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Physics 7CDiscussion/Lab Manual

PowerFrequency f1

Volume

(L1 = L2 ≈ 0)

PowerFrequency f2

Volume

Power Turn “VOLTS/DIV” to 2 m - 10 m settings

Turn “SEC/DIV” to 0.1 s

Flip both toggle switches up

Always use “~” and “10V” toggle settings; make sure speaker volumes are equal

Winter Quarter 2003 ArchivesUniversity of California, Davis

©Dr. Patrick M. Len, Ph.D

03.03.15

What's on the cover?Beats is the phenomenon of superposition of two sound waveswith different wavelengths .

In this experiment, an oscilloscope displays the sounds detectedby a microphone, which is located near two speakers that producesounds with different wavelengths. By varying the differencebetween the frequencies of the two generators, the beat andcarrier frequencies of the superposed waves will vary.

This is one of the several experiments you will perform and writeup as lab reports in Physics 7C. However, these lab reports areinformal in the sense that they are definitely not graded onformatting, but instead the emphasis is on conceptual understanding,identically to how a quiz question will be graded. Thus these labreports should be considered an opportunity to gauge yourunderstanding midway through a Block, well before the end-of-Block quiz actually takes place!

(See beat frequency , beats , carrier frequency ,superposition , wavelength , waves (sound) .)

Dedicated to my wonderful wife, H. M.

A "Waifer X® Industries, Inc. Book"™

Copyright © 2003 by Patrick M. Len([email protected]). This material may bedistributed only subject to the terms andconditions set forth in the Open PublicationLicense v1.0 without options A or B(http://www.opencontent.org/openpub/).

Physics 7C Winter 2003: Discussion/Lab Manual 1

03.03.18

Physics 7C Discussion/Lab ManualWinter Quarter 2003Constants and Conversion Factors 2Block 11 Discussion/Lab Activities 3

DLM 01 3DLM 02 7DLM 03 15

Block 12 Discussion/Lab Activities 19DLM 04 19DLM 05 24DLM 06 30DLM 07 37


Block 14 Discussion/Lab Activities 64DLM 12 64DLM 13 70DLM 14 76


Winter 2003 Quiz Archives 101Quiz 11 102Quiz 12 104Quiz 13 106Quiz 14 107

2 Physics 7C Winter 2003: Discussion/Lab Manual

03.03.18

Constants and Conversion FactorsConstants

G gravitational constant 6.67 ×10−11 N ⋅ m2 / kg2

k electric force constant 8.99×109 N ⋅ m2 / Coul2

µ0 magnetic permeability 1.26 ×10−6 Tesla ⋅ m / Ampsc velocity of light 3.00 ×108 m/sme mass of the electron 9.11×10−31 kg = 0.0005486 ump mass of the proton 1.6726 × −10 27 kg = 1.00728 umn mass of the neutron 1.6750 × −10 27 kg = 1.00866 ue fundamental charge 1.602 ×10−19 Coulh Planck's constant 6.626 ×10−34 J·skB Boltzmann's constant 1.38 ×10−23 J/K

Terrestrial constantsgE gravitational field magnitude9.8 N / kg

(at or near Earth's surface)ME mass of the Earth 5.98 ×1024 kgRE radius of the Earth 6.37 ×106 m

Conversion factorsEnergy1 eV = 1.602 ×10−19 J1 MeV = 1×106 eV1 "kiloton" of TNT = 4.184 ×1012 J1 cal = 4.184 J1 kcal ("food Calorie") = 4,184 J

Length1 m = 39.37 in = 3.281 ft1 km = 0.6214 mile1 Å (angstrom) = 10−10 m1 nm = 10−9 m1 fm = 10 15− m

Speed1 m/s = 3.28 fps (ft/s) = 2.24 mph (miles/hr) = 3.60 kph (km/hr)

Force1 N = 0.225 lb

Mass1 kg = 0.0685 slugs

1 u = 1.66054×10−27 kg = 931.5 MeV/c 2 = 1.49242× −10 10 J

" "2c


03.03.18

Activity Cycle 11.1.1: Analyzing SHM parametersA. Experimental measurement of mass-spring periods. Work at the board as a group and

put your results up as you work, in order that your TA can gauge your progress.

* 1. Provide sufficient experimental proof that the period T is either proportional or inverselyproportional to each of the mass-spring system parameters listed below:(a) Amplitude A.(b) Mass m.(c) Spring strength k. (You can "reduce" spring strength relative to a single spring by

hooking two springs in series, and "increase" spring strength by hooking twosprings in parallel, or "folding" a spring in half).

(d) The maximum velocity vmax that the mass has as it passes through equilibrium.(e) The gravitational constant g.

(Hint: when you measure your periods, pull your mass back from equilibrium, and start yourcount with "0" as soon as you let go of the mass (while starting your timing). Each time themass comes back to your starting position, count "1", "2", "3", etc. Stop counting/timing whenit comes back to your starting position for the tenth time. The period is your time divided by10. Look for significant dependencies, and not random experimental variation in yourresults.)

* 2. From your results in (1), decide whether each of the parameters (a)-(e) are "restoringforce" parameters, "inertial" parameters, or parameters that have no significant effect onthe period T of a mass-spring system.

* 3. Choose one specific set of measurements from (1), and calculate the expected value of theperiod of your mass-spring system (find k for this from the force diagram of the mass, atrest). What is the percent error with your experimentally measured period?

B. Experimental measurement of pendulum periods. Work at the board as a group andput your results up as you work, in order that your TA can gauge your progress.

* 4. Provide sufficient experimental proof that the period T is either proportional or inverselyproportional to each of the pendulum system parameters listed below:(a) Amplitude A.(b) Mass m.(c) String length L. (This is measured from where it hangs to the CM of the mass!).(d) The maximum velocity vmax that the mass has as it passes through equilibrium.(e) The gravitational constant g.

* 5. From your results in (4), repeat (2) above, but for the period T of a pendulum system.

* 6. Choose one specific set of measurements from (3), and calculate the expected value of theperiod of your pendulum system. What is the percent error with your experimentallymeasured period?


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Activity Cycle 11.1.2: Graphical representations of SHM

A. Constructing experimental SHM systems. Your TA will assign your group one of thefollowing SHM systems (a)-(f) to demonstrate to the whole class. You do notnecessarily have go through (1)-(3) in order. Work at the board as a group and putyour results up as you work, in order that your TA can gauge your progress.

(a) A mass-spring system with an amplitude of 2.0 cm, period of 0.5 s, and starts off atequilibrium at t = 0.0 s, with a negative velocity.

(b) A mass-spring system that starts off at y = +5.0 cm at t = 0.0 s, and then passesthrough equilibrium at t = 0.25 s.

(c) A mass-spring system with an amplitude of 5.0 cm, period of 2.0 s, and starts off atsome unknown positive y location at t = 0.0 s, already heading towards equilibrium,which it then passes through at t = 0.25 s.

(d) A pendulum system starts off at θ = –60° at t = 0.0 s, and then passes throughequilibrium at t = 0.125 s.

(e) A pendulum system with an amplitude of 30°, period of 1.0 s, and starts off atequilibrium at t = 0.0 s, with a positive velocity.

(f) A pendulum system with an amplitude of 45°, period of 2.0 s, and starts off at someunknown positive y location at t = 0.0 s, already heading away from equilibrium,which it then passes through at t = 0.75 s.

If your group has a mass-spring system, you must experimentally determine the strengthk (in N/m) of your spring. (You can use your data from the previous activity, or make anew measurement using the stretch distance of the spring, and a force diagram.) If yourgroup has a pendulum system, the angle between 6:00 and 5:00 on an analog clock face(how many ° is that?) can be used to measure off your θ angles.)

* 1. Determine the following physical and SHM parameters for your system:A = ______ m (or °).T = ______ s.ψ = ______ rad.m = ______ kg.L = ______ m (if a pendulum system).k = ______ N/m (if a mass-spring system).

* 2. Re-enact your SHM system, to be demonstrated later to the whole class. Ensure that yourSHM system has the correct period, and starts off in the appropriate manner at t = 0.0 s.Be sure to specify where your equilibrium is, and where the ± directions are with respectto the equilibrium.

* 3. Graph your SHM system motion on a y(t) or θ(t) graph, from t = 0.0 to 2.0 s. Indicate onyour graph the first instant in time that your mass passes through equilibrium. (It isprobably easiest if you draw a generic sine curve first, and then put in on your graph theaxes and scales after you are sure of where it "starts" and how big/long it is.)


03.03.18

DLM 01 Exit handoutAnnouncements The Physics 7C Student Packet, Winter Quarter 2003 (P. M. Len,2003) is available from Navin's Copy Shop (231 Third Street; 758-2311)for a nominal fee. Quiz 11 will be given during lecture 9:00-9:35 am on Friday,January 24, and will cover the material in Block 11. (Note that January 24is an "Academic Monday," and by decree of the Office of the Registraryou are required to attend all of your Monday classes on that day.) Bringa pen or pencil, calculator, and prepare to show your UC-Davis student IDcard (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Read the Academic Calendar and Course Policy (pp. 3-13) in the Physics 7C Student Packet,

Winter 2003 (or download the Course Policy excerpt from the Physics 7C website athttp://physics7.ucdavis.edu). Students are to be considered informed of the dates and times ofthe quizzes and Final Exam, and of any and all of the contents of the Course Policy.

2. Review the Block 11 Glossary (pp. 25-31) in the Physics 7C Student Packet, Winter Quarter 2003,and familiarize yourself with the following terms that will were introduced here in DLM 01.

amplitude Aconstant phase angle ψSHM

derivatives (trigonometric)displacement y, θequilibriumfrequency fgravitational field

constant g

mass-spring SHMoscillationspendulum SHMperiod Tsimple harmonic motion

(SHM)spring constant kvelocity vy

3. Read the Block 11 Glossary (pp. 32-48) in the Physics 7C Student Packet, Winter Quarter 2003,and familiarize yourself with the following terms that will be used extensively in DLM 02.

amplitude Aconstant phase angle ψwave

"coordinated motion"dependent wave parameterdisplacement yequilibriumfrequency fharmonic waveindependent wave

parameters

location xmediumperiod Tpolarizationpulse wave"snapshot"wave velocity vwave

waves, pressure/density("sound")

wavelength λ


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4. The general form of the equation that describes any harmonic wave is given by:

y x t At x

wave, sin( ) = π ± π +

2 2T λ

ψ .

Let's "freeze out" time in this complicated equation (by setting t equal to a specific time), andthen simplify as much as possible. Use the (+) sign for the (±) choice, amplitude A = 0.5 m,period T = 0.4 s, wavelength λ = 2.0 m, and constant phase ψwave = π in order to rewrite thiswave equation as a function of x only, using the above parameters, for the following timesbelow. For the t and ψwave terms, cancel and simplify as much as possible. For the x term, donot cancel out the 2π factor. Also plot each of these y(x) graphs.

(a) t1 = 0.0 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.0 s

1.0 2.00.0

+0.5

–0.5x [m]

(b) t2 = 0.1 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.1 s

1.0 2.00.0

+0.5

–0.5x [m]

(c) t3 = 0.2 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.2 s

1.0 2.00.0

+0.5

–0.5x [m]

(d) t4 = 0.3 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.3 s

1.0 2.00.0

+0.5

–0.5x [m]


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Activity Cycle 11.2.1: Analyzing harmonic wave motion

A. Summarizing FNT results. Put up your graphs 1(a)-(d) up on the board, in orderthat your TA can gauge your progress. Leave space on the board for the activities onthe back of this page.

* 1. "Freeze out" time t in the harmonic wave equation, and then simplify as much as possible,use the (+) sign for the (±) choice, amplitude A = 0.5 m, period T = 0.4 s, wavelengthλ = 2.0 m, and constant phase ψwave = π in order to rewrite this wave equation as afunction of x only, using the above parameters, for the following times below. Also plotthese y(x) graphs for each time.

(a) t1 = 0.0 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.0 s

1.0 2.00.0

+0.5

–0.5x [m]

(b) t2 = 0.1 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.1 s

1.0 2.00.0

+0.5

–0.5x [m]

(c) t3 = 0.2 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.2 s

1.0 2.00.0

+0.5

–0.5x [m]

(d) t4 = 0.3 s

y xx( ) = ( ) ( )

+

0 2

2 0.5 m

m sin

.π

y(x) [m] at t = 0.3 s

1.0 2.00.0

+0.5

–0.5x [m]

This activity concludes on the other side of this page. Your TA may elect to have a whole-classdiscussion here before moving on to the rest of this activity, in order to move every group along atthe same pace, and to clear up board space.


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Activity Cycle 11.2.1: Analyzing harmonic wave motion(continued)

B. Another parameter to "freeze" (i.e., hold constant). Discuss (2)-(3) in your group,and then put your group's answers up on the board. These require more thought andjustification than (1).

* 2. Start over from the complete harmonic wave function y(x,t) again (where ψwave = π).Instead of "freezing out" time, "freeze out" position for the value of x = ____ m assignedto your group by the TA. Write out your group's y(t) equation, then make a y(t) graph foryour x = ____ m position. Pretend that you are a particle on a rope wave, at yourspecified x location. Later in the whole class discussion, a volunteer from yourgroup will demonstrate what the particle at your x location does as timeprogresses from t = 0.0 s.

x = _____ m

y tt( ) = ( ) ( )

+

0 2

0.5 m

.4 s sin .π

y(t) [m] at x = ___ m

0.2 0.40.0

+0.5

–0.5t [s]

* 3. What is the constant phase ψ for your group's y(t) equation? Exactly how did each of theother groups' different x position wind up getting a different value for their constant phaseψ for their y(t) equation? What would happen if each different x position had the samevalue for ψ?

C. Analyzing your results. Discuss (4)-(5) in your group, and then put your group'sanswers up on the board.

* 4. Which graph (y(x) or y(t)) is a "snapshot" of a wave? Which variable (x or t) is "frozen"in a "snapshot" of a wave?

* 5. Which graph (y(x) or y(t)) describes simple harmonic motion? Which variable (x or t) is"frozen" in SHM?

D. Challenge questions. Discuss (6)-(7) in your group, but unless instructed by the TA,you do not have to put these up on the board.

6. What is the magnitude (in m/s) and direction of the wave described by the y(x,t) harmonicwave equation? Which graph(s) can you get this information from? Instead of usinggraph(s), how would you "read" this information directly off of the y(x,t) harmonic waveequation?

7. Can a y(x,t) harmonic wave equation be graphed without "freezing" one of the (x or t)variables? Explain how, or why not.


03.03.18

Activity Cycle 11.2.2: Slinky™ waves and wave velocity

A. Creating wave motion and observing wave velocities. Work at the board as a groupand put your results up as you work, in order that your TA can gauge your progress.

Pull out your Slinky™ and then lay it across the floor such that it is about half the length of thelab room. Gently make waves go down the Slinky™ by disturbing one of the ends. (Be kind toyour Slinky™—treat it nicely; and don't get too spastic!) Make and observe the followingtypes of transverse (sideways displacement) waves (more details below):

(a) A small transverse amplitude pulse wave.(b) A medium transverse amplitude pulse wave.(c) A packet of transverse small amplitude harmonic waves (f = 0.5 Hz).(d) A packet of transverse small amplitude harmonic waves (f = 1.0 Hz).

* 1. Make two separate schematic drawings (not graphs) of the Slinky™ for (a) and (b).

* 2. Qualitatively (i.e., just "eyeball" it!), which wave travels faster down the Slinky™—(a) or(b)? (Hint: watch how long it takes for a pulse to make a round trip down theSlinky™, and back. Repeat this as much as possible until your entire group isconvinced, and convince your TA of your conclusions as well.)

* 3. Make two separate schematic drawings (not graphs) of the Slinky™ for (c) and (d). (Thewaves should have the same amplitude.)

* 4. Qualitatively (i.e., just "eyeball" it!), which wave travels faster down the Slinky™—(c) or(d)? (Hint: watch how long it takes for a packet of crests to make a round tripdown the Slinky™, and back.)

* 5. In your drawing (and in your experiment), which harmonic wave ((c) or (d)) has a smallerwavelength? Carefully explain this using the relation v fwave = λ .

B. Interdependence of wave velocity with other wave parameters. Work at the board as agroup and put your results up as you work. No explanation necessary, but you shouldbe able to support your answers based on your observations.

* 6. Wave speed vwave is dependent on

independent of

the amplitude A.


independent of

the frequency f.


independent of

whether the wave is pulse or harmonic.

* 9. Wave speed vwave is dependent on the characteristics of the source, and not on the

properties of the medium it travels through. Yeah way.

No way.


03.03.18

Activity Cycle 11.2.3: Sound waves and wave parameters

A. Creating wave motion. Discuss (1) in your group, do not put anything up the board,but be prepared to be called on as a group in the whole-class discussion todemonstrate your wave to the rest of the class.

1. Your TA will assign your group one of the following waves to demonstrate to the wholeclass on your Slinky™. Take turns practicing your group's assigned wave. In themeanwhile, move onto answering questions (2)-(6) below.(a) Single longitudinal wave pulse with an amplitude of 5 cm;

single transverse wave pulse with an amplitude of 5 cm.(b) A packet of longitudinal harmonic waves with an amplitude of 5 cm.(c) A packet of transverse harmonic waves with an amplitude of 5 cm.(d) A packet of longitudinal harmonic waves with a period of 0.5 s.(e) A packet of transverse harmonic waves with a period of 0.5 s.

B. Analyzing sound waves as ideal harmonic waves. Work at the board as a group andput your results up as you work, in order that your TA can gauge your progress.

Observe the front surface of a speaker as it creates sound waves in the air in this room.* 2. If the coils on a Slinky™ represent the density of air molecules in this room, which of the

above waves ((a)-(e)) best represents a sound wave?

* 3. In order to make a lower or higher pitch sound wave, how would the front surface of thespeaker have to move differently? Be able to demonstrate this with a Slinky™.

* 4. In order to make a quieter or louder sound wave, how would the front surface of thespeaker have to move differently? Be able to demonstrate this with a Slinky™.

* 5. Explain how you make a sound wave in the following types of media, or why this wouldnot be possible.(a) In outer space (i.e., a vacuum).(b) Underwater.

C. Understanding independent and dependent wave parameters. Work at the board inyour group; you may find it easier to fill in a big chart on the board as you go along,such that your TA can gauge your group's progress. No explanation required.

* 6. Depends onwave source

Depends onmedium

Depends on bothsource/medium

amplitude Afrequency f

period Tphase shift ψvelocity vwavewavelength λ

polarization type


03.03.18

DLM 02 Exit handoutAnnouncements The Physics 7C Student Packet, Winter Quarter 2003 (P. M. Len,2003) is available from Navin's Copy Shop (231 Third Street; 758-2311)for a nominal fee. Quiz 11 will be given during lecture 9:00-9:35 am on Friday,January 24, and will cover the material in Block 11. (Note that January 24is an "Academic Monday," and by decree of the Office of the Registraryou are required to attend all of your Monday classes on that day.) Bringa pen or pencil, calculator, and prepare to show your UC-Davis student IDcard (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")X. Determine the values of the harmonic wave function

parameters for waves (a) and (b), described below. You willdiscuss your results and confirm them by graphing thesewaves using a computer program. See how manyparameters you can get on your own before then (althoughyou should be able to determine all of these parameters onyour own for Quiz 11!).

(a) Two graphs that depict a one-dimensional water wave, as a function of position, at twoseparate times (t = 0.0 s, and t = 1.0 s) are shown below. Assume that the intervalbetween these two times is "small."

0.5 1.0 1.5 2.0

y(x) [m] at t = 0.0 s

0.0

+0.1

–0.1x [m]

0.5 1.0 1.5 2.0

y(x) [m] at t = 1.0 s

0.0

+0.1

–0.1x [m]

(b) A y(x) graph that depicts a one-dimensional water wave, as a function of position at thetime t = 0.0 s; and a y(t) graph that depicts the vertical displacement of a buoy atx = 0.0 m, due to this one-dimensional water wave, as a function of time are shown below.

(a) (b)

ATλψwave

vwave

±


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y(x) [m] at t = 0.0 s

0.0

+0.1

–0.1x [m]

0.5 1.0 1.5 2.0

y(t) [m] at x = 0.0 m

0.0

+0.1

–0.1t [s]

5 10 15 20.

DLM 03 is a problem-solving session that will consolidate the material covered in Block 11. Thefollowing five problems represent actual or sample quiz or final exam questions given in previousquarters.

Keep in mind that your Quiz 11 grade will explicitly depend on the methodical application ofthe analytical tools developed in Block 11, and being able to demonstrate this understanding inwords and equations. Generous partial credit will be given for starting the correct approach in aconscientious manner, much less partial credit will be given for blind plugging-and-chugging.

These question/problems were completely new situations that were never seen before by thestudents who took these quizzes in the past. Similarly, you should expect completely new situationson Quiz 11 that you have never seen before as well. However, no matter how strange and differentyour Quiz 11 will appear to you at first, you must learn to rely on the analytical tools developed inBlock 11. Don't fixate on a "solving-problems-like-these" mentality, you should concentrate on aformulating a "general-approach-to-any-problem" strategy when doing these question/problemsand when studying for Quiz 11.

(Quiz 11, Fall 2002)1. Consider a mass-spring system with a mass m1 and a

spring strength k, which is stretched horizontally tothe right a distance x from its equilibrium position,and then released at t = 0.0 s.

For another mass-spring system, a smaller mass m2

is glued to the top of the original mass m1, and isstarted in the same manner at t = 0.0 s.

Determine which of the SHM parameters A, T, ψ, andmaximum vy are the same, or different, for the singlemass or the two-mass system. If a parameter is thesame for either system, determine what it is, in termsof the parameters k, x, m1, m2, and gEarth = 9.8 N/kg.If a parameter is different for either system, determinethe factor by which it is smaller or larger in terms ofthe given parameters. Ignore the effects of frictionand air resistance. Credit is assigned for the completeness and clarity of your justifications, andnot necessarily for your answers and numerical results.

t = 0.0 s

m1

equi

libriu

m

x

m1

x

m2

t = 0.0 s


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(Quiz 11, Fall 2001)2. Two rubber duckies float on the surface of the water in a rather large bathtub. Rubber ducky (1)

is located at x = +0.875 m; rubber ducky (2) is located at x = +1.125 m. A transverse wavemoves horizontally through the water in this bathtub from a wave source located at x = +2.000 m.The vertical displacements of these rubber duckies as functions of time are given below. Credit isassigned for the completeness and clarity of your justifications, and not necessarily for youranswers and numerical results.

y tt

rubber ducky m s1 0 5

23 0 6

( ) = ( ) π( )

+ π

. sin.

,

y tt

rubber ducky m s2 0 5

23 0 2

( ) = ( ) π( )

+ π

. sin.

.

(a) What is the wavelength (in m) of this water wave?(b) What is the constant phase ψ (in radians) of the wave?(c) Suppose that the bathtub is now filled with chocolate pudding, such that the velocity of

transverse waves decreases by a factor of two. The same wavemaker is used (assume theamplitude and period remain as before), and the rubber duckies are placed at the same xpositions. Choose and defend one statement only.

(A) The maximum vertical velocity of the rubber duckies will be slower in the puddingthan in the water.

(B) The maximum vertical velocity of the rubber duckies will be faster in the puddingthan in the water.

(C) The maximum vertical velocity of the rubber duckies will remain the same in thepudding as in the water.

(Quiz 11, Fall 1998)3. The front end of a speaker located at x = 0 creates (gauge) pressure fluctuations as a function of

time:

P tt( ) = ( ) π

( )+ π

10 0

20 002

32

. sin.

Pa s

.

These sound waves move down a straight tube filled with air (vwave = 340 m/s), so they can beconsidered one-dimensional harmonic waves. Credit is assigned for the completeness andclarity of your justifications, and not necessarily for your answers and numerical results.(a) Write out an equation for the pressure P(t) as a function of time at the x = +10 m

position. Fill in values for all the parameters. Show all your work.(b) Now this tube is completely filled with water (vwave = 1,440 m/s; the equilibrium pressure

in this tube is still 1 Atm), and the speaker is operated in exactly the same manner. Writeout an equation for the pressure P(t) as a function of time at the x = +10 m position. Fillin values for all the parameters. Show all your work and explain your reasoning.

(Quiz 11, Fall 2000)4. A harmonic wave is created by hand by a Physics 7C student along a rope. It is observed that

waves move at a speed of 16 m/s along this rope, but it is unknown whether this wave is movingto the left along the rope, or to the right along the rope. A graph of the wave at t = 2.0 s is shown


03.03.18

below. Credit is assigned for the completeness and clarity of your justifications, and notnecessarily for your answers and numerical results.

y(x) [m] at t = 2.0 s

0.5 1.00.0

+0.01

–0.01x [m]

1.5

(a) What is the period T (in seconds) of this wave?(b) What is the maximum vertical velocity (in m/s) of the hand of the Physics 7C student?

Show all your steps. Explain whether your answer depends on if the wave is moving tothe left, or to the right.

(c) Now suppose that this rope is then made more taut, and as a result, waves move fasteralong this rope. Choose and defend one statement only.(A) After the rope is made more taut, the wavelength λ of the waves created by this same

Physics 7C student will be longer than before.(B) After the rope is made more taut, the wavelength λ of the waves created by this same

Physics 7C student will be the same as before.(C) After the rope is made more taut, the wavelength λ of the waves created by this same

Physics 7C student will be shorter than before.

(Quiz 11, Spring 2001)5. Two graphs that depict a one-dimensional wave, as a function of position, at two separate times

(t = 0.0 seconds, and t = 1.5 seconds) are shown below. The direction of this wave is unknown,and it is also unknown whether the interval between these two times is "small" or not. Credit isassigned for the completeness and clarity of your justifications, and not necessarily for youranswers and numerical results.

y(x) [cm] at t = 0.0 s

50.0

+1.0

–1.0x [cm]

10 15 20

y(x) [cm] at t = 1.5 s

50.0

+1.0

–1.0x [cm]

10 15 20

(a) Explain in words and/or equations why it is possible to find at least two different possiblewave velocities and directions, given the two y(x) graphs above.

(b) Find the two slowest possible ±values for the velocity of this wave. Show your work,and/or explain your reasoning.

(c) For each of your two possible slowest values for the velocity of the wave in (b), draw avertical position versus time graph for the position x = 0.0 cm. Be sure to scale and labelyour horizontal time axes, and plot at least one period of oscillation.


03.03.18

Activity Cycle 11.2.4: Analysis of harmonic wave functions

* A. Summarizing FNT results. Put up your parametersfor waves (a)-(b) up on the board. Leave space onthe board for the rest of the activities on this page.

B. Animating harmonic waves, in order to check yourresults in (A). Discuss (1)-(5) in your group, andthen put your group's answers up on the board, inorder that your TA can gauge your progress.

Use Graphing Calculator (as shown atright) to plot and animate the harmonicwave equation using the parameters A, T, ±,λ, and ψwave determined from (a). Check tosee that your Graphing Calculator plotexactly matches the y(x) graphs for t =0.0 s, and for t = 1.0 s. There is nothingwrong with "guess-and-check," as long asyou check each of your guesses!

* 1. What is the meaning of letting n runfrom 0 to 100?

* 2. The Graphing Calculator will also runn back down from 100 to 0. Is thisphysically realistic? What does itmean with respect to a wave movingthrough time?

* 3. What would happen to the wave ifyou changed the (+) or a (–) of the(±) in the equation? (Try this!)

* 4. Explain how you can tell if the wavewas moving to the left or right, giventwo y(x) graphs.

Now use the Graphing Calculator to plot your results from (b). Make sure your answer for ψwave iscorrect.

* 5. Explain how you can tell if the wave was moving to the left or right from only just oney(x) graph and just one y(t) graph.

(a) (b)

ATλψwave

vwave

±

y = A sin ( 2π ± 2π + ψ) xn

T λ

Type in the equation (with your numerical values for A, T, ±, λ, and ψ); use “option-P” to enter “π,” “n” is used instead of t

Set 0 ≤ n ≤ 100, with 100 steps; press “play” to animate your wave

Rescale your graph

“Grab” the origin to move it

“Grab” the divider upwards to see the graph


03.03.18

Activity Cycle 11.3.1: Analyzing SHM/harmonic wave systems

A. (50 minutes.) Summarizing FNT results. Your TA will assign one of the sample quizquestion/problems (1)-(5) for your group to discuss, put up on the board, and presentto the whole class.

When working on your assigned question/problem:• Make sure you clearly show the following!

I. List and circle the (relevant) given information you used.II. List and circle the assumptions/laws/equations you used.III. State what you were asked to solve for.IV. Write your solution to the question/problem on the board. In order to conserve space,

do not show every math step (e.g., show the equation; solve it in terms of everythingelse; then show the numerical answer).

B. (40 minutes.) Presenting FNT results. Your TA will call on one or a number ofpeople at random in your group to present your group's solution to your assignedquestion/problem (1)-(5).

When presenting your assigned question/problem:• Make sure everyone in your group is able to explain your question/problem when called

upon! Your TA will either call on a person at random from your group; or may call oneveryone in turn to present your group's question/problem.

• After your question/problem is on the board, and you are ready to present your solution, thenyou can compare your individual work to the question/problems assigned to the other groups.


03.03.18

DLM 03 Exit handout

Announcements Quiz 11 will be given during lecture 9:00-9:35 am on Friday, January 24, and will cover thematerial in Block 11. (Note that January 24 is an "Academic Monday," and by decree of the Officeof the Registrar you are required to attend all of your Monday classes on that day.) Bring a pen orpencil, calculator, and prepare to show your UC-Davis student ID card (or similar photo ID) uponentering, and/or during the quiz.

FNT ("For Next Time")1. Consider two waves (y1 and y2) of the same amplitude, period and wavelength, as they travel

along their respective path lengths L1 and L2. For each of the following cases (a)-(f), statewhether these two waves interfere constructively or destructively. We will get into themathematics involved later in DLM 04.

(a) y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

(b) y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

(c)

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]


03.03.18

(d)

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]

(e)

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]

(f)

y2(x) [m] at t = 0.0 s

0+A

–AL2 [m]

y1(x) [m] at t = 0.0 s

0+A

–AL1 [m]

3. Read the Block 12 Glossary (pp. 49-55) in the Physics 7C Student Packet, Winter Quarter2003, and familiarize yourself with the following terms that will be used extensively in DLM04.

constructive interferencedestructive interference"in-phase"interference conditions"out-of-phase"path-length L

path-length difference ∆Lreflection phase shift ψreflection

total phase angle Ψtotal phase difference ∆Ψwave superposition


03.03.18

Activity Cycle 12.1.1: Experimenting with interference

A. Summarizing FNT results. Put up your "constructive/destructive" answers for (a)-(f)up on the board. Leave space on the board for the experiment below.

* 1. Consider two waves (y1 and y2) of the same amplitude, period and wavelength, as theytravel along their respective path lengths L1 and L2. For each of the cases (a)-(f), simplystate whether these two waves interfere constructively or destructively (no explanationnecessary).

B. Experimental observations of constructive/destructive interference. Discuss andperform the experiment described below (2) in your group, summarize yourmeasurements up on the board, and be prepared to be called on as a group in thewhole-class discussion to demonstrate your experimental results to the rest of theclass.

2. Set your sound frequency to any value between 1,000 Hz < f < 1,200 Hz (as long as itdoes not coincide with another group's frequency). Make sure your speakers are wiredin the same way (red-to-red, black-to-black). Place each speaker such that each soundwave travels the same path-length of 0.05 m to the microphone. Make sure youroscilloscope is able to detect a sound signal at this location. (Continued on other side...)

L1

PowerFrequency

Volume

L1 L2

Power

(start with L1 = L2 = 0.05 m)

Turn “VOLTS/DIV” clockwise all the way

Turn “SEC/DIV” to ≈ 1 ms

Always use “~” and “10V” toggle settings


03.03.18

Activity Cycle 12.1.1: Experimenting with interference (continued)

* 2. (Continued.) The objective here is to experimentally recreate each of the constructive anddestructive cases in 1(a)-(f), at the location of the microphone. You are free to doeither/both of two things: varying the path-lengths; and/or switching the red/black wiresthat go into the speakers. Record your observations and measurements on the board,using the table below.

Oscilloscope display? Speakers wiredsame/differently?

Path lengthL1 [m]

Path lengthL2 [m]

(a)

(b)

(c)

(d)

(e)

(f)

C. Analysis of experimental procedures. Work at the board as a group and put youranswers up for (3)-(5) as you work, in order that your TA can gauge your progress.

* 3. Explain whether the oscilloscope displays a y(t) or a y(x) graph of pressure displacementat location of the microphone. How do you know whether constructive/destructiveinterference takes place at the microphone location?

* 4. Recall that the front of a speaker moves longitudinally back and forth in order to createsound waves, as signaled by the frequency generator. Explain what wiring a speaker the"wrong way" does to the speaker.

* 5. Does it really matter whether your speakers are set face-to-face towards the microphone,or can you get the same constructive/destructive interference results even if you had bothspeakers facing in the same direction towards the microphone? Why is this so?

D. Challenge question. Discuss (6) in your group, but unless instructed by the TA, youdo not have to put this up on the board.

6. Suppose you are in a room with a large high-fidelity stereo sound system. Where is thebest place to sit, relative to the two speakers? If this turns out to be a "dead" spot, what iswrong with the speakers?

.


03.03.18

Activity Cycle 12.1.2: Applying interference conditions

A. Applying the interference conditions for same wavelength/period wave superposition.This is merely re-interpreting your experimental results from activity 12.1.1. Work atthe board as a group and put your results up as you work, in order that your TA cangauge your progress. Once you have completed the questions on this activity sheet, goonto the next (and last) activity 12.2.1.

Refer to the interference conditions on pp. 51-52 of the Physics 7C Student Packet, WinterQuarter 2003, specifically for the superposition of two waves with the same wavelength/period(referred to here as (A) and (B)):

(A) ∆ =( )

+( )

L

#

#

λλ

constructive,

destructive.1

2

(B) ∆ =+( )

( )

L

#

#

1

2λ

λ constructive,

destructive.

* 1. For each of the constructive/destructive interference cases (a)-(f) from your DLM 03 FNTand activity 12.1.1, which interference condition should be used, and why?

* 2. For each of the constructive/destructive interference cases (a)-(f) from your DLM 03 FNTand activity 12.1.1, explicitly calculate ∆L in order to show how each interferencecondition correctly predicts (or rather, is consistent with) your experimentalconstructive/destructive results.

Interference condition used(A) or (B), and why?

∆L = ?,and ∴ [constructive?/destructive?]

(a)

(b)

(c)

(d)

(e)

(f)

Your TA may elect to have a whole-class discussion here before moving on to the next activity, inorder to move every group along at the same pace, and to clear up board space.


03.03.18

Activity Cycle 12.1.3: Reflection phase shifts for sound waves

A. Recording constructive/destructive interference data. Discuss and perform theexperiment described below (1) in your group, do not put anything up the board, butbe prepared to be called on as a group in the whole-class discussion to demonstrateyour experimental results to the rest of the class.

1. Set your sound frequency to any value between 1,800 Hz < f < 2,000 Hz (as long as itdoes not coincide with another group's frequency). Place your microphone up against theedge of a wall (or any hard surface, such as the side of the frequency generator box) asshown below, such that it is able detect a sound wave directly from the speaker, and areflected sound wave. Make sure your oscilloscope is able to detect a sound signal at thislocation. Slowly move the microphone away from the reflecting surface (and towards thesound speaker). Record the nearest distance from the center of the microphone to thereflecting surface when it detects constructive interference, and the nearest destructiveinterference distance.

Power

Turn “VOLTS/DIV” clockwise all the way

Turn “SEC/DIV” to ≈ 1 ms

distance = ?

direct wave

reflected wave

ψre

flect

ion =

?

PowerFrequency

Volume

speaker-to-wall distance (≈ 0.50 m)

B. Interpreting your results to determine the reflection phase shift (either 0 or ππππ) for thereflected sound wave. You only have to discuss this in your groups, and then getpermission to be dismissed by your TA. The following question (2) below is a "labreport" question to be handed in for credit as soon as you walk in to the next DLM 04.It is your responsibility to have enough data to answer this question before leaving DLtoday.

2. Determine what the phase shift is (either 0 or π) for a sound wave reflected off of a hardsurface. Make sure your results are consistent for each of your measured distancesfrom (1). Clearly show your reasoning, which may be rather involved.


03.03.18

DLM 04 Exit handoutAnnouncements Quiz 11 will be given during lecture 9:00-9:35 am on Friday, January 24, and will cover thematerial in Block 11. (Note that January 24 is an "Academic Monday," and by decree of the Officeof the Registrar you are required to attend all of your Monday classes on that day.) Bring a pen orpencil, calculator, and prepare to show your UC-Davis student ID card (or similar photo ID) uponentering, and/or during the quiz.

FNT ("For Next Time")The following question is a "lab report" question to be handed in as you come into the next DLM 05.Answer this as you would a quiz question; it will be graded similar to a quiz question, and thensubsequently handed back to you. You will receive credit towards your DL grade. Be sure to writeout your answer on a separate page.

X. Determine what the phase shift is (either 0 or π) for a sound wave reflected off of a hardsurface. (Note that on pp. 54-55 of the Physics 7C Student Packet, Winter Quarter 2003, thereflection phase shifts for light waves are given. The reflection phase shifts for sound waveswere deliberately not given, and may or may not be the same as for light waves!).

The following FNTs are only to be checked off by your TA; you are not going to turn these in.

1. Which of the following types of waves (traveling through air) are humanly detectable?(Cf. p. 42 and 45 of the Block 11 Glossary.)(a) λ = 3.0 cm light.(b) λ = 3.0 cm sound.(c) λ = 633 nm light.(d) λ = 633 nm sound.


"diffraction grating"double-slit interference


03.03.18

Activity Cycle 12.1.4: Path-length interference of light

A. Summarizing FNT results. Put up your answers to (1) on the board, in order thatyour TA can gauge your progress. Leave space on the board for the activitiesdescribed below, and on the back of this page.

1. Which of the following types of waves (traveling through air) are humanly detectable?(a) λ = 3.0 cm light.(b) λ = 3.0 cm sound.(c) λ = 633 nm light.(d) λ = 633 nm sound.

B. Recording constructive/destructive data. Discuss and perform the experimentalmeasurements described below (2)-(4) in your group, summarize your measurementson the board, and be prepared to be called on as a group in the whole-class discussionto demonstrate your experimental results to the rest of the class.

2. Turn on your microwave source and detector. Line them up such that initially θ = 0°.Verify that this angle has constructive interference, by moving the detector angle slightly(±5°) to the left/right. Now move the detector as shown to find a destructive interferenceangle somewhere in the range of θ = 8°-13° (again, move your detector angle aroundslightly to find the exact location of this destructive angle). Record this experimentaldestructive interference angle on the board.

3. Repeat (2) above, but for a constructive interference angle somewhere in the range ofθ = 16°-25°.

Power (turn off/unplug when done)

λ = 3 cm light source

Each slit spreads microwave light out in all directions, but only certain directions will result in constructive interference

d

λ = 3 cm light detector

θ Detector setting (use 1× or 10×); turn off when done

Keep source near end of short ruler arm

Keep detector near end of long ruler arm

4. Find how many constructive interference angles there are in the complete range of –90° to+90° (i.e., in a complete sweep from side-to-side). (These will be easier to discern thandestructive interference angles.)


03.03.18

Activity Cycle 12.1.4: Path-length interference of light

C. Interpreting your experimental measurements. Work at the board as a group and putyour results up as you work, in order that your TA can gauge your progress.

* 5. Go back to yourdestructive interferenceangle from (2). Use atape measure or ruler tomeasure the individualpath-lengths L1 and L2

from each slit, to theback of the detectorfunnel, as shown at right.Does the path-lengthdifference ∆L matchwhat you would expectfor destructiveinterference?

* 6. Repeat (5), but for your constructive interference angle from (3).

* 7. A useful approximation to find ∆L directly for a given θ angle is ∆L ≈ dsinθ, where d isthe center-to-center spacing between the two slits. Determine ∆L from this approximationusing your experimental destructive and constructive angles. Does the calculated path-length difference ∆L ≈ dsinθ match what you would expect for constructive anddestructive interference? (From now on, we will consider this approximation as validunless explicitly noted otherwise.)

* 8. Manipulate the ∆L ≈ dsinθ approximation and the appropriate interference condition(s) tofind how many constructive interference angles there are in the complete range of –90° to+90° (i.e., in a complete sweep from side-to-side). Is it possible to find all of theseconstructive interference angles experimentally? What is the (#) used for each of theseconstructive interference angles?

* 9. Destructive interference angles/detector locations are sometimes referred to as "minima,"while constructive interference angles/detector locations are sometimes referred to as"maxima." Come up with a plausible reason for this, in terms of the detector dial readingsat those locations.

θ

L1

L2

Where microwaves interfere inside the detector

slit 1

slit 2


03.03.18

Activity Cycle 12.1.5: Diffraction grating interferenceA. Recording constructive interference ("maxima") angles. Discuss and perform the

experiment described below (1) in your group, summarize your measurements up onthe board, and be prepared to be called on as a group in the whole-class discussion todemonstrate your experimental results to the rest of the class.1. Set up the laser such that it passes through your diffraction grating, and creates one

central and two (#) = ±1 side maxima on your white board. Use a tape measure for thedistances you need to use with the Arctan function to find the (#) = ±1 θ angle (do thisfor both (#) = ±1 maxima, in order to average the two θ angles).

Power

θ

Each etch groove spreads light out in all directions, but only certain directions will result in constructive interferenceλ = 633 nm laser

d

B. Analysis of experimental measurements. Work at the board as a group and put youranswers up for (2)-(6) as you work, in order that your TA can gauge your progress.

* 2. Draw the triangles and legs used to find θ with the Arctan function for the left (#) = +1maximum. Do the same for the right (#) = –1 maximum. Average your two θ angles.

* 3. What on your experiment should be adjusted if your two θ maxima angles in (2) are notthe same? (You do not have to actually make any readjustments, as long as you averageyour left and right θ maxima angles.)

* 4. How many multiples of wavelengths should ∆L be for the (# = ±1) maxima?

* 5. Use the ∆L ≈ dsinθ approximation to find the spacing between etch grooves on yourdiffraction grating. (Check your result with the TA, who knows the actual valuefor d. Troubleshoot your measurements and calculations if necessary.)

* 6. Explain why the ∆L ≈ dsinθ approximation can here be considered an exact relation(∆L ≡ dsinθ) for this experiment, compared with activity 12.3.1.

Your TA may elect to have a whole-class discussion here before moving on to the back of this page,in order to move every group along at the same pace, and to clear up board space.


03.03.18

Activity Cycle 12.1.5: Diffraction grating interference (continued)

C. Recording more constructive interference ("maxima") angles. Discuss and performthe experiment described below (7) in your group, do not put anything up the board,but be prepared to be called on as a group in the whole-class discussion todemonstrate your experimental results to the rest of the class.

7. Carefully reverse the direction of your laser such that it reflects back off of the undersideof a commercially-produced compact disc (CD), and creates one central and two (#) = ±1maxima on your white board. Use a tape measure for the distances you need to use withthe Arctan function to find the (#) = ±1 θ angle (do this for both (#) = ±1 maxima, inorder to average the two θ angles).

θ

Each track reflects laser light back in all directions, but only certain directions will result in constructive interference λ = 633 nm laser

d

Power

D. Interpreting your results to determine the spacing between consecutive data tracks ona CD. You only have to discuss this in your groups, and then get permission to bedismissed by your TA. The following question (8) below is a "lab report" question tobe handed in for credit as soon as you walk in to the next DLM 04. It is yourresponsibility to have enough data to answer this question before leaving DL today.

8. Determine the spacing between consecutive data tracks on a CD. Make sure you show allyour steps, similar to (2), (4), and (5) for the earlier diffraction grating "dry run" inactivity 12.1.5. Clearly show all your steps and the reasoning for each step.


03.03.18

DLM 05 Exit handout

Announcements Quiz 11 will be given during lecture 9:00-9:35 am on Friday, January 24, and will cover thematerial in Block 11. (Note that January 24 is an "Academic Monday," and by decree of the Officeof the Registrar you are required to attend all of your Monday classes on that day.) Bring a pen orpencil, calculator, and prepare to show your UC-Davis student ID card (or similar photo ID) uponentering, and/or during the quiz. There will be no DLs for all lab sections that have start times from 10:30 am on Thursday,January 23, to 8:00 am on Tuesday, January 28. The normal DL cycle will resume starting 10:30 amon Tuesday, January 28.


X. Determine the spacing between consecutive data tracks on a CD. Make sure you show all yoursteps, similar to (2), (4), and (5) for the earlier diffraction grating "dry run" in activity 12.1.5.Clearly show all your steps and the reasoning for each step.

The following FNTs are only to be checked off by your TA; you are not going to turn these in.

1. Two waves in the same medium that have the same period, must have the same

different

wavelengths.

2. Two waves in the same medium that have different periods, must have the same

different

wavelengths.

3. The frequency of a wave traveling in a fast medium will

increase

remain the same

decrease

as it enters a slower

medium.

4. The wavelength of a wave traveling in a fast medium will

increase

remain the same

decrease

as it enters a slower

medium.


03.03.18

5. Consider two harmonic waves of different wavelengths/periods, y1 and y2 , which meet at onespecific x location. The displacements of both these waves at this x location is plotted versustime on the same graph below. The horizontal time axis is scaled with 1.0 second intervals.

y1

+A

y2

0–A

y(t) at x = 0.0 m

t [s]+A

5 10 15 20 25 30 35

(a) Determine the periods Τ1 and Τ2 (in s) of the two waves y1 and y2 .(b) Determine the specific instance(s) in time (in s) when the two waves are exactly in-phase

with each other.(c) Determine the specific instance(s) in time (in s) when the two waves are exactly out-of-

phase with each other. (As a check, the amount of time between in-phase times should bethe same amount of time between out-of-phase times.)


beatsbeat frequency f beat

beat period Τbeat

carrier frequency f carrier

carrier period Τcarrier

interference conditions(pp. 51-52)

thin film interference


03.03.18

Activity Cycle 12.1.6: Same wavelength/period interference

A. Summarizing FNT results. Put up your answers to the multiple choice questions (1)-(4), and a brief explanation why. (Leave space on the board for the activities on theback of this page.)

* 1. Two waves in the same medium that have the same period, must have the same

different

wavelengths.

* 2. Two waves in the same medium that have different periods, must have the same

different

wavelengths.

* 3. The frequency of a wave traveling in a fast medium will

increase

remain the same

decrease

as it enters a

slower medium.

* 4. The wavelength of a wave traveling in a fast medium will

increase

remain the same

decrease

as it enters a

slower medium.

Your TA may elect to have a whole-class discussion here before moving on to the rest of the activityon the other side of this page, in order to move every group along at the same pace, and to clear upboard space.


03.03.18

Activity Cycle 12.1.6: Same wavelength/period interference

B. Re-interpretation of interference conditions, using the difference in total phase ∆∆∆∆ΨΨΨΨinstead of ∆∆∆∆L. Work at the board as a group and put your results up as you work, inorder that your TA can gauge your progress.

Recall that different interference conditions for ∆L were used, whether in-phase or out-of-phasesources/reflections were considered. However, there is actually only one interference conditionfor two waves of the same wavelength/period, if the difference in total phase is used:

∆ = π∆ + ∆ + ∆

=±( )π±( )π

Ψ –2

L even

oddsources reflectionsλψ ψ

constructive,

destructive.

Apply this single interference condition to all of the phenomena from DLM 04-05.

5. Your TA will assign you one of the following experiments (a)-(e) to re-analyze using ∆Ψ.Insert your experimentally measured quantities in evaluating ∆Ψ, to show howconstructive or destructive interference resulted.

* (a) Activity 12.1.1, question 2(b).* (b) Activity 12.1.1, question 2(f).* (c) Activity 12.1.3, question 1 (for the nearest destructive interference microphone

location).* (d) Activity 12.1.4, question 2 (the destructive interference angle).* (e) Activity 12.1.4, question 3 (the constructive interference angle).

C. Application of ∆∆∆∆ΨΨΨΨ interference condition to a new phenomenon. Work at the board asa group and put your results up as you work, in order that your TA can gauge yourprogress.

* 6. Consider the superposition of light with a wavelengthof 550 nm in air, reflecting off of the outside and insidesurfaces of a soap bubble. Shown at right is a cross-section of the soap bubble wall (its thickness is greatlyexaggerated). Light travels 1.329× slower throughsoapy water than through air.(a) What is the wavelength λ water (in nm) of this

light wave, while it travels through the water/soapmixture?

(b) Determine the minimum thickness (in nm) of thebubble such that the superposition of thereflected light from the inner and outer surfacesconstructively interferes for green light waves( λ air = 550 nm).

(c) Note that other colors besides green are seen in the soap film. What varies inside∆Ψ to account for this?

soap

/wat

er fi

lm

thic

knes

s

air outside bubble

air inside bubble

wav

e 1

wav

e 2

"sof

t" r

efle

ctio

n

"hard" reflection


03.03.18

Activity Cycle 12.2.1: Different wavelength/period interference

A. Summarizing FNT results, and extending your answers. Put up your answers to (1)on the board. (Leave space on the board for the activities described on the back of thispage.)

* 1. Consider two harmonic waves of different wavelengths/periods, y1 and y2 .(a) Determine the periods Τ1 and Τ2 (in s) of the two waves y1 and y2 . Then determine

the frequencies f1 and f2 in (Hz) of the two waves.(b) Determine the specific instance(s) in time (in s) when the two waves are exactly in-

phase with each other. Would you be able to hear anything then?(c) Determine the specific instance(s) in time (in s) when the two waves are exactly out-

of-phase with each other. Would you be able to hear anything then?(d) Check your results by verifying that the amount of time between in-phase times is

the same amount of time between out-of-phase times. Then demonstrate that thebeat period Τbeat (constructive-destructive-constructive time) is equal to the inverseof fbeat , which is the difference between frequencies f1 and f2.

(e) Demonstrate that the carrier period Τcarrier (peak-to-peak cycle time) is equal to theinverse of the carrier frequency fcarrier , which is the average between frequences f1

and f2,.

0 t [s]

beat period

beatT

Tcarriercarrier (pitch) period

imaginary lines drawn to show maximum extent of constructive/destructive superposition

0 t [s]–A

ytotal(t) = y1 + y2, at x = 0.0 m

+A+2A

–2A

–A

ytotal(t) = y1 + y2, at x = 0.0 m

+A+2A

–2A

y1

+A

y2

0–A

y(t) at x = 0.0 m

t [s]+A

5 10 15 20 25 30 35



03.03.18

Activity Cycle 12.2.1: Different wavelength/period interference(continued)

B. Experimentally observing and listening to "beats." Discuss and perform theexperiment described below (2)-(3) in your group, summarize your measurements onthe board, and be prepared to be called on as a group in the whole-class discussion todemonstrate your experimental results to the rest of the class.

2. Set your two sound frequency generators to the frequencies f 1 and f 2 listed below, andplace your speakers face-to-face up against the microphone. Make sure that each speakeris set to the same volume level, and that your oscilloscope is initially able to detect a soundsignal. Don't get "woozy" or seasick!

PowerFrequency f1

Volume

(L1 = L2 ≈ 0)

PowerFrequency f2

Volume

Power Turn “VOLTS/DIV” to 2 m - 10 m settings

Turn “SEC/DIV” to 0.1 s

Flip both toggle switches up

Always use “~” and “10V” toggle settings; make sure speaker volumes are equal

* 3. Fill in the chart below to summarize your results.Carrier frequency,beat period

Oscilloscope display—watch for a while!(with Τbeat and Τcarrier intervals identified)

(a) f 1 = 220 Hzf 2 = 200 Hz

f carrier = Τbeat =

(b) f 1 = 210 Hzf 2 = 200 Hz


(c) f 1 = 201 Hzf 2 = 200 Hz


(d) f 1 = 200 Hzf 2 ≈ 200 Hz


C. Interpreting your experimental measurements. Put your results up on the board.

* 4. What happens to the intervals between "quiet" instances in time, as two sounds arebrought in-tune with each other?

* 5. If the two sounds had exactly the same frequency, what should the oscilloscope displaylook like? What is probably wrong with your experiment if your oscilloscope displaywere completely "flatline" all the time, when you finally made f 1 ≡ f 2?


03.03.18

DLM 06 Exit handoutAnnouncements Quiz 12 will be given during lecture 9:00-9:35 am on Monday, February 10, and will cover thematerial in Block 12. Bring a pen or pencil, calculator, and prepare to show your UC-Davis studentID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")—to be checked offX. Consider a medium where the magnitude of wave velocities is vwave = 2.0 m/s. Write out the

harmonic wave equations for the following two waves. (You will superpose these two waves onGraphing Calculator in the next DLM 07—can you guess what will result?)(a) A harmonic wave traveling to the right, with a wavelength λ = 0.20 m, zero constant phase,

and an amplitude of 0.5 m.(b) A harmonic wave traveling to the right, with a wavelength λ = 0.24 m, a constant phase of

π, and an amplitude of 0.5 m.


Keep in mind that your Quiz 12 grade will explicitly depend on the methodical application ofthe analytical tools developed in Block 12, and being able to demonstrate this understanding inwords and equations. Generous partial credit will be given for starting the correct approach in aconscientious manner, much less partial credit will be given for blind plugging-and-chugging.

These question/problems were completely new situations that were never seen before by thestudents who took these quizzes in the past. Similarly, you should expect completely new situationson Quiz 12 that you have never seen before as well. However, no matter how strange and differentyour Quiz 12 will appear to you at first, you must learn to rely on the analytical tools developed inBlock 12. Don't fixate on a "solving-problems-like-these" mentality, you should concentrate on aformulating a "general-approach-to-any-problem" strategy when doing these question/problemsand when studying for Quiz 12.

(Fina1 Exam, Spring 1997)1. Two microwave emitters are sitting side by side, both emitting microwaves of the same

wavelength. The wavelength of these microwaves is known to be between 2.0 cm and 3.0 cm.As you move a detector around in front of them, you find that when the detector is an equaldistance from each emitter, the detector reading is a minimum. You also note that when you are3.75 cm closer to one emitter than the other, the detector reads a maximum. Credit is assignedfor the completeness and clarity of your justifications, and not necessarily for your answersand numerical results.(a) Are the two emitters in phase with each other or not? Explain how you determined this.(b) What is the frequency of the microwaves coming from the two emitters?


03.03.18

(Quiz 11, Fall 1997)2. Radio station KPHY uses two antennae to transmit its signal at an AM

frequency of 1,148 kHz. While driving by on a semi-circular roadaround these antennae, you notice that there is only one location wherethe signal from both antennae is totally destructive. At this location(X), you are 49 m from antenna 1, and 147 m from antenna 2. Creditis assigned for the completeness and clarity of your justifications,and not necessarily for your answers and numerical results.(a) Prove that the radio antennae are not sources that are in phase

with each other.(b) If ψ1 = 0, what is ψ2 (in radians)?(c) If ψ1 = ψ2 , would you be able to detect a radio signal at

location (X)?

(Quiz 11, Spring 2001)3. A microphone is placed at a

certain location between twosound speakers that face eachother. This experiment happenson Earth, in air at standardtemperature and pressure. The microphone detects a sound that has a frequency of 550 Hz, butthis sound is loud at t = 0.00 s, quiet at 0.05 s, and then loud again at 0.10 s, quiet again at0.15 s, etc. Neglect all reflections of sound waves. Credit is assigned for the completeness andclarity of your justifications, and not necessarily for your answers and numerical results.(a) Explain in words and/or equations (i) what must be happening at the location of the

microphone, and (ii) how the different quantities (A, λ, T, ψ) in the wave equation for eachspeaker compare relative to each other (e.g., same as/different than) for this to happen. If itcannot be determined whether two quantities are the same or different than each other, explainwhy.

(b) Consider now a different situation where the two speakers have the same constant phase,and have the same frequency (which may or may not necessarily have been the casebefore in (a)). As a result, there is no sound detected at the location of the microphone.What is the lowest possible frequency of both speakers such that the microphone detectsno sound?

antenna 2

antenna 1

(X)

road

49 m

147

m

speaker 1 microphone speaker 2

0.6 m 0.3 m


03.03.18

(Quiz 11, Fall 2001)4. Two radio sources are spaced a

horizontal distance of 45.0 m apart, andboth emit λ = 30.0 m radio waves in alldirections. A distant satellite at an angleof 60° from the horizontal receives aconstructive interference signal fromthese two sources. The drawing at rightis not to scale. Credit is assigned forthe completeness and clarity of yourjustifications, and not necessarily foryour answers and numerical results.(a) Determine the smallest positive

value for the constant phase ψ1 (in radians) of source 1, if the constant phase ψ2 ofsource 2 is +π/6.

(b) Now consider the case where both radio sources have exactly the same constant phase.Determine whether the satellite will now be able to detect a radio signal or not. Choosethe most correct statement below, and then explain your answer. Choose and defend onestatement only.(A) The satellite will be able to detect a radio signal from source 1 and source 2.(B) The satellite will be not able to detect any radio signal from source 1 and source 2.

(Quiz 11, Fall 1999)5. Light will reflect off of the top (1) and bottom

(2) surfaces of a butterfly/moth scale toconstructively interfere. However, light can passthrough this top scale layer, and also reflect offthe top surface of the next consecutive scale (3),and cause constructive interference as well (thisis why scales seem to made up of a mixture ofseveral different colors). The index of refractionfor the scale material is 1.30. Recall that visiblewavelengths of light are in the range of 400-700 nm. Credit is assigned for the completeness and clarity of your justifications, and notnecessarily for your answers and numerical results.(a) Calculate the visible wavelength (in air) of visible light that will have constructive

interference between reflected light paths [1] and [2].(b) Calculate the visible wavelength (in air) of visible light that will have constructive

interference between reflected light paths [2] and [3].(c) Decide if this scale belongs to a butterfly or to a moth (assuming that there is also no

visible wavelength (in air) that will have constructive interference between light paths [1]and [3]).

source 1

60°

to distantsatellite

60°

1ψ = ? 2ψ = π6

source 2

45.0 m

side view

140 nm200 nm

(1)

(2)

(3)


03.03.18

Activity Cycle 12.2.2: Graphing different wavelength/period int.

A. Summarizing FNT results. Put up your two harmonic wave equations for waves (a)-(b) up on the board. Leave space on the board for the rest of the activities on thispage. Make sure your TA checks your equations, before going on.

* 1. Consider a medium where the magnitude of wave velocities is vwave = 2.0 m/s. Write outthe harmonic wave equations for the following two waves.(a) A harmonic wave traveling to the right, with a wavelength λ = 0.20 m, zero constant

phase, and an amplitude of 0.5 m.(b) A harmonic wave traveling to the right, with a wavelength λ = 0.24 m, a constant

phase of π, and an amplitude of 0.5 m.

B. Animating the superposition of two harmonic waves. Discuss (2)-(5) in your group,and then put your group's answers up on the board, in order that your TA can gaugeyour progress.

Use Graphing Calculator (as shown at right)to plot and animate the addition of the twoharmonic wave equations using your resultsfrom (1).

* 2. What parameter is being plotted on thehorizontal axis? What is the physicalinterpretation of "staying" at one locationon the horizontal axis, and letting nprogress from 0 to 10?

* 3. At t = 0.0 s, does an observer atx = 0.0 m detect constructive ordestructive interference? Demonstratethat you can predict your observation ofthis directly from solving the ∆Ψinterference condition equation.

* 4. At what time does the observer atx = 0.0 m next experience constructiveinterference? Destructive interference?Demonstrate that your observations ofthis from Graphing Calculator matchesthe expected value from Τbeat

calculations.

* 5. Describe what would happen if the two waves had the same wavelength of λ = 0.20 m.Test your prediction with Graphing Calculator.

y = A sin ( 2π ± 2π + ψ) xn

T λ

Type in your two harmonic wave equations added together (with your numerical values for A, T, ±, λ, and ψ); use “option-P” to enter “π,” “n” is used instead of t

Set 0 ≤ n ≤ 10, with 100 steps; press “play” to animate your wave

Rescale your graph

“Grab” the origin to move it

“Grab” the divider upwards to see the graph

+ ...


03.03.18

Activity Cycle 12.3.1: Analyzing wave superposition










03.03.18

DLM 07 Exit handout

Announcements Quiz 12 will be given during lecture 9:00-9:35 am on Monday, February 10, and will cover thematerial in Block 12. Bring a pen or pencil, calculator, and prepare to show your UC-Davis studentID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Read the Block 13 Glossary (pp. 71-80) in the Physics 7C Student Packet, Winter Quarter

2003, and familiarize yourself with the following terms that will be used extensively in DLM08.

direct model of forceselectric field

rE

fieldfield model of forcesforceforce, electric (direct model)force, electric (field model)force, gravitational

(direct model)force, gravitational

(field model)

gravitational field rg

potential energy, electricalPEelec

potential energy,gravitational PEgrav

source objecttest objectvector superposition (review)

2. There will be a lot of repetitious calculations in the next DLM 08, which will require the use ofthe following parameters. In order to streamline these calculations, look them up on page 2 ofthe Physics 7C Student Packet, Winter Quarter 2003, and highlight them and/or list them forfuture reference below.(a) Radius of the Earth: _____________ m.(b) Mass of the Earth: _____________ kg.(c) Charge of a proton: _____________ Coul.(d) Mass of a proton: _____________ kg.(e) Charge of an electron: _____________ Coul.(f) Mass of an electron: _____________ kg.(g) Universal gravitational constant: G = _____________ N ⋅ m2 / kg2 .(h) Conversion between meters and feet: 1 m = _____________ ft.(i) Conversion between kilometers and miles: 1 km = _____________ mi.(j) Conversion between "Ångstroms" and meters: 1 Å = _____________ m.(k) Electric force constant: k = _____________ N ⋅ m2 / Coul2 .(l) Conversion between "electronvolts" and Joules: 1 eV = _____________ J.

3. Calculate the magnitude (in N/kg) and direction (up or down) of the gravitational field vector gat these locations specified below (keep as many significant digits as necessary).(a) Sea level (calculate the exact theoretical value, which is close to, but not the given standard

approximation of "9.8 N/kg").(b) Aboard the International Space Station (orbiting 120 miles above sea level). (Interestingly

enough, this value is not zero!)


03.03.18

Activity Cycle 13.1.1: The field model (for gravitational forces)

A. Summarizing FNT results: characterization of gravitational field vectors created bymasses—the first step of the two-step field model. Put your group's FNT results up onthe board, and go on to the rest of this activity below.

* 1. Calculate the magnitude (in N/kg) and direction (up or down) of the gravitational fieldvector g at the locations specified below (keep as many significant digits as necessary).(a) Sea level.(b) Aboard the International Space Station (orbiting 120 miles above sea level)1.

B. Forces exerted by gravitational fields on masses—the second step of the two-step fieldmodel. Work at the board as a group and put your results up as you work, in orderthat your TA can gauge your progress.

* 2. Use the field model to find the magnitude (in N) and direction (up or down) of thegravitational force exerted on a 50.0 kg student, at the various locations listed above. In thisimplementation of the two-step field model, clearly indicate the following for each location:

(a) Source object: ___________.Test object: ___________.Magnitude (in N/Coul) and direction of relevant gravitational field vector: _________.Magnitude (in N) and direction of force on student: ___________.

(b) Source object: ___________.Test object: ___________.Magnitude (in N/Coul) and direction of relevant gravitational field vector: _________.Magnitude (in N) and direction of force on student: ___________.

* 3. Now use the field model to find the magnitude (in N) and direction (up or down) of thegravitational force exerted on the 454,000 kg International Space Station itself, in its orbit120 miles above the surface of the Earth. In this implementation of the two-step field model,clearly indicate the following for each location:

Source object: ___________.Test object: ___________.Magnitude (in N/Coul) and direction of relevant gravitational field vector: _________.Magnitude (in N) and direction of force on ISS: ___________.

Comment: this should all seem straightforward, once you get the idea—in fact, you have already beenusing the second part of the field model (as applied to gravitational forces) since Physics 7A and 7B.Later in this DL, you will be extending these concepts to electric forces. Move on! 1 "Space isn't remote at all. It's only an hour's drive away if your car could go straight upwards."

—Fred Hoyle


03.03.18

Activity Cycle 13.1.2: Superposition of fields (for elec. forces)

A. Characterization of electric field vectors created by point charges—the first step of thetwo-step field model. Work at the board as a group and put your results up as youwork, in order that your TA can gauge your progress.

Consider H+ nuclei (i.e., protons) at a certain locations for the specific cases shown below(note that 1 Å = 10 10− m). Keep in mind that a source object is always considered to be fixed,for the purposes of the field model.

* 1. Calculate the magnitude (in N/Coul) and direction (left or right) of the electric field Evectors at each and every x location, for the lone H+ nucleus in system (a). (One such Efield vector is already done for you—does it match what you calculate for that location?)For which location(s) is it irrelevant to define an electric field vector?

0 Å

+

x = –0.90 Å

H+

–0.37 Å +0.37 Å +0.90 Å

(a) 8.93×10 N/Coul

10E =

* 2. Repeat (1), but now for the lone H+ nucleus in system (b). (Hint: do not make any newcalculations—exploit symmetry and similarities with system (a).) For which location(s)is it irrelevant to define an electric field vector?

+H+

0 Åx = –0.90 Å –0.37 Å +0.37 Å +0.90 Å

(b)

* 3. Repeat (1), but now for the system of two H+ nuclei in system (c). (Hint: exploitsuperposition, symmetry, and similarities with systems (a) and (b).) For whichlocation(s) is the (total) electric field vector zero? For which location(s) is it irrelevant toeven define an electric field vector?

0 Å

+

x = –0.90 Å

H+

–0.37 Å

+H+

+0.37 Å +0.90 Å

(c)



03.03.18

Activity Cycle 12.1.2: Superposition of fields (for elec. forces)(continued)

B. Forces exerted by electric fields on point charges—the second step of the two-step fieldmodel. Work at the board as a group and put your results up as you work, in orderthat your TA can gauge your progress.

* 4. Use the field model to find the magnitude (in N) and direction (left or right) of the electricforce exerted by the H+ nucleus located at x = +0.37 Å, on an electron located atx = +0.90 Å (this is the attractive force between a proton and a 1s orbital electron in aneutral hydrogen atom). In this implementation of the two-step field model, clearlyindicate the following:

Source object(s): ___________.Test object(s): ___________.Set of electric field vectors used (choose one): (a)-(b)-(c).Magnitude (in N/Coul) and direction of relevant electric field vector: ___________.Magnitude (in N) and direction of force on electron: ___________.

* 5. Use the field model to find the magnitude (in N) and direction (left or right) of the electricforce exerted by the H+ nucleus at x = –0.37 Å, on the H+ nucleus at x = +0.37 Å (this isthe repulsive force between the two hydrogen nuclei in a hydrogen molecule). In thisimplementation of the two-step field model, clearly indicate the following:

Source object(s): ___________.Test object(s): ___________.Set of electric field vectors used (choose one): (a)-(b)-(c).Magnitude (in N/Coul) and direction of relevant electric field vector: ___________.Magnitude (in N) and direction of force on H+ nucleus: ___________.

C. Challenge questions. Discuss (6)-(9) in your group, but unless instructed by the TA,you do not have to put these up on the board.

6. What would the electric field vectors for (a) look like in all two dimensions? All three-dimensions?

7. Can the same charge be both a source object and a test object? Why or why not?

8. Why can't you use the set of total electric field vectors from (c) to answer (5)?

9. What is similar about the units of gravitational field vectors, and electric field vectors?


03.03.18

Activity Cycle 13.2.1: Potential energy, revisited

A. Changes in various potential energy systems, in a fundamental chemical process.Work at the board as a group and put your results up as you work, in order that yourTA can gauge your progress.

Consider the following exothermic chemical process where a proton and an electron combine toform neutral hydrogen:

H e H ++ + →− energy .

Assume that the initial position of the electron was moving very slowly at an infinite distanceaway from the proton, and that the final position of the electron is in the 1s hydrogen orbital(r = 0.53 Å).

* 1. Calculate the change in gravitational potential energy (in J, and in eV) of the proton-electron system. Specify how the ± result tells you whether PEgrav increased ordecreased in this initial-to-final process.

* 2. Calculate the change in electrical potential energy (in J, and in eV) of the proton-electronsystem. Specify how the ± result tells you whether PEelec increased or decreased in thisinitial-to-final process. Are the ± signs of the charges important?

* 3. What should be the total amount of energy (in eV) released to the environment, taking intoaccount your results from (2) and (3)? Which contribution to the amount of energyreleased (∆ PEgrav or ∆ PEelec ) is greater, and by what factor more than the other?

B. Challenge questions. Discuss (4)-(5) in your group, but unless instructed by the TA,you do not have to put these up on the board.

4. Recall from Chem 2A that the actual amount of energy given off in the above process is13.6 eV, which is not the same as your answer in (3), thus indicating that there is animportant energy system in this process that we have not properly accounted for. Frominspection of your answer in (3) being larger/smaller than 13.6 eV, would this be anenergy system that increased in energy, or decreased in energy during this process?

5. What is this energy system? (Hint: as in Physics 7A, you need to account for alldifferences in initial-to-final states. What (else) is the electron doing differently in itsfinal state that its initial state?


03.03.18

DLM 08 Exit handout

Announcements Quiz 12 will be given during lecture 9:00-9:35 am on Monday, February 10, and will cover thematerial in Block 12. Bring a pen or pencil, calculator, and prepare to show your UC-Davis studentID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Familiarize yourself with the following terms that will be used extensively in DLM 09, from the

Block 13 Glossary (pp. 81-87) in the Physics 7C Student Packet, Winter Quarter 2003.

gradient relationpotential energy,

gravitational PEgrav

potential energy, inter-atomicwork (review)

2. On the back of the DLM 08 exit handout is a (sideways) graph of the gravitational potentialenergy PEgrav for an Earth-1.0 kg mass system for various center-to-center separationdistances. For each of the following three separation distances, use the |slope| of the tangentlines to find the gravitational force (magnitude and direction) exerted on the 1.0 kg mass:(a) At sea level (center-to-center separation distance r = 6.37×106 m).(b) At a center-to-center separation distance of r = 10.0×106 m.(c) At a center-to-center separation distance of r = 15.0×106 m.

3. Familiarize yourself with the following terms that will be used extensively in DLM 09, from theBlock 13 Glossary (pp. 71-80) in the Physics 7C Student Packet, Winter Quarter 2003.

field model of forcesforce, magnetic

(field model)magnetic field

rB



03.03.18

center-to-center separation distance r between the E

arth and 1.0 kg mass [× 10 m

]6

67

89

1011

1213

1415

gravitational potential energy PE of Earth-1.0 kg system [× 10 J]7grav

–1–2–3–4–5–6–7


03.03.18

Activity Cycle 13.2.2: Forces and PE gradients

A. Summarizing FNT results: forces as potential energy "gradients." Put your group'sFNT results up on the board, and go on to the rest of this activity below.

* 1. On the back of the DLM 08 exit handout is a (sideways) graph of the gravitationalpotential energy PEgrav for an Earth-1.0 kg mass system for various center-to-centerseparation distances. For each of the following three separation distances, use the |slope|of the tangent lines to find the gravitational force (magnitude and direction) exerted on the1.0 kg mass:(a) At sea level (center-to-center separation distance r = 6.37×106 m).(b) At a center-to-center separation distance of r = 10.0×106 m.(c) At a center-to-center separation distance of r = 15.0×106 m.

B. Connections between gravitational forces and potential energy "gradients." Work atthe board as a group and put your results up as you work, in order that your TA cangauge your progress.

* 2. Use the relation between gravitational forces and PEgrav "gradients" to answer thefollowing questions:(a) Why does the slope of the graph flatten out at ∞?(b) Can a PEgrav graph (for a two-mass system) ever have a negative slope?

* 3. How would the PEgrav versus r graph for an Earth-2.0 kg mass system compare to aEarth-1.0 kg mass system? Draw both PEgrav curves on the same axes, and then explainhow your PEgrav graphs show that the Earth always exerts twice as much force on a2.0 kg mass than on a 1.0 kg mass, at any one given location. (Hint: both graphs havePEgrav = 0 at r = ∞.)

* 4. By reading values off of the PEgrav graph (no need to calculate anything), determineapproximately how much work (in J) each of these processes requires. Also explain whythese processes require different amounts of work, even though the changes in distancesare approximately the same.(A) Lifting a 1.0 kg mass from (a) sea level to location (b).(B) Lifting a 1.0 kg mass from location (b) to location (c).

* 5. Draw a PEgrav graph for the Earth-1.0 kg mass system, for a range of separationdistances of y = 0.0 m (TB 114 floor) to y = +2.7 m (TB 114 ceiling). Explain why thisPEgrav graph has a constant slope, unlike the curving slope of the PEgrav graph from theDLM 08 exit handout.)



03.03.18

Activity Cycle 13.2.2: Forces and PE gradients

C. Connections between inter-atomic forces and potential energy "gradients." Workat the board as a group and put your results up as you work, in order that your TAcan gauge your progress.

+0.4

+0.2

0.0

–0.4

–0.6

–0.8

–0.2

–1.0

0.6 0.7 0.8 0.9 1.0separation distance r between atoms [× 10 m]–10

PE

inte

r-at

omic fo

r H

-H [

× 10

J]–1

9

1.1

H

r

H

6. Use the relations between forces and potential energy "gradients" to explain the following:* (a) For what range of separation distances are there H-H repulsive forces? At what

specific r is the repulsive force a maximum?* (b) For what range of separation distances are there H-H attractive forces? At what

specific r (to the nearest 0.1 Å) is the attractive force a maximum?* (c) For what separation distances (to the nearest 0.01 Å) are no H-H forces whatsoever?

* 7. By reading values off of the PEinter atomic− graph (no need to calculate anything), determineapproximately how much work (in J) it would take to dissociate (break apart) a typical H2

molecule to an ∞ separation distance, and discuss whether this would be a minimum or amaximum amount of work to do so.

* 8. Suppose that the dissociation energy for H2 were one-half of the value you determined in(7). Draw a new PEinter atomic− versus r graph for this "weak H2" system on the same axesas the original H2 system. Explain which of your answers in (6) will change, and whetherthe magnitude of the forces will be increased/decreased for the "weak H2" system.


03.03.18

Activity Cycle 13.3.1: Characterizing magnetic fields

A. Preliminary stuff. Set up the experiment described below, and follow the directionson the other side of this page.

LabPro interface (nothing to adjust) Probe interface

(high sensitivity setting)

Voltage source

Laptop (start Logger Pro after everything else is ready; automatically starts measuring magnetic field magnitudes)

Telegraph key switch(hold down to turn on current)

+ –

Magnetic probe (center of dot at distance r from center of current)

ruler (to measure r )

Current-carrying white wire

Hint: record magnetic field when current is off, then when current is on, then you can subtract the background of the Earth’s magnetic field!

Hint: keep other parts of the current wire as far away from the probe as possible

Note: probe only detects magnetic fields that are perpendicular to its dot

I = 2.0 Amps

Slowly turn up from zero to produce 2 A of current when telegraph key is held down

Limiting resistors


03.03.18

Activity Cycle 13.3.1: Characterizing magnetic fields (continued)

B. Taking (careful) data, and subtracting out the background. Perform and discuss theexperiments (1)-(3) described below in your group, summarize your measurements onthe board, and be prepared to be called on as a group in the whole-class discussion todemonstrate your experimental results to the rest of the class.

1. Hold the magnetic field probe such that the white dot is held as close to the wire aspossible, facing towards the wire. Record the magnetic field (in relative arbitrary units(i.e., not really "milliTeslas")) when the current is turned on, and then when it is turned off(this is so you can subtract out the background magnetic field of the Earth, in order to getonly the magnetic field created by the wire).

2. Repeat (1), with the white dot held as close to the wireas possible, but with the white dot alongside the wireinstead of facing towards it.

* Fill in the charts below to summarize your results (you can repeat multiple measurements).Magnetic fieldmagnitude ofwire and Earth(arbitrary units)

Magnetic fieldmagnitude ofjust the Earth(arbitrary units)

Magnetic fieldmagnitude ofjust the wire(arbitrary units)

1. Dot facing wire

2. Dot beside wire

3. Repeat (2), with the white dot alongside the wire (i.e., face up on ruler), for various rdistances from 1.0 cm to 10.0 cm (as measured from center of the wire to the center of thedot).

Bwire Earth+ (arb. units) BEarth (arb. units) Bwire (arb. units)

r = 1.0 cmr = 2.0 cm (etc.)

C. Interpreting your results to characterize the magnetic field created by current in awire. You only have to discuss this in your groups, and then get permission to bedismissed by your TA. The following question (4) below is a "lab report" questionsto be handed in for credit as soon as you walk in to the next DLM 10. It is yourresponsibility to have enough careful data to answer this question before leaving DLtoday.4. (a) From your results in (1)-(2), support your conclusion whether magnetic field

directions point tangentially sideways to or radially away from the current in a wire.

(b) Magnetic field magnitudes are inversely dependent on the distance r away from thecurrent in a wire. Calculate (Bwire ·r) and (Bwire ·r2) for all measurements in (3), andinterpret your results to support your conclusion of either 1/r or 1/r2 dependence.


03.03.18

DLM 09 Exit handoutAnnouncements Quiz 12 will be given during lecture 9:00-9:35 am on Monday, February 10, and will coverthe material in Block 12. Bring a pen or pencil, calculator, and prepare to show your UC-Davisstudent ID card (or similar photo ID) upon entering, and/or during the quiz. There is no lecture on Monday, February 17, due to the President's Day holiday. Note thatDLs will be unaffected, and will continue as scheduled.


X. Analyze your results from (1)-(3) of Activity Cycle 13.3.1.(a) From your results in (1)-(2), support your conclusion whether magnetic field directions

point tangentially sideways along or radially away from the current in a wire.(b) Magnetic field magnitudes are inversely dependent on the distance r away from the

current in a wire. Calculate (Bwire ·r) and (Bwire ·r2) for all measurements in (3), andinterpret your results to support your conclusion of either 1/r or 1/r2 dependence.Explain why and how this analytical trick works.

(c) Discuss how your results in (a)-(b) demonstrates the magnitude and direction propertiesof magnetic fields around a current-carrying wire, as given by RHR1 and the first step ofthe two-step field model of magnetic forces.

The following FNTs are only to be checked off by your TA; you are not going to turn these in.1. Consider the following arrangements (a)-(e) of current-carrying wires.

Use the convention at right for drawing vector directions on a page.When drawing all of your vectors, clearly label whether it representscurrent I or magnetic field B. (The vectors at right can be used torepresent any kind of quantity, so please specify what they represent.)Determine the magnitude (in Teslas) and direction of the magneticfield B at each and every "?" location (some have been done for youalready).

out of page

into page

up

down

left

right


03.03.18

8.0×10 Tesla

6B =

Ι = 4.0 Ax = –0.1 m

+0.1 m +0.2 m

y = +0.1 m

–0.1 m

(a) Current going into the page

× +0.3 m

?

?

?8.0×10 Tesla

6B =

4.0×10 Tesla

6B =

0 m

(b) Current coming out of the page

Ι = 4.0 A

x = –0.1 m +0.1 m +0.3 m

?? ??

Ι = 4.0 A

x = –0.1 m +0.1 m +0.2 m

(c) Current up in the plane of the page

+0.3 m

?? ? ?

(d) Two currents going into plane of the page

Ι1 = 4.0 A

x = –0.1 m +0.3 m

??

+0.1 m

? Ι2 = 4.0 A× ×

(e) Two currents, into/out of the page

Ι1 = 4.0 A

x = –0.1 m +0.3 m

??

+0.1 m

? Ι2 = 4.0 A×


03.03.18


field model of forcesforce, magnetic

(field model)magnetic field

rB


3. Come to the next DLM 10 with the fingers on your right hand labeled asshown (this is for RHR2, the second step in the two-step field model ofmagnetic forces). We mean it.

v

F

B


03.03.18

Activity Cycle 13.3.2: Superposition of fields (for mag. forces)

A. Summarizing FNT results: characterization of magnetic field vectors created bycurrent-carrying wires—the first step of the two-step field model. Your TA will assignone of the fields (a)-(e) for your group to put up on the board, and then go on to therest of this activity on the other side of this page.

* 1. Determine the magnitude (in Teslas) and direction of the magnetic field B at each andevery "?" location for the current-carrying wires placed at the specific locations shown on1(a)-(e) of the DLM 09 exit handout. Keep in mind that a source object is alwaysconsidered to be fixed, for the purposes of the field model.



03.03.18

Activity Cycle 13.3.2: Superposition of fields (for mag. forces)(continued)

B. Forces exerted by magnetic fields on moving charges—RHR2, the second step of thetwo-step field model. Work at the board as a group and put your results up as youwork, in order that your TA can gauge your progress, and practice RHR2 with yourfingers to explain the following magnetic force directions.

* 2. For the situation shown below, use RHR2 to show why the direction of the magneticforce on the proton is exerted out of the plane of the page. Clearly indicate:Source object(s): ___________.Test object(s): ___________.Set of magnetic field vectors used (choose one): 1(a)-(b)-(c)-(d)-(e).Magnitude (in Teslas) and direction of relevant magnetic field vector: ___________.(Then rehearse a demonstration of RHR2 to explain the direction of force on proton.)

Ι1 = 4.0 A

x = –0.1 m +0.3 m+0.1 m×

protonv = 0.1 m/sΙ2 = 4.0 A

*3 . For the situation shown below, use RHR2 to show why the direction of the magneticforce on the wire located at x = +0.2 m is exerted to the right along the plane of the page.Clearly indicate:Source object(s): ___________.Test object(s): ___________.Set of magnetic field vectors used (choose one): 1(a)-(b)-(c)-(d)-(e).Magnitude (in Teslas) and direction of relevant magnetic field vector: ___________.(Then rehearse a demonstration of RHR2 to explain the direction of force on thex = +0.2 m wire.)

Ι1 = 4.0 A

x = –0.1 m +0.3 m+0.1 m

Ι2 = 4.0 A×


4. What would the magnetic field vectors for 1(a) and 1(b) look like in all two dimensions?All three-dimensions?

5. Can the same current-carrying wire be both a source object and a test object? Why orwhy not?

6. Why can't you use the set of magnetic field vectors from 1(e) to answer (3)?

7. Which direction did you point your thumb in RHR2 for the moving test charge in (2)?Which direction did you point your thumb in RHR2 for the moving test charge in (3)?


03.03.18

Activity Cycle 13.3.3: The field model (for mag. forces)A. Preliminary stuff. Set up the three experiments (a)-(c) described below one at a time,

and follow the directions on the other side of this page.

electron beam

v

∆V I

power source

2.00

+–

Telegraph key switch(hold down to turn on current)

Current-carrying white wire

Hint: keep other parts of the current wire as far away from the electron tube as possible

I = 2.0 Amps

Slowly turn up from zero to produce 2 A of current when telegraph key is held down

Limiting resistors

highon(a) Current parallel to electron beam

“Cathode ray tube (CRT)” control box

Brightness (turn up all the way)

Focus (make spot small as possible)

Deflection (center spot on screen)

(b) Current antiparallel to electron beam

electron beam

v

(c) Current perpendicular to electron beam

Always keep “DC out” switch on

electron beam

v


03.03.18

Activity Cycle 13.3.3: The field model (for mag. forces)(continued)

B. Making predictions using the first part of the two-step model, and then taking(careful) data for the second part of the two-step model. Perform and discuss theexperiments (1)-(3) described below in your group, summarize your measurements onthe board, and be prepared to be called on as a group in the whole-class discussion todemonstrate your experimental results to the rest of the class.

1. For each of the experimental set-ups in (a)-(c), make the necessary distance and currentmeasurements in order to determine the magnitude and direction of the magnetic fieldvector B created by the wire, at the location of the green dot in the cathode ray tube.

2. For each of the experimental set-ups in (a)-(c), carefully watch what happens to the greendot in the cathode ray tube when the current is turned on, compared to when there is nocurrent in the wire.

* Fill in the chart below to summarize your results.Experimental measurements: Predictions of Bwire : Exp. observ.:distance rfrom wire[m]

current Ithrough wire[Amp]

magnitude ofmagnetic field[Tesla]

direction ofmagnetic field[vector arrow]

direction ofgreen dotdeflection

(a)(b)(c)

C. Interpreting your results using the two-step field model. You only have to discuss thisin your groups, and then get permission to be dismissed by your TA. The followingquestion (3) below is a "lab report" question to be handed in for credit as soon as youwalk in to the next DLM 10. It is your responsibility to have enough careful data toanswer this question before leaving DL today.

* 3. Use the two-step field model (RHR1 and RHR2) to analyze your results in (1)-(2) for asingle electron inside the cathode ray tube (as they travel at a speed of 1.68×107 m/s), foreach of the experimental set-ups in (a)-(c). Show your three-dimensional drawings in aclear and concise manner as possible.

Source object: ___________.Test object: ___________.Magnitude (in Teslas) and direction of relevant magnetic field vector: _________.Magnitude (in m/s) and direction of velocity of a cathode ray tube electron: ___________.Magnitude (in N) and direction of force on a cathode ray tube electron: ___________.(Hint: electrons have negative charge!)


03.03.18

DLM 10 Exit handoutAnnouncements There is no lecture on Monday, February 17, due to the President's Day holiday. Note thatDLs will be unaffected, and will continue uninterrupted as scheduled. Quiz 13 will be given during lecture 9:00-9:35 am on Monday, February 24, and will coverthe material in Block 13. Bring a pen or pencil, calculator, and prepare to show your UC-Davisstudent ID card (or similar photo ID) upon entering, and/or during the quiz.


X. Use the two-step field model (RHR1 and RHR2) to analyze your results in (1)-(2) of ActivityCycle 13.3.3 for a single electron inside the cathode ray tube (as they travel at a speed of1.68×107 m/s), for each of the experimental set-ups in (a)-(c). Show your three-dimensionaldrawings in a clear and concise manner as possible.

Source object: ___________.Test object: ___________.Magnitude (in Teslas) and direction of relevant magnetic field vector: _________.Magnitude (in m/s) and direction of velocity of a cathode ray tube electron: ___________.Magnitude (in N) and direction of force on a cathode ray tube electron: ___________.(Hint: electrons have negative charge!)


(Quiz 13, Spring 2000)1. A rock of unknown mass from

very, very far away crashes ontothe surface of the Moon.Credit is assigned for thecompleteness and clarity ofyour justifications, and notnecessarily for your answersand numerical results.(a) What is the minimum

velocity (in m/s) of the rock just ast it crashes onto the surface of the Moon? Explainwhat assumptions must be made in order for your answer to be the minimum velocity ofthe rock. (Hint: when finding the velocity, your energy balance equation should havethree terms that together sum to zero.)

DEarth-Moon = 3.85 × 10 m8

REarth = 6.37 × 10 mMEarth = 5.98 × 10 kg

6

24

path of rock

RMoon = 1.73 × 10 mMMoon = 7.35 × 10 kg

6

22


03.03.18

(b) Which gravitational potential energy system (Earth-rock or Moon-rock) contributes moreenergy to the kinetic energy system of the rock? Determine the factor by which it is largerthan the other.

(Quiz 13, Fall 2001)2. [50%] The inter-atomic potential energy graph versus separation distance r between the

hydrogen atom (fixed) and fluorine (moveable) atom in an HF molecule is shown below.Credit is assigned for the completeness and clarity of your justifications, and not necessarilyfor your answers and numerical results.

+0.4

+0.2

0.0

–0.4

–0.6

–0.8

–0.2

–1.0

0.8 0.9 1.0 1.1 1.2separation distance r between atoms [× 10 m]–10

PE

inte

r-at

omic fo

r H

F [×

10

J

]–1

9

r

H F

1.67

4 ×

10

kg

–27

31.1

55 ×

10

k

g–2

7

(a) Determine the (total) inter-atomic force (magnitude (in N), and direction (whetherattractive/repulsive)) exerted on the fluorine atom, when the HF separation distance isr = 1.00×10−10 m.

(b) Recall that inter-atomic interactions between H and F are due to the contributions ofgravitational, electric, and quantum-mechanical orbital interactions. At the separationdistance r = 1.00×10−10 m, rank the following forces from smallest magnitude to largestmagnitude.(A) The gravitational force between H and F.(B) The electric force between the nuclei of H and F.(C) The quantum-mechanical orbital interactions between H and F.


03.03.18

(Quiz 13, Summer Session I, 2000)2

3. Two electric charges (+1 µCoul and –8 µCoul) are placed and rigidly held at their respectivelocations along the x-axis (–4.0 cm and +4.0 cm), as shown below. Credit is assigned for thecompleteness and clarity of your justifications, and not necessarily for your answers andnumerical results.

+1 µCoul –8 µCoul

–4 cm 0 cm +4 cm

+

x = –8 cm +8 cm

(a) In what region(s) would their total electric field be zero? Defend your choice(s) for zerototal electric field regions.(A) Somewhere to the left of the +1 µCoul charge.(B) Between the two charges.(C) Somewhere to the right of the –8 µCoul charge.

(b) Rank the following total electric fields at the locations listed below, from smallestmagnitude to largest magnitude.(A) The total electric field at x = –8 cm.(B) The total electric field at x = 0 cm.(C) The total electric field at x = +8 cm.

(Quiz 11, Fall 2001)3

4. Two wires carry currenteither into or out of the planeof this page, as shown atright. Wire 2 carries 0.2 Amps of current, while wire 1 carries an unknown amount of current.When an electron is placed at x = +10 cm, and moves to the right with a speed of v = 2.0 cm,there is no magnetic force exerted on it by the two wires.

Determine the magnitude (in N) and direction of the total magneticforce exerted on an electron located at x = +20 cm, as it moves to theright with a speed of v = 2.0 cm/s. Choose and defend one of thedirections indicated. Credit is assigned for the completeness andclarity of your justifications, and not necessarily for your answers andnumerical results.

2 Also given on Midterm 2 for Physics 210B at Sonoma State University, Spring 2002.3 Also given on Final Exam for Physics 210B at Sonoma State University, Spring 2002.

Ι1Ι 2

x = –10 cm 0 cm +10 cm +20 cm

×

out of page

into page

up

down

left

right


03.03.18

(Final Exam, Summer Session I, 2000)5. A (neutrally charged) Physics 7C student (carefully) carries an

electron horizontally to the right at a constant velocity of 0.3 m/sthrough a magnetic field, as shown in this side view. Shenotices that the apparent weight of the electron decreases to halfof its expected value as she does this (i.e., "the electron feelslighter!"). This entire experiment takes place at sea level on this(neutrally charged) planet. Shown below are four magnetic fields (A)-(D) that may or may notsurround the electron as the student carries it horizontally to the right. Credit is assigned forthe completeness and clarity of your justifications, and not necessarily for your answers andnumerical results.

electron v

B

(A)

electronelectron electronvv v

B B B

(B) (C) (D)

(a) Which of the above magnetic fields (A)-(D) depicts the magnetic field created by theelectron? Choose and defend one field only.

(b) Which of the above magnetic fields (A)-(D) depicts the magnetic field that exerts amagnetic force on the electron? Choose and defend one field only.

(c) What is the magnitude (in Teslas) of the magnetic field vectors that exerts a magneticforce on the electron?

region of magnetic field vectors


03.03.18

Activity Cycle 13.4.1: Analyzing fields and potentials










03.03.18

DLM 11 Exit handout

Announcements There is no lecture on Monday, February 17, due to the President's Day holiday. Note thatDLs will be unaffected, and will continue uninterrupted as scheduled. Quiz 13 will be given during lecture 9:00-9:35 am on Monday, February 24, and will coverthe material in Block 13. Bring a pen or pencil, calculator, and prepare to show your UC-Davisstudent ID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Calculate the amount of energy released (in J) for the two (exothermic) nuclear reactions listed

below. (Hint: calculate the mass decrement, then convert from u to J by the conversion factor1 u = 1.49×10–10 J/"c2". Your answers should correspond to the values on the inter-nuclearPE graphs on pages 92 and 94 of the Physics 7C Student Packet.)(a) n U Rb Cs +2n92

2353793

55141+ → + .

(b) 12

13

24H H He n+ → + .

Table of atomic masses:

n = 1.008 664 923 u

12H = 2.014 101 778 u

13H = 3.016 049 268 u

24 He = 4.002 603 250 u

3793 Rb = 92.922 032 765 u

55141Cs = 140.920 043 984 u

92235U = 235.043 923 062 u

2. Calculate the change in electrical PE for each of the processes listed below, and state whether itis an increase or decrease. Assume that the nuclei involved act like simple positive charges.(Hint: your answers should correspond to the values on the inter-nuclear PE graphs on pages92 and 94 of the Physics 7C Student Packet.)(a) A rubidium nucleus (containing 37 protons and 56 neutrons) and a cesium nucleus

(containing 55 protons and 86 neutrons) approach each other from an initial separationdistance of ∞, until just before they touch (center-to-center separation distance of11.7× −10 15 m).

(b) A deuterium nucleus (containing a proton and a neutron) and a tritium nucleus (containinga proton and two neutrons) approach each other from an initial separation distance of ∞,until just before they touch (center-to-center separation distance of 3.24× −10 15 m).


03.03.18

3. Read the Block 14 Glossary (pp. 89-104) in the Physics 7C Student Packet, Winter Quarter2003, and familiarize yourself with the following terms that will be used extensively in DLM12. (Note that for Winter 2003, the Block 14 material in the Student Packet will completelyreplace the obsolescent material in the Physics 7C Course Notes. Future quarters of Physics7C will not cover any of the material from the Student Packet, and will instead return to thematerial covered in the Physics 7C Course Notes.)

binding energyfemtometer (fm)fissionfusionmass decrementmass defectmass-energy equivalencemegaelectron-volt (MeV)nuclear radius R

nucleonnucleon number Anucleuspotential energy,

inter-nuclearproton number ZQ-valueunified atomic mass unit (u)


03.03.18

Activity Cycle 14.1.1: Nuclear fission processesA. Summarizing FNT results: energetics of an exothermic fission process. Put your

group's FNT results up on the board, and go on to the rest of this activity below.

Consider the fusion process 92235

3793

55141U +n Rb Cs +2n→ + , as shown by 1 → 2 → 3 on the

inter-nuclear PE graph shown below (cf. page 92 of the Physics 7C Student Packet, Winter2003).

+10

+20

+30

0.0 5.0 10.0 15.0 20.0

distance r [fm]

Inte

r-n

ucle

ar P

E (

×10

)

[J]

–12

+40

+50

net energy released

(Q-value)

initiation energy

3 r = ∞

1

2

* 1. Calculate the net amount of energy (in J) released in this process.* 2. Calculate the change in electrical PE (increase/decrease in J) from 2 → 3 .

B. Further analysis of this process. Work at the board as a group and put your resultsup as you work, in order that your TA can gauge your progress.

* 3. What is the initiation energy cost (in J) to start this process?

* 4. Describe what is happening in each of the processes listed below:(a) What does the 92

235 U nucleus look like at 1 ? Verify that this distance is equal to

the nuclear radius of 92235 U .

(b) What is happening to the 92235 U nucleus from 1 → 2 ?

(c) What is happening to the 92235 U nucleus right at 2 ? Verify that this distance is

equal to the nuclear radii of 55141Cs and 37

93Rb added together.

(d) What is happening to the 55141Cs and 37

93Rb nuclei from 2 → 3 ?



03.03.18

Activity Cycle 14.1.1: Nuclear fission processes (continued)

* 5. Inspect the slope of the inter-nuclear PE graph from 1 → 2 , which tells you the

direction of the total force exerted between the rubidium and cesium nuclei just beforethey completely separate from each other. In this region, which is stronger—the attractivestrong force between their nucleons, or the repulsive forces between just their protons?

* 6. Strong bonds are interactions between nucleons in contact with each other (regardless ofwhether they are p-p, p-n, or n-n). Explain whether strong bonds are being made orbroken in 1 → 2 . Does this mean that strong bond energy is increasing or

decreasing?

C. Summary of results. No new calculations are required; your answers should directlyfollow from all of your work from previously answering (1)-(6).

* 7. Complete the following statement. For process 1 → 2 :

the increase

decrease

in electric PE is

more than

the same amount as

less than

the

increase

decrease

in strong bond energy.


electric PE

increases

remains the same

decreases

, and strong bond energy

increases

remains the same

decreases

.

* 9. Complete the following statement. For the entire fission process 1 → 3 :

the increase

decrease

in electric PE is

more than

the same amount as

less than

the

increase

decrease


D. Challenge questions. Discuss (10)-(11) in your group, but unless instructed by yourTA, you do not have to put these up on the board.

10. What would the inter-nuclear PE graph look like for an endothermic fusion process?

11. Neutron masses were included in your Q-value calculations, but why were the neutronsinvolved in this fission process not shown on an inter-nuclear PE graph?


03.03.18

Activity Cycle 14.1.2: Nuclear fusion processesA. Summarizing FNT results: energetics of an exothermic fusion process. Put your

group's FNT results up on the board, and go on to the rest of this activity below.Consider the fusion process 1

213

24H H He n+ → + , as shown by 1 → 2 → 3 on the inter-

nuclear PE graph shown below (cf. page 94 of the Physics 7C Student Packet, Winter 2003,shown below is a correction to the initiation energy value).

+1.0

+2.0

+3.0

0.0

–1.0

–2.0

–3.0

5.0 10.0 15.0 20.0distance r [fm]

Inte

r-n

ucle

ar P

E (

×10

)

[J]

–12

net energy released(Q-value)

initiation energy

2

1 r = ∞

3

* 1. Calculate the net amount of energy (in J) released in this process.* 2. Calculate the change in electrical PE (increase/decrease in J) from 1 → 2 .

B. Further analysis of this process. Work at the board as a group and put your resultsup as you work, in order that your TA can gauge your progress.

* 3. What is the initiation energy cost (in J) to start this process? Why is this initiation energycost calculated differently here than for fission?

* 4. Describe what is happening in each of the processes listed below:(a) What is happening to the 1

2H and 13H nuclei from 1 → 2 ?

(b) What is happening to the 12H and 1

3H nuclei right at 2 ? Verify that this distance

is equal to the nuclear radii of 12H and 1

3H added together.

(c) What is happening to the 24 He nucleus from 2 → 3 ?

(d) What does the 24 He nucleus look like at 3 ? Verify that this distance is equal to

the nuclear radius of 24 He.



03.03.18

Activity Cycle 14.1.2: Nuclear fusion processes (continued)

* 5. Inspect the slope of the inter-nuclear PE graph from 2 → 3 , which tells you the

direction of the total force exerted between the deuterium and tritium nuclei just after theirsurfaces touch. In this region, which is stronger—the attractive strong force betweentheir nucleons, or the repulsive forces between just their protons?

* 6. Strong bonds are interactions between nucleons in contact with each other (regardless ofwhether they are p-p, p-n, or n-n). Explain whether strong bonds are being made orbroken in 2 → 3 . Does this mean that strong bond energy is increasing or

decreasing?

C. Summary of results. No new calculations are required; your answers should directlyfollow from all of your work from previously answering (1)-(6).


electric PE

increases

remains the same

decreases

, and strong bond energy

increases

remains the same

decreases

.


the increase

decrease

in electric PE is

more than

the same amount as

less than

the

increase

decrease

in strong bond

energy.

* 9. Complete the following statement. For the entire fusion process 1 → 3 :

the increase

decrease

in electric PE is

more than

the same amount as

less than

the

increase

decrease


D. Challenge questions. Discuss (10)-(11) in your group, but unless instructed by yourTA, you do not have to put these up on the board.

10. What would the inter-nuclear PE graph look like for an endothermic fusion process?

11. Even though the initiation energy cost for this fusion process is much lower than for thefission process in activity cycle 14.1.1, explain why it is easier in practice to initiateuranium fission than tritium-deuterium fusion. (Hint: why is it easier to combine aneutron with a certain amount of energy with a uranium nucleus, than a deuterium anda tritium nucleus?)


03.03.18

Activity Cycle 14.2.1: α decay versus nuclear fissionA. Comparison of two possible nuclear processes. Work at the board as a group and put

your results up as you work, in order that your TA can gauge your progress.

Shown below is the inter-nuclear PE graph of two possible (exothermic) processes that bring anunstable 92

236U nucleus to a lower energy state:

"Pd-Pd fission:" 92236

46118

46118U Pd Pd→ + (process 1 → 2 → 3 )

"α decay:" 92236

90232

24U Th He→ + (process 1 → 2’ → 3’ ).

* 1. Which process (Pd-Pd fissionor α decay) releases a greaternet amount of energy?Explain how you can read thisoff of an inter-nuclear PEgraph, and relate this to whichprocess has a greater netdecrease in PEelec .

* 2. Which process (Pd-Pd fissionor α decay) has a higherinitiation energy cost?Explain how you can read thisoff of an inter-nuclear PEgraph, and relate this to whichprocess must break apartmore strong bonds betweennucleons in order for the 92

236Unucleus to split apart.

* 3. Explain why the fission distanceat 2 is greater than the

α emission distance at 2’ ?

(Hint: draw a picture of whathappens at 2 and at 2’ , and

calculate the radii for all of thenuclei involved, cf. activity14.1.1, question 4(c).)

* 4. Which of the factors (1)-(3) helps explain why α-decay for the specific case of anunstable 92

236U nucleus is favored over Pd-Pd fission? Which of the factors (1)-(3) doesnot help explain α-decay for the specific case of an unstable 92

236U nucleus is favored overPd-Pd fission?

inte

r-nu

clea

r po

tent

ial e

nerg

y P

Ein

ter-

nucl

ear (r

) [J

]

distance r [m]

3

2

3’

2’

1


03.03.18

DLM 12 Exit handoutAnnouncements Quiz 13 will be given during lecture 9:00-9:35 am on Monday, February 24, and will coverthe material in Block 13. Bring a pen or pencil, calculator, and prepare to show your UC-Davisstudent ID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Fill in the proton and neutron "box model" energy levels for each of the five (stable) nuclei (a)-

(e) below. Remember that there can only be a maximum of two protons or two neutrons (spinup and spin down) per energy level.

37Li

p n

36Li

p n

24He

p n

(d)(c)(b)23He

p n

(a)

2. Read the Block 14 Glossary (pp. 105-119) in the Physics 7C Student Packet, Winter Quarter2003, and familiarize yourself with the following terms that will be used extensively in DLM13. (Note that for Winter 2003, the Block 14 material in the Student Packet will completelyreplace the Physics 7C Course Notes. Future quarters of Physics 7C will not cover any of thematerial from the Student Packet, and will instead return to the material covered in the Physics7C Course Notes.)

"antielectron" ( e+ )antimatterantineutrino ( ν )beta decaybeta particles (β− , β+ )box modelelectron capture (ε)

neutrino ( ν)nuclear weak interactionpositron (e+ )potential energyQ-value (radioactive decay)radioactive decayweak interaction process


03.03.18

Activity Cycle 14.3.1: Box model and nuclear stabilityA. Summarizing FNT results: filling "box model" nuclear energy levels. Put your

group's FNT results up on the board, and go on to the rest of this activity below.

* 1. Fill in the proton and neutron "box model" energy levels for each of the five nuclei (a)-(e)below. Remember that there can only be a maximum of two protons or two neutrons(spin up and spin down) per energy level.

37Li

p n

36Li

p n

24He

p n

(d)(c)(b)23He

p n

(a)

B. The "box model" and nuclear stability of oxygen isotopes. Work at the board as agroup and fill in your nuclear energy levels as you work, in order that your TA cangauge your progress.

* 2. Fill in the proton and neutron "box model" energy levels for each of the five isotopes ofoxygen (a)-(e) below. (Note for oxygen nuclei, the proton ground state is raised higherdue to there being more internal proton-proton repulsion than in helium and lithium.)Then decide which of these nuclei are stable or unstable. For the nuclei that are unstable:• Describe whether it would reach a more stable state by transforming a proton into a

neutron, or a neutron into a proton.• Write out the notation for the new nucleus that it becomes after stabilizing itself.

(d)(c)(b) 818O

p n

817O

p n

816O

p n

(e) 819O

p n

(a) 815O

p n



03.03.18

Activity Cycle 14.3.1: Box model and nuclear stability (continued)

C. Conditions for nuclear stability in the "box model." Work at the board as a groupand put your results up as you work, in order that your TA can gauge your progress.

* 3. Explain in words why a nucleus with a given amount of Z protons cannot have too few ortoo many neutrons.

4. 83209Bi is the largest stable nucleus, with 83 protons and 126 neutrons. (Any nucleus withmore than 83 protons has too much internal proton-proton repulsion to be permanentlystable, and thus all Z > 83 elements are radioactive, regardless of how their topmostnuclear energy levels are filled.)

* (a) Which of the proton and neutron energy levels shown below best depicts thetopmost proton and neutron energy levels for 83

209Bi? (Hint: eliminate two choicesbecause they are inherently unstable—then decide which of the two remainingchoices will give you the right number of protons and neutrons in 83

209Bi.)

20983Bi?209

p n

83Bi?

p n

(filled below) (filled below)

20983Bi?209

p n

83Bi?

p n

(filled below) (filled below)

* (b) Note for oxygen nuclei, the proton ground state lies between the first and secondneutron energy levels. Between which neutron energy levels is the (significantlyraised) proton ground state for 83

209Bi? (Hint: count carefully!)

* 5. Summarize your results in (3) and (4) to give a plausible explanation why small nucleithat are stable have nearly equal numbers of protons and neutrons; while larger nucleithat are stable have much more neutrons than protons.


03.03.18

Activity Cycle 14.3.2: Beta decay processesA. Completing the nuclear reaction equations for beta decay processes. Work at the

board as a group and put your results up as you work, in order that your TA cangauge your progress.

1. The basic nuclear reaction equation for a neutron turning into a proton is given by:

n p e→ + +– ν (electron emission—β– , or "beta-minus" decay).

Note that charge is conserved, while the "antineutrino" has such a small mass that it isessentially negligible (it assists in conserving spin).

* (a) For the oxygen isotope in activity cycle 14.3.1,question (2) that would reach a lower energyconfiguration by a neutron-to-proton conversion,write out the nuclear reaction equation that describesthis process (the "n" and "p" are "inside" the initialand final nucleus, respectively).

* (b) Calculate the Q-value = (minitial atom – m final atom )c2

(in J) of this reaction, and verify that it is positive.(Recall that 1 u = 1.49×10–10 J/"c2".)

2. There are two possible nuclear reactions for a proton turning into a neutron:

p e n+ → +– ν (absorption of an inner shell electron—ε, or "electron capture");p n e→ + ++ ν (positron emission—β+ , or "beta-plus" decay).

* (a) Show how each of these two reactions can be derived from the basic neutron-to-proton process for β– decay. What happens to particles that are "switched" fromone side of a reaction equation to the other?

* (b) For the oxygen isotope in activity cycle 14.3.1, question (2) that would reach a lowerenergy configuration by a proton-to-neutron conversion, write out the two possiblenuclear reaction equations that would describe this process (the "p" and "n" are"inside" the initial and final nucleus, respectively).

* (c) Calculate the Q-values (in J) for each of these two reactions (for electron captureQ-value = (minitial atom – m final atom )c2; but for positron emission Q-value =( minitial atom – m final atom – 2me)c

2 . Determine which of these proton-to-neutronprocess is possible/impossible.


3. For the two proton-to-neutron processes, why is electron capture (ε) able to release moreenergy than positron emission (β+)? That is, why is there an the "extra energy cost"for β+ decay?

4. There is an alternative process of converting a neutron into a proton (for a total of twoneutron-to-proton processes, similar to the two proton-to-neutron processes). Write outthe basic nuclear reaction for the process, and then argue why the likelihood of thisparticular neutron-to-proton process is very small.


e± = 0.000 548 6 u

715N = 14.003 074 005 u

815O = 15.003 065 386 u

819O = 19.003 578 730 u

919F = 18.998 403 205 u


03.03.18

DLM 13 Exit handout

Announcements Quiz 13 will be given during lecture 9:00-9:35 am on Monday, February 24, and will coverthe material in Block 13. Bring a pen or pencil, calculator, and prepare to show your UC-Davisstudent ID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")DLM 14 is a problem-solving session that will consolidate the material covered in Block 14.

(New problem)1. Consider the following two fusion processes that produce 7

14 N:

Process [1]: p C N +613

714+ → γ.

Process [2]: 36

48

714Li+ Be N→ .

Given below is a table of atomic (not nuclear masses) for several nuclei, in unified atomic massunits. Credit is assigned for the completeness and clarity of your justification using theproperties of the box model, inter-nuclear potential energy, mass-energy equivalence andnuclear processes, and not necessarily for finding the correct choice.


11H = 1.007 825 032 u

36Li = 6.015 122 281 u

48Be = 8.005 305 094 u

613C = 13.003 354 838 u

714 N = 14.003 074 005 u

(a) Draw the transitions between box model energy levels for process [1] (assuming that theproton and neutron energy levels are not appreciably shifted relative to each other, and thatthe only transitions that occur are between consecutive energy levels), starting from 6

13C .Discuss whether the wavelength value of the gamma ray represents the maximum possiblevalue, minimum possible value, or is a fixed value no matter how much KE the proton hadin colliding with the carbon atom.

(b) Recall that a fusion nuclear reaction (regardless if it is exo/endothermic) requires a certainamount of energy to initiate. Choose and defend one statement only.(A) Process [1] will require a greater amount of initiation energy.(B) Process [2] will require a greater amount of initiation energy.(C) Both processes [1] and [2] will require the same amount of initiation energy.


03.03.18

(New problem)2. Consider two stable (non-radioactive) molecules:

CO (carbon monoxide), with 612C and 8

16O nuclei.N2 ("di-nitrogen"), with two 7

14 N nuclei.

Note that each of these molecules contains a total of 14 protons and 14 neutrons (and14 electrons, but their mass contribution is basically negligible for the purposes of thisdiscussion). Given below is a table of mass defects per nucleon, in MeV units. Credit isassigned for the completeness and clarity of your justification using the properties of mass-energy equivalence and nuclear processes, and not necessarily for finding the correct choice.

Table of (mass defects)·c2 per nucleon:

612C = 7.680 146 MeV

714 N = 7.475 616 MeV

816O = 7.976 209 MeV

(a) Rank the three nuclei listed above in order of the "dissociation" energy required to break itapart into separated protons and neutrons.

(b) A carbon monoxide molecule and a di-nitrogen molecule are now singly ionized, and thenboth put through a mass spectrometer. Choose and defend one statement only:(A) The spectrometer will show that the singly-ionized CO molecule has slightly more

mass than the singly-ionized N2 molecule.(B) The spectrometer will show that the singly-ionized CO molecule has slightly less

mass than the singly-ionized N2 molecule.(C) The spectrometer will show that the singly-ionized CO molecule has exactly the

same mass as the singly-ionized N2 molecule (i.e., the mass spectrometer cannottell the difference between these two molecules).

(New problem)3. Quiz 13 archive problem (2), page 147 of the Physics 7C Student Packet. Note that the nuclear

reaction equation should be corrected to read "ν+ →1737Cl ____ + ____."

(New problem)4. Consider the following two possible processes observed in nature that bring radioactive 83

210Bi tostable 82

206Pb:

Process [1]: α decay, followed by β− decay.Process [2]: β− decay, followed by α decay.

Given below is a table of atomic (not nuclear masses) for several nuclei, in unified atomic massunits. Credit is assigned for the completeness and clarity of your justification using theproperties of mass-energy equivalence and nuclear processes, and not necessarily for findingthe correct numerical answers.


03.03.18


83210Bi = 209.984 104 944 u

82210Pb = 209.984 173 129 u

84210Po = 209.982 857 396 u

83209Bi = 208.980 383 241 u

81206 Tl = 205.976 095 321 u

82206Pb = 205.974 449 002 u

80204 Hg = 203.973 475 640 u

24 He = 4.002 603 250 u

(a) Give a completely qualitative argument (no calculations!) why process [1] and process [2]would release the same net amount of energy.

(b) Rank the following Q-values, from smallest to largest of energy released. If two or moreprocesses have the same Q-values, then explicitly state so.(A) Process [1] α decay.(B) Process [1] β− decay.(C) Process [2] β− decay.

(D) Process [2] α decay.

5. Consider the following exothermic fission process that breaks apart a large, unstable nucleusinto two daughter nuclei, resulting in a Q-value of +27.8× −10 12 J. Recall that the presence ofneutrons can be ignored on the inter-nuclear potential energy graph for this process. You arenot given a table of atomic masses for this problem. Credit is assigned for the completenessand clarity of your justification using the properties of inter-nuclear potential energy and PEgradients, and not necessarily for finding the correct numerical answer.

n U Ba+ Kr + 3n92235

56141

3692+ → .

(a) Calculate the change in electrical PE (in J) just as the two daughter nuclei begin toseparate from each other, to when they separate out to an infinite distance from each other.

(b) Determine the minimum velocity (in m/s) that the neutron must originally have to in orderto initiate this fission process.

(c) Calculate the total strong force between nucleons (magnitude and direction) when thecenter-to-center distance r between the 56

141Ba and 3692 Kr nuclei is 9.00 fm (i.e., when the

two daughter nuclei have not yet fully separated from each other). Just how strong is thestrong force?


03.03.18

Activity Cycle 14.3.1: Nuclear toolbox

A. Relating concepts, models, and methods to nuclear processes. Work at the board as agroup and put your results up as you work, in order that your TA can gauge yourprogress.

1. For each of the five processes (a)-(e) listed below, check off which of the followingconcepts, models, and methods apply to them. There are not necessarily right/wronganswers; the important thing here is to make connections within the material in Block 14.

(a)

fusi

on

(b)

fissi

on

(c) α

dec

ay

(d) β

dec

ay

(e) γ

dec

ay

Exothermic

Endothermic

Initiation energy cost

Strong interactions (p-p, n-n, p-n strong bonds)

Weak interactions (p→ n, n→p reactions)

Final state is lower in energy

Final state is higher in energy

∆PEelec can be calculated/is relevant

Modeled by inter-nuclear PE graphs

Modeled by box model energy levels

Q-value is positive

Q-value is negative


03.03.18

Activity Cycle 14.4.1: Analyzing nuclear processes










03.03.18

DLM 14 Exit handout

Announcements Quiz 14 will be given during lecture 9:00-9:35 am on Monday, March 10, and will cover thematerial in Block 14. Bring a pen or pencil, calculator, and prepare to show your UC-Davis studentID card (or similar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")

1. The frequency of a wave will

increase

remain the same

decrease

as it enters a medium with a higher index of

refraction.

2. The wavelength of a wave will

increase

remain the same

decrease

as it enters a medium with a higher index of

refraction.


critical angle θc

index of refraction nLaw of Reflection

("Hero's Law")raysrefractionreflection

Snell's Law("Descartes' Law")

specular reflectionsurface normaltotal internal reflection (TIR)wheel axle model


03.03.18

Activity Cycle 15.1.1: Refraction of light

A. Perform the experiments (1)-(2) described below in your group, and summarize yourmeasurements on the board, in order that your TA can gauge your progress.

In this experimental setup, you are going to study the angles of a light ray in air as it enterslucite, or a light ray in lucite as it exits out into air. The flat surface of your semicircular lucitesample you have will simulate the air-lucite interface; for now ignore the circular surface ofthe lucite sample. Once your TA has set up your experiment, you should only have torotate your protractor table in order take all of your measurements.

* 1. Consider a light ray in air that hits the flat surface of the lucite sample. Rotate the entireprotractor table to get the range of incident angles in air (0° ≤ θair ≤ 80°) listed below, andthen record your experimental angles in lucite. Fill in the "Tinkertoy™ analog" columnlater; instructions are on the other side of this page.

Angle in airθair

Angle in luciteθlucite

Tinkertoy™ analog[A]-[B]-[C]-[D]

0°20°40°60°80°

airlucite

θair

θlucite

refracted ray

incident ray

* 2. Consider a light ray in air that first hits the circular surface of the lucite sample, and thenexits out into air through the flat surface. Rotate the entire protractor table to get therange of incident angles in lucite (0° ≤ θlucite ≤ 80°) listed below, and then record yourexperimental angles in lucite. If something happens (or does not happen), make carefulnotes of your observations.

Angle in luciteθlucite

Angle in airθair

Tinkertoy™ analog[A]-[B]-[C]-[D]

0°20°40°60°80°

θair

θluciteincident ray

lucite

refracted ray

air

Your TA may elect to have a whole-class discussion here before moving on to the rest of this activity,in order to move every group along at the same pace, and to clear up board space.


03.03.18

Activity Cycle 15.1.2: Refraction of light (continued)B. Tinkertoy™ wheel axle analogs of light refraction. Work at the board as a group and

put your results up as you work, in order that your TA can gauge your progress.3. Shown below are four different cases [A]-[D] of a Tinkertoy™ wheel axle as it rolls

across a fast surface (such as concrete) onto a slow surface (such as grass), or across aslow surface onto a fast surface. Demonstrate (with an actual wheel axle on a drawing onthe board) how both wheels move differently in either medium, and explain why the entireaxle will make the paths indicated. Make this convincing enough for a whole classdiscussion.

slow

[C]

slow

[D]

fast fast

fastslow

[B]

fastslow

[A]

* 4. Match these wheel axle demonstrations [A]-[D] withtheir analogous experimental situations for each ofyour measurements in (1)-(2).

* 5. For [B], derive a relation between the θ1 and θ2 anglesand the v1 and v2 velocities on the fast and slowsurfaces. The diagram at right shows the ∆x distancesthat each wavefront/axle travels in the same amount of∆t time. (Hint: use the fact that these two trianglesshare the same hypotenuse, and that v = ∆x/∆t.)

C. Summary of results. Your answers should directly follow from all of yourobservations from part (A).

6. As light travels from a fast to a slow medium, its ray bends towards

away from

the normal.

7. As light travels from a slow to a fast medium, its ray bends towards

away from

the normal.

8. If light starts from a fast

slow

medium, its ray may reflect back into the

fast

slow

medium.

incident

wavefront

∆x2

refracted

wavefront

∆x1

θ2

θ1


03.03.18

Activity Cycle 15.1.2: Snell's Law and total internal reflection

A. Re-analysis of experimental data from Activity Cycle 15.1.1. Work at the board as agroup and put your results up as you work, in order that your TA can gauge yourprogress.

* 1. Show how your "velocity form" of Snell's Law from (5) of Activity Cycle 15.1.1 turnsinto the "index of refraction form" of Snell's Law. (You can look up Snell's Law on page124 of the Physics 7C Student Packet.) Then find an average experimental value for theindex of refraction for lucite (nlucite), using all of your experimental data from (1)-(2) ofActivity Cycle 15.1.1, and the fact that nair ≈ 1.

* 2. Calculate the critical angle θc, which is the maximum angle in lucite that will make arefracted ray of 90° in air. Experimentally observe and describe the following:(a) What happens to the lucite incident ray when θlucite < your calculated θc value?(b) What happens to the lucite incident ray when θlucite > your calculated θc value?

* 3. Describe in words which of these objects youwould see (Sun, man, fish?), and where theywould appear to be located, if you areunderwater at the Rec Pool, and are looking backup at the surface. (Be sure to show the directionthe each and every light ray travels.)4

B. Challenge questions. Discuss (4)-(6) in your group, but unless instructed by yourTA, you do not have to put these up on the board.

4. You have been observing refraction occurring at the flat surface of the lucite sample.Explain why there is no refraction occurring at the circular surface.5

5. If you were stranded on a deserted island like Tom Hanks in Castaway, and had to speara fish that you saw (while above water), would you poke your spear just above or justbelow where you see the underwater fish?

6. Repeat (5) above, but supposing you had a lethal laser gun instead of a spear. Would youaim your laser just above or just below where you see the underwater fish?

4 DLM 15 for Physics 7C, Summer Session I, 1997, was held at the Rec Pool.5 This was given on the Final Exam for Physics 7C, Summer Session I, 1997.

(you)


03.03.18

Activity Cycle 15.2.1: Prisms and lensesA. Measuring incident and exiting light ray angles for a prism. Make the measurements

described below with a protractor.

1. Align your equilateral (60°-60°-60°) prism and laser for the three following cases. Tracethe incident and exiting rays, and the outline of the prism onto your own piece of paper,and then measure the angles indicated with a protractor.

(a)

exiting ray

leaves

right face

incident ray parallel to bottom face

prism

trace prism and rays; measure acute angle between incident/exiting rays

(c)

incident ray (⊥ to bottom face, off-center from middle)

exiting ra

y

leaves right

face

prism

trace prism and rays; measure acute angle between incident/exiting rays

(b)

incident ray exiting rayprism

trace prism and rays; measure incident/exiting ray angles with surface

incident/exiting rays are “symmetric” on left/right faces

incident ray ⊥ to bottom face

B. Extending your results from (A) to consider prismsas lens components. Work at the board as a groupand put your results up as you work, in order thatyour TA can gauge your progress.

2. Consider parallel light rays incident on two typesof lenses, as shown at right. Sketch what theselenses will do to each of these incident light rays,using the information from 1(a)-(c). Describewhich lens is a "converging" or "diverging" lens,and define a "focal point" for either lens.

Your TA may elect to have a whole-class discussion here before moving on to the rest of this activity,in order to move every group along at the same pace, and to clear up board space.

incident rays

incident rays


03.03.18

Activity Cycle 15.2.1: Prisms and lenses (continued)C. Extending your results from (A)-(B) to consider the effect of lenses on different types

of incident light rays. Work at the board as a group and put your results up as youwork, in order that your TA can gauge your progress.

3. From the following incident light rays shown below, choose the appropriate path of theexiting light ray, using the information from 1(a)-(c), and your results in (2).

bent upwards?

°f°f

away from f ?

straight across?bent downwards?

through f ?

°f°f

away from f ?


through f ?

°f°f

away from f ?


through f ?

(a)

(b)

(c)

°f°f

away from f ?

straight across?bent upwards?

through f ?

°f°f

away from f ?

straight across?bent upwards?

through f ?

°f°f

away from f ?

straight across?

through f ?

(e)

(f)

(d)

D. Interpreting your results from (A) to determine the index of refraction for the prism.You only have to discuss this in your groups, and then get permission to be dismissedby your TA. The following question (4) below is a "lab report" question to behanded in for credit as soon as you walk in to the next DLM 16. It is yourresponsibility to have enough data to answer this question before leaving DL today.

4. (a) Consider your data from 1(c). This set-up only allows you to determine a range ofpossible values for n prism . Calculate the minimum and maximum possible values forn prism , as determined from this set-up.

(b) Consider your data from 1(b). This set-up does allow you to determine a specificexperimental value for n prism . Calculate the numerical value for n prism , as determinedfrom this set-up.


03.03.18

DLM 15 Exit handout



The following question is a "lab report" question to be handed in as you come into the next DLM 16.Answer this as you would a quiz question; it will be graded similar to a quiz question, and thensubsequently handed back to you. You will receive credit towards your DL grade. Be sure to writeout your answers on a separate page.

X. (a) Consider your data from 1(c) of Activity Cycle 15.2.1. This set-up only allows you todetermine a range of possible values for n prism . Calculate the minimum and maximumpossible values for n prism , as determined from this set-up.

(b) Consider your data from 1(b) of Activity Cycle 15.2.1. This set-up does allow you todetermine a specific experimental value for n prism . Calculate the numerical value forn prism , as determined from this set-up.


converging lensdiverging lensfar focal pointfocal lengthfocal point fimageimage distance iimage height hi

lensmagnification, linear Mlinear

near focal point

objectobject distance oobject height ho

optical axisprincipal raysray tracingreal imagesign conventionsthin lens equationthin lens modelvirtual image


03.03.18

Activity Cycle 15.2.2: Ray tracing and image formation

A. Your TA will assign to your group one of the single lens systems [A]-[F] that werediscussed in Lecture 15.1. Perform the ray tracing for your group's assigned system,and put up a 2:1 scale (i.e., twice normal size) drawing up on the board, with o and idistances clearly labeled, in order that the rest of the class can record your work.

* 1. Use a ray tracing to estimate the following quantities (a)-(c) for your assigned lenssystem [A]-[F]. Neatly draw your ray tracing on the boards, as every group will have topresent their results in the whole-class discussion.(a) Approximate image distance i (the distance from the lens to the image) = _____ cm.(b) Approximate linear magnification factor M (how much bigger/smaller the image is

than the object) = _____.(c) Decide whether your image is a real image (actual intersection of

converging/diverging light rays) or a virtual image ("traced-back" (inferred)intersection of light rays).

B. Summary of results. Your answers for (2)-(6) should directly follow from makinggeneralizations from each and every other group's results from part (A).

2. An object placed outside a converging lens focal point creates a real

virtual

image.

3. An object placed inside a converging lens focal point creates a real

virtual

image.

4. An object placed outside a diverging lens focal point creates a real

virtual

image.

5. An object placed inside a diverging lens focal point creates a real

virtual

image.

6. When is it not possible for a converging lens to create an image?7. When is it not possible for a diverging lens to create an image?

far fnear fobject

[A] f = +15 cm lenso = +32 cm from lensi = ?M = ?×

2 cm

Additional lens systems [B]-[F] are shown on the back of this page.


03.03.18

far fnear f

far fnear f object

object

far fnear f

object

far fnear f object

2 cm

2 cm

[C]

[D]

[E]

[F]

f = –15 cm lenso = +32 cm from lensi = ?M = ?×



f = +15 cm lenso = +4 cm from lensi = ?M = ?×

far fnear f

object [B] f = +15 cm lenso = +15 cm from lensi = ?M = ?×

Activity Cycle 15.2.2: Ray tracing and image formation (continued)


03.03.18

Activity Cycle 15.2.3: Thin lens equations and experimentsA. Your TA will assign to your group one of the single lens systems [A]-[F] from Activity

15.2.2. Perform the calculations and experiments (1)-(2) described below for yourgroup's assigned system, and summarize your results on the board, in order that therest of the class can record your work.

* 1. Use the thin lens equation to calculate the following quantities (a)-(b) for your assignedlens system [A]-[F]. Neatly summarize your results on the boards, as every group willhave to present their results in the whole-class discussion.(a) Image distance i (the distance from the lens to the image) = _____ cm.(b) Linear magnification factor M (how much bigger/smaller the image is than the

object) = _____.

* 2. Actually set up your system [A]-[F] using the lenses provided, with your given value for o(the object to lens distance). Be sure to demonstrate your experimental observations tothe other groups in the whole class discussion. If your image is real, locate it with ascreen. If it is virtual, then you must be able to look through the lens to see it.

i

f = +15.0 cm or –15.0 cm

o

lens (#2xx) or (#4xx)illuminated object slidelight

sourcescreen (only if image is real)

±, ?

B. Summary of results. Your answers for (3)-(8) should directly follow from makinggeneralizations from each and every other group's results from part (A).

3. A positive value for i corresponds to a real

virtual

image.

4. A negative value for i corresponds to a real

virtual

image.

5. A positive value for M corresponds to an upright

inverted

image.

6. A negative value for M corresponds to an upright

inverted

image.

7. An M > 1 value corresponds to a(n) enlarged

diminished

image.

8. An M < 1 value corresponds to a(n) enlarged

diminished

image.


03.03.18

Activity Cycle 15.2.4: Camera versus eyeA. Analysis of single lens systems, using the thin lens equations. Work at the board as a

group and put your results up as you work, in order that your TA can gauge yourprogress.Consider a simple camera with a f = +50.0 mm lens, which can be modeled by a singleconverging lens projecting a real image onto a screen (in order to expose either film or acharge-coupled device (CCD), as in a "digital" camera).

* 1. Ideally, a camera should be able to create real images on film for a range of objectdistances. Of the three parameters in the thin lens equation (o, i, f), discuss which two areallowed to vary for a camera, and which one must remained fixed, and why.

2. For each the following situations, determine all three parameters in the thin lens equation(o, i, f), and draw a separate ray tracing with clearly labeled o and i distances.

* (a) The camera is taking a picture of an object at an ∞ distance away from its lens.* (b) The camera is taking a picture of an object at the "closest focusable distance" of

30 cm away from its lens. (Is this consistent with what camera lenses do whenfocusing on nearby objects rather than far away objects?)

Consider your eye, with a diameter of 17.1 mm, which can be modeled by a single converginglens projecting a real image onto your retina (in order to expose light-sensitive cells).

* 3. Ideally, your eye should be able to create real images on its retina for a range of objectdistances. Of the three parameters in the thin lens equation (o, i, f), discuss which two areallowed to vary for your eye, and which one must remained fixed, and why.

4. For each the following situations, determine all three parameters in the thin lens equation(o, i, f), and draw a separate ray tracing with clearly labeled o and i distances.

* (a) Your eye is looking at an object at an ∞ distance away from its cornea/lens.* (b) Your eye is looking at an object at its "closest focusable distance" of 250 mm away

from its cornea/lens. (What do your ciliary muscles do to your eye here?)

* 5. Make a chart for everyone in your group.(a) If you cannot focus sharply on o = ∞ objects, then roughly estimate the furthest

distance (in m) that you can focus sharply at.(b) Measure the closest distance (in m) you can focus sharply at (focus on your

fingerprints and close one eye, as this is not a test of how "cross-eyed" you can get).(c) Diagnose whether each person in your group is either nearsighted, farsighted, or both.

Name(a) far point

ofar

(b) near pointonear

(c) nearsighted?farsighted?both?

"Nominal vision" ∞ 0.25 m (n/a, normal)


03.03.18

DLM 16 Exit handout


FNT ("For Next Time")Perform the following thin lens equaution calculations for the following object distances and lensesbelow (you may also do ray tracings to check your results, but exact calculations must be foundfrom the thin lens equations.) These preliminary results will be used for Activity Cycle 15.3.1 at thebeginning of the next DLM 17.

1. An object is placed 25.0 cm to the left of a f = +10.0 cm lens.(a) Locate the image, and state whether it will be found to the left or to the right of the lens.(b) Determine how much larger or smaller the image will be, as compared to the object.

2. An object is placed 25.0 cm to the left of a f = +33.6 cm lens.(a) Locate the image, and state whether it will be found to the left or to the right of the lens.(b) Determine how much larger or smaller the image will be, as compared to the object.

3. An object is placed 25.0 cm to the left of a f = –15.0 cm lens.(a) Locate the image, and state whether it will be found to the left or to the right of the lens.(b) Determine how much larger or smaller the image will be, as compared to the object.

4. Read the Block 15 Glossary (pp. 139) in the Physics 7C Student Packet, Winter Quarter 2003,and familiarize yourself with the following terms that will be used extensively in DLM 17.

multiple lens system


03.03.18

Activity Cycle 15.3.1: Multiple lens systemsA. Your TA will assign to your group one of the following multiple lens systems

[A]-[E] (not drawn to scale). Perform the calculations and experiments (1)-(5)described below for your group's assigned system, and summarize your results on theboard, in order that the rest of the class can record your work.

* 1. Use the thin lens equation for each lens to calculate the following quantities (a)-(f) foryour assigned system [A]-[E] (note that (a)-(b) are from the DLM 16 FNT). Neatlysummarize your results on the boards, for the whole class discussion.(a) Image distance i1 (the distance from lens 1 to image 1, which now becomes the

object 2 for lens 2).(b) Linear magnification factor M1 (how much bigger/smaller image 1 is than object 1).(c) Object distance o2 (the distance from object 2 to lens 2).(d) Image distance i2 (the distance from lens 2 to image 1).(e) Linear magnification factor M2 (how much bigger/smaller image 2 is than object 2).(f) Total magnification factor M M Mtotal = ⋅1 2 (how much bigger/smaller image 2 is than

object 1).

* 2. Actually set up your system [A]-[E] using the lenses provided, and with your given o1

(object 1 to lens 1 distance) and d (lens 1 to lens 2 distance) values. Be sure to demonstrateyour experimental set-up to the other groups in the whole class discussion.(a) If your image 1 (i.e., object 2) is real, locate it with a screen. If it is virtual, you

must be able to look through lens 1 to see it.(b) If your image 2 (your final image) is real, locate it with a screen. If it is virtual, then

you must be able to look through lens 2 to see it.

* 3. Image 1 is real

virtual

, and is

upright

inverted

and

enlarged

diminished

with respect to object 1.

* 4. Image 2 is real

virtual

, and is

upright

inverted

and

enlarged

diminished

with respect to image 1.

* 5. Therefore, image 2 is upright

inverted

and

enlarged

diminished

with respect to object 1.

* 6. Our system [A-B-C-D-E] demonstrates a real

virtual

image being made of a

real

virtual

image.

i2 +___ cm

i1 +___ cm

o2+___ cm

lens 2 (#2xx)f1 = +10.0 cm

o1+25.0 cm

f2 = +15.0 cmlens 1 (#1xx)object 1

light source

d = 40.0 cm[A]


03.03.18

lens 2 (#2xx)f1 = +10.0 cm

o1+25.0 cm

f2 = +15.0 cmlens 1 (#1xx)object 1

light source

d = 20.0 cm[B]

i1 +___ cm

o2 = +___ cm

i2 = –___ cm

lens 2 (#2xx)f1 = +33.6 cm

o1 = +25.0 cmf2 = +15.0 cm

lens 1 (#3xx)object 1light source

[C]

i2 +___ cm

o2+___ cm

i1–___ cm

d = 20.0 cm

f1 = +33.6 cmo1 = +25.0 cm

lens 1 (#3xx)object 1light source

[D]

i1–___ cm

d = 20.0 cm

lens 2 (#4xx)f2 = –15.0 cm

o2 = +___ cm

i2 = –___ cm

f2 = +10.0 cmlens 2 (#1xx)

o1 = +25.0 cm

object 1light source

[E]

i1–___ cm

d = 20.0 cm

lens 1 (#4xx)f1 = –15.0 cm

i2 +___ cm

o2+___ cm


03.03.18

Activity Cycle 15.3.2: Experimental determination of f

A. Consolidating group information from the previous Activity Cycle 15.3.1. The spacebelow is provided such that you can summarize your group's and the other groups'results for the systems [A]-[E] from the previous Activity Cycle 15.3.1.

Case o1 f1 (a) i1 (c) o2 f2 (d) i2

[A][B][C][D][E]

Case (b), 3. M1 image (e), 4. M2 image (f), 5. Mtotal 6.

[A] ± _____[real | virtual]

[upright | inverted][enlarged | dim.]

± _____[real | virtual]


± _____


[real | virtual]image of a[real | virtual]image

[B] ± _____[real | virtual]




± _____



[C] ± _____[real | virtual]




± _____



[D] ± _____[real | virtual]




± _____



[E] ± _____[real | virtual]




± _____



After the whole-class discussion from the previous Activity Cycle 15.3.1 is over, and after you havesummarized every group's results, and after you have looked at/through every lens system to see the finalimages for yourself, then go on to the last lab report of Physics 7C on the back of this page.


03.03.18

Activity Cycle 15.3.2: Experimental determination of fB. Experimental determination of the focal lengths of converging and diverging lenses.

The following question (1) below is a "lab report" question to be handed in for creditas soon as you walk in to the next DLM 18. It is your responsibility to have enoughdata to answer this question before leaving DL today.

Note that your thin lens equation calculations for object and image locations may be slightlyinaccurate compared to your experimental observations, due to the fact that the focal lengthsof your converging and diverging lenses will not be exactly f = +15.0 cm and f = –15.0 cm.

1. (a) Open the blinds on your window, and place the white screen paddle behind your"f ≈ +15.0 cm" converging lens such that the projected real image of the distantoutside scenery is as sharply focused as possible. Record this lens-to-screendistance. Explain how this allows you to calculate an exact value for the focallength of your "f ≈ +15.0 cm" converging lens, and then calculate this exactexperimental value.

converging lensf1 ≈ +15.0 cm(#2xx)

screen

to window

(b) Now use the illuminated object slide, your exact value "f = +___ cm" converginglens from (a), and a "f ≈ –15.0 cm" diverging lens to create a real final image on thewhite screen paddle. (You decide the spacing between the lenses.) Record yourobject slide to lens 1 distance; the lens 1 to lens 2 distance; and lens 2 to screendistance. Explain how this allows you to calculate an exact value for the focallength of your "f ≈ –15.0 cm" diverging lens, and then calculate this exactexperimental value.

f2 ≡ +____ cm(#2xx)

converging lensobject 1light source

d = ?

diverging lensf1 ≈ –15.0 cm(#4xx)

o1 = ? i2 = ?

screen


03.03.18

DLM 17 Exit handout



The following question is your last "lab report" question to be handed in as you come into the nextDLM 18. Answer this as you would a quiz question; it will be graded similar to a quiz question,and then subsequently handed back to you. You will receive credit towards your DL grade. Be sureto write out your answers on a separate page.

X. (a) Explain how your experimental observations from Activity Cycle 15.3.2 allows you tocalculate an exact value for the focal length of your "f = +15.0 cm" converging lens, andthen calculate this exact experimental value.

(b) Explain how your experimental observations from Activity Cycle 15.3.2 allows you tocalculate an exact value for the focal length of your "f = –15.0 cm" diverging lens, andthen calculate this exact experimental value.

DLM 18 is your penultimate ("second-to-the-last") regularly scheduled discussion/lab meeting, andis a problem-solving session that will consolidate the material covered in Block 15. The following fiveproblems represent actual final exam questions given in previous quarters. (The last DLM 19 willbe a problem-solving session for the Quizzes 11-14 from this quarter.) Remember that credit isassigned for the completeness and clarity of your justifications, and not necessarily for youranswers and numerical results.

(Final Exam, Summer Session II, 2001)1. Shymu the Shy Killer Whale is

currently at a depth of 7.0 munderwater.(a) What vertical depth

underwater (in m) does theaudience apparently perceiveShymu to be at? (Forsimplicity, assume thatShymu is a point object, andconsider only the light that isoriginally specularly reflectedfrom the tip of its dorsal fin.)

(b) Shymu would like to swim up to a new shallower depth such that its dorsal fin cannot beseen by the audience. Calculate the new shallower depth underwater (in m) that Shymushould vertically swim to, in order for this to happen.

water

air

30°

Shymu

7.0

m

image of Shymu's dorsal fin


03.03.18

(Final Exam, Fall 1997)6

2. Similar to in DL, an illuminated object slide is placed 10.0 cm to the left of a f = –15.0 cm lens.A white screen paddle is placed 15.0 cm to the right of a f = +10.0 cm lens.

f2 = +10.0 cmconverging lensobject 1

light source

d = ?

diverging lensf1 = –15.0 cm

10.0 cm 15.0 cm

screen

(a) What should be the distance d between these two lenses, such that a real final image isprojected on the screen by the f = +10.0 cm lens?

(b) What should be the maximum distance d between these two lenses, such that a virtual finalimage is produced by the f = +10.0 cm lens?

(Final Exam, Spring 2000)3. Similar to in DL, an illuminated object slide is placed 10.0 cm to the left of a f = +33.6 cm lens.

(a) What isthe magnification of the image produced by the f = +33.6 cm lens, as measured withrespect to the object slide? Is the image upright or inverted compared to the object slide?

(b) Now, a f = –15.0 cm lens is placed 4.00 cm to the right of the f = +33.6 cm lens from part(a). What is the magnification of the final image produced by the f = –15.0 cm lens, asmeasured with respect to the object slide? Is this image upright or inverted compared tothe object slide?

(Final Exam, Summer Session I, 2001)7

6 Also given on Physics 210B Midterm 3 at Sonoma State University, Spring 2002.

object 1light source

4.00 cm

converging lensf1 = +33.6 cm

10.0 cm

f2 = –15.0 cmdiverging lens


03.03.18

4. You wake up early one morning and accidentally peek inside your roommate's medicine cabinet.You find the original container for her contacts, both labeled "+1.80 D."(a) What is (i) the uncorrected near point and (ii) uncorrected far point of your roommate's

eyes, assuming that she has perfect nominal vision when she wears these contacts in hereyes, and does not yet require bifocals.

(b) Decide whether your roommate will eventually have to wear bifocals in order to correcther vision as a result of aging.

(Final Exams, Summer Session I, 1997 and Fall 1998)5. Mzra the Öy is an extraterrestrial who has an eye that has a

radically different anatomy than humans. Mzra's relaxedeye has a curved shape such that she can look at nearbythings. By accommodating her ciliary muscles, Mzra canstretch and flatten her lens in order to focus on distantobjects. (Mzra's planet is shrouded in fog, and usuallyonly nearby object distances are important.)(a) Mzra's far point is 2.60 m. If she would like to see

objects that are up to 10.0 m away (it is impossible tosee further than that in the foggy atmosphere of herhome planet of Öy), find the optical strength of herprescription for contacts, and state whether these areconverging or diverging lenses.

(b) Describe what presbyopia (the loss of the ability to accommodate) will do to Mzra theÖy's vision as she grows older.

Read the Block 15 Glossary (pp. 127-140) in the Physics 7C Student Packet, Winter Quarter 2003,and familiarize yourself with the following terms that will be used extensively in DLM 19.

accommodationbifocalscorneacontact lensdiopter (D)far pointfarsightednessglasses

hyperopiamultiple lens systemmyopianear pointnearsightednessoptical strength Dpresbyopiaretina

7 Also given on Physics 210B Midterm 3 at Sonoma State University, Spring 2002. Typical replies such as,

"I cannot answer this question because my beliefs preclude me from using illicitly gained information," whilerefreshingly honest, did not receive much partial credit.

Mzra the Öy

Mzra's relaxed eye

4.25 cm

Mzra's accommo-dated eye

4.25 cm


03.03.18

Activity Cycle 15.3.3: Amateur optometry

A. Modeling corrected vision as a two lens system. Work at the board as a group and putyour results up as you work, in order that your TA can gauge your progress.

Choose one member of your group who is nearsighted (i.e., whose far point ofar < ∞). If noone at your table is nearsighted, use a fictitious person with a far point of ofar = +5.00 m.

* 1. Use the two-lens model to find the focal length (in m) and prescription (in diopters) of thecontact lens that would compensate for this vision defect. In this two-step implementation ofthe thin lens equation, clearly indicate the following ± signs and values for each lens:

(a) Object distance for contacts: o1 = +∞.Image distance for contacts: i1 = –|ofar |.Focal length of contacts: f1 = _________ m.Optical strength of contacts: Dcontacts = _________ diopters.

(b) Object distance for eye: o2 = _________ m.Image distance for eye: i2 = _________ m (location of retina).Focal length of eye: f2 = _________ m.

Choose one member of your group who is farsighted (i.e., whose near point onear > ∞). If noone at your table is farsighted, use a fictitious person with a far point of onear = +0.600 m.

* 2. Use the two-lens model to find the focal length (in m) and prescription (in diopters) of thecontact lens that would compensate for this vision defect. In this two-step implementation ofthe thin lens equation, clearly indicate the following ± signs and values for each lens:

(a) Object distance for contacts: o1 = +0.250 m.Image distance for contacts: i1 = –|onear|.Focal length of contacts: f1 = _________ m.Optical strength of contacts: Dcontacts = _________ diopters.

(b) Object distance for eye: o2 = _________ m.Image distance for eye: i2 = _________ m (location of retina).Focal length of eye: f2 = _________ m.

B. Challenge questions. Discuss (3)-(8) in your group, but unless instructed by yourTA, you do not have to put these up on the board.

3. Why is it not necessary for an optometrist to know the focal length or the diameter ofyour eye in order to prescribe corrective contact lenses?

4. Ideally what is the only mandatory parameter that your optometrist tests your eyes for inorder to prescribe the strength of your contact lenses?

5. Why must the image distance for the contacts always be negative?

6. Why is the focal length f2 of your eye different for (1) and for (2)? Which of these isyour relaxed eye's focal length? Which is your accommodated eye's focal length?

7. In which case (near/far-sighted) are diverging contacts required? Converging contacts?

8. Who will need to wear bifocals later, as a result of presbyopia? Near- or farsighted people?


03.03.18

Activity Cycle 15.4.1: Analyzing optical systems










03.03.18

DLM 19 Exit handout (the last one ever!)

AnnouncementsNo more homework! But if you need something to do,

why don't you download (http://physics7.ucdavis.edu) and getyour Physics 7ABC Certificate of Achievement signed? This isthe last quarter that Dr. Len will ever be allowed to teach atUC-Davis, so this collector's item would sure look nifty on yourrefrigerator door, and you'll be the envy of all your Physics 7Aand 7B roommates. Review sessions will be held in Temporary Building 114 as scheduled below. It is suggestedthat you come prepared to the review sessions to concentrate on this quarter's Quizzes, DLactivities, and general questions that you may have, in order to make the best use of the instructor'stime.

Temporary Building 114 Review Sessions:Saturday, March 159:00-10:30 AM Brooke Haag10:30-12:00 noon Randy Nelson12:00-1:30 PM Dr. Patrick M. Len1:30-3:00 PM Cary Allen

Sunday, March 164:00-5:30 PM David Michaels

Note that as always, Dr. Len will be also be available for informal short questions at CafeRoma, 231 "E" Street, Sunday, March 16 from 5:30-7:00 PM. The Final Exam will be held on Monday, March 17 at 8:00 AM-10:00 AM, and will becomprehensive with an equal emphasis on Blocks 11-14, with slightly more emphasis on Block 15.Bring a pen or pencil, calculator, and come early to show your UC-Davis student ID card (or similarphoto ID) before entering your Final Exam room. Room assignments for the Final Exam are asfollows:

Last 4 ID digits Room assignment0000-3999 2 Wellman4000-9999 179 Chemistry

Important note—if you have made extensive corrections and/or annotations to the Physics7C Student Packet (i.e., the Core Concepts and Glossaries), Dr. Len would be interested if youwould be willing to donate your Student Packet, along with any of your notes (or allow xeroxes to bemade) in order to improve physics instruction, in the event that he would ever be allowed to teachagain at another school. In the meanwhile, good luck to you in studying for your final exams thisquarter, and in all of your future endeavors.


03.03.18


03.03.18

Physics 7C Quiz ArchivesDisclaimer

Please carefully read the following information regarding these archivedPhysics 7C quizzes:

• These quizzes are presented "as is, where is" in as close to their originalform as possible, as it was presented to students in Physics 7C lecturesections taught by Dr. Patrick M. Len at the University of California atDavis in Winter quarter, 2003.

• The intent of presenting these quizzes is to provide to all students (and notjust those who are somehow able to procure class materials from formerPhysics 7C students) an additional resource in studying questions that havehistorically appeared on typical Physics 7C quizzes.

Be aware that these archived Physics 7C quizzes are not to be construedin any way, shape, or form as an indicator of the content, difficulty, or lengthof future Physics 7C quizzes.

• No effort has been or will be made to present worked-out solutions to thesearchived Physics 7C quizzes. This has been left to you as a unique andunprecedented opportunity to gauge your understanding relative to paststudents who have taken Physics 7C in previous quarters.

Be aware that your performance on these archived Physics 7C quizzes isnot to be construed in any way, shape, or form as an indicator of your actualperformance on future Physics 7C quizzes relative to current students.

By reading the following Physics 7C Quiz Archives, you acknowledge andaccept the above conditions and terms regarding the usage of these archivedPhysics 7C quizzes. If you neither understand nor accept the aboveconditions and terms, you are to tear out and discard these Physics 7C QuizArchives pages.


03.03.18

Quiz 111. [50%] Consider two pendulum systems, both with the same mass (m = 0.50 kg) on strings of

the same length (L = 0.80 m). Both pendulum systems hit barriers at θ = 0° such that thelength of either system is smaller (L = 0.40 m) when it swings up on the other side. Bothpendulum systems start from the same initial angle θ at t = 0.0 s.

One pendulum system is released from rest at t = 0.0 s, and is allowed to swing freely to theother side, and then returns back to its initial position. The other pendulum system is pushedsuch that it has a significant amount of velocity at t = 0.0 s, and is allowed to swing freely (to alarger angle) on the other side, and then returns back to its initial position. Ignore any and alleffects of air resistance.

L = 0

.80

m

m = 0.50 kg

L = 0.40 m

Pendulum released from rest at t = 0.0 s, swings up and returns back to its initial position

vinitial = 0

barrier

v = 0

L =

0.80

m

m = 0.50 kgPendulum released with forward velocity at t = 0.0 s, swings up and returns back to its initial position

vinitial

L = 0.40 m

barrier

v = 0

Decide which one of the following statements below must be true. Credit is assigned for thecompleteness and clarity of your justification, and not necessarily for finding the correct choicebelow.

Choose and defend one statement only.(A) The pendulum released from rest will return back to its initial position before the pushed

pendulum.(B) The pendulum released from rest will return back to its initial position at the same time as

the pushed pendulum.(C) The pendulum released from rest will return back to its initial position after the pushed

pendulum.(D) Not enough information is given to determine which pendulum will return to its initial

position first.

2. [50%] A source located somewhere produces transverse waves that travel to the right along avery long rope. The y(x) graphs for two very slightly different times is shown below, similar toletting time "run" on the Graphing Calculator program.


03.03.18

y(x) [m]

0.0

+0.1

–0.1x [m]

5 10 15 20

at t = 0.0 sat t = 0.1 s

However, something in this system is changed, such that the y(x) graphs for the two veryslightly different times is now as shown below.

y(x) [m]

0.0

+0.1

–0.1x [m]

5 10 15 20

at t = 0.0 sat t = 0.1 s

Decide which one of the following statements below must be true. Credit is assigned for thecompleteness and clarity of your justifications, and not necessarily for finding the correctchoice below.

Choose and defend one statement only.(A) Only properties of the source were changed (while properties of the medium remained

constant).(B) Only properties of the medium were changed (while properties of the source remained

constant).(C) Both the properties of the source and the medium were changed.(D) Both the properties of the source and the medium remained constant.

Useful equations and constants:

ySHM t( ) = Asin2πt

Τ+ ψSHM

; y x t A

t xwave, sin( ) = π ± π +

2 2T λ

ψ ; Ψ x tt x

wave,( ) = π ± π +

2 2T λ

ψ ;

d

dtA t A t

d

dtA t A t

sin cos

cos sin

β β β

β β β

( ) = ( )

( ) = − ( )

; T pendulum = 2π L

g; Fspring = −k ⋅ stretch( ) ; gEarth, at surface = 9.8

Nkg

;

Tmass-spring = 2π m

k; f = 1

Τ; λ = vwave

f; vparticle x,t( ) = d

dtyparticle x,t( ); vwave sound, ≈ 340

ms

;

vc

n nwave lightmedium medium

,

.

m/s= =

×( )3 00 108

.


03.03.18

Quiz 121. [60%] Consider the experimental

set-up at right, where amicrophone is held next to a wallof an unknown type of material,and is slowly moved away fromthe wall, towards a speakeremitting sound (in air) of a certainwavelength λ. The microphonedetects the superposition of asound wave that travels directlyfrom the speaker to the microphone, and the sound wave that travels from the speaker, reflectsoff of the wall, and then to the microphone.

A student who has already taken Physics 7C tells you the following:"All I needed to do was to place the microphone at a distance of one-quarter of a wavelengthfrom the wall. [1] If the microphone detected constructive interference there, the reflectionphase shift off the wall was π."[2] If the microphone detected destructive interference there, the reflection phase shift off thewall was 0."


Choose and defend one statement only.(A) Both statement [1] and statement [2] are true.(B) Statement [1] is true, and statement [2] is false.(C) Statement [1] is false, and statement [2] is true.(D) Both statement [1] and statement [2] are false.

direct wave

reflected wave

speaker(stationary)

microphone (λ/4 from the wall)

wal

l (un

know

n m

ater

ial)


03.03.18

2. [40%] Consider theexperimental set-up at right,where a laser of a certainwavelength λ illuminates thedata tracks on the underside ofa compact disc (CD). As aresult, on the whiteboard thereare two maxima spots spacedequally on either side of thereflected central spot.

A student who has alreadytaken Physics 7C tells you thefollowing:"Since a digital video disc(DVD) has data tracks thatare spaced closer togetherthan on a CD, then it wouldcreate maxima spots that arecloser together on either sideof the central spot."

Decide which one of thefollowing statements below must be true. Credit is assigned for the completeness and clarity ofyour justifications, and not necessarily for finding the correct choice below.

Choose and defend one statement only.(A) The statement is correct.(B) The statement is incorrect.(C) Not enough information is given to determine what will happen to the maxima spots

created by a DVD.


y L t At L

source reflection

wave

, sin –( ) = π π + +

2 2Τ λ

ψ ψψ

1 244 344; f = 1

Τ; λ = vwave

f; vwave sound, ≈ 340

ms

(air);

vc

n nwave lightmedium medium

,

.

m/s= =

×( )3 00 108

; ∆ = −L L L1 2; ∆ ≈L d sinθ; ψreflection =π

0 "soft" reflection

"hard" reflection.

∆ = − = π ∆( ) π∆

+ ∆ + ∆

=

±( )π±( )π

Ψ Ψ Ψ1 2 2 2t f

L even

oddsources reflections–λ

ψ ψ constructive

destructive;

f f f

f f fcarrier

beat

= +( )=

1

2 1 2

1 2–.

λ = 633 nm laserCD or DVD

central spot

first maxima

first maximaw

hite

boar

d


03.03.18

Quiz 131. [40%] Consider the process where a proton is brought from an initial position at a infinite

distance away, to be held stationary at a final location nearby a –4 µCoul and a +1 µCoulcharge.

°–+1 µCoul–4 µCoul

–1 cm 0 cm +1 cm

+

x = –2 cm +2 cm

proton

in from ∞

Decide which one of the following statements below must be true for this process. Credit isassigned for the completeness and clarity of your justifications, and not necessarily for findingthe correct choice below.

Choose and defend one statement only. Carefully read each choice.(A) The electrical potential energy of the proton increased from its initial to final position.(B) The electrical potential energy of the proton is the same for its initial and final positions.(C) The electrical potential energy of the proton decreased from its initial to final position.(D) There is not enough information to determine the initial-to-final change in electrical

potential energy of the proton.

2. [60%] Initially , a proton moves at a constantvelocity, at a speed of 0.1 m/s, horizontally tothe left, due to both the gravitational field andthe magnetic field of the Earth. However, aftera Physics 7C student turns on a circuit suchthat a current I = 2.0 Amps flows through ahorizontal wire, the trajectory of the proton isdeflected from its (initially) horizontaldirection.

Decide which one of the following statements below must be true after the current is turned on.Credit is assigned for the completeness and clarity of your justifications, and not necessarilyfor finding the correct choice below.

Choose and defend one statement only. Carefully read each choice.(A) At the location of the proton, the magnetic field of the Earth and the magnetic field of the

wire point in the same direction.(B) At the location of the proton, the magnetic field of the Earth and the magnetic field of the

wire point in opposite directions from each other.(C) At the location of the proton, the magnetic field of the Earth and the magnetic field of the

wire point in two completely different (but non-opposite) directions from each other.(D) Not enough information is given to determine the directions of the magnetic field of the

Earth and the magnetic field of the wire relative to each other, at the location of the proton.

°Ι = 2.0 A

y

v = 0.1 m/sproton

+3.0 m

+2.0 m

+1.0 m

0.0 m


03.03.18

Quiz 13 useful equations and constants:

out of page

into page

up

down

left

right

Ι

B

r

v

F

B θ

G = 6.67 ×10−11 N ⋅ m2

kg2 ; gM = GM

r2 ; gEarth, at surface = 9.8 Nkg

; REarth = 6.37 ×106 m ;

MEarth = 5.98 ×1024 kg ; Fon m = mg; k = 8 99 109. × ⋅ N mCoul

2

2 ; EQ = kQ

r2 ; Fon q = qE ;

qe = × −– .1 602 10 19 Coul ; µ0 = 1.26 ×10−6 Tesla ⋅ mAmps

; BI = µ0I

2πr; F qvBon qv = sinθ; F

PE

ralong r = −∆∆

;

∆PEelec = kQq∆ 1r

; ∆ = ∆

≈ ∆PE GMmr

mg hgrav –1

; m proton = × −1 6726 10 27. kg.

Quiz 141. [50%] Consider the following (reversible) nuclear reaction:

He

4.002 603 250 u

+ He

4.002 603 250 u

Be

8.005 305 094 u24

24

48

1 244 344 1 244 344 1 244 344↔ .

For this question you will determine whether the forward reaction (fusion) or the reversereaction (fission) will have the greater (or the same) initiation energy.


Choose and defend one statement only. Carefully read each choice.(A) The forward reaction (fusion) will have the greater initiation energy.(B) The reverse reaction (fission) will have the greater initiation energy.(C) The forward reaction and the reverse reaction both have the same initiation energy.(D) There is not enough information to determine which reaction will have the greater

initiation energy.


03.03.18

2. [50%] Consider all of the possible isotopes for magnesium (all of which have 12 protons), andthe possible isotopes for aluminum (all of which have 13 protons). Due to electrostaticrepulsion in their nuclei, it is known for both magnesium and aluminum nuclei that the protonground state lies halfway between the ground state and the first excited state for the neutrons.In this question you will determine how many of these magnesium and aluminum isotopes arestable (i.e., will not experience β+, β– , nor electron capture decay).


Choose and defend one statement only. Carefully read each choice.(A) The box model predicts that there will be a greater number of stable magnesium isotopes

than stable aluminum isotopes.(B) The box model predicts that there will be a greater number stable aluminum isotopes than

stable magnesium isotopes.(C) The box model predicts that there will be the same number of stable magnesium and

aluminum isotopes.(D) There is not enough information to determine whether magnesium or aluminum will have

a greater number of stable isotopes.


Z (protons)A(nucleons)X(element); R A A= ( ) = ×( )−1 2 1 2 101 3 15 1 3. ./ / fm m ; "Binding energy" mass defect= ( )c 2 ;

" - value" mass decrementQ c= ( ) 2; XE hfhc

photon photonphoton

= =λ

; h = 6.626 ×10−34 J·s;

n p e→ + +– ν ; ∆PEelec = kQq∆ 1r

; qe = × −– .1 602 10 19 Coul ; 8 99 109. × ⋅

N mCoul

2

2 ;

m

m

m

electron

proton

neutron

= × ×= ×= ×

− −

−

−

9 10939 10 5 4858 10

1 672623 10 1 007276

1 674929 10 1 008665

31 4

27

27

. .

. .

. .

kg = u

kg = u

kg = u

;1 u = 1.66054×10−27 kg = 1.49242× −10 10

J" "2c

;

c = 3×108 m/s; 1 eV = 1.602×10−19 J;1 MeV = 1×106 eV.

physics 7c discussion/lab manual - waifer x 7c discussion/lab manual ... graphical representations...

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