angle theta with the x axis calculate the path difference calculate the path difference as a multiple of lambda determine angles for which the path difference is an integer multiple of lambda determine angles for which the path difference is an integer multiple of lambda plus a half-wavelength apply to situations involving the two-slit phenomenon 17.05.  Analyze straight lines representing rays of light refracted by lenses and mirrors. Relate for two broken-line paths, each defined by three points in the coordinate plane, and apply to image formation by thin lenses. coordinates of the three defining points for each path x and y intercepts of the paths point(s) of intersection of the paths triangles formed by paths with one another and with the coordinate axes sets of similar triangles and relative dimensions 17.06.  Calculate the relatationships among image and object distances, focal lengths, magnifications for thin lenses. Relate for a thin converging or diverging lens image distance object distance focal distance magnification nature of image diagrams of principle rays 17.07.  Calculate the path difference from two given points to a third given point. Relate for a given point (x_0, 0) on the x axis of the coordinate plane, two points (0, y_1) and (0, y_2) on the y axis and a wavelength length of path 1 from (x_0, 0) to (0, y_1) length of path 2 from (x_0, 0) to (0, y_2) difference in path lengths difference in path lengths as a multiple of wavelength 17.08.  For points (0, -a/2) and (0, a/2) on the coordinate plane and a wavelength lambda < a using a sketch depict the path difference corresponding to a distant observer, along paths making angle theta with the x axis calculate the path difference calculate the path difference as a multiple of lambda determine angles for which the path difference is an integer multiple of lambda determine angles for which the path difference is an integer multiple of lambda plus a half-wavelength apply to situations involving the two-slit phenomenon   17.09.  Calculate image formation by a combination of two lenses. Relate for two lenses focal lengths position of object with respect to first lens position of image formed by first lens position of second lens position of image formed by second lens characteristics of each image 17.10.  Calculate the characterstics of refraction. Relate for a plane wave incident from one medium at a plane interface with a second: indices of refraction angle of incidence angle of refraction speed of light in each medium Objectives are addressed in Introductory Problem Sets, the text and the Class Notes.
  Asst #17	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  17	Set 6, Probs 22-24	Experiments to View	text_17		Class Notes #17, 18		query_17
  Assignment #18 Objectives 18.01.  Sketch and analyze the path of light incident on an reflected or refracted by a thin lens, a mirror or a prism.
  Asst #18	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  18		Resolving Images [2] Experiment 26:  Circular Lens and Circular Mirror   (do the experiment but don't write it up--just respond to the query program).  Note the summary document Index of Refraction from Focal Point of Liquid-Filled Cylinder [2]	text_18		Class Notes		query_18
  Assignment #19 Objectives 19.01  Sketch and analyze the path of light incident on a thick cylindrical interface.
  Asst #19	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  19		focusing_light_thru_cylindrical_lens [2]	text_19		Class Notes #20		query_19
  Assignment #20 Objectives 20.01.  Analyze image formation by a combination of thin lenses. 20.02.  Analyze interference patterns for thin films, single slits, double slits and diffraction gratings.
  Asst #20	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  20		Image Formation; Combining Lenses [2]  PHeT 25.26 Geometric Optics	text_20				query_20
  Assignment #21 Objectives 21.01.  Explain how radio waves could be polarized when passing through a series of vertical or horizontal metal posts, and whether the resulting waves would be polarized vertically or horizontally. 21.02.  Calculate Brewster's angle for light incident from a medium with index of refraction n_1 on a smooth flat surface with index of refraction n_2.
  Asst #21	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  21		Interference [2]	text_21		Class Notes #21		query_21
  Assignment #22 Objectives There are no new objectives for Assignment 22.  Review for Test #2 and take the test after completing Assignments 19-22.
  Asst #22	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  22			text_22			Partial Summary of Intro Problem Set	query_22
  Module 3, Assignments 23 - 33
  Electrostatics ·         Coulomb’s Law, electric fields, superposition of fields. ·         Gaussian surfaces ·         Energy, potential difference, potential functions. Electrical Circuits ·         Ohm’s Law, Series and Parallel Circuits, Kirchoff’s Laws, Energy Relationships Magnetism ·         Magnetic fields. ·         Interaction between magnetic fields and moving electric charges. ·         Magnetic fields as the result of moving charges. ·         Magnetic flux, EMF resulting from changing magnetic flux.
  Coulomb's Law and its Consequences: F = k * q1 * q2 / r^2, where k = 9 * 10^9 N m^2 / C^2, q1 and q2 are two point charges, r is the distance separating the charges and F is the force between the two charges. The force F is exerted on each charge by the other.  If q1 and q2 are of like sign the force will be one of attraction along the line between the two charges; otherwise the force will be one of repulsion in the direction of the line defined by the two charges. This law is known as Coulomb's Law. E = k q / r^2: The electric field E at a point P, due to a point charge q at another point Q, is the force experienced per Coulomb of test charge when the test charge is introduced at the point P. This field is directed along the line defined by P and Q, and is directed away from P if q is positive and toward P is q is negative. F = q * E: The force exerted on a charge q in electric field E is equal to the product q * E. If q is positive the force will be exerted in the direction of the field; if q is negative the force will be exerted in the direction opposite that of the field. Electrostatic Flux = 4 `pi k Q: The total electrostatic flux through a closed surface is 4 `pi k Q, where Q is the total charge enclosed by the surface. E = k Q / r^2:  If the charge distribution is spherically symmetric, then the electric field due to that distribution will be spherically symmetric about the same central point. The field will be directed radially outward from the center and will hence be perpendicular to the surface of any concentric sphere. Thus for any such sphere we have uniform electric field E = 4 `pi k Q / ( 4 `pi r^2) = k Q / r^2, where Q is the total charge enclosed by the sphere. Note that this agrees with Coulomb's Law in the case of a point charge q. E = 2 k `lambda / r:  If a charge distribution is cylindrically symmetric, then the electric field due to that distribution will be cylindrically symmetric about the central axis of the distribution. The field will be directed radially outward from the central axis and will hence be perpendicular to the curved surface of any coaxial cylinder. Thus if `lambda is the amount of charge per unit length enclosed by the cylinder, a cylinder of radius r and length L will enclose charge Q = `lambda * L. Since the curved surface of the cylinder will have area A = 2 `pi r * L, the field at the surface of the cylinder will be E = 4 `pi k Q / r^2 = 4 `pi k ( `lambda * L) / (2 `pi r * L) = 2 k `lambda / r. E = 2 `pi k `sigma:  If charge is uniformly distributed over a large plane area, then symmetry arguments show that near that plane but not close to its edges the electric field due to the distribution is very nearly perpendicular to the plane. It follows that if the charge per unit area is `sigma, then a rectangular box with its central axis oriented perpendicular to the plane, with the box intersecting the plane and having cross-sectional area A perpendicular to the plane, will contain charge Q = `sigma * A. The electrostatic flux will exit this box through its two ends and not through its sides, so the flux will be E * ( 2 A). We therefore have E ( 2 A) = 4 `pi k ( `sigma * A) and E = 4 `pi k ( `sigma * A ) / ( 2 A) = 2 `pi k `sigma. Note that as long as we remain near the plane, in the sense already specified, the electric field remains constant. Work, Energy, Potential Difference, Power: `dW(ON) = q * E * `ds: The work done ON a charge q which moves through a displacement `ds in the direction of a uniform electric field E is `dW = F * `ds = (q * E) * `ds.  The work done BY the charge against the field is the negative of this quantity. V = E * `ds. The potential difference V between two points is the work required per unit charge to move charge from the first point to the second. In a uniform electric field E the work to move a charge q through displacement `ds in the direction of the field is `dW(ON) = q * E * `ds, so the potential difference is V = `dW(ON) / q = q * E * `ds / q = E * `ds. The unit of this potential difference is the Joule / Coulomb, which is the Volt. F = q * `dV / `ds. If `dV is the potential difference corresponding to a displacement `ds in the direction of a constant electric field, then the potential gradient of the field is `dV / `ds. In this case the force on a charge q is the product of the charge and the potential gradient. `dKE = -`dW(BY). The change in the kinetic energy of a charge particle, in the absence of dissipative forces, is equal and opposite to the work done by the particle against an electrostatic field. Electrostatic fields are conservative, and the forces on charged subatomic particles within such fields usually exceed any dissipative forces to the extent that the dissipative forces are negligible. In this case energy conservation tells us that the kinetic energy change of such a particle will be equal to the work done on the system by the electrostatic field, or to the negative of the work done by the system against the electrostatic field. P = I * V: The power required to move charge at the rate I (standard unit Coulombs / sec or amps) through a potential difference V (standard unit Joules / Coulomb or volts) is the product I * V of the rate and potential difference (when we multiplied Coulombs/second by Joules/Coulomb we get Joules/second, or watts). Conduction by Charge Carriers: (Rate of charge passage = N / L * vDrift).  If there are N charge carriers uniformly distributed over a length L, then the number of charge carriers per unit length is N / L. If those charge carriers, which typically have small mass and which therefore have large thermal velocity, have an average net drift velocity vDrift along the length, then the number of charges passing a given point per unit of time is given by N / L * vDrift. Rate of charge passage = charge density * A * vDrift.  The number of charges per unit of length in a uniform conducting wire depends on the volume density of charge carriers in the wire and on the cross-sectional area A of the wire. We have N / L = charge density * A, so that the number of charges passing a given point per unit of time is charge density * A * vDrift. The average drift velocity of the charge carriers in a substance is proportional to the strength of the electric field, which is equal to the potential gradient. For a uniform conducting wire with potential difference `dV between its ends, the strength of this electric field or potential gradient is `dV / L. (Rate of Charge Passage proportional to A * `dV / L).  The drift velocity is affected by various factors that vary with temperature and from one substance to another. For given substance at a given temperature the drift velocity is proportional to `dV / L, so that the number of charges passing a given point per unit time is proportional to charge density * A * `dV / L. Since charge density also depends on the substance and temperature, we can say that the number of charges passing a given point per unit of time for a given substance and temperature is proportional to A * `dV / L. (`dV / R proportional to A * `dV / L).  The number of charges passing a given point per unit of time is the current, designated I. Thus for given substance at a given temperature I is proportional to A * `dV / L. Ohm's Law tells us that I = `dV / R, where R is the resistance of the conductor to the flow of current (see below; for the present model `dV is the voltage V across the conductor). Thus `dV / R is proportional to A * `dV / L, so 1 / R is proportional to A / L and R is proportional to L / A. R = `rho * L / A.  We call the proportionality constant between R and L / A the resistivity of the substance, and we use the symbol `rho for the resistivity. Thus R = `rho * L / A. The resistance to the flow of current is proportional to the length of the conductor (greater L implies lower potential gradient, or electrical field strength, `dV / L, which results in lower drift velocity and therefore lower current) and inversely proportional to its cross-sectional area (greater A implies more charge carriers and hence more current flow for a give drift velocity). Ohm's Law and Circuits: I = V / R. Ohm's Law expresses the fact that the current I in a conductor is proportional to the voltage across the conductor and inversely proportional to the quantity called resistance. Using V for the voltage and R for the resistance this is expressed as I = V / R. P = V^2 / R. If a voltage V is applied across a resistance R the resulting current is I = V / R. A current I passing through a potential difference V requires power P = I * V so P = (V / R) * V = V^2 / R. R = R1 + R2, series resistances. If a current I passes through two resistances R1 and R2 without branching, we say that the two resistances are in series. In this case voltages V1 = I * R1 and V2 = I * R2 are required across the resistances. Since the resistances, hence the voltages, are in series the total voltage across the combination is V1 + V2 = I * R1 + I * R2, or V = I * (R1 + R2). Thus I = V / ( R1 + R2) and we can say that the resistance of the series combination is R1 + R2. 1 / R = 1 / R1 + 1 / R2, parallel resistances: If a voltage V is maintained across a parallel combination of two resistances R1 and R2, then the entire voltage is experienced by both resistances. Hence current I1 = V / R1 flows through the first resistance and I2 = V / R2 flows through the second, giving a total current I = I1 + I 2 = V / R1 + V / R2. So I = V ( 1 / R1 + 1 / R2). Since I = V / R, we have 1 / R = 1 / R1 + 1 / R2. Capacitors and Capacitance: C = Q / V. A capacitor, when a potential difference is maintained between its terminals, stores charge in proportion to that potential difference. Capacitance is defined as C = stored charge / voltage = Q / V. C = A / (4 `pi k Q) (parallel-plate capacitor). A parallel-plate capacitor consists of two flat plates each with area A, with a uniform separation d. If charge Q is taken from one initially uncharged plate and placed on the other, then the plates will have charges Q and -Q and charge densities Q / A and -Q / A. The resulting electric fields will therefore be E1 = 2 `pi k Q / A, directed away from the first plate, and E2 = 2 `pi k Q / A directed toward the second plate. Provided d is small compared to the dimensions of the plates, between the plates the field will therefore be 4 `pi k Q / A, directed from the first plate toward the second, and outside the plates field will be zero. The voltage between the plates will be V = E * d = 4 `pi k Q / A * d, and the capacitance, defined as Q / V, will be C = Q / (4 `pi k Q / A * d) = A / (4 `pi k * d). C = C1 + C2 (capacitors in parallel). A parallel combination of two capacitors with capacitance C1 and C2 will maintain the same potential difference across both. The total charge is therefore the sum of the two charges that would result from that potential difference, and as a result capacitance is the sum of the two capacitances. 1/C = 1/C1 + 1/C1 (capacitors in series). A series combination of two capacitors with capacitance C1 and C2 will result in equal charges Q on both capacitors. This results in series voltages V1 = Q / C1 and V2 = Q / C2 so that total voltage is V = Q ( 1 / C1 + 1 / C2) and we have V / Q = 1 / C1 + 1 / C2. Since the capacitance of the combination is C = Q / V, we see than 1 / C = 1 / C1 + 1 / C2. Magnetism: B = k ' I * `dL / r^2: Magnetic fields are caused by electrical currents. A current I flowing thru a short straight segment `dL (think for example of a short segment of a straight conductor) will contribute k ' I `dL / r^2 to the magnetic field B at a point P, lying at distance r, provided that a line from the segment to P is perpendicular to the segment. k ' = 10^-7 Tesla / (amp meter). The direction of the field contribution at P is perpendicular to both `dL and to the line from the segment to P, according to the right-hand rule. B = k ' I * `dL / r^2 * sin(`theta): A current I flowing thru a short straight segment `dL will contribute k ' I `dL / r^2 sin(`theta) to the magnetic field B at a point P, lying at distance r, if the line from the segment to P makes angle `theta with the segment. If `theta is a right angle then this rule is identical to the rule of the preceding paragraph. k ' = 10^-7 Tesla / (amp meter). The direction of the field contribution at P is perpendicular to both `dL and to the line from the segment to P, according to the right-hand rule. B = 2 k ' * `pi I / a (field at the center of a single circular loop of radius a). If we add up all the k ' I `dL / r^2 contributions from a single loop of wire of radius a, adding to obtain the field at the center of the loop, we find that if the loop is in a horizontal plane and the current goes around the loop in the counterclockwise direction the magnetic field contributed by each segment is directed vertically upward. Thus all the individual k ' I `dL / r^2 contributions are in the same direction and their magnitudes add to the total magnitude of the magnetic field. Since the total `dL is equal to the circumference 2 `pi a of the loop and r = a we can replace `dL by 2 `pi a and r by a to get B = k ' I ( 2 `pi a ) / a^2 = 2 k ' * I / a. `phi = F * A * cos(`theta): The flux, designated `phi, of any constant field F which penetrate a planar surface whose area is A is equal to the product of the component of F perpendicular to the surface, and the area of the surface. Here `theta is the angle of the field F with a line perpendicular to the surface. The component of F perpendicular to the surface is therefore F * cos(`theta), and the flux is the product of this perpendicular component and the area: flux = F * cos(`theta) * A = F * A * cos(`theta). Vave = `d`phi / `dt (ave voltage = ave rate of change of electrostatic flux): When the electrostatic flux `phi = E * A cos(`theta) due to an electrostatic field E through a loop of area A is changed by amount `d`phi in a time interval of duration `dt, a potential difference with average value Vave = `d`phi / `dt is created around the loop. | Vave | = 4 * A * E * f (ave magnitude of a voltage produced when a loop of area A is rotated at frequency f in the presence of an electric field E): When a loop of area A is rotated with frequency f about an axis perpendicular to a constant electric field E, then the time required for the loop to rotate from perpendicular to parallel with the field is 1/4 of the period of rotation. The period of rotation is the reciprocal T = 1 / f of the frequency. So in `dt = 1/ 4 T = 1 / (4 f ) we have a change in flux from `phi = A * E to `phi = 0, a change of magnitude | `d `phi | = A * E. This implies average voltage vAve = `d`phi / `dt = A * E / (1 / (4 f) ) = 4 * A * E * f. F = q v B (force on a moving charge in the presence of the magnetic field, velocity and field perpendicular): When a charge q moves with velocity v perpendicular to a magnetic field B, it experiences a force F = q v B directed perpendicular to both the velocity v and the magnetic field B, with the direction determined by the right-hand rule. m v^2 / r = q v B (force on a moving charge in the presence of a perpendicular magnetic field is equal to the centripetal force on the charge): When a charge q moves with velocity v perpendicular to a uniform magnetic field B, the force being perpendicular to the velocity constitutes a centripetal force m v^2 / r. The particle will move in a circular orbit of radius r, where r is the solution to the equation m v^2 / r = q v B. v = | E / B | (velocity of a charge to particle moving in a straight line through 'crossed' electric and magnetic field): When a particle with charge q passes through uniform electric and magnetic fields which make right angles with one another, and the velocity of the particle is perpendicular to both of these fields, then if the particle travels in a straight line this means that net force on the particle is zero. This can only happen if the electrostatic force q E is equal and opposite to the magnetic force q v B, so that | q E | = | q v B |. Solving for v, the magnitude of the velocity, we easily obtain v = | E / B |. F = I L B sin(`theta) (force on a straight current segment in the presence of a uniform magnetic field): When a current I flows in a straight conductor of length L, in the presence of a magnetic field B making angle `theta with the conductor, then the field exerts a total force F = I L B sin(`theta), with the direction of the force perpendicular to both B and I, the direction determined by the right-hand rule.
  Assignment #23- 24 Objectives 23.01.  Use Coulomb's Law to determine the magnitudes of forces between charges in the coordinate plane.  Technically:   Relate each of the following sets: {q1, q2, k, epsilon_0, F, r} {q1, q2, k, epsilon_0, F, PE} where q_1 and q_2 are charges, (x_1, y_1) and (x_2, y_2) their positions in the plane, r the distance between them, F the magnitude of the force of their interaction, k = 1 / (4 pi epsilon_0) = 9 * 10^9 N m^2 / C^2, epsilon_0 the permittivity of free space, PE the electrostatic potential energy of the two-charge system relative to infinite separation (PE incorporated in asst 25). 23.02.  Use Coulomb's Law to determine the vector forces between charges in the coordinate plane.  Technically: Relate {q1, q2, k, epsilon_0, r, F_12, F_21, PE} where r is the vector from charge 1 to charge 2, F_12 the vector force exerted on charge 1 by charge 2, F_21, the force exerted by charge 1 on charge 2, PE the electrostatic potential energy of the two charges relative to infinite separation (quantities related to PE incorporated in asst 25) 23.03.  Calculate the potential energy change per unit of 'test charge' when moved through a small displacement in the vicinity of a system consisting of two charges. Technically: Relate {Q, q1, q2, (x_1, y_1), (x_2, y_2), (x, y), r_1, r_2, F_1, F_2, F, F / Q, PE, PE / Q} where (x, y) is a position different from the positions of q_1 and q_2, Q a hypothetical charge located at (x, y), r_1 and r_2 the vectors from q_1 and q_2, respectively, to (x, y), F_1 and F_2 the forces exerted on Q by q_1 and q_2, F (quantities related to PE incorporated in asst 25) 23.04.  Calculate the potential energy change per unit of 'test charge' when moved through a small displacement in the vicinity of a system consisting of a number of charges.  Technically: Relate {q_i, (x_i, y_i), F_i | i = 1, ..., n} U {Q, (x, y), F, E_i, E, PE_system} where q_i is the ith of n charges, (x_i, y_i) its position, F_i the force of the ith charge and F the net force exerted by the n charges on the charge Q at (x, y), PE_system the total electrostatic potential energy of the n charges relative to infinite separation, E_i the contribution of the ith charge to the electric field at (x, y), E the electric field at (x, y) due to the n charges.
  Asst #23	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  23	Set 1, Probs 1-5	Collaborative_labs_II [10]			Class Notes #26	Physics I Initial Problem Sets:  Vectors Overview of Electrostatic Forces, Fields and Energy	query_23
  Assignment #24 Objectives Assignment 24 Objectives Continue Assignment #23 Objectives
  Asst #24	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  24	Set 1, Probs 6-9	PHeT 18.10 Balloons and Static Electricity	text_24		Class Notes #27		query_24
  Assignment #25 Objectives 25.01.  Use the 'flux picture' to calculate the force per unit test charge, due to a single actual charge, at a given distance from that charge.  Technically: Relate for a sphere with a single point charge at its center, where phi is the electrostatic flux through the sphere, Q the charge, a the radius of the sphere, E the magnitude of the electric field at a point on the surface of the sphere, q a charge at distance r from the center, PE(r) the electrostatic potential energy of the system, V(r) the electrostatic potential at the position of q due to the charge Q. {Q, phi, A, E, q, r, PE(r),  V(r)} 25.02.  Calculate the change in electrostatic potential between two points in a field that can be considered uniform between the points.  Technically: Relate {F, E, `ds, q, `dW_on, `dPE_elec, `dV} where F is the force exerted on charge q at a certain position, E the field at that position, `ds a displacement of q small enough that the field E does not change significantly, `dPE_elec the change in the electostatic potential energy due to the displacement of q, `dW_on the done on q by the field during the displacement, `dV the change in electrostatic potential between the initial and final positions of q
  Asst #25	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  25	Set 1, Probs 10-23	PHeT 18.21 Electric Field of Dreams			Class Notes #28		query_25
  Assignment #26 Objectives 26.01.  Relate for current I in a short segment of length `dL in a charge carrier in the presence of magnetic field B, where `dF is the force exerted by the field on the segment: {I, B, `dL, `dF} 26.02.  Relate for a circuit element with resistance R, where I is the current through the element and V the potential difference across the element: {I, R, V} 26.03.  Relate {P, I, V, R} for a circuit element with resistance R, where I is the current through the element and V the potential difference across the element, and P is the power required to maintain the current. 26.04.  Relate for long cylinder carrying an axially symmetric charge distribution of density lambda, where phi_E is the electrostatic flux of the distribution, a its radius and E the magnitude of the electric field at distance r from the cylinder (where the distance from the point to the nearest end of the cylinder is much greater than r):  {Q_enclosed, lambda, L, phi_E, a, E, r} 26.05.  Relate for a plane distribution of constant charge density, at a point much closer to plane than to any of its edges:  {`dA, sigma, `dQ, phi_E, N, E} where sigma is the charge density, N a vector normal to the surface, `dA is the area of a cross section in a plane perpendicular to N of an appropriately positioned rectangular 'box' all of whose points are much closer to the plane than to any of its edges, `dQ the charge enclosed in the box, phi_E the electrostatic flux through an end of the box and E the electric field at the point. 26.06.  Relate for a parallel-plate capacitor in air, where A is the area of each plate, d the separation, E the electric field between the plates, V the potential difference between the plates, C the capacitance and Q the magnitude of the charge on each plate: {A, d, E, V, Q, C} 26.07.  Relate for two conducting elements of the same material, each of constant cross-section both subject to the same potential difference V between its ends: {A_cs_1, A_cs_2, I_1, I_2, L_1, L_2} where A_cs indicates cross-sectional area, I current, L length of the conductor in the direction normal to the cross-section.
  Asst #26	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  26	Set 2, Probs 1-5	Current Flow and Energy [3] PHeT 21.42 Circuit Construction Kit DC, 23.10 Faraday's Electromagnetic Lab	text_26		Class Notes #22		query_26
  Asst	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  Assignment #27 Objectives 27.01.  Relate {C, Q, I, R, V_s, V_c, `dt, `dQ, `dV_c}, for a series circuit consisting of a source, a capacitor and a resistance element, with V_s is the voltage of the source, C the capacitance, Q the charge on the capacitor, V_c the voltage of the capacitor, I the current, R the resistance, `dt a short time interval, `dQ the change in the charge on the capacitor, `dV_c the change in the voltage across the capacitor. 27.01.  Relate {V, R_1, R_2, `dV_1, `dV_2, I_1, I_2} for a series or a parallel circuit with two resistance elements, where V is the voltage of the course, R_1 and R_2 the two resistances, `dV_1 and `dV_2 the respective voltage drops, I_1 and I_2 the currents through the respective resistors.
  Asst #27	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  27	Set 3, Probs 1-6	Capacitors and Current, Voltage and Energy [3] PHeT 25.53 Circuit Construction Kit AC	text_27		Class Notes #30, 31		query_27
  Assignment #28 Objectives 28.01.  Relate for short current segment `dL, position r relative to `dL, the magnetic field contribution `dB at that position; theta is the angle of `dL with respect to r {`dL, `dB, I, r, theta} 28.02.  Relate {I, orientation, a, B}  for a circular current loop of radius a in which a current I flows with a given orientation, B the magnetic field at the center of the loop. 28.03.  Relate for a plane region of area A, electric field of magnitude E whose angle with respect to the specified normal of the plane is theta,  phi_E the flux of the electric field through the region {E, theta, A, phi_E}
  Asst #28	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  28	Set 4, Probs 1-7	Batteries, Circuits and Measurement of Voltage and Current. [3]	text_28		Class Notes #22		query_28
  Asst	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  Assignment #29 Objectives 29.01.  Solve problems related to voltage induced by changing magnetic flux. 29.02.  Explain self-induction. 29.03.  Relate for a plane region of area A, magnetic field of magnitude B whose angle with respect to the specified normal of the plane is theta,  phi_B the flux of the magnetic field through the region {B, theta, A, phi_B} 29.04.  Relate for a plane region of area A, magnetic field of magnitude B whose angle with respect to the specified normal of the plane changes from theta_1 to theta_2 it time interval `dt,  phi_B_1 the flux of the magnetic field through the region at the beginning of the interval and phi_B_2 the same quantity at the end, `dPhi_B the change in flux, ave_Rate the average rate of change of flux with respect to clock time, V_ave the approximate average induced voltage: {B, theta, A, phi_B_1, phi_B_2, `dPhi_B, ave_Rate, V_ave}
  Asst #29	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  29	Set 4, Probs 8-13	Charging and Discharging a Capacitor. [3]	text_29		Class Notes #23		query_29
  Assignment #30 Objectives 30.01.  Relate for charge q moving with velocity v in electric field E and magnetic field B, where F_E and F_B are the forces exerted by the respective fields {q, E, B, v, F_E, F_B} 30.02.  Relate for segment `dL carrying current I, in the presence of magnetic field B, where `dF is the force exerted on the segment, {`dL, B, I, `dF }
  Asst #30	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  30	Set 4, Probs 14-18	The RC Circuit [3]	text_30		Class Notes #24,25		query_30
  Assignment #31 Objectives Continue mastery of previous objectives.
  Asst #31	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  31	Set		text_31		Class Notes #31, 32		query_31
  Assignment #32 Objectives Continue mastery of previous objectives.
  Asst #32	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  32	Set
  Assignment #33 Objectives Continue mastery of previous objectives.  Complete review of Assignments 23-33.  Test #3 should be completed after Assignment 33.
  Asst #33	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  33	Set
  Module 4, Assignments 34 - 40 "Modern" Physics ·         Time dilation, length contraction, mass-energy. ·         Photoelectric effect, quantization of energy. ·         Uncertainty principle. ·         Atomic spectra, quantization of angular momentum, atomic structure. ·         Modes of nuclear decay, energy conservation.
  Quantization of Energy in Electromagnetic Radiation: c = `lambda * f: Light, and generally all electromagnetic radiation, is characterized by a uniform speed c of approximately 3 * 10^8 m/s in a vacuum, and by a spectrum of wavelengths `lambda, which can be measured using diffraction gratings and photographic plates. Frequencies are easily determined once wavelengths are measured. E = h * f: The photoelectric effect demonstrates that electromagnetic radiation with frequency f transfers energy in discrete amounts equal to the product of Planck's constant h = 6.63 * 10^-34 J s and the frequency of the radiation. In this sense electromagnetic radiation behaves as a stream of photons, particles which carry energy but which have no mass. p = E / c: A photon with energy E will have momentum p = E / c. Wave Properties of Particles: `lambda = h / p: A beam of massive particles (i.e., particles with mass) each with momentum p will exhibit interference effects identical to those of a wave having wavelength `lambda = h / p, where h is Planck's constant.  This wavelength `lambda is called the deBroglie wavelength. `dx * `dp = h (uncertainty principle): The uncertainty in x, the position of an object, and p, the momentum of the object, are denoted by `dx and `dp. It is not possible to measure both position and momentum to an arbitrarily high degree of precision. The more precisely one is measured the less precisely is possible to determine the other. The product of the uncertainties is approximately equal to Planck's constant. i.e., `dx * `dp = h. Quantization of Orbital Energies in Atoms: m v^2 / r = k q^2 / r^2 (condition relating velocity and radius of 'orbit' of electron around proton). If an electron 'orbits' a proton at a distance r, then the velocity must be such that the Coulomb attraction k q^2 / r^2 (q = charge of electron) between the proton and electron constitutes the centripetal force m v^2 / r required to maintain the circular path. This relationship can easily be solved for v in terms of r, obtaining r = k q^2 / (m v^2). m * v * r = n ( h / (2 `pi) ), n = 1, 2, 3, ... . (quantization condition for angular momentum): Angular momentum can occur only in whole-number multiples of h / ( 2 `pi ). Combining this quantization condition on the angular momentum m * v * r with m v^2 / r = k q^2 / r^2 we conclude that for an electron orbiting a proton, only certain orbital radii and their associated velocities and energies can occur. The resulting model explains to a high degree of precision the spectrum observed as a result of energy transitions within a hydrogen atom. r = n^2 h^2 / ( 4 `pi^2 k q^2 m) = n^2 * .509 *10^-10 m approx., n = 1, 2, 3, ... . (possible radii of electron orbit around proton) Combining m v r = n ( h / (2 `pi) ), the quantization condition on angular momentum, with m v^2 / r = k q^2 / r^2, which states that Coulomb Force = centripetal force, we obtain r = n^2 h^2 / ( 4 `pi^2 k q^2 m). Using h = 6.63 * 10^-34 J s, k = 9 * 10^9 N m^2 / C^2, q = 1.60 * 10^-19 Coulombs and m = 9.11 * 10^-31 kg (mass of electron) we find that h^2 / ( 4 `pi^2 k q^2 m) = .509 * 10^-10 m, approx., so we can write r = n^2 * .509 Angstroms (approx).  An Angstrom is 10^-10 meter. 2 `pi r = n * `lambda   (orbital radius contains an integer number of particle waves):  For an orbital radius satisfying the quantization condition, the circumference of the orbital is a whole number of deBroglie wavelengths, suggesting that the electron in forms allowed orbits by creating a standing wave in each. Conversion between Mass and Energy and Nuclear Decay Modes: E = m c^2: As predicted by Special Relativity and as confirmed by experiment, mass can be converted to energy and vice versa. The energy equivalent to mass m is E = m c^2. Alpha decay consists of the emission of a helium nucleus (2 protons and 2 neutrons all bound together) from the nucleus of a larger atom (i.e., one containing in its nucleus more than 2 protons and 2 neutrons). This process reduces the number of protons and neutrons in the larger nucleus each by 2. The mass of the resulting nucleus plus the mass of the alpha particle is less than the mass of the original nucleus. The resulting mass defect appears in the form of kinetic energy as the alpha particle and the remains of the original nucleus fly apart in opposite directions. In the usual case, where the alpha particle is much less massive then the remains of the original nucleus, almost all of this kinetic energy resides in the alpha particle. Beta decay consists of the emission of an electron from the nucleus of an atom. This process results when a neutron decays into a proton and an electron (note that the total charge is conserved--the original neutron has zero charge, and a proton and an electron have a net charge of zero). This process thus increases the number of protons in the nucleus by 1 and reduces the number of neutrons by 1. The mass of the resulting nucleus plus the mass of the beta particle (the electron) is less than the mass of the original nucleus. The resulting mass defect appears in the form of kinetic energy as the electron and the new nucleus fly apart in opposite directions. Since the electron is very much less massive then the new nucleus, virtually all of this kinetic energy resides in the electron. Gamma decay is analogous to a decrease in the orbital energy of an electron in an atom, but Gamma decay takes place within the nucleus and involves nuclear particles. The energies within the nucleus are much higher than the energies of atomic electrons, and the energies of the Gamma photons are hence much greater than the energies emitted by atomic electrons. The nucleus after a Gamma decay is less massive than before, and the mass defect is carry off by the energy of the photon. Special Relativity: `dt ' = `dt * 1 / (1 - v^2 / c^2) (time dilation): Einstein's Theory of Special Relativity is based on the assumption that the laws of physics are the same in all interial reference frames. One consequence of these laws is that the speed of light in a vacuum is c = 3 * 10^8 m/s, approx.. If we consider a photon bouncing back and forth in the vertical direction between two mirrors in a spaceship which passes at velocity v in the horizontal direction, we are led to the conclusion that the time between round trips as measured by an occupant of the spaceship will be different than the time between round trips as measured from our frame of referencet. Specifically if in our frame of reference we measure a time interval `dt ' between two events which occur at the same location as observed by the occupants of the passing spaceship while the occupants of the spaceship measure time interval `dt, our time interval `dt ' will be greater than `dt by factor 1 / (1 - v^2 /c^2).  The contraction of length and the increase of mass, as well as the relative nature of simultaneity, also follow (see below). `dx ' = `dx * `sqrt(1 - v^2 / c^2) (length contraction): If a spaceship passes us moving moving at velocity v relative to our frame of reference, and if as measured by the occupants of the ship its length in the direction of its velocity is `dx, then the most accurate measurements in our frame of reference will determine that the length of the ship is `dx ' , which is less than `dx by factor `sqrt(1 - v^2 / c^2). m ' = m * 1 / `sqrt( 1 - v^2 / c^2) (relativistic mass): If a spaceship passes us moving moving at velocity v relative to our frame reference has mass m, as measured by the occupants of the spaceship (who could, for example, measured the acceleration and the net force applied to the spaceship to determine its mass), then any measurement made in our frame of reference to determine the mass will indicated that the mass is m ' , which is greater than m by the factor 1 / `sqrt(1 - v^2 / c^2). Relative nature of simultaneity: If a spaceship passes us moving moving at velocity v relative to our frame reference, then two events that occur simultaneously but at different locations as measured by the occupants of the spaceship will not occur simultaneously in our reference frame. KE = m c^2 / `sqrt(1 - v^2 / c^2 ) - m c^2.  If a spaceship with mass m, as measured in the frame of reference of the spaceship, passes us moving moving at velocity v relative to our frame reference, then its kinetic energy will be m c^2 / `sqrt(1 - v^2 / c^2 ) - m c^2. For velocities v which are small compared to c, this expression reduces to .5 m v^2. The expression for kinetic energy can also be written by factoring the m c^2 out, obtaining m c^2 ( 1 / `sqrt(1-v^2/c^2) - 1). This form suggests a 'rest energy' of m c^2, to which kinetic energy is added as velocity increases. Correspondence Principle: The Correspondence Principle states that the results of relativistic mechanics reduce, at small relative velocities v, to the results of classical Newtonian mechanics. Stated another way, there must be a smooth transition from the everyday physics of low relative velocities to the relativistic physics of high relative velocities. Brief Notes about Particle Physics: If a particle such as a proton or and electron is accelerated, usually by means of electromagnetic forces, to a high relativistic velocity then the possibility exists that the total energy of the particle can be converted to other particles. This usually happens when the particle interacts with other particles. The rest mass of the particles so created can exceed the rest mass of the original particles as some of the kinetic energy of the original particles converts to mass. This conversion satisfies the equation E = m c^2. When new particles are created a number of conservation laws apply. The total energy of the particles involved is the same before as after collision, provided we include the energy equivalent E = m c^2 of the rest mass of the particles as part of the energy. Momentum must be conserved (keeping in mind that we're talking about relativistic momentum m v * 1 / `sqrt(1-v^2/c^2). Electric charge must be conserved (for example the total charge after a collision involving a proton and a neutron must be the same, +1, as before the collision). Other more subtle conservation laws also apply. These conservation laws lead to a classification of the hundreds of different particles observed and of their properties. This classification leads to a very successful mathematical model which successfully predicts the nature of particles prior to their being observed. This model is called the Quark Theory. It is believed that protons, neutrons and hundreds of other particles are in fact combinations of more fundamental particles called Quarks.
  Assignment #34 Objectives 34.01. Solve problems involving the particle nature of light and the wave nature of particles. 34.02. Apply the uncertainty principle to approximate the characteristics of an electron confined to the vicinity of a proton, and a proton confined within a nucleus. 34.03. Relate where h is Planck's Constant, f the frequency of electromagnetic radiation, lambda its wavelength and c its propagation velocity {h, f, c, lambda, photon energy, photon momentum} 34.04. Relate where m, v, KE and p are the mass, velocity, kinetic energy and momentum of a particle and lambda its deBroglie wavelength {m, v, KE, p, lambda, h} 34.05. Relate where `dp, `dx and `dv are the uncertainties in momentum position and velocity of a particle, m its mass {`dp, `dx, `dv, m, h}
  Asst #34	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  34	Set 7, Probs 1-6				Class Notes #34
  Assignment #35 Objectives 35.01.  Relate for an electron in a classical circular orbit about a proton, where m_e is the mass of electron, v its oribtal velocity, r its distance from the proton, F_coul the Coulomb attraction between the particles, F_centrip the classically-predicted centripetal force, KE and PE the kinetic and potential energies of the orbit (PE relative to infinite separation) {m_e, v, KE, r, F_coul, F_centrip} 35.02.  Relate for the preceding situation with the additional quantization condition on angular momentum, where lambda and circumf are the deBroglie wavelength of the electron and circumf the circumference of the classical orbit {m_e, v, KE, PE, r, F_coul, F_centrip, n, angular momentum, lambda, circumf} 35.03.  Relate where n_1 and n_2 are angular momentum quantum numbers, `dKE and `dPE the kinetic and potential energy changes for the Bohr model of the hydrogen atom, f the frequency of the photon associated with the change in orbit {n_1, n_2, `dKE, `dPE, f} 35.04.  Relate where E is the energy equivalent of mass m and c the speed of light {E, m, c}
  Asst #35	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  35	Set 7, Probs 7-12				Class Notes #35
  Assignment #36 Objectives 36.01.  Analyze masses of two given isotopes of a given element to determine if a given transition is possible. 36.02.  Given the information in a periodic table of elements and their isotopes, identify possible decay chains involving alpha, beta and gamma decays. 36.03.  Relate where E is the energy equivalent of mass m and c the speed of light, lambda the wavelength of a photon with equivalent energy {E, m, c, lambda} 36.04.  Relate where N_p is the number of protons and N_n the number of neutrons in a nucleus, m_p and m_n the masses of proton and neutron (masses in SI units, AMU or equivalents), m_nucleus the mass of the nucleus, ' indicates properties of the resulting nucleus after a nuclear transition, m_defect the mass defect associated with the transition and E the energy released by the transition: {N_p, N_n, m_p, m_n, m_nucleus, N_p', N_n', m_p, m_n, m_nucleus', E} 36.05.  Relate where N_p is the number of protons and N_n the number of neutrons in a nucleus, ' indicates properties of the resulting nucleus after a nuclear transition, and transitionType indicates the type of transition (alpha, beta, gamma) {N_p, N_n, N_p', N_n', atomicNumber, atomicNumber', transitionType} 36.06.  Relate where all quantities have been defined in preceding objectives {N_p, N_n, N_p', N_n', m_p, m_n, m_particle, atomicNumber, atomicNumber', transitionType} 36.07.  Relate where E_bind is total binding energy, E_per is binding energy per nucleon, other quantities as previously defined: {E_bind, E_per, m_p, m_n, m_nucleus}
  Asst #36	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  36	Set 7, Probs 13-19				Class Notes #36
  Assignment #37 Objectives 37.01.  Relate where v is the relative velocity of two reference frames, L and L ' the lengths of a given object as measured in the two frames, `dt and `dt' the time interval between two events as measured in the two frames, m and m ' the masses of a given object as measured in the two frames: {v, c, L, L', `dt, `dt', m, m'}
  Asst #37	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  37	Set 7, Probs 20-23				Class Notes #37
  Assignment #38 Objectives Continue mastering previous objectives, review.
  Asst #38	Introductory Problem Set	lab/activity	text	outline	Class Notes	other	query
  38	Set 7, Probs 24-27				Class Notes #38
  Assignment #39 Objectives Continue mastering previous objectives, review. Complete Test #4.  This test must be in the instructor's possession by the end of the last day of Final Exams.
  Asst #39	Introductory Problem Set	lab/activity	text	outline	Class Notes	other
  39
  Asst #40	Introductory Problem Set	lab/activity	text	outline	Class Notes	other
  40