QuestionNumber Unit Label Question Text Answer Choice A Choice B Choice C Choice D Choice E Justification Image name

1 Statics The electron volt is a measure of B Charge Energy Impulse Momentum Velocity by definition

2 StaticsA solid conducting sphere is given a positive charge Q. How is the charge Qdistributed in or on the sphere? E

It is concentratedat the center of thesphere.

It is uniformlydistributedthroughout thesphere.

Its densitydecreases radiallyoutward from thecenter.

Its densityincreases radiallyoutward from thecenter.

It is uniformlydistributed on thesurface of thesphere only.

Since charge is free to move aroundon/in a conductor, excess charges willrepel each other to theouter surface

3 Statics

A parallel–plate capacitor is charged by connection to a battery. If the batteryis disconnected and the separation between the plates is increased, what willhappen to the charge on the capacitor and the voltage across it? E Both remain fixed. Both increase Both decrease

The chargeincreases and thevoltage decreases.

The chargeremains fixed

When the battery is disconnected, Qremains constant. Since C decreaseswhen d increases andQ = CV, V will increase

4 StaticsA point P is 0.50 meter from a point charge of 5.0 × 10^(–8) coulomb. Theintensity of the electric field at point P is most nearly: D 2.5 × 10^(–8) N/C

2.5 × 10^1N/C

9.0 × 10^2N/C

1.8 × 10^3N/C

7.5 × 10^8N/C E = kQ/r^2

5 StaticsA point P is 0.50 meter from a point charge of 5.0 × 10^(–8) coulomb. Theelectric potential at point P is most nearly: C 2.5 × 10^(–8) N/C

2.5 × 10^1N/C

9.0 × 10^2N/C

1.8 × 10^3N/C

7.5 × 10^8N/C V = kQ/r

6 Statics

One joule of work is needed to move one coulomb of charge from one pointto another with no change invelocity. Which of the following is true between the two points? C

The resistance isone ohm.

The current is oneampere.

The potentialdifference is onevolt.

The electric fieldstrength is onenewton percoulomb.

The electric fieldstrength is onejoule per electron. W = qV

7 Statics

Two positive charges of magnitude q are each a distance d from the origin Aof a coordinate system as shownabove. At which of the following points is the electric field least in magnitude? A A B C D E

Since both charges are positive, theelectric field vectors point in oppositedirections at pointsbetween the two. At point A, themagnitudes of the electric field vectorsare equal and thereforecancel out, making E = 0 at point A 7.statics.png

8 Statics

Two positive charges of magnitude q are each a distance d from the origin Aof a coordinate system as shownabove. At which of the following points is the electric potential greatest inmagnitude? A A B C D E

V = ΣkQ/r and since both charges arepositive, the largest potential is at theclosest point to thetwo charges (it is more mathematicallycomplex than that, but this reasoningworks for thechoices given) 7.statics.png

9 Statics

A parallel–plate capacitor has a capacitance C. A second parallel–platecapacitor has plates with twice the area and twice the separation. Thecapacitance of the second capacitor is most nearly: C ¼C ½C C 2C 4C

C = ε0A/d; if A × 2, C × 2 and if d × 2, C ÷ 2 sothe net effect is C is unchanged

10 Statics

Two identical conducting spheres are charged to +2Q and –Q. respectively,and are separated by a distance d(much greater than the radii of the spheres) as shown above. The magnitudeof the force of attraction on the leftsphere is F1. After the two spheres are made to touch and then arereseparated by distance d, the magnitude of the force on the left sphere is F2.Which of the following relationships is correct? E 2F1=F2 F1=F2 F1=2F2 F1=4F2 F1=8F2

The net charge on the two spheres is+Q so when they touch and separate,the charge on eachsphere (divided equally) is ½ Q. F∝ Q1Q2 so before contact F ∝ (2Q)(Q) =2Q2and aftercontact F ∝ (½ Q)(½ Q) = ¼ Q2Eor 1/8 of the original force 10.statics.png

11 StaticsThe capacitance of a parallel–plate capacitor can be increased by increasingwhich of the following? C

The distancebetween the plates

The charge oneach plate

The area of theplates

The potentialdifference acrossthe plates None of the above

C = ε0A/d and changing Q or V has noeffect on the capacitance

12 Statics An electron volt is a measure of A energy electric field

electric potentialdue to oneelectron

force per unitelectron charge electric charge By definition

13 Statics

An electron is accelerated from rest for a time of 10^-9 second by a uniformelectric field that exerts a force of8.0 x 10–15 newton on the electron. What is the magnitude of the electricfield? A 8.0 × 10^–24 N/C 9.1 × 10^–22 N/C 8.0 × 10^–6 N/C 2.0 × 10^–5 N/C 5.0 × 10^4 N/C E = F/q

14 Statics

An electron is accelerated from rest for a time of 10^-9 second by a uniformelectric field that exerts a force of8.0 x 10–15 newton on the electron. The speed of the electron after it hasaccelerated for the 10^–9 second is most nearly D 10^1 m/s 10^3 m/s 10^5 m/s 10^7 m/s 10^9 m/s

Δv = at where a = F/m. So we have Δv= 10^–4 × 10^–9 ÷ 10^–30 = 10^(–14 +–9 –(–30))

15 Statics

A hollow metal sphere of radius R is positively charged. Of the followingdistances from the center of thesphere, which location will have the greatest electric field strength? C

0 (center of thesphere) 3R/2 5R/4 2R

None of the abovebecause the fieldis of constantstrength

Inside the metal sphere E = 0. Onceoutside the sphere E decreases as youmove away so thestrongest field will be the closest pointto the outside of the sphere

16 Statics

Two isolated charges, + q and – 2q, are 2 centimeters apart. If F is themagnitude of the force acting on charge–2Q, what are the magnitude and direction of the force acting on charge +q? C

(1/2) F Towardcharge – 2q

2 F Away fromcharge –2q

F Toward charge –2q

F Away fromcharge – 2q

2F Toward charge– 2q Newton’s third law

17 Statics Charges + Q and – 4Q are situated as shown above. The net electric field iszero nearest which point? A A B C D E

Where E is zero must be closer to thesmaller charge to make up for theweaker field. Thevectors point in opposite directionswhen outside the two opposite charges.These two criteriaeliminate 4 of the choices. 17.statics.png

18 Statics

A positive charge of 10–6 coulomb is placed on an insulated solid conductingsphere. Which of the following istrue? E

The chargeresides uniformlythroughout thesphere.

The electric fieldinside the sphereis constant inmagnitude, but notzero.

The electric field inthe regionsurrounding thesphere increaseswith increasingdistance from thesphere.

An insulated metalobject acquires anet positive chargewhen brought nearto, but not incontact with, thesphere

When a secondconducting sphereis connected by aconducting wire tothe first sphere,charge istransferred untilthe electricpotentials of thetwo spheres areequal.

Charges flow when there is a differencein potential. Analyzing the otherchoices: A is wrongbecause the charge resides on thesurface. For B, E = 0 in a chargedconducting sphere. E =kQ/r^2eliminates choice C. And for D, chargeseparation will occur, but the object willnotacquire any charge.

19 Statics

Two large parallel conducting plates P and Q are connected to a battery ofemf E, as shown above.A test charge is placed successively at points I, II, and III. If edge effects arenegligible, the force on the chargewhen it is at point III is B

of equal magnitudeand in the samedirection as theforce on thecharge when it isat point I

of equal magnitudeand in the samedirection as theforce on thecharge when it isat point II

equal in magnitudeto the force on thecharge when it isat point I, but in theopposite direction

much greater inmagnitude thanthe force on thecharge when it isat point II, but inthe same direction

much less inmagnitude thanthe force on thecharge when it isat point II, but inthe same direction

E is uniform between charged parallelplates therefore the force on a charge isalso uniformbetween the plates 19.statics.png

20 Statics

Forces between two objects which are inversely proportional to the square ofthe distance between the objectsinclude which of the following? I. Gravitational force between two celestialbodiesII. Electrostatic force between two electronsIII. Nuclear force between two neutrons C I only III only I and II only II and III only I, II, and III

Fg = Gm1m2/r2 and FE = kq1q2/r2.The nuclear force does not have asimilar relationship.

21 Statics

The diagram above shows an isolated, positive charge Q. Point (B) is twiceas far away from Q as point A. Theratio of the electric field strength at point A to the electric field strength atpoint B is B 8 to 1 4 to 1 2 to 1 1 to 1 1 to 2

E ∝ 1/r2so if r × 2, E ÷ 4 21.statics.png

22 Statics

Which of the following is true about the net force on an uncharged conductingsphere in a uniform electricfield? A It is zero

It is in the directionof the field

It is in the directionopposite to thefield

It produces atorque on thesphere about thedirection of thefield.

It causes thesphere to oscillateabout anequilibriumposition.

While the charges may separate, theforces on the opposite charges are inopposite directions,canceling out

23 Statics

Two conducting spheres of different radii, as shown above, each have charge–Q. Which of the followingoccurs when the two spheres are connected with a conducting wire? E No charge flows

Negative chargeflows from thelarger sphere tothe smaller sphereuntil the electricfield at the surfaceofeach sphere is thesame.

Negative chargeflows from thelarger sphere tothe smaller sphereuntil the electricpotential of eachsphere is thesame.

Negative chargeflows from thesmaller sphere tothe larger sphereuntil the electricfield at the surfaceofeach sphere is thesame.

Negative chargeflows from thesmaller sphere tothe larger sphereuntil the electricpotential of eachsphere is thesame.

V = kQ/r so the smaller sphere is at thelower potential (more negative = lower)Negative chargeflows from low to high potential so thecharge will flow from the smaller sphereto the larger.The flow of charge ceases when thereis no difference in potential. 23.statics.png

24 Statics

Two parallel conducting plates are connected to a constant voltage source.The magnitude of the electric fieldbetween the plates is 2,000 N/C. If the voltage is doubled and the distancebetween the plates is reduced to 1/5the original distance, the magnitude of the new electric field is E 800N/C 1,600N/C 2,400N/C 5,000N/C 20,000N/C

E = V/d so if V × 2, E × 2 and if d ÷ 5, E× 5 so the net effect is E × 10

25 Statics

The figure above shows two particles, each with a charge of +Q, that arelocated at the opposite corners of asquare of side d. What is the direction of the net electric field at point P ? C northeast east southeast south southwest

The electric field vectors from the twocharges point down and to the left(away from thecharges) so the resultant field pointsdown and left 25.statics.png

26 Statics

The figure above shows two particles, each with a charge of +Q, that arelocated at the opposite corners of asquare of side d. What is the potential energy of a particle of charge +q that isheld at point P ? D zero

SQRT(2)qQ/(4πε0d) 1qQ/(4πε0d) 2qQ/(4πε0d)

2SQRT(2)qQ/(4πε0d)

The potential energy of a particle at alocation is the potential at that locationtimes the charge.In this case, the potential is kQ/d +kQ/d = (2kQ/d) 25.statics.png

27 Statics

. Two parallel conducting plates, separated by a distance d, are connected toa battery of emf E. Which of thefollowing is correct if the plate separation is doubled while the battery remainsconnected? B

The electric chargeon the plates isdoubled.

The electric chargeon the plates ishalved

The potentialdifference betweenthe plates isdoubled.

The potentialdifference betweenthe plates ishalved

The capacitance isunchanged.

If the battery remains connected, thepotential remains constant. Cdecreases as the separationincreases soothe charge Q = CV willalso decrease

28 StaticsA 4 µF capacitor is charged to a potential difference of 100 V. The electricalenergy stored in the capacitor is E 2 × 10^–10 J 2 × 10^–8 J 2 × 10^–6 J 2 × 10^–4 J 2 × 10^–2 J UC = ½ CV^2

29 Statics

The hollow metal sphere shown above is positively charged. Point C is thecenter of the sphere and point P isany other point within the sphere. Which of the following is true of the electricfield at these points? A

It is zero at bothpoints.

It is zero at C, butat P it is not zeroand is directedinward

It is zero at C, butat P it is not zeroand is directedoutward.

It is zero at P, butat C it is not zero.

It is not zero ateither point.

In metals under electrostatic conditions,the electric field is zero everywhereinside. 29.statics.png

30 Statics

Charges –Q and +Q are located on the x– and y–axes, respectively, each ata distance d from the origin O, asshown above. What is the direction of the electric field at the origin O ? D east west northwest southeast southwest

The electric field vector from the +Qcharge points down and from the –Qcharge points to theright so the resultant field points downand right 30.statics.png

31 Statics

Charges –Q and +Q are located on the x– and y–axes, respectively, each ata distance d from the origin O, asshown above. What is the magnitude of the electric field at the origin O? D kQ/(2d^2) kQ/(2^(1/2)d^2) kQ/d^2 2^(1/2)kQ/d^2 2kQ/d^2

The two vectors, each of magnitude E =kQ/d2, point at right angles to eachother so the resultant field is √2E 30.statics.png

32 Statics

An electron e and a proton p are simultaneously released from rest in auniform electric field E, as shown above.Assume that the particles are sufficiently far apart so that the only force actingon each particle after it isreleased is that due to the electric field. At a later time when the particles arestill in the field, the electron andthe proton will have the same E direction of motion speed displacement

magnitude ofacceleration

magnitude of forceacting on them

Since the electron and the proton haveequal charge, the forces on them areequal. Since theyhave different masses, theaccelerations, speeds anddisplacements will not be equal. 32.statics.png

33 Statics

Two large, flat, parallel, conducting plates are 0.04 m apart, as shown above.The lower plate is at a potential of2 V with respect to ground. The upper plate is at a potential of 10 V withrespect to ground. Point P is located0.01 m above the lower plate. The electric potential at point P is D 10 V 8 V 6 V 4 V 2 V

The electric field between chargedparallel plates is uniform, which meansthe potential changesuniformly with distance. For a change of8 V over 4 cm means the change ofpotential withposition (and the electric field strength)is 2 V/cm, which gives the potential 1cm away from the2 V plate as 4 V 33.statics.png

34 Statics

Two large, flat, parallel, conducting plates are 0.04 m apart, as shown above.The lower plate is at a potential of2 V with respect to ground. The upper plate is at a potential of 10 V withrespect to ground. Point P is located0.01 m above the lower plate. The magnitude of the electric field at point P is D 800 V/m 600 V/m 400 V/m 200 V/m 100 V/m E=V/d 33.statics.png

35 Statics

A particle of charge Q and mass m is accelerated from rest through apotential difference V, attaining a kineticenergy K. What is the kinetic energy of a particle of charge 2Q and mass m/2that is accelerated from restthrough the same potential difference? D 1/4 K 1/2 K K 2K 4K

W = ΔK = QV (mass doesn’t have aneffect on the kinetic energy, just on thespeed in this case)

36 Statics

The diagram above shows electric field lines in an isolated region of spacecontaining two small chargedspheres, Y and Z. Which of the following statements is true? D

The charge on Y isnegative and thecharge on Z ispositive.

The strength of theelectric field is thesame everywhere.

The electric field isstrongest midwaybetween Y and Z.

A small negativelycharged objectplaced at point Xwould tend tomove toward theright.

Both chargesspheres Y and Zcarry the charge ofthe same sign.

The field lines point away from Y andtoward Z making Y positive and Znegative. 36.statics.png

37 Statics

A hollow metal sphere 1.0 m in diameter carries a charge of 4.0 μC. Theelectric field at a distance of 2.0 mfrom the center of the sphere is most nearly A 9.0 x 10^3 N/C 1.8 x 10^4 N/C 2.4 x 10^4 N/C 3.6 x 10^4 N/C 1.4 x 10^5 N/C E = kQ/r2

38 Statics

A parallel–plate capacitor has a capacitance Co. A second parallel–platecapacitor has plates with twice the area and twice the separation. Thecapacitance of the second capacitor is most nearly C 1/4 Co 1/2 Co Co 2 Co 4 Co C = ε0A/d; ε0(2A)/(2d) = ε0A/d

39 Statics The electric field E just outside the surface of a charged conductor is A

directedperpendicular tothe surface

directed parallel tothe surface

independent of thesurface chargedensity zero infinite

Charges arrange themselves onconductors so there is no electric fieldinside, and no electric fieldcomponent along the surface

40 Statics

Points R and S are each the same distance d from two unequal charges, + Qand +2Q, as shown above. The work required to move a charge -Q from pointR to point S is D

dependent on thepath taken from Rto S

directlyproportional to thedistance betweenR and S positive zero negative

By symmetry VR = VS so ΔVRS = 0and W = qΔV 40.statics.png

41 StaticsA rigid insulated rod, with two unequal charges attached to its ends, is placedin a uniform electric field E as shown above.The rod experiences a B

net force to the leftand a clockwiserotation

net force to the leftand acounterclockwiserotation

net force to theright and aclockwise rotation

net force to theright and acounterclockwiserotation

rotation, but no netforce

The force on the upper charge is to theleft and twice the magnitude of theforce on the bottom charge, which is tothe right. This makes the net force tothe left and the torque on the rod to becounterclockwise. 41.statics.png

42 Statics

The electric field of two long coaxial cylinders is represented by lines of forceas shown above. The charge onthe inner cylinder is +Q. The charge on the outer cylinder is E positive 3Q positive Q 0 negative Q negative 3Q

Compared to the +Q charge at thecenter, the charge on the outer surfaceof the outer cylinder has twice themagnitude and is of opposite sign (so itis –2Q). There is also an equal andopposite charge induced on the innersurface of the outer cylinder making thetotal charge on the outer cylinder –2Q +–Q 42.statics.png

43 Statics

An isolated capacitor with air between its plates has a potential difference Voand a charge Qo. After the space between the plates is filled with oil, thedifference in potential is V and the charge is Q. Which of the following pairs ofrelationships is correct? B Q = Qo and V > Vo Q = Qo and V < Vo Q > Qo and V = Vo Q < Qo and V < Vo Q > Qo and V > Vo

Since the capacitor is isolated, Qremains constant. Filling the place withoil (a dielectric) will increase thecapacitance, causing the potential (V =Q/C) to decrease

44 Statics

Two small spheres have equal charges q and are separated by a distance d.The force exerted on each sphere by the other has magnitude F. If the chargeon each sphere is doubled and d is halved, the force on each sphere hasmagnitude E F 2F 4F 8F 16F

FE∝ q1q2/r2; if q1 and q2 × 2; F ×4 and if r ÷ 2, F × 4 making thenet effect F × 4 × 4

45 StaticsWhich of the following statements about conductors under electrostaticconditions is true? E

Positive work isrequired to move apositive chargeover the surface ofa conductor

Charge that isplaced on thesurface of aconductor alwaysspreads evenlyover the surface

The electricpotential inside aconductor isalways zero.

The electric field atthe surface of aconductor istangent to thesurface.

The surface of aconductor isalways anequipotentialsurface.

Since there is no component of theelectric field along a conducting surfaceunder electrostatic conditions, no workis done moving the charge around thesurface, meaning no differencesinpotential

46 StaticsA charged particle traveling with a velocity v in an electric field E experiencesa force F that must be D parallel to v perpendicular to v

perpendicular to vand E parallel to E perpendicular to E

Regardless of velocity, the force on acharge in an electric field is parallel tothe field (F = qE)

47 Statics

A positive charge of 3.0 × 10^ -8 coulomb is placed in an upward directeduniform electric field of 4.0 × 10^4 N/C.When the charge is moved 0.5 meterupward,the work done by the electric force on the charge is A 6 × 10^ -4 J 12 × 10^ –4 J 2 × 10^ 4 8 x 10^ 4 J 12 x 10^4 J W = Fd = qEd

48 Statics

The following configurations of electric charges are located at the vertices ofan equilateral triangle.Point P is equidistant from the charges. In whichconfiguration is the electric field at P equal to zero? A A B C D E

E points away from + charges andtoward – charges. Use symmetry. 48.statics.png

49 Statics

The following configurations of electric charges are located at the vertices ofan equilateral triangle. Point P is equidistant from the charges. In whichconfiguration is the electric field at P pointed at the midpoint between two ofthe charges? C A B C D E

D and E are not symmetric so the fieldwill not point at the midpoint of anyside. The field inchoice B points at the bottom charge. 48.statics.png

51 StaticsA sheet of mica is inserted between the plates of an isolated chargedparallel–plate capacitor. Which of the B

The capacitancedecreases.

The potentialdifference acrossthe capacitordecreases.

The energy of thecapacitor does notchange.

The charge on thecapacitor platesdecreases

The electric fieldbetween thecapacitor platesincreases.

Since the capacitor is isolated, Qremains constant. Filling the place withoil (a dielectric) willincrease the capacitance, causing thepotential (V = Q/C) to decrease.

52 Statics

Two conducting spheres, X and Y have the same positive charge +Q, butdifferent radii(rx > ry) as shown above. The spheres are separated so that thedistance between them is large compared witheither radius. If a wire is connected between them, in which direction willelectrons be directed in the wire? A From X to Y From Y to X

There will be noflow of charge inthe wire.

It cannot bedetermined withoutknowing themagnitude of Q.

It cannot bedetermined withoutknowing whetherthe spheres aresolid or hollow.

V = kQ/r so the smaller sphere (Y) is atthe higher potential. Negative chargeflows from low tohigh potential so the charge will flowfrom X to Y. 52.statics.png

53 Statics

A sphere of radius R has positive charge Q uniformly distributed on itssurface. Which of the following represents the magnitude of the electric fieldE and the potential V as functions of r, thedistance from the center of the sphere, when r < R ? A E = 0, V = kQ/R E = 0, V = kQ/r E = 0, V = 0 E = kQ/r^2, V = 0 E = kQ/R^2, V = 0

Once inside a uniform sphere ofcharge, the electric field is zero. SinceE = 0 the potential doesnot change within the sphere (meaningit is the same value as the surface)

54 Statics

A sphere of radius R has positive charge Q uniformly distributed on itssurface. Which of the following represents the magnitude, of the electric fieldE and the potential V as functions of r, thedistance from the center of sphere, when r > R ? D

E = kQ/R^2, V =kQ/R

E = kQ/R, V =kQ/R E = kQ/R, V = kQ/r

E = kQ/r^2, V =kQ/r

E = kQ/r^2, V =kQ/r^2

Outside a uniform sphere of charge, itbehaves as a point charge.

55 Statics

From the electric field vector at a point, one can determine which of thefollowing?I. The direction of the electrostatic force on a test charge of known sign at thatpointII. The magnitude of the electrostatic force exerted per unit charge on a testcharge at that pointIII. The electrostatic charge at that point C I only III only I and II only II and III only I, II, and III

E = F/q. The vector nature of theequation allows one to find the directionof F and the equationitself allows one to find the ratio F/q, butnot q specifically

56 Statics

A conducting sphere of radius R carries a charge Q. Another conductingsphere has a radius R/2, but carries thesame charge. The spheres are far apart. The ratio of the electric field near thesurface of the smaller sphere tothe field near the surface of the larger sphere is most nearly E 0.25 0.5 1 2 4

Outside a uniform sphere of charge, itbehaves as a point charge. E = kQ/r2

57 Statics

A circular ring made of an insulating material is cut in half. One half is given acharge –q uniformly distributedalong its arc. The other half is given a charge + q also uniformly distributedalong its arc. The two halves arethen rejoined with insulation at the junctions J, as shown above. If there is nochange in the chargedistributions, what is the direction of the net electrostatic force on an electronlocated at the center of the circle? B

Toward the top ofthe page

Toward the bottomof the page To the right To the left Into the page.

By symmetry, the force on an electronat the center from the top half will bestraight down andthe force from the bottom half will alsobe straight down 57.statics.png

58 Statics

Four positive charges of magnitude q are arranged at the corners of a square,as shown above. At the center C of the square, the potential due to one charge alone is Vo and the electricfield due to one charge alone hasmagnitude Eo. Which of the following correctly gives the electric potential andthe magnitude of the electricfield at the center of the square due to all four charges? D

Electric Potential =zero, Electric Field= zero

Electric Potential =zero, Electric Field= 2Eo

Electric Potential =2Vo, Electric Field= 4Eo

Electric Potential =4Vo, Electric Field= zero

Electric Potential =4Vo, Electric Field= 2Eo

E is a vector so all the individual E fieldvectors from the four charges willcancel. V is a scalarand will add since they are all positivecharges. 58.statics.png

59 Statics

Two charges, –2Q and +Q, are located on the x–axis, as shown above. PointP, at a distance of 3D from theorigin O, is one of two points on the positive x–axis at which the electricpotential is zero. How far from theorigin O is the other point? D 2/3D D 3/2D 5/3D 2D

The points where V = 0 must lie closerto the smaller charge. Unlike electricfield vectors whichalso require the individual vectors pointin opposite directions, there are a locusof points (in thiscase in a ring surrounding the +Qcharge) where V = 0 as the twocharges are opposite in signand V is a scalar. So the other point onthe x axis is between the two charges,but closer to the+Q charge. This must be a valuebetween 1.5 D and 2 D 59.statics.png

50 Statics

Two concentric, spherical conducting shells have radii r1 and r2 and chargesQ1 and Q2, as shown above. Let rbe the distance from the center of the spheres and consider the region r1 < r< r2. In this region the electric fieldis proportional to A Q1/r^2 (Q1 + Q2)/r^2 (Q1 + Q2)/r Q1/r1 + Q2/r Q1/r + Q2/r2

When inside a uniform shell of charge,there is an electric field due to the shell.When outside auniform shell of charge, the electric fieldis as if the shell was a point charge. 60.statics.png

60 Statics

61 StaticsWhich of the following configurations is most likely to produce theseequipotential lines? D A B C D E

The potential difference between theplates is 4 V and the right side is thepositive plate. Weneed the batteries pointing in the samedirection with the positive terminal onthe right. 62.statics.png

62 Statics The force on an electron located on the 0 volt potential line is D 0N1N, directed to theright

1N, directed to theleft

to the right, but itsmagnitude cannotbe determinedwithout knowingthe distancebetween the lines

to the left, but itsmagnitude cannotbe determinedwithout knowingthe distancebetween the lines

The electron experiences a forcetoward the positive plate of magnitudeF = Eq. E = V/d andcannot be calculated without knowing d. 62.statics.png

63 Statics

Two metal spheres that are initially uncharged are mounted on insulatingstands, as shown above. A negativelycharged rubber rod is brought close to, but does not make contact with,sphere X. Sphere Y is then broughtclose to X on the side opposite to the rubber rod. Y is allowed to touch X andthen is removed some distanceaway. The rubber rod is then moved far away from X and Y. What are thefinal charges on the spheres? D

Sphere X:Zero Sphere Y:Zero

Sphere X:Negative SphereY: Negative

Sphere X:Negative SphereY: Positive

Sphere X:Positive SphereY: Negative

Sphere X:Positive SphereY: Positive

While spheres X and Y are in contact,electrons will repel away from the rodout of sphere X intosphere Y. 63.statics.png

64 Statics

Which of the following capacitors, each of which has plates of area A, wouldstore the most charge on the topplate for a given potential difference V? E A B C D E

The capacitor with the largestcapacitance will store the most charge.C = κε0A/d where κglass >κair and Kvacuum 64.statics.png

65 Statics

A parallel–plate capacitor has charge +Q on one plate and charge –Q on theother. The plates, each of area A,are a distance d apart and are separated by a vacuum. A single proton ofcharge +e, released from rest at thesurface of the positively charged plate, will arrive at the other plate withkinetic energy proportional to A (edQ)/A Q^2/(eAd) (AeQ)/d Q/ed eQ^2/Ad

K = qΔV. To find ΔV we use Q = CV (Vis ΔV in this case) which gives K = e(Q/C) and if weuse C = ε0A/d we have K = e(Qd/ε0A)

66 Statics

Two initially uncharged conductors, 1 and 2, are mounted on insulatingstands and are in contact, as shownabove. A negatively charged rod is brought near but does not touch them.With the rod held in place, conductor2 is moved to the right by pushing its stand, so that the conductors areseparated. Which of the following is nowtrue of conductor 2? C It is uncharged

It is positivelycharged

It is negativelycharged

It is charged, butits sign cannot bepredicted

It is at the samepotential that itwas before thecharged rod wasbrough near

While spheres 1 and 2 are in contact,electrons will repel away from the rodout of sphere 1 intosphere 2. 66.statics.png

67 Statics

As shown above, two particles, each of charge +Q, are fixed at oppositecorners of a square that lies in the planeof the page. A positive test charge +q is placed at a third corner. What is thedirection of the force on the testcharge due to the two other charges? E A B C D E

The force vectors from the two +Qcharges point down and to the left(away from the charges) sothe resultant force points down and left 67.statics.png

68 Statics

If F is the magnitude of the force on the test charge due to only one of theother charges, what is the magnitudeof the net force acting on the test charge due to both of these charges? D Zero F/2^(1/2) F [2^(1/2)]F 2

The two vectors, each of magnitude F,point at right angles to each other sothe resultant field is√2F 67.statics.png

69 Statics

Two charges are located on the line shown in the figure below, in which thecharge at point I is +3q and thecharge at point III is +2q. Point II is halfway between points I and III....Otherthan at infinity, the electric field strength is zero at a point on the line in whichof the following ranges? C To the left of I Between I and II Between II and III To the right of III

None; the field iszero only at infinity

Where E is zero must be closer to thesmaller charge to make up for theweaker field. Thevectors point in opposite directionswhen between the two like charges.These two criteriaeliminate 4 of the choices 69.statics.png

70 StaticsThe electric potential is negative at some points on the line in which of thefollowing ranges? E To the left of I Between I and II Between II and III To the right of III

None; thispotential is nevernegative.

Since both charges are positive and Vis a scalar equal to ΣkQ/r, the potentialwill never be zeroin the vicinity of these two charges 69.statics.png

71 Statics

The work that must be done by an external agent to move a point charge of 2mC from the origin to a point 3 m away is 5 J. What is the potential differencebetween the two points? C 4×10–4 V 10–2 V 2.5×103 V 2×106 V 6×106 V W=q∆V

72 Statics

The graph above shows the electric potential V in a region of space as afunction of position along the x–axis.At which point would a charged particle experience the force of greatestmagnitude? D A B C D E

The electric field (and hence, theelectric force on a charge) is greatestwhere the potential changes mostrapidly with position (the greatestgradient) since E = V/d. On this graph,thiswould be the point where the slope isthe greatest 72.statics.png

73 Statics

Suppose that an electron (charge –e) could orbit a proton (charge +e) in acircular orbit of constant radius R. Assuming that the proton is stationary andonly electrostatic forces act on the particles, which of the following representsthe kinetic energy of the two–particle system? B A B C D E

FE =FC andq1 =q2 =e so we haveke2/R2 =mv2/R and we multiply bothsides by 1⁄2R so the B right sidebecomes 1⁄2 mv2 (the kinetic energy).Choices C and E could have beeneliminatedbecause they are negative, and kineticenergy cannot be negative. Choices A& D aredimensionally incorrect (D has the unitsof a force, not energy, and A has theunits of electricpotential) 73.statics.png

74 StaticsIf the only force acting on an electron is due to a uniform electric field, theelectron moves with constant A

acceleration in adirection oppositeto that of the field

acceleration in thedirection of thefield

acceleration in adirectionperpendicular tothat of the field

speed in adirection oppositeto that of the field

speed in thedirection of thefield

If F is constant and F = ma, theacceleration is also constant. Negativecharges experience forces A oppositein direction to electric field lines.

75 Statics

Two charged particles, each with a charge of +q, are located along the x–axisat x = 2 and x = 4, as shownabove. Which of the following shows the graph of the magnitude of theelectric field along the x–axis from theorigin to x = 6? A A B C D E

By symmetry, E = 0 at the midpoint andgoes to infinity near each charge (E =kQ/r2) 75.statics.png

76 Statics

A positive electric charge is moved at a constant speed between twolocations in an electric field, with no workdone by or against the field at any time during the motion. This situation canoccur only if the... D

charge is moved inthe direction of thefield

charge is movedopposite to thedirection of thefield

charge is movedperpendicular toan equipotentialline

charge is movedalong anequipotential line

electric field isuniform

If no work is done by the field and thereis a field present, the motion must beperpendicular to the field, along anequipotential line, making the forceperpendicular to the displacement ofthecharge (a requirement for zero work).Along an equipotential line, ∆V = 0 andW = q∆V.

77 Statics

The nonconducting hollow sphere of radius R shown above carries a largecharge +Q, which is uniformlydistributed on its surface. There is a small hole in the sphere. A small charge+q is initially located at point P. adistance r from the center of the sphere.If k = 1/4πεo, what is the work thatmust be done by an external agentin moving the charge +q from P through the hole to the center O of thesphere? E Zero kqQ/r kqQ/R kq(Q – q)/r kqQ(1/R – 1/r)

Inside the sphere, E = 0 which meansthe potential does not change withposition and is the same value as thesurface, which is kQ/R. At point P, thepotential is kQ/r. W = q∆V = q(kQ/R –kQ/r) 77.statics.png

78 Statics

A capacitor is constructed of two identical conducting plates parallel to eachother and separated by a distance d. The capacitor is charged to a potentialdifference of V0 by a battery, which is then disconnected. If any edge effectsare negligible, what is the magnitude of the electric field between the plates? B V0d V0/d d/V0 V0/d2 V02/d E=V/d

79 Statics

A capacitor is constructed of two identical conducting plates parallel to eachother and separated by a distance d. The capacitor is charged to a potentialdifference of V0 by a battery, which is then disconnected. A sheet ofinsulating plastic material is inserted between the plates without otherwisedisturbing the system. A

It causes thecapacitance toincrease

It causes thecapacitance todecrease

None; thecapacitance doesnot change

Nothing can besaid about theeffect withoutknowing thedielectric constantof the plastic

Nothing can besaid about theeffect withoutknowing thethickness of thesheet

If the battery is disconnected, Qremains constant. If a dielectric isinserted between the plates, thecapacitance increases and since Q =CV, the potential difference decreases.

80 Statics

A point charge +Q is inside an uncharged conducting spherical shell that inturn is near several isolated pointcharges, as shown above. The electric field at point P inside the shelldepends on the magnitude of A Q only

the chargedistribution on thesphere only

Q and the chargedistribution on thesphere

all of the pointcharges

Conductors under electrostaticconditions will arrange their changes sono electric field exists inside (otherthan those created by charges placedinside the empty cavity). Fields fromexternalcharges will not penetrate intoconducting enclosures. 80.statics.png

81 StaticsA 20 μF parallel–plate capacitor is fully charged to 30 V. The energy stored inthe capacitor is most nearly... B 9 × 10^3 J 9 × 10^–3 J 6 × 10^–4 J 2 × 10^–4 J 2 × 10^–7 J UC = ½ CV^2

82 Statics

A potential difference V is maintained between two large, parallel conductingplates. An electron starts fromrest on the surface of one plate and accelerates toward the other. Its speedas it reaches the second plate isproportional to... C 1/V 1/V^(1/2) V^(1/2) V V^2 W = K = q∆V and K = ½ mv^2

83 Statics

Particles of charge Q and –4Q are located on the x–axis as shown in thefigure above. Assume the particles areisolated from all other charges. Which of the following describes the directionof the electric field at point P? E positive x positive y negative y

Components inboth the –x and +ydirections

Components inboth the +x and –ydirections

At point P, the field due to charge Qpoints up and to the right and the fielddue to charge –4Q islarger in magnitude and points downand to the right. Due to the asymmetry,no components willcancel. 83.statics.png

84 Statics

Particles of charge Q and –4Q are located on the x–axis as shown in thefigure above. Assume the particles are isolated from all other charges. Atwhich of the labeled points on the x–axis is the electric field zero? A A B C D E

Where E is zero must be closer to thesmaller charge to make up for theweaker field. Thevectors point in opposite directionsoutside the two opposite charges.These two criteria eliminate3 of the choices. For the magnitudes ofthe electric fields to be zero the ratiosQ/r2must be equalgiving (in units along the x axis) Q/r2= 4Q/(r + 4 units)2Agiving r = 4 units 83.statics.png

85 Statics

A solid metallic sphere of radius R has charge Q uniformly distributed on itsouter surface. A graph of electricpotential V as a function of position ris shown above. Which of the followinggraphs best represents themagnitude of the electric field E as a function of position rfor this sphere? C A B C D E

Since E = ∆V/d, E represents the slopeof the line on the graph which could bechoice C or D.since V ∝ 1/r the slope isproportional to ∆V/r = (1/r)/r =1/r^2 which is choice C

85.statics.png 85.staticsquestion.png

86 Statics

As shown in the figure above, six particles, each with charge +Q, are heldfixed and ate equally spaced aroundthe circumference of a circle of radius R. What is the magnitude of theresultant electric field at the center of the circle? A 0

6^(1/2) / 4πε *Q/R^2

12^(1/2) / 4πε *Q/R^2

18^(1/2) / 4πε *Q/R^2

3^(1/2) / 2πε *Q/R^2 By symmetry, all the vectors cancel 86.statics.png

87 Statics

As shown in the figure above, six particles, each with charge +Q, are heldfixed and ate equally spaced aroundthe circumference of a circle of radius R. With the six particles held fixed, howmuch work would be required to bring a seventh particle of charge + Qfrom very far away and place it at the center of the circle? D 0 6^(1/2) / 4πε * Q/R 3 / 2πε * Q^2/R^2 3 / 2πε * Q^2/R 9 / πε * Q^2/R

W = q∆V = +Q(Vcenter – V∞) =+QVcenter where Vcenter = ΣV = ΣkQ/r= 6kQ/R 86.statics.png

88 Statics

The diagram above shows equipotential lines produced by an unknowncharge distribution. A, B, C, D, and Eare points in the plane. Which vector below best describes the direction of theelectric field at point A ? A northeast southwest southeast northwest

None of these; thefield is zero.

E points from high potential to lowpotential, perpendicular to equipotentiallines (the direction ofthe force on a positive charge) 88.statics.png

89 Statics

The diagram above shows equipotential lines produced by an unknowncharge distribution. A, B, C, D, and Eare points in the plane. At which point does the electric field have the greatestmagnitude? B A B C D E

E points from high potential to lowpotential, perpendicular to equipotentiallines (the direction ofthe force on a positive charge) 88.statics.png

90 Statics

The diagram above shows equipotential lines produced by an unknowncharge distribution. A, B, C, D, and Eare points in the plane. How much net work must be done by an externalforce to move a –1 μC point charge from rest at point C to restat point E ? B –20 μJ –10 μJ 10 μJ 20 μJ 30 μJ

∆VCE = VE – VC = 10 V. The amountof work, W = q∆V = 1 µC × 10 V = 10µC. Since the Bexternal force must push against thenegative charge to keep it fromaccelerating and bring it torest at point E, the work done by theexternal force must be negative. 88.statics.png

91 Statics

The plates of a parallel–plate capacitor of cross sectional area A areseparated by a distance d, as shown above.Between the plates is a dielectric material of constant K. The plates areconnected in series with a variableresistance R and a power supply of potential difference V. The capacitance Cof this capacitor will increase ifwhich of the following is decreased? D A R K d V

C = KεoA/d. Only changes in thegeometry of the capacitor will changethe capacitance, not changes to thebattery or resistor. 91.statics.png

92 Statics

A physics problem starts: "A solid sphere has charge distributed uniformlythroughout. . . " It may be correctlyconcluded that the E

electric field is zeroeverywhere insidethe sphere

electric field insidethe sphere is thesame as theelectric fieldoutside

electric potentialon the surface ofthe sphere is notconstant

electric potential inthe center of thesphere is zero

sphere is not madeof metal

For charge to be distributed throughouta material, it must be non-conducting

93 Statics

A uniform spherical charge distribution has radius R.. Which of the followingis true of the electric fieldstrength due to this charge distribution at a distance r from the center of thecharge? D

It is greatest whenr = 0.

It is greatest whenr = R/2.

It is directlyproportional to rwhen r > R.

It is directlyproportional to rwhen r < R.

It is directlyproportional to r2.

Advanced question (not exactly in the Bcurriculum, but interesting). Like gravityinside a uniform sphere of mass, thefield is directly proportional to r wheninside the sphere (and proportional to1/r2 when outside) 93.statics.png

94 Statics

When a negatively charged rod is brought near, but does not touch, theinitially uncharged electroscope shownabove, the leaves spring apart (I). When the electroscope is then touchedwith a finger, the leaves collapse (II).When next the finger and finally the rod are removed, the leaves spring aparta second time (III). The charge onthe leaves is D

positive in both Iand III

negative in both Iand III

positive in I,negative in III

negative in I,positive in III

impossible todetermine in eitherI or III

In I, charge separation occurs (negativecharges repel to the leaves). The wholeprocess describes charging byinduction, where the electrons leave theelectroscope to ground (the finger) andonce contact with ground is broken, theelectroscope is left with a positivecharge (III)

95 Statics

A positively charged conductor attracts a second object. Which of thefollowing statements could be true?I. The second object is a conductor with negative net charge.II. The second object is a conductor with zero net charge.III. The second object is an insulator with zero net charge.. E I only II only III only I & II only I, II & III

Charged objects attract object with anopposite charge, but also neutralobjects by separation of charges.

96 Statics

A point charge of +4.0 μC is placed on the negative x–axis 0.20 m to the leftof the origin, as shown in theaccompanying figure. A second point charge q is placed on the positive x–axis 0.30 m to the right of the origin. If the net electric field at the origin iszero. What is q? A 9.0 μC 6.0 μC 0 –6.0 μC –9.0 μC

If E = 0, the field vectors point inopposite directions, making q positive.In magnitude we can find q by (+4 µC)/(0.2 m)2= q/(0.3 m)2 96.statics.png

97 Statics

A point charge of +4.0 μC is placed on the negative x–axis 0.20 m to the leftof the origin, as shown in theaccompanying figure. A second point charge q is placed on the positive x–axis 0.30 m to the right of the origin. If the net electric potential at the origin iszero, what is q? D 9.0 μC 6.0 μC 0 –6.0 μC –9.0 μC

If V = 0 and V = ΣkQ/r then q must benegative and (+4 µC)/(0.2 m) = q/(0.3m) 96.statics.png

98 Statics

Which of the following statements about solid conductors in electrostatics aretrue?I. The electric field inside the conductor is always zero.II. The electric potential inside the conductor is always zero.III. Any net charge is on the surface. D I only II only III only I & III only II & III only

by definition of conductors underelectrostatic conditions

99 Statics

A small object with charge q and weight mg is attached to one end of a stringof length L. The other end isattached to a stationary support. The system is placed in a uniform horizontalelectric field E, as shown in theaccompanying figure. In the presence of the field, the string makes a constantangle q with the vertical. What isthe sign and magnitude of q? B

positive withmagnitude(mg)/E

positive withmagnitude(mg)/(Etan(theta))

negative withmagnitude(mg)/E

negative withmagnitude(mg)/(Etan(theta))

negative withmagnitude(E)/(mgtan(theta))

Since the electrostatic force pushes thecharge to the right, with the field line, itis a positive charge. ΣFy= 0 gives T cosθ = mg and ΣFx= 0 gives T sin θ = FE=qE. Divide the two expressions toeliminate T. 99.statics.png

100 Statics

An isolated conducting sphere of radius R has positive charge + Q. Whichgraph best depictsthe electricpotential as a function of r, the distance from the center of the sphere? A A B C D E

V is constant inside and on the surfaceof a charged conductor and isproportional to 1/r outside a chargedconducting sphere. 100.statics.png

101 Statics

In the figure to the right, equipotential lines are drawn at 0, 20.0 V, and 40.0V. The total work done in movinga point charge of + 3.00 mC from position a to position b is: E 4.00 mJ 8.00 mJ 12.0 mJ 24.0 mJ 120 mJ

W = qΔV (motion along an equipotentialline requires no work so only ΔVmatters, not the path) 102.statics.png

102 Statics

Two positive point charges repel each other with force 0.36 N when theirseparation is 1.5 m. What force dothey exert on each other when their separation is 1.0 m? A 0.81 N 0.54 N 0.36 N 0.24 N 0.16 N F ∝ 1/r2

103 StaticsAn amber rod is given a net negative charge and held at rest. Which of thefollowing statements is true? C

The amber rod issurrounded only bya magnetic fieldthat circles the rod.

The amber rod issurrounded only byan electric fieldthat is directed outfrom the rod.

The amber rod issurrounded only byan electric fieldthat is directed intothe rod.

The amber rod issurrounded byboth a magneticfield that circlesthe rod and anelectric field that isdirected out fromthe rod.

The amber rod issurrounded byboth a magneticfield that circlesthe rod and anelectric field that isdirected into therod.

In a later topic, you will learn magneticfield are created by moving charges.Electric field linespoint toward negative charges.

104 Statics

Two isolated conducting spheres (S1 of radius 0.030 m and initial charge +6.0 nC and S2of radius 0.040 m and initial charge + 2.0 nC) are connected by a conductingwire. Charge will flow in the wire until: E

both spheres areequally charged.

the net charge iszero.

the force ofrepulsion betweenthe two spheresbecomes equal.

both spheres havethe same surfacecharge density.

both spheres areat the samepotential.

Charges flow when there is a differencein potential.

105 Statics

A point charge +q is placed midway between two point charges +3q and –qseparated by a distance 2d. IfCoulomb’s constant is k, the magnitude of the force on the charge +q is: B 2kq^2/d^2 4kq^2/d^2 6kq^2/d^2 8kq^2/d^2 10kq^2/d^2

The distance between the +q chargeand each charge is d. The force on the+q charge from eachcharge is in the same direction, makingthe net force kq2/d2 + k(3q2)/d2

106 StaticsHow much work is required to move – 24 mC of charge 4.0 m parallel to auniform 6.0 N/C electric field? E 1.0 mJ 16 mJ 36 mJ 62 mJ 576 mJ W = Fd = qEd

107 Statics

An isolated conducting sphere of radius R has positive charge + Q. Whichgraph best depicts the electric fieldas a function of r, the distance from the center of the sphere? D A B C D E

E is zero inside a charged conductorand is proportional to 1/r2 outside acharged conducting sphere. 108.statics.png

108 Statics

Point charges 1 and 2 have equal magnitude. The diagram to above showsthe electric field lines surroundingthem. Which of the following statements is true? A

Charge 1 ispositive, charge 2is negative.

Charge 1 isnegative, charge 2is positive.

Both charges 1and 2 are positive.

Both charges 1and 2 arenegative.

Both charges 1and 2 have thesame sign, but it isimpossible to tellwhich.

Electric field lines point in the directionof the force on a positive charge (awayfrom positive charges and towardnegative charges) 109.statics.png

109 Statics

A charged rod is placed between two insulated conducting spheres as shown.The spheres have no net charge.Region II has the same polarity as Region B I only III only IV only I & III only I & IV only

The rod will attract the same chargefrom each sphere to the side closer tothe rod. 110.statics.png

110 Statics

A charged rod is placed between two insulated conducting spheres as shown.The spheres have no net charge.Region II has the same polarity as Region B I only III only IV only I & III only I & IV only

The rod will attract the same chargefrom each sphere to the side closer tothe rod. 110.static.png

111 Statics

Two large oppositely charged insulated plates have a uniform electric fieldbetween them. The distance between the plates is increased. Which ofthefollowing statements is true? I. The field strength decreases.II. The field strength increases.III. The potential difference between the plates increases. C I only II only III only I and III only II and III only

Since the plates are insulated, thecharge remains constant. If thedistance is increased, thecapacitance will decrease (C ∝ A/d)and since Q = CV, the potentialdifference must increase by thesame factor that the distanceincreases. This means E = V/dremains the same.

112 Statics

When two charged point–like objects are separated by a distance R, the forcebetween them is F. If the distance between them is quadrupled, the forcebetween them is E 16 F 4 F F F/4 F/16 F ∝ 1/r2 ; if r × 4, F ÷ 16

113 Statics

An electroscope is given a positive charge, causing its foil leaves to separate.When an object is brought near the top plate of the electroscope, the foilsseparate even further. We could conclude A

that the object ispositively charged.

that the object iselectrically neutral.

that the object isnegativelycharged.

only that the objectis charged.

only that the objectis uncharged

If the leaves are positive, furtherseparation means they are becomingmore positive, whichimplies electrons are leaving theleaves, attracted to the top plate of theelectroscope. This willoccur if the object is positively charged.

114 Statics

Four positive point charges are arranged as shown in the accompanyingdiagram. The force between charges 1and 3 is 6.0 N; the force between charges 2 and 3 is 5.0 N; and the forcebetween charges 3 and 4 is 3.0 N. Themagnitude of the total force on charge 3 is most nearly A 6.3 N 8.0 N 10 N 11 N 14 N

Vector addition. Since all the chargesare positive, the forces due to charges2 and 4 point inopposite directions, making themagnitude of the net force along the xaxis 2 N. Combine thiswith a net force along the y axis of 6 Nusing the Pythagorean theorem 114.statics.png.png

115 Statics

Two isolated parallel plates are separated by a distance d. They carryopposite charges Q and each has surfacearea A. Which of the following would increase the strength of the electric fieldbetween the plates? I. Increasing QII. Increasing AIII. Increasing d A I only II only III only I & III only II & III only

Q = CV and V = Ed and using C = ε0A/d gives E = Q/ε0A

116 Statics

Consider the two oppositely charged plates asshown in the diagram. At whichof the marked pointsshown inthe diagram would a positively charged particle have the greatest electricalpotential energy? E A B C D E

The greatest potential energy would bewhere the charge is at the point with thegreatest potentialsince UE= qV (at a point). This is closest to thepositive plate. 116.statics.png

117 StaticsHow much work would be required to move a 4 coulomb charge 6 metersparallel to a 24 N/Celectric field? E 0 J 24 J 96 J 144 J 576 J W = Fd = qEd

118 Statics

. When a positive electrically charged glass rod is brought near a neutralhollow metal sphere suspended by aninsulating string, the sphere will be attracted to the rod because: D

the rod is muchlarger than thesphere

the rod removeselectron from thesphere

the electric chargeproduces amagnetic field toattract the sphere

the charge on therod causes aseparation ofcharge in thesphere

some of theprotons from therod have beengiven to the sphere

Charged objects attract neutral objectsby separating the charges within theneutral object.

119 Statics

An alpha particle and a proton are placed equal distance between two largecharged metal plates as shown.Which of the following would best describe the motion of the two particles ifthey were free to move? E

The alpha particlewill travel upwardswith twice thevelocity of theproton.

Both particles willtravel upwardswith the samevelocity.

The alpha particlewill accelerateupwards with twicethe acceleration ofthe proton.

Both particles willaccelerateupwards with thesame acceleration.

The alpha particlewill accelerateupwards with halfthe acceleration ofthe proton.

An alpha particle has twice the chargeand four times the mass of a proton.Twice the chargemeans twice the electric force. This,combined with four times the massgives half theacceleration. 119.statics.png

120 Statics

Two parallel metal plates carry opposite electrical charges each with amagnitude of Q. The plates are separatedby a distance d and each plate has an area A. Consider the following:I. increasing QII. increasing dIII. increasing AWhich of the following would have the effect of reducing the potentialdifference between the plates? C I only II only III only I and III II and III

Q = CV and C = ε0A/d which gives V =Qd/ε0A

121 Statics

A positive point charge of +q and a negative point charge of –q are separatedby a distance d. What would bethe magnitude of the electric field midway between the two charges? E E = 0 E=kq/d^2 E=2kq/d^2 E=4kq/d^2 E=8kq/d^2

At a point midway between the chargesE = kq/(d/2)2 from each charge. Sincethey are oppositecharges, the field vectors between thecharges point in the same direction. 121.statics.png

122 Statics

A positive charge +Q located at the origin produces an electric field E0 atpoint P (x = +1, y = 0). A negativecharge –2Q is placed at such a point as to produce a net field of zero at pointP. The second charge will beplaced on the C x-axis where x > 1

x-axis where 0 < x< 1 x-axis where x < 0 y-axis where y > 0 y-axis where y < 0

For the E field vectors to point inopposite directions, point P must lieoutside the two charges.For the magnitudes of E due to eachcharge to cancel, Point P must becloser to the smallercharge 122.statics.png

123 Statics

A 300 eV electron is aimed midway between two parallel metal plates with apotential difference of 400 V. Theelectron is deflected upwards and strikes the upper plate as shown. Whatwould be the kinetic energy of theelectron just before striking the metal plate? C 360 eV 400 eV 500 eV 700 eV 740 eV

The extra kinetic energy gained by theelectron is W = K = qΔV, where ΔV isthe potentialdifference between the midway line andthe upper plate, which is 200 V. Thismakes theadditional kinetic energy 200 eV.Kinetic energy is a scalar so the totalKE of the electron is now300 eV + 200 eV 123.statics.png

124 Statics

Two small hollow metal spheres hung on insulating threads attract oneanother as shown. It is known that apositively charged rod will attract ball A.I. Ball A has a positive chargeII. Ball B has a negative chargeIII. Ball A and Ball B have opposite chargesWhich of the above can be correctly concluded about the charge on theballs? E I only II only III only all of these none of these

If a positive rod attracts ball A, it iseither negative or neutral. For ball B toalso attract ball Ameans ball B can be charged positiveor negative (if ball A is neutral) orneutral (if ball A ispositive)

125 Statics

A 5 × 10–6 coulomb electric charge is placed midway between two parallelmetal plates connected to a 9–voltbattery. If the electric charge experiences a force of 1.5 × 10–4 newtons,what is the separation of the metalplates? D 6.75 × 10–9 m 2.7 × 10–4 m 3.7 × 10–3 m 0.30 m 3.3 m F = Eq and E = V/d giving d = qV/F

126 Statics

A parallel–plate capacitor is connected to a resistanceless circuit with abattery having emf E until the capacitoris fully charged. The battery is then disconnected from the circuit and theplates of the capacitor are moved tohalf of their original separation using insulated gloves. Let Vnew be thepotential difference across the capacitorplates when the plates are moved together. Let Vold be the potentialdifference across the capacitor plates whenconnected to the battery. Vnew/Vold= B ¼ ½ 1 2 4

Since the battery is removed, thecharge remains constant. If thedistance is decreased, thecapacitance will increase (C ∝ A/d)and since Q = CV, the potentialdifference must decrease bythe same factor that the distancedecreases. 126.statics.png

127 Statics

A solid, uncharged conducting sphere of radius 3a contains a hollowedspherical region of radius a. A pointcharge +Q is placed at the common center of the spheres. Taking V = 0 as rapproaches infinity, the potential atposition r = 2 a from the center of the spheres is: C 0 2kQ/3a kQ/3a kQ/a kQ/2a

Since the spherical shell is conducting,a charge of –Q is induced on the innersurface. This givesa charge of +Q on the outer surfacesince the spherical shell is neutral. As E= 0 inside theconducting shell, the potential inside isconstant and the same as on thesurface, which is kQ/r

128 Statics

Two identical electrical point charges Q, separated by a distance d producean electrical force of F on oneanother. If the distance is decreased to a distance of 0.40d, what is thestrength of the resulting force? B 16F 6.3F 2.5F 0.40F 0.16F F ∝ 1/r2; if r × 0.4 then F ÷ 0.42

129 Statics

The most convincing proof of the fact that electrical charge comes in afundamentally–sized basic amount wasprovided by the work of E Crookes Lorentz Rutherford Faraday Millikan

The oil drop experiment not only foundthe charge of the electron, but also thefact that chargewas quantized. 129.statics.png

130 Statics

Four electrical charges are arranged on the corners of a 10 cm square asshown. What would be the direction of the resulting electric field at the centerpoint P? B Right Up Left Down Northeast

The force vectors from each chargeand their relative magnitude are goingfrom P to the outer dots. 130.statics.png

131 Statics

A proton is released between the two parallel plates of the fully chargedcapacitor shown above. What wouldbe the resulting acceleration of the proton? E 1.0 × 10–7 m/s2 7.3 × 1013 m/s2 9.6 × 108 m/s2 6.3 × 1019 m/s2 3.8 × 1011 m/s2

Using F=ma=qE and E=V/d givesa=qV/md 131.statics.png

132 Statics

A circular parallel–plate capacitor is connected to a battery in a circuit. Thecapacitor is fully charged beforethe battery is disconnected from the circuit. A uniform material of dielectricconstant κ is inserted between theplates of the capacitor, effectively filling the space between the plates. LetUold be the energy stored by thecapacitor before the dielectric was inserted, while Unew is the energy storedafter the dielectric was inserted.The ratio of Unew/Uold is: B 1/(k^2) 1/k 1 k k^2

Since the battery is disconnected, Qremains constant. UC = Q2/2C soUnew/Uold = Cold/Cnew = (ε0A/d)/(κε0A/d) = 1/κ

133 Statics

A solid uncharged conducting sphere has radius 3a contains a hollowedspherical region of radius 2a. A pointcharge +Q is placed at a position a distance a from the common center of thespheres. What is the magnitude ofthe electric field at the position r = 4a from the center of the spheres asmarked in the figure by P? B 0 kQ/16a^2 3kQ/16a^2 kQ/9a^2 None of the above.

Since the spherical shell is conducting,a charge of –Q is induced on the innersurface. This gives a charge of +Q onthe outer surface since the sphericalshell is neutral and the field outside theshell is as if the shell was a pointcharge. 133.statics.png

134 Statics The potential energy of two like charges A

decreases as thecharges areseparated.

depends on thesign of the charge.

is proportional tothe square of therelative speed.

is inverselyproportional to thesquare of theseparation. is repulsive. UE = kq1q2/r

135 Statics

A positively charged object is brought near but not in contact with the top ofan uncharged gold leafelectroscope. The experimenter then briefly touches the electroscope with afinger. The finger is removed,followed by the removal of the positively charged object. What happens to theleaves of the electroscope whena negative charge is now brought near but not in contact with the top of theelectroscope? B

they remainuncharged

they move fartherapart

they move closertogether

they remainpositively chargedbut unmoved

they remainnegatively chargedbut unmoved

The process described is charging byinduction which gives the electroscopein this case a net negative charge.Bringing a negative charge near the topof the electroscope will cause electronsto repel to the leaves. Since the leavesare already negative, this will causethem to separate further.

136 Statics

A solid spherical conducting shell has inner radius a and outer radius 2a. Atthe center of the shell is located apoint charge +Q. What must the excess charge of the shell be in order for thecharge density on the inner andouter surfaces of the shell to be exactly equal? A -5Q 3Q -4Q 4Q -3Q

The charge density is Q/area which isQ/4πr2 so for the inner surface it isQinner/4πa2 and for the outer surface itis Qouter/16πa2. For these to be equalQouter must be 4Qinner. Because ofthe +Q charge inside, there is a chargeof –Q induced on the inner surface,which means the outer surface musthave charge -4Q. Thus the total chargeon the shell is -5Q. 136.statics.png

137 Statics

A small positive test charge is placed at point P in the region near twocharges. Which of the following arrowsindicates the direction of the force on the positive test charge? C Right Down Left Southeast Up

The force on a positive charge is in thedirection of the electric field at thatlocation. 137.statics.png

138 Statics

A portable radio that is playing is placed inside a screen cage as shown.When inside the cage the radio stopsplaying because D

the electricpotential of thebatteries isneutralized.

the charge on theradio is zero.

the sound cannottravel through thecage.

the electric field ofthe radio wavescannot penetratethe cage.

none of the abovereasons.

Conductors under electrostaticconditions will arrange their changes sono electric field exists D inside (otherthan those created by charges placedinside the empty cavity). Fields fromexternal sources will not penetrate intoconducting enclosures. 138.statics.png

139 Statics

A spherical conducting shell has a net charge +Q placed on it. Which of thefollowing is the correctrelationship for the electric potential at the points labeled A, B, and C? Point Ais at the center of the sphere,point B is at the surface of the shell, a distance R from point A, and point C isa distance R from point B outsidethe sphere. As r goes to infinity, V = 0. E VC <VB <VA VA <VB <VC VC =VB =VA VC =VB <VA VC <VB =VA

Once inside a uniform sphere ofcharge, the electric field is zero.Since E = 0 the potential does notchange within the sphere(meaning it is the same value asthe surface). V ∝ 1/r outside thesphere. 139.statics.png

140 StaticsWhich statement about a system of point charges that are fixed in space isnecessarily true? A

If the potentialenergy of thesystem is negative,net positive workby an externalagent is requiredto take the chargesin the system backto infinity.

If the potentialenergy of thesystem is positive,net positive work isrequired to bringany new chargenot part of thesystem in frominfinity to its finalresting location.

If the potentialenergy of thesystem is zero, nonegative chargesare in theconfiguration.

If the potentialenergy of thesystem is negative,net positive workby an externalagent was requiredto assemble thesystem of charges.

If the potentialenergy of thesystem is zero,then there is noelectric forceanywhere in spaceon any othercharged particlenot part of thesystem.

141 Statics

A positive point charge exerts a force of magnitude F on a negative pointcharge placed a distance x away. If the distance between the two pointcharges is halved, what is the magnitude of the new force that the positivepoint charge exerts on the negative point charge? A 4F 2F F F/2 F/4 F ∝ 1/r^2

142 Statics

Two uniformly charged non–conducting spheres on insulating bases areplaced on an air table. Sphere A has a charge +3Q coulombs and sphere Bhas a charge +Q coulombs. Which of the following correctly illustrates themagnitude and direction of the electrostatic force between the spheres whenthey are released? D A B C D E

. Newton’s third law requires the forcesbe equal and opposite. This eliminateschoices A, B andC. Since they both positive, the force isrepulsive. 142.statics.png

143 Statics

For the diagram shown below, what is the ratio of the charges q2/q1 wherethe diagram shown has a representation of the field lines in the space nearthe charges. B -3/2 -2/3 0.666 1.5 1

q2/q1= lines on q2/lines on q1 and since thelines point toward q2 and away from q1they are Boppositely charged, making the rationegative. 143.statics.png

144 StaticsIn which Region(s) is there a place on the x–axis (aside from infinity) at whichthe electric potential is equal to zero? E Only in Region II Only in Region III

In both Regions Iand II

In both Regions Iand III

In both Regions IIand III

The points where V = 0 must lie closerto the smaller charge. Unlike electricfield vectors whichalso require the individual vectors pointin opposite directions, there are a locusof points (in thiscase in a ring surrounding the –Qcharge) where V = 0 as the twocharges are opposite in signand V is a scalar. 144,145.statics.png

145 StaticsIn which Region(s) is there a place on the x–axis (aside from infinity) at whichthe electric field is equal to zero? B Only in Region II Only in Region III

In both Regions Iand II

In both Regions Iand III

In both Regions IIand III

For E to be zero, the electric fieldvectors from each charge must point inopposite directions andmust therefore occur at a point outsidethe charges. For the electric fieldvectors from eachcharge to be equal in magnitude sothey can cancel, it must also occur at apoint closer to thesmaller charge to make up for theweaker field. 144,145.statics.png

146 Statics

A parallel–plate capacitor is connected to a battery. Without disconnecting thecapacitor, a student pulls the capacitor’s plates apart so that the plateseparation doubles. As a result of this action, what happens to the voltageacross the capacitor and the energy stored by the capacitor? D

the voltagedoubles; theenergy stays thesame

the voltage halves;the energy doubles

the voltagedoubles; theenergy halves

the voltage staysthe same; theenergy halves

the voltage staysthe same; theenergy doubles

Since the battery remainsconnected, V remains constant. Cdecreases as d increases (C ∝ 1/d)and UC = ½ CVD2

147 Statics

A person rubs a neutral comb through their hair and the comb becomesnegatively charged. Which of the following is the best explanation for thisphenomenon? C

The hair gainsprotons from thecomb.

The hair gainsprotons from thecomb while givingelectrons to thecomb.

The hair loseselectrons to thecomb.

The comb losesprotons to theperson’s handholding the comb.

The comb losesprotons to theperson’s handwhile also gainingelectrons from thehair.

Only electrons are transferred in staticcharging processes.

148 Statics

A charge of +Q is located on the x–axis at x = –1 meter and a charge of –2Qis held at x = +1 meter, as shown in the diagram above. At what position onthe x–axis will a test charge of +q experience a zero net electrostatic force? A – (3 + √8) m –1/3 m 0 0.333 (3 + √8) m

Any charge will experience a net forceof zero where the electric field is zero.This must bewhere the fields from each charge pointin opposite directions and also closer tothe smallercharge, which is to the left of the +Qcharge (the answer will be to the left of–1 m). Let thedistances to the +Q and the –2Qcharge be x and (X + 2), respectively.This gives E1= E2 andkQ/x2= k(2Q)/(x + 2)2Solve for x and add the extra 1 m to theorigin 148.statics.png

149 Statics

The two plates of a parallel-plate capacitor are a distance d apart and aremounted on insulating supports. Abattery is connected across the capacitor to charge it and is thendisconnected. The distance between theinsulated plates is then increased to 2d. If fringing of the field is still negligible,which of the followingquantities is doubled? D

The capacitance ofthe capacitor

The total chargeon the capacitor

The surfacedensity of thecharge on theplates of thecapacitor

The energy storedin the capacitor

The intensity of theelectric fieldbetween the platesof the capacitor

Since the battery is removed, thecharge remains constant. If thedistance is increased, thecapacitance will decrease (C ∝ A/d)and since Q = CV, the potentialdifference must increase bythe same factor that the distanceincreases and Uc= ½ QV

150 Statics

Four point charges are each brought from infinity into a region of empty spaceand are "attached in place" into asquare arrangement of side length a as shown below. The location marked Pis at the center of the square andhas no charge associated with it. Which is a true statement about theconfiguration of charges? E

The net electricfield at point P isdirected to the left

The net electricfield at point P isdirected to theright.

The total force oneach charge fromthe other three inthe configuration iszero.

The electricpotential at thepoint P is (√2Q)/[(pi)Ea)]

The outside agentthat assembled thecharges didnegative net work

UE = Σkq1q2/r where we are summingeach pair of charges. Computing UEgives a totalpotential energy that is negative. Thismeans negative work must have beendone by an outsideagent to keep the chargesfrom collidinginto each other and stop them in theirrespectivelocations. The net field and the potentialat the center is zero due to symmetry 150.statics.png

151 Statics

Two point objects each carrying charge 10Q are separated by a distance d.The force between them is F. If halfthe charge on one object is transferred to the other object while at the sametime the distance between them isdoubled, what is the new force between the two objects? A 0.19 F 0.25 F 0.75 F 4.0 F no change in F

F ∝ q1q2/r2; the original force F ∝100Q2/d2. The new charges are15Q and 5Q making the new forceF ∝ 75Q2/(2d)2= 19Q2/d

152 Statics

2.A parallel plate capacitor is charged to a voltage V. To double the energystored on the capacitor, what wouldthe voltage between the plates have to become? C 0.25 V 0.50 V 1.4 V 2.0 V 4.0 V

Assuming C remains constant and UC= ½ CV2, for UC to double V mustincrease by √2

153 Statics

Two identical spheres carry identical electric charges. If the spheres are set adistance d apart they repel one another with a force F. A third sphere,identical to the other two but initially uncharged is then touched to one sphereand then to the other before being removed. What would be the resultingforce between the original two spheres? D ¾ F 5/8 F ½ F 3/8 F ¼ F

When one sphere is touched, thecharged divides equally (½ Qeach). When this sphere is thentouched to the second sphere, thenet charge (3/2 Q) is dividedequally (¾ Q each). Since F ∝q1q2,the original force is proportional toQ2 and the new force is thenproportional to (½ Q)(¾Q) = 3/8 Q

154 Statics

Two parallel metal plates 0.04 meters apart are connected to a 1.5 voltbattery. When fully charged, each metalplate has a charge of magnitude 9.0 x10–4coulombs. What is the capacitanceof the two plates? D 1.5 × 10–2 F 1.2 × 10–3 F 3.0 × 10–4 F 6.0 × 10–4 F 9.0 × 10–4 F Q = CV

155 Statics

An alpha particle is accelerated to a velocity v in a particle accelerator by apotential difference of 1200 V.Which of the following potential differences would be needed to give thealpha particle twice the velocity? B 7200 V 4800 V 4100 V 2400 V 1700 V

W = K = q∆V so ∆V ∝ v^2 and forv to double, ∆V must increase by 4

156 Statics

An electrical charge Q is placed at one vertex of an equilateral triangle. Whenan identical charge is placed atanother vertex, each charge feels a force of 15 N. When a third chargeidentical to the first two, is placed at thethird vertex, what would be the magnitude of the force on each charge? B 15 N 26 N 30 N 42 N 45 N

Adding the force vectors shown (each15 N) with x components that canceland y-components that equal 15 N cos30º gives F= 2 × 15 N cos 30º = 26 N

157 Statics

Two conducting spheres with the same charge Q are separated by an infinitedistance. Sphere A has a radius of10 cm while sphere B has a radius of 20 cm. At what distance from thecenters of the spheres would themagnitude of the electric field be the same? E

15 cm from A and15 cm from B

20 cm from A and34 cm from B

20 cm from A and40 cm from B

30 cm from A and40 cm from B

40 cm from A and40 cm from B

Once outside the spheres, they act aspoint charges and their difference insize is irrelevant 157.Statics.png

158 Statics

A large conducting sphere labeled X contains an electrical charge Q. SphereX is connected by a metal wire toa small uncharged conducting sphere labeled Y. The wire is then removed.How does the electrical field (Ey) at the surface of sphere Y compare to theelectrical field (Ex) at the surface of sphere X? D Ey= 0 Ey= Ex Ey< Ex Ey> Ex Ex= 0

When connected, the potentialsbecome equal. This gives kQX/rX =kQY/rY and since E = kQ/r2, dividingthe potentials by their respective radiigives kQX/(rX)^2< kQY/(rY)^2

159 Statics

9.What voltage would be required across a 8.9 nF capacitor to accumulate1.5 × 10^12excess electrons on one plate of the capacitor? E 0.17 V 3.7 V 5.9 V 14 V 27 V

1.5 × 10^12 excess electrons is acharge of magnitude (1.5 × 10^12) ×(1.6 × 10^–19) = 2.4 × 10^–7C.Use Q =CV

160 Statics

A hollow metal sphere is uniformly charged with positive charge. Points K andL are inside the sphere andpoints M and N are outside the sphere as shown in the diagram. At whichpoint would the field be the smallest? C points K and N points L and M points K and L points M and N point K only

The field is zero everywhere inside ametal sphere. 160.Statics.png

161 Statics

Two circular metal plates, each having an area A are placed to one another adistance d apart. When a potentialdifference is applied across the two plates, an electric field E is measuredhalfway between the two plates attheir centers. What is the magnitude of the potential difference between thetwo plates? A (A) Ed (B) E/d (C) EA/d (D) Ed/A (E) EA ∆V = Ed

162 Statics

Three electric charges (Q1, Q2, and Q3) are arranged at three corners of arectangle as shown in the diagram andeach has a charge of –40 nC. What is the magnitude of the net force on Q2? D (A) 1.4 × 10^–5 N (B) 1.7 × 10^–5 N (C) 4.2 × 10^–5 N (D) 4.6 × 10^–5 N (E) 1.47 × 10^–4 N

The force on Q2 from Q1 pointsdownward and the force from Q3 pointsat right angles to the left. Computeeach force using F = kq1q2/r2and usethe Pythagorean theorem. 162.statics.png

163 Statics What would be the magnitude of the total electric field at center point X? A (A) 1440 N/C (B) 720 N/C (C) 360 N/C (D) 180 N/C (E) 90 N/C

The field at the center due to Q1 andQ3 cancels. The only contribution to thefield then is that due to Q2. E =kQ/r^2where r2= 0.3^2+ 0.4^2 162.statics.png

164 Statics

Which of the following graphs would best represent the electric field of ahollow Van de Graff sphere as afunction of distance from its center when it is charged to a potential of400,000 volts? E A B C D E E inside = 0 and outside E ∝ 1/r^2 164.statics.png

165 Statics

Three metal spheres A, B, and C are mounted on insulating stands. Thespheres are touching one another, asshown in the diagram below. A strong positively charged object is broughtnear sphere A and a strong negativecharge is brought near sphere C. While the charged objects remain nearspheres A and C, sphere B is removedby means of its insulating stand. After the charged objects are removed,sphere B is first touched to sphere Aand then to sphere C. The resulting charge on B would be of what relativeamount and sign? C

(A) the same signbut 1/2 themagnitude asoriginally onsphere A

(B) the oppositesign but 1/2 themagnitude asoriginally onsphere A

(C) the oppositesign but 1/4 themagnitude asoriginally onsphere A

(D) the same signbut 1/2 themagnitude asoriginally onsphere C

(E) neutrallycharged

Initially, when B is removed, A and Care equally and oppositely charged andB is neutral.Touching B to A gives B ½ the chargeof A (split equally). The charge on B isthen ½ that of Cand oppositely charged. When B and Ctouch, the total charge between them is½ the charge ofC and the same sign as C. Each spherethen has ¼ of the charge of C aftercontact is made. Thismakes the end result that the charge onsphere B is ¼ the original charge of Aand the same signas sphere C, which is opposite that of A 165.statics.png

166 Statics

A charge is uniformly distributed through a volume of radius a. Which of thegraphs below best represents themagnitude of the electric field as a function of distance from the center of thesphere? D A B C D E

Advanced question (not exactly in the Bcurriculum, but interesting). Like gravityinside auniform sphere of mass, the field isdirectly proportional to r when inside thesphere (andproportional to 1/r^2 when outside) 166.statics.png

167 Statics

Four point charges are placed at the corners of a square with diagonal 2a asshown in the diagram. What is thetotal electric field at the center of the square? B

(A) kq/a2 at anangle 45° abovethe +x axis.

(B) kq/a2 at anangle 45° belowthe –x axis.

(C) 3kq/a2 at anangle 45° abovethe –x axis.

(D) 3kq/a2 at anangle 45° belowthe +x axis.

(E) 9kq/a2 at anangle 45° abovethe +x axis.

The field due to the two +3q chargescancel. The –q in the upper rightcounters –q from thelower left, leaving the net contribution tothe field a –q from the lower left. 167.statics.png

168 Statics

A free electron and a free proton are placed between two oppositely chargedparallel plates. Both are closer tothe positive plate than the negative plate. See the diagram below. Which ofthe following statements is true? I. The force on the proton is greater than theforce on the electron.II. The potential energy of the proton is greater than that of the electron.III. The potential energy of the proton and the electron is the same. B (A) I only (B) II only (C) III only (D) I & II only (E) I & III only

With equal charge, the forces are thesame. The potential energy of thecharges is equal in magnitude, butpositive for the proton and negative forthe electron. For scalars, positivenumbers are higher than negativenumbers. 168.statics.png

169 Statics How is the charge –q distributed after it has reached equilibrium? C

(A) +Q on the innersurface, – q – Q onthe outer surface.

(B) The charge –qis spread uniformlybetween the innerand outer surface.

(C) –Q on theinner surface, – q+ Q on the outersurface.

(D) –Q on theinner surface, –qon the outersurface.

(E) Zero charge onthe inner surface,–q on the outersurface.

The charge Q in the middle will inducea charge –Q on the inner surface of theshell. For the net charge of the shell tobe –q, the outer surface must have therest of the charge such that qouter +qinner = –q so qouter= –q – qinner= –q– (–Q) = Q – q 169.statics.png

170 StaticsWhat is the electrostatic potential at a distance R from the center of the shell,where b < R < a? E (A) 0 (B) kQ/a (C) kQ/R (D) k(Q – q)/R (E) k(Q – q)/b

The potential inside the shell is thesame as the potential at the surface ofthe shell since E = 0 inside the shell. V= kqouter/b

171 Statics

Conducting sphere X is initially uncharged. Conducting sphere Y has twicethe diameter of sphere X andinitially has charge q. If the spheres are connected by a long thin wire, whichof the following is true onceequilibrium has been reached? B

(A) Sphere Y hashalf the potential ofsphere X.

(B) Spheres X andY have the samepotential.

.(C) Sphere Y hastwice the potentialof sphere X

.(D) Sphere Y hashalf the charge ofsphere X

.(E) Spheres X andY have the samecharge

Charges flow when there is a differencein potential.

172 Statics

Four positive charges are fixed at the corners of a square, as shown above.Three of the charges have magnitude Q, and the fourth charge has amagnitude 2Q. Point P is at the center of the square at a distance r from eachcharge. What is the electric potential at point P? E (A) Zero (B) kQ/r r (C) 2kQ/r (D) 4kQ/r (E) 5kQ/r V = ΣkQ/r 172.statics.png

173 Statics What is the magnitude of the electric field at point P ? B (A) Zero (B) kQ/r2 (C) 2kQ/r2 (D) 4kQ/r2 (E) 5kQ/r2

The electric field cancels fromsymmetry all but +Q remaining in theupper right corner and E = B kQ/r2 173.statics.png

174 Statics

If the separation between the plates of an isolated charged parallel-platecapacitor is increased slightly, which ofthe following also increases? B

(A) Thecapacitance

(B) The storedelectrostaticenergy

(C) The force ofattraction betweenthe plates

(D) The magnitudeof the charge oneach plate

(E) The magnitudeof the electric fieldin the regionbetween the plates

Since the plates are insulated, thecharge remains constant. If thedistance is increased, the Bcapacitance will decrease (C ∝ A/d)and since Q = CV, the potentialdifference must increase bythe same factor that the distanceincreases. UC = 1⁄2 QV 174.statics.png

175 Statics

The two charged metal spheres X and Y shown above are far apart, and eachis isolated from all other charges.The radius of sphere X is greater than that of sphere Y, and the magnitudesof the electric fields just outside theirsurfaces are the same. How does the charge on sphere X compare with thaton sphere Y? A (A) It is greater. (B) It is less. (C) It is the same.

D) It cannot bedetermined withoutknowing the actualradii of thespheres.

(E) It cannot bedetermined withoutknowing the actualvalue of theelectric field justoutside the sphere

If the E fields are the same, that meanskQX/rX2 = kQY/rY2, or QX/QY =rX2/rY2

176 Statics

Two negative point charges are a distance x apart and have potential energyU. If the distance between the pointcharges increases to 3x, what is their new potential energy? D (A) 9U (B) 3U (C) U (D) 1/3 U (E) 1/9 U UE∝1/r

177 Statics

Sphere X of mass M and charge +q hangs from a string as shown above.Sphere Y has an equal charge +q and isfixed in place a distance d directly below sphere X. If sphere X is inequilibrium, the tension in the string is mostnearly E (A) Mg (B) Mg + kq/d (C) Mg – kq/d (D) Mg + kq2/d2 (E) Mg – kq2/d2

ΣF=0sowehaveT+k(q)(q)/d2 –Mg=0givingT=Mg–kq2/d2 177.statics.png

178 Statics

A small positively charged sphere is lowered by a nonconducting thread intoa grounded metal cup withouttouching the inside surface of the cup, as shown above. The grounding wireattached to the outside surface isdisconnected and the charged sphere is then removed from the cup. Which ofthe following best describes thesubsequent distribution of excess charge on the surface of the cup? B

(A) Negativecharge resides onthe inside surface,and no chargeresides on theoutside surface.

(B) Negativecharge resides onthe outsidesurface, and nocharge resides onthe inside surface.

(C) Positive chargeresides on theinside surface, andno charge resideson the outsidesurface.

(D) Positive chargeresides on theoutside surface,and no chargeresides on theinside surface.

(E) Negativecharge resides onthe inside surface,and positivecharge resides onthe outsidesurface.

When lowered inside, the chargedsphere induces a negative charge onthe inner surface of the B cup. Theouter surface remains neutral since it isgrounded. When the grounding wire isremoved, the cup has a net negativecharge, which when the sphere isremoved, will move to theouter surface of the cup. 178.statics.png

179 Statics

A helium nucleus (charge +2q and mass 4m) and a lithium nucleus (charge+3q and mass 7m) are acceleratedthrough the same electric potential difference, V0. What is the ratio of theirresultant kinetic energies, K Lithium/ K Helium? E (A) 2/3 (B) 6/7 (C) 1 (D) 7/6 (E) 3/2 K=q∆VsoK1/K2=q1/q2 179.statics.png

180 Statics

A point charge −Q is located at the origin, while a second point charge +2Q islocated at x = d on the x-axis, as shown above. A point on the x-axis wherethe net electric field is zero is located in which of the following regions? A (A)-∞<x<0 (B)0< x<d/2 (C)d/2<x<d (D)d<x<∞

(E)Noregiononthex-axis

The field is zero where the fields fromeach charge point in opposite directionsand also closer to Athe smaller charge, which is to the leftof the –Q charge 181.static.png

181 StaticsWhich of the following expressions best represents the magnitude of theelectric field at point P ? B 10 V/0.14 m 10 V/0.04 m 25 V/0.14 m 25 V/0.04 m 40 V/0.25 m E=∆V/d 182.183.static.png

182 Statics The direction of the electric field at point P is most nearly A toward the left toward the righttoward the bottomof the page

toward the top ofthe page

perpendicular tothe plane of thepage

E fields point from high potential to lowpotential, perpendicular to theequipotential lines. 182.183.static.png

183 StaticsThe electric field E0 and potential V0 at the surface of each drop is given bywhich of the following? C 0 0 kQ/R2 kQ/R^2 kQ/R^2 kQ/R 0 kQ/R kQ/R 0 Forasphere,E=kQ/r2andV=kQ/r 184.185.static.png

184 StaticsIf two droplets happen to c2ombine into a single larger droplet, the newpotential V at the surface of the larger droplet is most nearly equal to C 3 V 2 V 2/3square root2 V 3square root 2 V V

Combining two droplets doubles thecharge. The volume is doubled, whichmeans the radius is multiplied by 3square root 2 184.185.static.png

185 Statics

Two protons and an electron are assembled along a line, as shown above.The distance between the electron and each proton is a. What is the workdone by an external force in assembling this configuration of charges? B –2ke2/a –3ke2/2a ke2/2a 3ke2/2a 3ke2/a

The work to assemble the charges isthe potential energy of the system,which is the sum of the potentialenergies of each pair of charges UE = –ke2/a – ke2/a + ke2/2a 186.static.png

186 statics

A conducting sphere with a radius of 0.10 meter has 1.0 × 10–9 coulomb ofcharge deposited on it. The electric field just outside the surface of the sphereis C zero 450 V/m 900 V/m 4,500 V/m 90,000 V/m E = kQ/r2

1 circuitsWhich two arrangements of resistors shown above have the same resistancebetween the terminals? B I and II I and IV II and III II and IV III and IV

The resistances are as follows: I: 2 Ω,II: 4 Ω, III: 1 Ω, IV: 2 Ω 1.circuits.png

2 circuitsIn the circuit shown above, what is the value of the potential differencebetween points X and Y if the 6–volt battery has no internal resistance? B 1 V 2 V 3 V 4 V 6 V

The total resistance of the 3 Ω and 6 Ωin parallel is 2 Ω making the total circuitresistance 6 Ω BandthetotalcurrentE/R=1A.This1Awilldivideintheratioof2:1throughthe3Ωand6Ω respectively sothe 3 Ω resistor receives 2/3 A makingthe potential difference IR = (2/3 A)(3Ω)= 2 V. 2.circuits.png

3 circuits

A lamp, a voltmeter V, an ammeter A, and a battery with zero internalresistance are connected as shown above. Connecting another lamp inparallel with the first lamp as shown by the dashed lines would A

increase theammeter reading

decrease theammeter reading

increase thevoltmeter reading

decrease thevoltmeter reading

produce nochange in eithermeter reading

Adding resistors in parallel decreasesthe total circuit resistance, thisincreasing the total current A in thecircuit. 3.circuit.png

4 circuits

The five resistors shown below have the lengths and cross–sectional areasindicated and are made of material with the same resistivity. Which has thegreatest resistance? B A B C D E

R = ρL/A. Greatest resistance is thelongest, narrowest resistor. 4.circuits.png

5 circuits

Two capacitors are connected in parallel as shown above. A voltage V isapplied to the pair. What is the ratio of charge stored on C1 to the chargestored on C2, when C1 = 1.5C2 ? D 4/9. 2/3. 1 3/2. 9/4.

In parallel V1 = V2. Q1 = C1V1 and Q2= C2V2 so Q1/Q2 = C1/C2 = 1.5 5.circuits.png

6 circuits

The five incomplete circuits below are composed of resistors R, all of equalresistance, and capacitors C, all ofequal capacitance. A battery that can be used to complete any of the circuitsis available. Into which circuit should the battery be connected to obtain thegreatest steady power dissipation? D A B C D E

For steady power dissipation, the circuitmust allow current to slow indefinitely.For the greatestpower, the total resistance should bethe smallest value. These criteria aremet with the resistorsin parallel. 6-7.circuits.png

7 circuits

The five incomplete circuits below are composed of resistors R, all of equalresistance, and capacitors C, all ofequal capacitance. A battery that can be used to complete any of the circuitsis available. Which circuit will retain stored energy if the battery is connectedto it and then disconnected? B A B C D E

To retain energy, there must be acapacitor that will not discharge througha resistor. Capacitorsin circuits C and E will dischargethrough the resistors in parallel withthem. 6-7.circuits.png

8 circuits

The circuit shown above left is made up of a variable resistor and a batterywith negligible internal resistance. Agraph of the power P dissipated in the resistor as a function of the current Isupplied by the battery is givenabove right. What is the emf of the battery? C 0.025 V .67 V 2.5 V 6.25 V 40 V P = IE

9 circuits

An immersion heater of resistance R converts electrical energy into thermalenergy that is transferred to theliquid in which the heater is immersed. If the current in the heater is I, thethermal energy transferred to theliquid in time t is B IRt I^2Rt IR^2t IRt^2 IR/t W = Pt = I2Rt

10 circuitsThe total equivalent resistance between points X and Y in the circuit shownabove is A 3 Ω 4 Ω 5 Ω 6 Ω 7 Ω

The resistance of the two 2 Ω resistorsin parallel is 1 Ω. Added to the 2 Ωresistor in series withthe pair gives 3 Ω 10.circuits.png

11 circuits

The five resistors shown below have the lengths and cross–sectional areasindicated and are made of materialwith the same resistivity. Which resistor has the least resistance? E A B C D E

R = ρL/A. Least resistance is thewidest, shortest resistor 11.circuits.png

12 circuitsIn the circuit shown above, the value of r for which the current I is 0.5 ampereis E 0 Ω 1 Ω 5 Ω 10 Ω 20 Ω

The resistance of the two resistors inparallel is r/2. The total circuitresistance is then 10 Ω + 1⁄2 E r, whichis equivalent to E/I = (10 V)/(0.5 A) = 20Ω = 10 Ω + r/2 12.circuits.png

13 circuits

Which of the following will cause the electrical resistance of certain materialsknown as superconductors tosuddenly decrease to essentially zero? C

Increasing thevoltage applied tothe materialbeyond a certainthreshold voltage

Increasing thepressure applied tothe materialbeyond a certainthreshold pressure

Cooling thematerial below acertain thresholdtemperature

Stretching thematerial to a wireof sufficiently smalldiameter

Placing thematerial in asufficiently largemagnetic field

Resistance varies directly withtemperature. Superconductors have aresistance that quickly goes C to zeroonce the temperature lowers beyond acertain threshold

14 circuitsKirchhoff’s loop rule for circuit analysis is an expression of which of thefollowing? B

Conservation ofcharge

Conservation ofenergy Ampere's law Faraday's law Ohm's law

The loop rule involves the potential andenergy supplied by the battery and it’suse around acircuit loop.

15 circuits The equivalent capacitance for this network is most nearly D 10/7 μF 3/2 μF 7/3 μF 7 μF 14 μF

The capacitance of the 4 μF and 2μF inparallel is 6 μF. Combined with the 3μFin series gives 2μF for the right branch. Added to the 5μF in parallel gives a total of 7 μF 15.circuits.png

16 circuits The charge stored in the 5–microfarad capacitor is most nearly B 360 μC 500 μC 710 μC 1,100 μC 1,800 μC

Since the 5 μF capacitor is in parallelwith the battery, the potential differenceacross it is 100 V.Q = CV 15.circuits.png

17 circuits What is the emf of the battery? D 1.2 V 6.0 V 10.8 V 12.0 V 13.2 V

Total circuit resistance (includinginternal resistance) = 40 Ω; total current= 0.3 A. E = IR 17.circuits.png

18 circuits What is the potential difference across the terminals X and Y of the battery? C 1.2 V 6.0 V 10.8 V 12.0 V 13.2 VVXY = E – Ir where r is the internalresistance 17.circuits.png

19 circuits What power is dissipated by the 4–ohm internal resistance of the battery? A 0.36 W 1.2 W 3.2 W 3.6 W 4.8 W P = I2r 17.circuits.png

20 circuits

In the diagrams above, resistors R1 and R2 are shown in two differentconnections to the same source of emf εthat has no internal resistance. How does the power dissipated by theresistors in these two cases compare? B

It is greater for theseries connection.

It is greater for theparallelconnection.

It is the same forboth connections.

It is different foreach connection,but one must knowthe values of R1and R2 to knowwhich is greater.

It is different foreach connection,but one must knowthe value of ε toknow which isgreater.

With more current drawn from thebattery for the parallel connection, morepower is dissipated inthis connection. While the resistors inseries share the voltage of the battery,the resistors inparallel have the full potential differenceof the battery across them. 20.circuits.png

21 circuits The product (2 amperes × 2 volts × 2 seconds) is equal to C 8 coulombs 8 newtons 8 joules 8 calories 8 newton–amperes

Amperes = I (current); Volts = V(potential difference); Seconds = t(time): IVt = energy

22 circuitsThe electrical resistance of the part of the circuit shown between point X andpoint Y is A 4/3 Ω 2 Ω 2.75 Ω 4 Ω 6 Ω

Resistance of the 1 Ω and 3 Ω in series= 4 Ω. This, in parallel with the 2 Ωresistor gives (2 × 4)/(2 + 4) = 8/6 Ω. Also notice theequivalent resistance must be less than2 Ω (the 2 Ω resistor isin parallel and the total resistance in 22.circuits.png

23 circuitsWhen there is a steady current in the circuit, the amount of charge passing apoint per unit of time is C

the sameeverywhere in thecircuit

greater in the 1 Ωresistor than in the2 Ω resistor

greater in the 2 Ωresistor than in the3 Ω resistor

greater at point Xthan at point Y

greater in the 1 Ωresistor than in the3 Ω resistor

The upper branch, with twice theresistance of the lower branch, willhave ½ the current of thelower branch. 22.circuits.png

24 circuits

A certain coffeepot draws 4.0 A of current when it is operated on 120 Vhousehold lines. If electrical energy costs 10 cents per kilowatt–hour, howmuch does it cost to operate the coffeepot for 2 hours? D 2.4 cents 4.8 cents 8.0 cents 9.6 cents 16 cents

Power = IV = 480 W = 0.48 kW. Energy= Pt = (0.48 kW)(2 hours) = 0.96 kW-h 24.circuits.png

25 circuits

A battery having emf E and internal resistance r is connected to a loadconsisting of two parallel resistors each having resistance R. At what value ofR will the power dissipated in the load be a maximum? D 0 r/2 r 2r 4r

Total circuit resistance of the load =R/2. Total circuit resistance includingthe internal resistance D = r + R/2. Thecurrent is then E/(r + R/2) and the totalpower dissipated in the load is P =I2Rload= (E2R/2)/(r + R/2)2. Using calculusmax/min methods or plotting this on agraph gives the valueof R for which this equation ismaximized of R = 2r. This max/minproblem is not part of the B curriculumbut you should be able to set up theequation to be maximized. 25.circuits.png

26 circuits

Two concentric circular loops of radii b and 2b, made of the same type ofwire, lie in the plane of the page, as shown above. The total resistance of thewire loop of radius b is R. What is the resistance of the wire loop of radius2b? D R/4 R/2 R 2R 4R

The larger loop, with twice the radius,has twice the circumference (length)and R = ρL/A

27 circuitsThe total capacitance of several capacitors in parallel is the sum of theindividual capacitances for which of the following reasons? A

The charge oneach capacitordepends on itscapacitance, butthe potentialdifference acrosseach is the same.

The charge is thesame on eachcapacitor, but thepotential differenceacross eachcapacitor dependson its capacitance.

Equivalentcapacitance isalways greaterthan the largestcapacitance.

Capacitors in acircuit alwayscombine likeresistors in series.

The parallelcombinationincreases theeffectiveseparation of theplates.

By process of elimination, A is the onlypossible true statement.

28 circuits

A wire of length L and radius r has a resistance R. What is the resistance of asecond wire made from the same material that has a length L/2 and a radiusr/2? B 4R 2R R R/2 R/4

R=ρL/A. IfL÷2,R÷2andisr÷2thenA÷4andR×4makingtheneteffectR÷2×4

29 circuitsThe operating efficiency of a 0.5 A, 120 V electric motor that lifts a 9 kg massagainst gravity at an average velocity of 0.5 m/s is most nearly E 7% 13% 25% 53% 75%

ThemotorusesP=IV=60WofpowerbutonlydeliversP=Fv=mgv=45Wofpower.The E efficiency is “what you get” ÷“what you are paying for” = 45/60

30 circuits What is the current I1? D 0.8mA 1.0mA 2.0mA 3.0mA 6.0mA

Resistance of the 2000 Ω and 6000 Ωin parallel = 1500 Ω, adding the 2500 Ωin series gives a total circuit resistanceof 4000 Ω. Itotal = I1 = E/Rtotal 30.circuits.png

31 circuits How do the currents I1, I2, and 13 compare? A I1 > I2 > I3 I1 > I3 > I2 I2 > I1 > I3 I3 > I1 > I2 I3 > I2 > I1

I1 is the main branch current and is thelargest. It will split into I2 and I3andsince I2 moves through the smallerresistor, it will be larger than I3. 30.circuits.png

32 circuitsWhen lighted, a 100–watt light bulb operating on a 110–volt household circuithas a resistance closest to E 10–2 Ω 10–1 Ω 1Ω 10Ω 100Ω P=V2/R 32.circuits.png

33 circuits In the circuit shown above, what is the resistance R? B 3 Ω 4 Ω 6 Ω 12 Ω 18 Ω

The current through R is found usingthe junction rule at the top junction,where 1 A + 2 A enter giving I = 3 A.Now utilize Kirchhoff’s loop rule throughthe left or right loops: (left side) + 16V – (1 A)(4 Ω) – (3 A)R = 0 giving R = 4Ω 33.circuits.png

34 circuits35 circuits36 circuits37 circuits38 circuits39 circuits40 circuits41 circuits42 circuits43 circuits

44 circuits Which graph best represents the voltage across the capacitor versus time? B A B C D E

When the switch is closed, the circuitbehaves as if the capacitor were just awire and all thepotential of the battery is across theresistor. As the capacitor charges, thevoltage changes overto the capacitor over time, eventuallymaking the current (and the potentialdifference across theresistor) zero and the potentialdifference across the capacitor equal tothe emf of the battery 44.circuits.png

45 circuitsThree 6–microfarad capacitors are connected in series with a 6–volt battery.The equivalent capacitance of the set of capacitors is B 0.5 μF 2 μF 3 μF 9 μF 18 μF in series (1/Ct)= E(1/c)

46 circuits The energy stored in each capacitor is C 4 μJ 6 μJ 12 μJ 18 μJ 36 μJ

There are several ways to do thisproblem. We can find the total energystored and divide it intothe three capacitors: UC = ½ CV2= ½(2 µF)(6 V)2= 36 µJ ÷ 3 = 12 µJ each

47 circuits

The power dissipated in a wire carrying a constant electric current I may bewritten as a function of the length lof the wire, the diameter d of the wire, and the resistivity ρ of the material inthe wire. In this expression, thepower dissipated is directly proportional to which of the following? C l only d only l and ρ only d and ρ only l, d, and ρ

P = I^2R and R = ρL/A giving P ∝ρL/d^2

48 circuits

A wire of resistance R dissipates power P when a current I passes through it.The wire is replaced by anotherwire with resistance 3R. The power dissipated by the new wire when thesame current passes through it is D P/9 P/3 P 3P 6P P = I^2 R

49 circuits

Two resistors of the same length, both made of the same material, areconnected in a series to a battery asshown above. Resistor II has a greater cross. sectional area than resistor I.Which of the following quantitieshas the same value for each resistor? E

Potentialdifference betweenthe two ends

Electric fieldstrength within theresistor Resistance

Current per unitarea Current

Since these resistors are in series, theymust have the same current. 49.circuits.png

50 circuitsBelow is a system of six 2–microfarad capacitors. The equivalent capacitanceof the system of capacitors is C 2/3μF 4/3 μF 3 μF 6 μF 12 μF

Each branch, with two capacitors inseries, has an equivalent capacitanceof 2 µF ÷ 2 = 1 µF.The three branches in parallel have anequivalent capacitance of 1 µF + 1 µF +1 µF = 3 µF 50.circuits.png

51 circuits

What potential difference must be applied between points X and Y so that thecharge on each plate of eachcapacitor will have magnitude 6 microcoulombs? C 1.5 V 3 V 6 V 9 V 18 V

For each capacitor to have 6 µC, eachbranch will have 6 µC since the twocapacitors in series ineach branch has the same charge. Thetotal charge for the three branches isthen 18 µC. Q = CVgives 18 µC = (3 µF)V 51.circuits.png

52 circuits

In the circuit above, the emf's and the resistances have the values shown.The current I in the circuit is 2 amperes.The resistance R is A 1 Ω 2 Ω 3 Ω 4 Ω 6 Ω

Utilizing Kirchhoff’s loop rule starting atthe upper left and moving clockwise: –(2 A)(0.3 Ω) +12 V – 6 V – (2 A)(0.2 Ω) – (2A)(R) –(2A)(1.5 Ω) = 0 52.circuits.png

53 circuits The potential difference between points X and Y is C 1.2 V 6.0 V 8.4 V 10.8 V 12.2 VSumming the potential differences: – 6V – (2 A)(0.2 Ω) – (2A)(1 Ω) = – 8.4 V 53.circuits.png

54 circuits How much energy is dissipated by the 1.5–ohm resistor in 60 seconds? C 6 J 180 J 360 J 720 J 1440 JEnergy = Pt = I2Rt 54.circuits.png

55 circuits Immediately after the switch is closed, the current supplied by the battery is B V/(R1+ R2) V/R1 V/R2 V(R1+R2)/R1R2 zero

When the switch is closed, the circuitbehaves as if the capacitor were just awire, shorting out the resistor on theright. 55.circuits.png

56 circuitsA long time after the switch has been closed, the current supplied by thebattery is A V/(R1+R2) V/R1 V/R2 V(R1+R2)/R1R2 zero

When the capacitor is fully charged, thebranch with the capacitor is “closed” tocurrent, effectively removing it from thecircuit for current analysis. 56.circuits.png

57 circuits

A 30–ohm resistor and a 60–ohm resistor are connected as shown above to abattery of emf 20 volts and internal resistance r. The current in the circuit is0.8 ampere. What is the value of r? C 0.22 Ω 4.5 Ω 5 Ω 16 Ω 70 Ω

Total resistance = E/I = 25 Ω.Resistance of the 30 Ω and 60 Ωresistors in parallel =20 Ω adding theinternal resistance in series with theexternal circuit gives Rtotal= 20 Ω + r =25 Ω 57.circuits.png

58 circuits

A variable resistor is connected across a constant voltage source. Which ofthe following graphs represents the power P dissipated by the resistor as afunction of its resistance R? A A B C D E

P = V2/R and if V is constant P ∝1/R 58.circuits.png

59 circuits If the ammeter in the circuit above reads zero, what is the resistance R ? E 1.5 Ω 2 Ω 4 Ω 5 Ω 6 Ω

For the ammeter to read zero meansthe junctions at the ends of theammeter have the same potential. Forthis to be true, the potential dropsacross the 1 Ω and the 2 Ω resistormust be equal, which means thecurrent through the 1 Ω resistor mustbe twice that of the 2 Ω resistor. Thismeans the resistance of the upperbranch (1 Ω and 3 Ω) must be ½ that ofthe lower branch (2 Ω and R) giving 1 Ω+ 3 Ω = ½ (2 Ω + R) 59.circuits.png

60 circuits

A resistor R and a capacitor C are connected in series to a battery of terminalvoltage V0. Which following equations relating the current I in the circuit andthe charge Q on the capacitor describes this circuit? B V0+ QC – I2R = 0 V0 – Q/C – IR = 0 V02-Q2/2C-I2R=0 V0-CI-I2R=0 Q/C – IR = 0

Kirchhoff’s loop rule (V = Q/C for acapacitor)

61 circuits

Which of the following combinations of 4Ω resistors would dissipate 24 Wwhen connected to a 12 Voltbattery? E A B C D E

To dissipate 24 W means R = V2/P = 6Ω. The resistances, in order, are: 8 Ω,4/3 Ω, 8/3 Ω, 12 Ω and 6 Ω 61.circuits.png

62 circuits

A narrow beam of protons produces a current of 1.6 × 10–3 A. There are 109protons in each meter along the beam. Of the following, which is bestestimate of the average speed of the protons in the beam? D 10^–15 m/s 10^–12 m/s 10^–7 m/s 10^7 m/s 10^12 m/s

Dimensional analysis: 1.6 × 10–3A = 1.6 × 10–3 C/s ÷ 1.6 × 10–19C/proton = 1016 protons/sec ÷ 109protons/meter = 107 m/s

63 circuits The equivalent capacitance between points X and Z is B 1.0 µF 2.0 µF 4.5 µF 6.0 µF 9.0 µF

The equivalent capacitance of the two 3µF capacitors in parallel is 6 µF,combined with the 3 µF in series givesCtotal = 2 µF 63.circuits.png

64 circuits

Three identical capacitors, each of capacitance 3.0 μF, are connected in acircuit with a 12 V battery as shown above.The potential difference betweenpoints Y and Z is D Zero 3V 4V 8V 9V

The equivalent capacitance between Xand Y is twice the capacitance betweenY and Z. This means the voltagebetween X and Y is 1⁄2 the voltagebetween Y and Z. For a total of 12 V,this gives 4 V between X and Y and 8 Vbetween Y and Z. 64.circuits.png

65 circuits

The circuit in the figure above contains two identical lightbulbs in series with abattery. At first both bulbs glow with equal brightness. When switch S isclosed, which of the following occurs to the bulbs? B

Bulb 1:Goes outBulb 2:Getsbrighter

Bulb 1:Getsbrighter Bulb 2:Goes out

Bulb 1:Getsbrighter Bulb 2:Gets slightlydimmer

Bulb 1:Getsslightly dimmerBulb 2:Getsbrighter

Bulb 1:NothingBulb 2:Goes out

Closing the switch short circuits Bulb 2causing no current to flow to it. Sincethe bulbs wereoriginally in series, this decreases thetotal resistance and increases the totalcurrent, making bulb1 brighter. 65.circuits.png

66 circuitsThree 1/2 μF capacitors are connected in series as shown in the diagramabove. The capacitance of the combination is E 0.1 μF 1 μF 2/3 μF 1⁄2 μF 1/6 μF In series 1/CT = = Σ 1/C 66.circuits.png

67 circuits A hair dryer is rated as 1200 W, 120 V. Its effective internal resistance is C 0.1Ω 10Ω 12 Ω 120Ω 1440Ω P = V^2/R

68 circuitsWhen the switch S is open in the circuit shown above, the reading on theammeter A is 2.0 A. When the switch is closed, the reading on the ammeter is B doubled

increased slightlybut not doubled the same

decreased slightlybut not halved halved

Closing the switch reduces theresistance in the right side from 20 Ω to15 Ω, making the totalcircuit resistance decrease from 35 Ω to30 Ω, a slight decrease, causing aslight increase incurrent. For the current to double, thetotal resistance must be cut in half. 68.circuits.png

69 circuits

Two conducting cylindrical wires are made out of the same material. Wire Xhas twice the length and twice the diameter of wire Y. What is the ratio Rx/Ryof their resistances? B "1/4" 1⁄2 1 2 4

R = ρL/A ∝ L/d^2 where d is thediameter. Rx/Ry = Lx/dx^2 ÷Ly/dy^2 = (2Ly)d^2/[Ly(2dy)^2]= ½

70 circuitsYou are given three 1.0 Ω resistors. Which of the following equivalentresistances CANNOT be produced using all three resistors? C 1/3Ω 2/3Ω 1.0Ω 1.5Ω 3.0Ω

Using all three in series = 3 Ω, all threein parallel = 1/3 Ω. One in parallel withtwo in series =2/3 Ω, one in series with two in parallel= 3/2 Ω

71 circuits

The figures above show parts of two circuits, each containing a battery of emfε and internal resistance r. The current in each battery is 1 A, but the directionof the current in one battery is opposite to that in the other. If the potentialdifferences across the batteries' terminals are 10 V and 20 V as shown, whatare the values of ε and r ? C E = 5 V, r = 15 Ω E =10 V, r = 100 Ω E = 15 V, r = 5 Ω E = 20 V, r = 10 Ω

The values cannotbe computedunless thecomplete circuitsare shown.

Summing the potential differences frombottom to top:left circuit: – (1 A)r + E = 10 Vright circuit: + (1 A)r + E = 20 V, solvesimultaneous equations 71.circuits.png

72 circuits In the circuit shown above, the equivalent resistance of the three resistors is D 10.5 Ω 15Ω 20 Ω 50 Ω 115 Ω

The equivalent resistance of the 20 Ωand the 60 Ω in parallel is 15 Ω, addedto the 35 Ω resistorin series gives 15 Ω + 35 Ω = 50 Ω 72.circuits.png

73 circuitsWhat is the current through the 6.0 Ω resistor shown in the accompanyingcircuit diagram? Assume all batteries have negligible resistance. A 0 A 0.40 A 0.50 A 1.3 A 1.5 A

If you perform Kirchhoff’s loop rule forthe highlighted loop, you get a currentof 0 A throughthe 6 Ω resistor. 73.circuits.png

74 circuitsFour identical light bulbs K, L, M, and N are connected in the electrical circuitshown. Rank the current through the bulbs. D K > L > M > N L = M > K = N L > M > K > N N > K > L = M N > L = M > K

N is in the main branch, with the mostcurrent. The current then divides intothe two branches,with K receiving twice the current as Land M. The L/M branch has twice theresistance of the Kbranch. L and M in series have thesame current. 74.circuits

75 circuits

Four identical light bulbs K, L, M, and N are connected in the electrical circuitshown. In order of decreasing brightness (starting with the brightest), thebulbs are: D K = L > M > N K = L = M > N K > L = M > N N > K > L = M N > K = L = M

Current is related to brightness (P =(I^2)R) ("N is in the main branch, withthe most current. The current thendivides into the two branches,with K receiving twice the current as Land M. The L/M branch has twice theresistance of the K branch. L and M inseries have the same current.") 75.circuits

76 circuitsFour identical light bulbs K, L, M, and N are connected in the electrical circuitshown. Bulb K burns out. Which of the following statements is true? E

All the light bulbsgo out.

Only bulb N goesout.

Bulb N becomesbrighter

The brightness ofbulb N remains thesame

Bulb N becomesdimmer but doesnot go out.

If K burns out, the circuit becomes aseries circuit with the three resistors, N,M and L all inseries, reducing the current throughbulb N. 76.circuits

77 circuitsFour identical light bulbs K, L, M, and N are connected in the electrical circuitshown. Bulb M burns out. Which of the following statements is true? E

All the light bulbsgo out.

Only bulb M goesout.

Bulb N goes outbut at least oneother bulb remainslit

The brightness ofbulb N remains thesame

Bulb N becomesdimmer but doesnot go out.

If M burns out, the circuit becomes aseries circuit with the two resistors, Nand K in series, withbulb L going out as well since it is inseries with bulb M. 77.circuits

78 circuits

The voltmeter in the accompanying circuit diagram has internal resistance10.0 kΩ and the ammeter has internalresistance 25.0 Ω. The ammeter reading is 1.00 mA. The voltmeter reading ismost nearly: D 1.0 V 2.0 V 3.0 V 4.0 V 5.0 V

Using Kirchhoff’s loop rule around thecircuit going through either V or R sincethey are inparallel and will have the samepotential drop gives: – V – (1.00 mA)(25Ω) + 5.00 V – (1.00mA)(975 Ω) = 0 78.circuits

79 circuits

When two resistors, having resistance R1 and R2, are connected in parallel,the equivalent resistance of thecombination is 5 Ω. Which of the following statements about the resistancesis correct? A

Both R1 and R2are greater than 5Ω.

Both R1 and R2are equal to 5 Ω.

Both R1 and R2are less than 5 Ω.

The sum of R1 andR2 is 5 Ω.

One of theresistances isgreater than 5 Ω,one of theresistances is lessthan 5 Ω.

The equivalent resistance in parallel issmaller than the smallest resistance.

80 circuits

See the accompanying figure. What is the current through the 300 Ω resistorwhen the capacitor is fullycharged? C zero 0.020 A 0.025 A 0.033 A 0.100 A

When the capacitor is fully charged, thebranch on the right has no current,effectively makingthe circuit a series circuit with the 100 Ωand 300 Ω resistors. RtotalC= 400 Ω, E = 10 V = IR 80.circuits

81 circuits

Three resistors – R1, R2, and R3 – are connected in series to a battery.Suppose R1 carries a current of 2.0 A, R2has a resistance of 3.0 Ω, and R3 dissipates 6.0 W of power. What is thevoltage across R3? C 1.0 V 2.0 V 3.0 V 6.0 V 12 V

In series, they all have the samecurrent, 2 A. P3= I3V3

82 circuits

When a single resistor is connected to a battery, a total power P is dissipatedin the circuit. How much totalpower is dissipated in a circuit if n identical resistors are connected in seriesusing the same battery? Assume the internal resistance is zero. D (n^2)P nP P P/n P/(n^2)

P = (E^2)/R. Total resistance of nresistors in series is nR making thepower P = (E^2)/nR = P/n

83 circuits

Consider the compound circuit shown above. The three bulbs 1, 2, and 3 –represented as resistors in thediagram – are identical. Which of the following statements are true? I. Bulb 3is brighter than bulb 1 or 2.II. Bulb 3 has more current passing through it than bulb 1 or 2.III. Bulb 3 has a greater voltage drop across it than bulb 1 or 2. E I only II only I and II only I and III only I, II, and III

The current through bulb 3 is twice thecurrent through 1 and 2 since thebranch with bulb 3 ishalf the resistance of the upper branch.The potential difference is the sameacross each branch,but bulbs 1 and 2 must divide thepotential difference between them. 83.circuits

84 circuitsWhen any four resistors are connected in parallel, the _______ each resistoris the same. E charge on current through power from resistance of voltage across by definition of a parallel circuit

85 circuits

Wire I and wire II are made of the same material. Wire II has twice thediameter and twice the length of wire I. If wire I has resistance R, wire II hasresistance C R/8 R/4 R/2 R 2R

R = ρL/A ∝ L/d^2 where d is thediameter. RII/RI = LII/dII^2 ÷LI/dI^2 = (2LI)dI^2/[LI(2dI)^2] =½

86 circuitsA heating coil is rated 1200 watts and 120 volts. What is the maximum valueof the current under these conditions? A 10.0 A 12.0 A 14.1 A 0.100 A 0.141 A P = IV

87 circuitsIn the accompanying circuit diagram, the current through the 6.0–Ω resistor is1.0 A. What is the power supply voltage V? D 10 V 18 V 24 V 30 V 42 V

If the current in the 6 Ω resistor is 1 A,then by ratios, the currents in the 2 Ωand 3 Ω resistor are 3 A and 2 Arespectively (since they have 1/3 and1/2 the resistance). This makes thetotal current 6 A and the potential dropacross the 4 Ω resistor 24 V. Now useKirchhoff’s loop rule for any branch. 87.circuits.png

88 circuitsIn the circuit diagrammed above, the 3.00–μF capacitor is fully charged at18.0 μC. What is the value of the power supply voltage V? C 4.40 V 6.00 V 8.00 V 10.4 V 11.0 V

The voltage across the capacitor is 6 V(Q = CV) and since the capacitor is inparallel with the 300 Ω resistor, thevoltage across the 300 Ω resistor isalso 6 V. The 200 Ω resistor is notconsidered since the capacitor ischarged and no current flows throughthat branch. The 100 Ω resistor inseries with the 300 Ω resistor has 1/3the voltage (2 V) since it is 1/3 theresistance. Kirchhoff’s loop rule for theleft loop gives E = 8 V. 88.circuits.png

89 circuitsWhat is the resistance of a 60 watt light bulb designed to operate at 120volts? D 0.5 Ω 2 Ω 60 Ω 240 Ω 7200 Ω P = V^2/R

90 circuitsGiven the simple electrical circuit above, if the current in all three resistors isequal, which of the following statements must be true? C

X, Y, and Z allhave equalresistance

X and Y haveequal resistance

X and Y addedtogether have thesame resistanceas Z

X and Y each havemore resistancethan Z

none of the abovemust be true

For the currents in the branches to beequal, each branch must have thesame resistance. 90.circuits.png

91 circuits

Wire Y is made of the same material but has twice the diameter and half thelength of wire X. If wire X has a resistance of R then wire Y would have aresistance of A R/8 R/2 R 2R 8R

R ∝ L/A = L/d^2. If d × 2, R ÷ 4and if L ÷ 2, R ÷ 2 making the neteffect R ÷ 8

92 circuits

The diagram above represents a simple electric circuit composed of 5identical light bulbs and 2 flashlight cells. Which bulb (or bulbs) would youexpect to be the brightest? D V only V and W only V and Z only V, W and Z only

all five bulbs arethe samebrightness

Bulbs in the main branch have the mostcurrent through them and are thebrightest. 92.circuits.png

93 circuits

Three different resistors R1, R2 and R3 are connected in parallel to a battery.Suppose R1 has 2 V across it, R2 = 4 Ω, and R3 dissipates 6 W. What is thecurrent in R3? D 0.33 A 0.5 A 2 A 3 A 12 A

In parallel, all the resistors have thesame voltage (2 V). P3 = I3V3

94 circuitsWhich of the following statements is NOT true concerning the simple circuitshown where resistors R1, R2 and R3 all have equal resistances? A

the largest currentwill pass throughR1

the voltageacross R2is 5 volts

the powerdissipated inR3 could be 5watts

if R2 were to burnout, current wouldstill flow throughboth R1 and R3

the net resistanceof the circuit is lessthan R1

If the resistances are equal, they will alldraw the same current. 94.circuits.png

95 circuits

If all of the resistors in the above simple circuit have the same resistance,which would dissipate the greatestpower? D Resistor A Resistor B Resistor C Resistor D

They would alldissipate the samepower

Resistor D is in a branch by itself whileresistors A, B and C are in series,drawing less currentthan resistor D. 95.circuits.png

96 circuits

The following diagram represents an electrical circuit containing two uniformresistance wires connected to asingle flashlight cell. Both wires have the same length, but the thickness ofwire X is twice that of wire Y.Which of the following would best represent the dependence of electricpotential on position along the length ofthe two wires? E A B C D E

Even though the wires have differentresistances and currents, the potentialdrop across each is1.56 V and will vary by the samegradient, dropping all 1.56 V along thesame length. 96.circuits.png

97 circuits

Each member of a family of six owns a computer rated at 500 watts in a 120V circuit. If all computers areplugged into a single circuit protected by a 20 ampere fuse, what is themaximum number of the computers canbe operating at the same time? D 1 2 3 4 5 or more

Each computer draws I = P/V = 4.17 A.4 computers will draw 16.7 A, while 5will draw over 20A.

98 circuits

Three identical capacitors each with a capacitance of C are connected asshown in the following diagram. Whatwould be the total equivalent capacitance of the circuit? B 0.33 C 0.67 C 1.0 C 1.5 C 3.0 C

The capacitance of the two capacitorsin parallel is 2C. Combined with acapacitor in seriesgives C=(Cx2C)/(C+2C)=2C/3 98.circuits.png

99 circuits

An electric heater draws 13 amperes of current when connected to 120 volts.If the price of electricity is$0.10/kWh, what would be the approximate cost of running the heater for 8hours? D $0.19 $0.29 $0.75 $1.25 $1.55

P = IV = 1.56 kW. Energy = Pt = 1.56kW × 8 h = 12.48 kW-h

100 circuitsThe steady current in the above circuit would be closest to which of thefollowing values? B 0.2 amp 0.37 amp 0.5 amp 2.0 amp 5.0 amp

Resistance of bulbs B & C = 20 Ωcombined with D in parallel gives 6.7 Ωfor the right side.Combined with A & E in series gives atotal resistance of 26.7 Ω. E = IR 100-101.circuits.png

101 circuitsWhich bulb (or bulbs) could burn out without causing other bulbs in the circuitto also go out? A only bulb D only bulb E only bulbs A or E only bulbs C or D bulbs B, C, or D

A and E failing in the main branchwould cause the entire circuit to fail. Band C would affecteach other. 100-101.circuits.png

102 circuitsWith the switch open, what would be the potential difference across the 15ohm resistor? A 30 V 40 V 60 V 70 V 110 V V = IR 102-104.circuits.png

103 circuits With the switch open, what must be the voltage supplied by the battery? D 30 V 40 V 60 V 70 V 110 V E = IRtotal where Rtotal = 35 Ω 102-104.circuits.png

104 circuits When the switch is closed, what would be the current in the circuit? D 1.1 A 1.7 A 2.0 A 2.3 A 3.0 A

With the switch closed, the resistanceof the 15 Ω and the 30 Ω in parallel is10 Ω, making thetotal circuit resistance 30 Ω and E = IR 104.circuits.png

105 circuitsHow much current flows through a 4 ohm resistor that is dissipating 36 wattsof power? B 2.25 amps 3.0 amps 4.24 amps 9.0 amps 144 amps P = I^(2)R

106 circuitsHow would the current through the 2 ohm resistor compare to the currentthrough the 4 ohm resistor? E one–forth as large one–half as large four times as large twice as large equally as large

The equivalent resistance through pathACD is equal to the equivalentresistance through pathABD, making the current through thetwo branches equal 106.circuits.png

107 circuitsWhat would be the potential at point B with respect to point C in the abovecircuit? D "+7 V" "+3 V" "0 V" "-3 V" "-7 V"

The resistance in each of the two pathsis 9 Ω, making the current in eachbranch 1 A. Frompoint A, the potential drop across the 7Ω resistor is then 7 V and across the 4Ω resistor is 4 V,making point B 3 V lower than point C 107.circuits.png

108 circuits

A cylindrical resistor has length L and radius r. This piece of material is thendrawn so that it is a cylinder withnew length 2L. What happens to the resistance of this material because ofthis process? E

the resistance isquartered.

the resistance ishalved.

the resistance isunchanged.

the resistance isdoubled.

the resistance isquadrupled.

Since the volume of material drawn intoa new shape in unchanged, when thelength is doubled,the area is halved. R = ρL/A

109 circuits

A circuit is connected as shown. All light bulbs are identical. When the switchin the circuit is closedilluminating bulb #4, which other bulb(s) also become brighter? A Bulb #1 only Bulb #2 only

Bulbs #2 and #3only

Bulbs #1, #2, and#3 None of the bulbs.

Closing the switch reduces the totalresistance of the circuit, increasing thecurrent in the mainbranch containing bulb 1 109.circuits.png

110 circuits

A cylindrical graphite resistor has length L and cross–sectional area A. It is tobe placed into a circuit, but itfirst must be cut in half so that the new length is ½ L. What is the ratio of thenew resistivity to the oldresistivity of the cylindrical resistor? C 4 2 1 0.5 0.25

Resistivity is dependent on the material.Not to be confused with resistance

111 circuits Through which resistor(s) would there be the greatest current? D J only M only N only J&N only K&L only

Resistors J and N are in the mainbranch and therefore receive thelargest current 111.circuits.png

112 circuits Which resistor(s) have the greatest rate of energy dissipation? D J only M only N only J&N only K&L only P = I^(2)R 112.circuits.png

113 circuits

The circuit shown has an ideal ammeter with zero resistance and fouridentical resistance light bulbs which areinitially illuminated. A person removes the bulb R4 from its socket therebypermanently breaking the electricalcircuit at that point. Which statement is true of the circuit after removing thebulb? A

The voltage from Bto C increases

The powersupplied by thebattery increases

The voltageaccross R1increases

The ammeterreading isunchanged

The bulb R2maintains thesame brightness

Breaking the circuit in the lower branchlowers the total current in the circuit,decreasing thevoltage across R1. Looking at the upperloop, this means R2Anow has a larger share of the batteryvoltage and the voltage across AD isthe same as the voltage across BC 113.circuits.png

114 circuits

A current through the thin filament wire of a light bulb causes the filament tobecome white hot, while thelarger wires connected to the light bulb remain much cooler. This happensbecause B

the largerconnecting wireshave moreresistance than thefilament.

the thin filamenthas moreresistance than thelarger connectingwires.

the filament wire isnot insulated.

the current in thefilament is greaterthan that throughthe connectingwires.

the current in thefilament is lessthan that throughthe connectingwires.

In series circuits, larger resistorsdevelop more power

115 circuitsIn the circuit above the voltmeter V draws negligible current and the internalresistance of the battery is 1.0 ohm. The reading of the voltmeter is C 10.5 V 12.0 V 10.8 V 13.0 V 11.6 V

With a total resistance of 10 Ω, the totalcurrent is 1.2 A. The terminal voltageVT = E – Ir 115.circuts.png

116 circuits

Suppose you are given a constant voltage source V0 and three resistors R1,R2, and R3 with R1 > R2 > R3. If you wish to heat water in a pail which of thefollowing combinations of resistors will give the most rapid heating? E A B C D E

Most rapid heating requires the largestpower dissipation. This occurs with theresistors inparallel. 116.circuts.png

117 circuitsA household iron used to press clothes is marked “120 volt, 600 watt.” Innormal use, the current in it is D 0.2 A 2 A 4 A 5 A 7.2 A P = IV

118 circuits

For the circuit shown, a shorting wire of negligible resistance is added to thecircuit between points A and B.When this shorting wire is added, bulb #3 goes out. Which bulbs (all identical)in the circuit brighten? C Only Bulb 2 Only Bulb 4 Only Bulbs 1 and 4 Only Bulbs 2 and 4 Bulbs 1, 2 and 4

Shorting bulb 3 decreases theresistance in the right branch,increasing the current through bulb 4and decreasing the total circuitresistance. This increases the totalcurrent in the main branchcontaining bulb 1. 118.circuts.png

119 circuits

For the configuration of capacitors shown, both switches are closedsimultaneously. After equilibrium isestablished, what is the charge on the top plate of the 5 μF capacitor? E 100 μC 50 μC 30 μC 25 μC 10 μC

The total charge to be distributed is+100 μC – 50 μC = + 50 μC. In parallel,the capacitors musthave the same voltage so the 20 μFcapacitor has four times the charge ofthe 5 μF capacitor.This gives Q20 = 4Q5 and Q20 + Q5 =4Q5 + Q5 = 5Q5 = 50 μC, or Q5 = 10 μC 119.circuts.png

120 circuitsHow many coulombs will pass through the identified resistor in 5 secondsonce the circuit was closed? E 1.2 12 2.4 24 6

The equivalent resistance of the two 4Ω resistors on the right is 2 Ω makingthe total circuitresistance 10 Ω and the total current2.4 A. The 2.4 A will divide equallybetween the twobranches on the right. Q = It = (1.2 A)(5s) = 6 C 120.circuts.png

121 circuits

A junior Thomas Edison wants to make a brighter light bulb. He decides tomodify the filament. How shouldthe filament of a light bulb be modified in order to make the light bulb producemore light at a given voltage? B

Increase theresistivity only.

Increase thediameter only.

Decrease thediameter only.

Decrease thediameter andincrease theresistivity.

Increase the lengthonly.

For more light at a given voltage, morecurrent is required, which requires lessresistance. R =ρL/A

122 circuitsIn the circuit diagram above, all of the bulbs are identical. Which bulb will bethe brightest? C A B C D

The bulbs all havethe samebrightness.

Bulb C in the main branch receiving thetotal current will be the brightest 122.circuts.png

123 circuitsFor the circuit shown, the ammeter reading is initially I. The switch in thecircuit then is closed. Consequently: C

The ammeterreading decreases.

The potentialdifference betweenE and F increases.

The potentialdifference betweenE and F stays thesame.

Bulb #3 lights upmore brightly.

The powersupplied by thebattery decreases.

Wire CD shorts out bulb #3 so it willnever light. Closing the switch merelyadds bulb #2 inparallel to bulb #1, which does notchange the potential difference acrossbulb #1. 123.circuts.png

124 circuits

Approximately how much would it cost to keep a 100 W light bulb litcontinuously for 1 year at a rate of $0.10per kW ⋅ hr? C $1 $10 $100 $1000 $100000

1 year = 365 days × 24 hours/day =8760 hours. W (energy) = Pt = 0.1 kW× 8760 hours = 867kW-h × $0.10 per kW-h = $ 86.7

125 circuits

.In the circuit shown above, the potential difference between points a and b iszero for a value of capacitance Cof A 1/3 microfarad 2/3 microfarad 2 microfarads 3 microfarads 9 microfarads

For points a and b to be at the samepotential, the potential drop across the3 Ω resistor must beequal to the potential drop acrosscapacitor C. The potential drop acrossthe 3 Ω resistor is threetimes the drop across the 1 Ω resistor.For the potential drop across capacitorC to be three timesthe crop across the 1 µF capacitor, Cmust be 1/3 the capacitance, or 1/3 µF 125.circuits.PNG

126 circuitsThe equivalent resistance of the circuit shown to the right with resistances R1= 4.00 Ω, R2 = 3.00 Ω, and R3 B 0.111 Ω 0.923 Ω 1.08 Ω 3.00 Ω 9.00 Ω In parallel 126.circuits.PNG

127 circuits

For the circuit shown, when a shorting wire (no resistance) connects thepoints labeled A and B, which of thenumbered light bulbs become brighter? Assume that all four bulbs areidentical and have resistance R . D Bulb 1 only Bulb 2 only Bulb 3 only Bulbs 1 and 3 only Bulbs 1, 2, and 3

Shorting bulb 4 decreases theresistance in the right branch,increasing the current through bulb 3and in the main branch containing bulb1. 127.circuits.PNG

128 circuitsIn terms of the seven fundamental SI units in the MKS system, the Ohm iswritten as A

(kgm^2)/(A^2s^3)

(kgm^2s)/C^2 kgm/Cs (kgm^2)/As^2

R = V/I where V = W/Q and Q = Itgiving R = W/I2t and W = joules = kg m2/s2

129 circuits

.Consider a simple circuit containing a battery and three light bulbs. Bulb A iswired in parallel with bulb B andthis combination is wired in series with bulb C. What would happen to thebrightness of the other two bulbs ifbulb A were to burn out? C

There would be nochange in thebrightness of eitherbulb B or bulb C.

Both would getbrighter.

Bulb B would getbrighter and bulb Cwould get dimmer.

Bulb B would getdimmer and bulb Cwould get brighter.

Only bulb B wouldget brighter

If A were to burn out, the totalresistance of the parallel part of thecircuit increases, causing lesscurrent from the battery and lesscurrent through bulb A. However, A andB split the voltagefrom the battery in a loop and with lesscurrent through bulb A, A will have asmaller share ofvoltage, increasing the potentialdifference (and the current) throughbulb B.

130 circuits

For the RC circuit shown, the resistance is R = 10.0 Ω, the capacitance is C =5.0 F and the battery has voltage ξ= 12 volts . The capacitor is initially uncharged when the switch S is closed attime t = 0. At some time later, thecurrent in the circuit is 0.50 A. What is the magnitude of the voltage acrossthe capacitor at that moment? D 0 volts 5 volts 6 volts 7 volts 12 volts

When the current is 0.5 A, the voltageacross the resistor is V = IR = 5 V.According to the looprule, the remaining 7 V must be acrossthe capacitor. 130.circuits.PNG

131 circuits

In the circuit shown above, the 10 µF capacitor is initially uncharged. After theswitch S has been closed for along time, how much energy is stored in the capacitor? D 0 µJ 100 µJ 250 µJ 500 µJ 1000 µJ

When the switch has been closed along time, the voltage across thecapacitor is 10 V as thecurrent has stopped and the resistorhas no potential drop across it. UC = ½CVD2 131.circuits.PNG

132 circuits

.In the circuit shown above, a constant current device is connected to someidentical light bulbs. After the switchS in the circuit is closed, which statement is correct about the circuit? D

Bulb #2 becomesbrighter.

Bulb #1 becomesdimmer.

All three bulbsbecome equallybrighter.

The voltagebetween points Cand D isdecreased.

The power fromthe current deviceis increased.

Since there is constant current, bulb 1remains unchanged and bulbs 2 andthree must now splitthe current. With half the currentthrough bulb 2, the potential differencebetween A and B isalso halved. 132.circuits.PNG

133 circuits

Two 1000 Ω resistors are connected in series to a 120–volt electrical source.A voltmeter with a resistance of1000 Ω is connected across the last resistor as shown. What would be thereading on the voltmeter? D 120 V 80 V 60 V 40 V 30 V

The voltmeter is essentially anotherresistor. The voltmeter in parallel withthe 100 Ω resistoracts as a 500 Ω resistor, which will half½ the voltage of the 100 Ω resistor onthe left. Thus the120 V will split into 80 V for the 1000 Ωresistor and 40 V for the voltmetercombination. 133.circuits.PNG

134 circuits

Two resistors, one with resistance R and the second with resistance 4R areplaced in a circuit with a voltage V. If resistance R dissipates power P, whatwould be the power dissipated by the 4R resistance? A 4P 2P P .5P .25P

P = I^2 * R and the current is the samethrough each resistor. 134.circuits.PNG

135 circuits Which resistor has the greatest electric current through it? A 1Ω 2Ω 3Ω 4Ω 5ΩThe greatest current is in the mainbranch. 135.circuits.png

136 circuits Which resistor has the greatest potential difference across it? C 1Ω 2Ω 3Ω 4Ω 5Ω

Let the current through the 1 Ω be x.The potential difference across the 1 Ωresistor is then xvolts. The current will divide betweenthe upper branch (5 Ω) and the lowerbranch (9 Ω) with(using the current divider ratio method)9/(9 + 5) = 9/14 x in the upper branchand 5/14 x in thelower branch. The potential differencesare then IR giving for the 2, 3, 4, 5 Ωresistors,respectively 18/14 x, 27/14 x, 20/14 xand 25/14 x volts. 135.circuits.png

137 circuits

A battery, an ammeter, three resistors, and a switch are connected to formthe simple circuit shown above. When the switch is closed what wouldhappen to the potential difference across the 15 ohm resistor? C

it would equal thepotential differenceacross the 20 ohmresistor

it would be twicethe potentialdifference acrossthe 30 ohmresistor

it would equal thepotential differenceacross the 30 ohmresistor

it would be half thepotential differenceacross the 30 ohmresistor none of the above

The 15 Ω resistor would be in parallelwith the 30 Ω resistor when the switchis closed. 137.circuits.png

138 circuits What would be the current at point E in the circuit? A 2 amp 4 amp 5 amp 7 amp 9 amp

ACD = 9 Ω, ABD = 9 Ω so the totalresistance is 4.5 Ω making the totalcurrent E/R = 2 A. 138.circuits.png

139 circuits What would be the potential at point B with respect to point D? A positive 2 V positive 4 V positive 5 V positive 7 V positive 9 V

The 2 A will divide equally between thetwo branches with 1 A going througheach branch.From B to D we have – (1 A)(2 Ω) = –2V, with B at the higher potential 138.circuits.png

140 circuits

Two resistors and a capacitor are connected with a 10 volt battery, a switchand an ideal ammeter to form the simple electrical circuit shown. After theswitch is closed and the current in the circuit reaches a constant value, whatis the reading on the ammeter in the circuit? C 9.2 × 10–2A 8.1 × 10–2A 7.5 × 10–2A 6.9 × 10–2A Zero

When the capacitor is charged, thebranch is effectively removed from thecircuit, making it asimple parallel circuit. The totalresistance is 133.3 Ω and V = IR 140.circuits.png

141 circuitsWhen the switch is closed, what would be the current in the circuit shown inthe diagram above if the two batteries are opposing one another? E 1.25 A .75 A .5 A .3 A .2 A

In a simple series circuit with twobatteries opposing one another thevoltages subtract from oneanother. The total effective voltage forthis circuit is then 4 V. With a totalresistance of 20 Ωthe total current is (4 V)/(20 Ω) 141.circuits.png

142 circuits

Four resistors, R1, R2, R3, and R4, are connected in the circuit diagramabove. When the switch is closed, current flows in the circuit. If no currentflows through the ammeter when it is connected as shown, what would be thevalue of R3? D

(R1+R4)/[(R1+R2)*(R3+R4)]

[(R1+R2)*(R4)]/(R2+R4) (R1+R2)/R4 (R1*R4)/R2 R1

For no current to flow, the potentialdrop across R1 must equal the potentialdrop across R2. Forthis to occur I1R1 = I2R2. Since the twobranches also have the same potentialdifference as awhole (they are in parallel) we alsohave I1(R1 + R3) = I2(R2 + R4). Solvefor R3 142.circuits.png

143 circuits

The diagram above shows an electrical circuit composed of 3 resistors and 1capacitor. If each resistor has aresistance of 10 Ω and the capacitor has a value of 10 μF, what would be thecharge stored in the capacitorwhen an EMF of 10 V is maintained in the circuit for a sufficient time to fullycharge the capacitor? C 23 μC 40 μC 67 μC 100 μC 150 μC

When the capacitor is charged, thebranch is effectively removed from thecircuit, making thecircuit a 10 Ω resistor in series with two10 Ω resistors in parallel. The lone 10 Ωresistor hastwice the voltage of the two 10 Ωresistors in parallel with an effectiveresistance of 5 Ω. The 10volts will then divide with 3.3 V going tothe parallel combination and 6.7 Vgoing to the single10 Ω resistor. The capacitor is inparallel with the single 10 Ω resistor. Q= CV 143.circuits.png

144 circuitsGiven 4 identical resistors of resistance R, which of the following circuitswould have an equivalent resistance of 4/3 R? A A B C D E

The resistances are, respectively, 4/3R, 2/5 R, R, and 5/3 R 144.statics.png

145 circuits

The three lightbulbs in the circuit above are identical, and the battery has zerointernalresistance. When switch S is closed to causebulb 1 to light, which ofthe other two bulbs increase(s) in brightness? C Neither bulb Bulb 2 only Bulb 3 only Both bulbs

It cannot bedetermined withoutknowingthe emf ofthe battery.

Closing the switch adds another parallelbranch, increasing the total currentdelivered by the battery. Bulb 3 will getbrighter. Bulb 2, in its own loop withbulb 3 and the battery will then losesome of its share of the potentialdifference from the battery and will getdimmer 145.statics.png

146 circuitsWhat would be the equivalent capacitance of the circuit shown if eachcapacitor has a capacitance of C? C ¼ C ¾ C 4/3 C 3C 4C

For the 3 capacitors in series on theright CTC= C/3. Adding to thecapacitor in parallel gives C + C/3 =4C/3 146.statics.png

147 circuitsWhich of the following graphs would best represent the resistance versustemperature relationship for a superconductor? A A B C D E

Superconductors have a propertywhere the resistance goes to zerobelow a certain threshold temperature 147.statics.png

148 circuitsWhat would be the total current being supplied by the battery in the circuitshown above? D 3.0 amperes 2.25 amperes 2.0 amperes 1.5 amperes 1.0 amperes

On the right, the 6 Ωand 3 Ωresistor inparallel have an equivalent resistanceof 2 Ω. Added to the 4 Ωresistance inthe middle branch which is in serieswith the pair gives 6 Ωacross themiddle. This is in parallel with the 3Ωresistor at the top giving an equivalentresistance of 2 Ω. Lastly add the 4Ωresistor in the main branch giving atotal circuit resistance of 6 Ω. V = IR 148.statics.png

149 circuitsIn the electric circuit shown above, the current through the 2.0 Ω resistor is3.0 A. Approximately what is the emf of the battery? B 51V 42V 36V 24V 21V

Using ratios, the currents in the 6Ωand3 Ωresistors are 1 A and 2 A. Theyhave three times and 3/2 times theresistance of the 2 Ωresistor so they willhave 1/3 and 2/3 the current. The totalcurrent is then 6 A giving a potentialdrop of 36 V across the 6 Ωresistor inthe main branch and adding any one ofthe branches below with the loop rulegives 36 V + 6 V = 42 V for the battery 149.statics.png

150 circuits

Which of the following wiring diagrams could be used to experimentallydetermine R using Ohm's Law? Assume an ideal voltmeter and an idealammeter. B A B C D E

Voltmeters must be placed in paralleland ammeters must be placed in series 150.statics.png

151 circuitsIf B2 were to burn out, opening the circuit, which voltmeter(s) would read zerovolts? B

none would readzero Only V2 only V3 and V4

only V2, V4, andV5

The would all readzero

Even though B2 burns out, the circuit isstill operating elsewhere as there arestill closed paths 151.statics.png

152 circuits

If B2 were to burn out, opening the circuit, what would happen to the readingof V1? Let V be its original reading when all bulbs are functioning and let V(underline) be its reading when B2 has burnt out. D V > 2V 2V> V> V V= V V> V>V/2 V/2 > V

With B2 burning out, the totalresistance of the circuit increases as itis now a series circuit. This decreasesthe current in the main branch,decreasing V1. For V1 to be halved,the current must be halved whichmeans the total resistance must bedoubled, which by inspection did nothappen in this case (total before = 5/3R, total after = 3 R) 152.statics.png

153 circuitsClosing which of the switches will produce the greatest power dissipation inR2? C S1 only S2 Only S1 and S2 only S1 and S3 only S1, S2, and S3

S1 must be closed to have any current.Closing S2 will allow current in R2 butclosing R3 would short circuit R2. 153.statics.png

154 circuitsClosing which of the switches will produce the greatest reading on theammeter? E S1 only S2 only S3 only S1 and S2 S1 and S3

S1 must be closed to have any current.Closing S3 will short circuit R3, leavingonly resistor R1, Ewhich is the lowest possible resistance. 154.circuits.png

155 circuits Closing which of the switches will produce the greatest voltage across R3? A S1 only S2 only S1 and S2 only S1 and S3 only S1, S2, and S3

S1 must be closed to have any current.The greatest voltage will occur with thegreatest currentthrough R3 but closing S2 or S3 willdraw current away from R3. 155.circuits.png

156 circuits

Two cables can be used to wire a circuit. Cable A has a lower resistivity, alarger diameter, and a differentlength than cable B. Which cable should be used to minimize heat loss if thesame current is maintained ineither cable? D Cable A Cable B

The heat loss isthe same for both.

It cannot bedetermined withoutknowing the lengthof each cable.

It cannot bedetermined withoutknowing thematerialscontained in eachcable123. R = ρL/A

157 circuits What would be the reading on a voltmeter connected across points A and C ? A 12 V 6 V 3 V 2 V

0 V, since the fusewould break thecircuit

Starting at A and summing potentialdifferences counterclockwise to point Cgives 12 V 157.cicuits.png

158 circuits What would be the reading on an ammeter inserted at point B ? C 9 A 6 A 3 A 2 A

0 A, since the fusewould break thecircuit

The branch with two 2 Ω resistors has atotal resistance of 4 Ω and a potentialdifference of 12 V.V = IR 158.circuits.png

159 circuits The equivalent capacitance for the circuit is D 1/11 μF 11/18 μF 1 μF 4 μF 11 μF

For the 6 μF and 3 μF capacitor inseries, the equivalent capacitance is 2μF. Adding the 2 μF inparallel gives a total capacitance of 4μF 159.circuits.png

160 circuitsHow do the charge Q3 stored in the 3 μF capacitor and the voltage V3 acrossit compare with those of the 6 μF capacitor? C Q3 < Q6 V3 = V6 Q3 = Q6 V3 < V6 Q3 = Q6 V3 > V6 Q3 > Q6 V3 = V6 Q3 > Q6 V3 > V6

In series the capacitors have the samecharge, but the smaller capacitor willhave the largerpotential difference (to force the samecharge on a smaller area)

161 circuits

A length of wire of resistance R is connected across a battery with zerointernal resistance. The wire is then cutin half and the two halves are connected in parallel. When the combination isreconnected across the battery,what happens to the resultant power dissipated and the current drawn fromthe battery? E

No change Nochange Doubles Doubles

QuadruplesDoubles

DoublesQuadruples

QuadruplesQuadruples

Before cutting the resistance is R. Aftercutting we have two wires of resistance½ R which inparallel is an equivalent resistance of ¼R. P = V2/R and I = V/R

162 circuits

A fixed voltage is applied across the length of a tungsten wire. An increase inthe power dissipated by the wirewould result if which of the following could be increased? B

The resistivity ofthe tungsten

The cross-sectional area ofthe wire

The length of thewire

The temperature ofthe wire

The temperature ofthe wire’ssurroundings

P = V2/R and R = ρL/A giving P =V2A/ρL

163 circuits

In a 30-minute interval, one kilowatt-hour of electrical energy is dissipated in aresistance of 20 ohms by acurrent of A 10 amp. 20 amp. 14.1 amp. 36 amp. 18 amp.

1 kW-h = 1000 W × 60 min = 60,000 W-min = I2Rt = I2(20 Ω)(30 min)

1 magnetostatics

Four infinitely long wires are arranged as shown in the accompanying figureend–on view. All four wires are perpendicular to the plane of the page andhave the same magnitude of current I. The conventional current in the wire inthe upper right–hand corner is directed into the plane of the page. The otherconventional currents are out of the plan of the page. Point P is a distance afrom all four wires. What is the total magnetic field at point P? C

μo I / 2πa towardthe upper left handcorner

μo I / 2πa towardthe lower left handcorner

2(μo I / 2πa)toward the upperleft hand corner

2(μo I / 2πa)toward the lowerleft hand corner 0

Each wire contributes a B field given byμoI / 2πa in a direction found usingRHRcurl. Thedirection of each B field is as follows,(1)Top right wire: B up&left, (2)Top leftwire: Bup&right, (3)Bottom left wire: B up&left,(4)Bottom right wire: B down&left.Forces from1 and 4 cancel leaving both 3 and 4 Bfields acting up and left and addingtogether. 1.magnetostatics.png

2 magnetostatics

The conventional current I in a long straight wire flows in the upward directionas shown in the figure. (Electron flow is downward.) At the instant a proton ofcharge +e is a distance R from the wire and heading directly toward it, theforce on the proton is: E

(μo/2π)I^2 towardthe wire

(μoI^2L)/(2πR)upward (in thesame direction asI)

(μoI^2L)/(2πR)downward (in theopposite directionas I)

ev(μoI)/(2πR)upward (in thesame direction asI)

ev(μoI)/(2πR)downward (in theopposite directionas I)

The B field at the location of the charge+e is created by the wire next to it andgiven byB = μoI / 2πR. Based on RHRcurl thedirection of that B field is into the pageat thatlocation. Then the force on that chargeis given by Fb=qvB, with q=e and Bfrom beforeso Fb = ev(μoI / 2πR). Using theRHRflat for the + charge, the forcecomes out as down. 2.magnetostatics.png

3 magnetostatics

A charged particle with constant speed enters a uniform magnetic field whosedirection is perpendicular to theparticles velocity. The particle will: E Speed up Slow down

Experience nochange in velocity

Follow a parabolicarc

Follow a circulararc

Charges moving through magneticfields move in circles

4 magnetostatics

A long straight wire conductor is placed below a compass as shown in the topview figure.When a large conventional current flows in the conductor as shown, the Npole of thecompass: D

remainsundeflected points to the south points to the west points to the east

has its polarityreversed

The compass is ABOVE the wire. UsingRHRcurl on the wire, the B field pointstowards theright at the location above the wire.Since compasses follow B field lines,the compass willalso point right, which is east. 4.magnetostatics.png

5 magnetostatics

A proton of mass M and kinetic energy K passes undeflected through aregion with electric and magnetic fieldsperpendicular to each other. The electric field has magnitude E. Themagnitude of the magnetic field B is D √ME^2/K √ME/2K √2ME^2/K √ME^2/2K √ME^2/K^2

To be undeflected, the electric andmagnetic forces must balance.Fe = Fb Eq = qvB B = E / v With vrelated to K by K = ½ mv2gives B = E / √(2K/m) … which isequivalent to choice D

6 magnetostatics

An electric current flows through a horizontal wire as shown.Which option best represents the direction of the magnetic fieldat point P A into the page out of the page

to the right of thepage

toward the top ofthe page

toward the bottomof the page

Focus on + charge direction and useRHRcurl and you get into page 6.magnetostatics.png

7 magnetostaticsTwo bar magnets are to be cut in half along the dotted lines shown. Noneof the pieces are rotated. After the cut: E

None of the halveswill attract anyother

The two halves ofeach magnet willattract each other

The two halves ofeach magnet willrepel each other

The two halves ofthe top magnet willrepel, the twohalves of thebottom magnet willattract

The two halves ofthe top magnet willattract, the twohalves of thebottom magnet willrepel

When cutting a magnet, you must endup with two new magnets having 2poles each. For the topmagnet the current N and S must stayas is, so the left of center part becomesa S and theright of center part becomes a N. Thereare now two opposite poles that attract.For thebottom magnet, by slicing it down thecenter you now have two magnets ontop of eachother. The poles would not change theircurrent locations so you have two northand twosouth poles near each other on top andbottom which makes repulsion. 7.magnetistatics.png

8 magnetostatics

An ion with charge q, mass m, and speed V enters a magnetic field B and isdeflected into a path with a radiusof curvature R. If a second ion has speed 2V, while m, q, and B areunchanged, what will be the radius of thesecond ion’s path? B 4R 2R R R/2 R/4

For this scenario, The circular motion isprovided by the magnetic force. So thatFnet(C) = mv2/rqvB = mv2/r qBr = mv 2 x V --> 2 x r

9 magnetostatics

A wire moves through a magnetic field directed into thepage. The wire experiences an induced charge separationas shown. Which way is the wire moving? E to the right to the left out of the page

toward the top ofthe page

toward the bottomof the page

Focus on a single + charge in the wirethat gets pushed to the right. So this +charge is moving ina magnetic field pointing into the pagewith a force directed right, based onRHRflat, thecharge must be moving down. 9.magnetostatics.png

10 magnetostatics

A charged particle with constant velocity enters a uniform magnetic fieldwhose direction is parallel to theparticle’s velocity. The particle will C speed up slow down

experience nochange in velocity

follow a parabolicarc

follow a circulararc

When moving parallel to magneticfields, no forces are experienced.

11 magnetostaticsThe diagram to the right depicts iron filings sprinkled around three permanentmagnets. Pole R is the same pole as D T and Y T and Z X and Y X and Z S, T, and Z

Assume R is north. Based on the lines,T would have to be north and so wouldY.This makes X and Z south and S north.

11.magnetostatics.png

12 magnetostaticsIf conventional electric current flows from left to right in a wire as shown, whatis the direction of the magnetic field at point P? C

towards the top ofthe paper

towards the bottomof the paper into the paper out of the paper to the right Using RHRcurl, we get into the page

12.magnetostatics.png

13 magnetostaticsTwo light wires are hung vertically. With electrical current in both wiresdirected upwards A

the wires willexperience a forceof attraction

the wires willexperience a forceof repulsion

the force on theright hand wire willcancel the force onthe left hand wire

both wires willexperience atorque until theyare at right anglesto each other none of the above

Parallel current wires with samedirection current attract.

14 magnetostatics

A wire moves with a velocity v through a magnetic field andexperiences an induced charge separation as shown. What is thedirection of the magnetic field? A into the page

towards the bottomof the page towards the right out of the page

towards the top ofthe page

Focus on a single + charge in the wirethat gets pushed to the right. So this +charge is movingdown with a force directed right, basedon RHRflat, the magnetic field mustpoint into thepage.

14.magnetostatics.png

15 magnetostatics

A positively charged particle moves to the right. It enters aregion of space in which there is an electric field directed up theplane of the paper as shown. In which direction does themagnetic field have to point in this region so that the particlemaintains a constant velocity? B

into the plane ofthe page

out of the plane ofthe page to the right to the left

up the plane of thepage

By definition, E fields exert forces on +charges in the same direction as the Efield. So the forcefrom the E field must be UP. Tomaintain a constant velocity, thisupwards force must becounterbalanced by a downwards force,which in this case it is to be provided bythemagnetic field. With a + charge movingright, and a magnetic force down,RHRflat gives amagnetic field pointing out of the page.

15.magnetostatics.png

16 magnetostatics

A compass is placed near a coil of wire. A conventional electricalcurrent is then run through the coil from left to right as shown. Thiswill cause the North pole of the compass to: A

point toward theleft

point toward theright

point toward thebottom of thepaper

not move since themagnetic field ofthe coil is into thepaper

not move since themagnetic field ofthe coil is out ofthe paper

A coil of wire (solenoid) like thisbecomes an electromagnet when thecurrent runs through it.Use the RHR–solenoid to determinethat the right side of this electromagnetbecomes thenorth side. Now pretend that theelectromagnet is simply a regularmagnet with a N pole onthe right and a S pole on the left anddraw the field lines. In doing so, thelines end uppointing to the left at the location of thecompass. Since compasses followmagnetic fieldlines, the compass will also point left.

16.magnetostatics.png

17 magnetostatics

Two parallel wires are carrying different electric current in the same directionas shown. How does themagnitude of the force of A from B compare to the force of B from A E

FB on A = 4 FA onB

FB on A = ¼ FA onB

FB on A = 2 FA onB

FB on A = ½ FA onB FB on A = FA on B

Due to action reaction the forces mustbe the same. Another way to look at itis that wire Acreates the field that wire B is sitting inbased on its current I, Ba= µoIa/ 2πR. The force onwire B is dependent on the field from A,and also the current in wire B itself andis given byFb=BaIbL Fb= (µoIa/ 2πR) IbL. So since both currents from A and Baffect eachrespective force, they should share thesame force.

17.magnetostatics.png

18 magnetostatics

A positively charged particle of mass M is at rest on a table. A non–zeroelectric field E is directed into theplane of the table. A non–zero magnetic field B is directed out of the plane ofthe table. What is true about themagnitude of the electric force on the particle FE compared to the magneticforce on the particle FB? A FE > FB FE<FB FE<FB

It cannot bedetermined withoutknowing the exactvalue of the chargeof the particle

The relative sizesof the electric andmagnetic fields areneeded to answerthis question

Think about this as if you are lookingdown at a table top with the + particleon it. An E field ispointed down into the table so anelectric force acts down into the tablealso. The electricforce pushing down will not move thecharge. A magnetic field comes up outof the table,but since the charge is at rest, themagnetic field exerts zero force on it.So Fe> Fb

19 magnetostatics

A positive electric charge of negligible weight is released from rest betweenthepoles of a horseshoe magnet as shown. What would be the direction of theacceleration of the charge caused by the magnetic field? E

towards the northpole

towards the southpole upwards downwards none of the above

As described above, a charge notmoving will not experience a magneticforce

19.magnetostatics.png

20 magnetostatics

Two very long current–carrying wires are shown end on in the figure. Thewire on the left has a 4A currentgoing into the plane of the paper and the wire on the right has a 3A currentcoming out of the paper.Disregarding the case of x --> ∞, in which region(s) could the magnetic fieldfrom these two wires add to zeroon the x–axis. C Region I only Region II only Region III only

Regions I and IIIonly none

First of all we should state that a largercurrent makes a bigger B field and thefurther from thewire the less the B field. UsingRHRcurl, the 4A wire has decreasingmagnitude B fieldspointing down in regions II and III onthe axis and upwards on region I. The3A wire has Bfields pointing upwards in region III anddownwards in regions II and I. Tocancel, fieldswould have to oppose each other.Region I is a possibility but since thedistance from the 4Awire is smaller at every point and it alsohas a larger current it will always havea larger Bfield so there is no way to cancel.Region II has fields in the samedirection and cannotcancel. Region III has opposing fields.Since the 4A wire has a larger currentbut also alarger distance away from any point inRegion III and the 3A wire has asmaller current but acloser distance to any point in RegionIII it is possible that these two factorscompensate tomake equal B fields that oppose andcould cancel out.

20.magnetostatics.png

21 magnetostatics The magnetic field line passing through point P inside the solenoid is directed D to the right to the left

downward towardthe bottom of thepage

upward toward thetop of the page

in no directionsince the magneticfield is zero

Using RHR–solenoid the top of the loopis N and the bottom is S. Drawing afield line out of thetop and looping outside down to thebottom, you have to continue upthrough the solenoid tocomplete the field line so the directionis UP. (Note: this may seemcounterintuitive becausethe field line points from the south tothe north which is opposite of what youmight think butthis is INSIDE the solenoid (magnet).Only outside, do lines come out of Nand into S.)

21.magnetostatics.PNG

22 magnetostatics

The diagram below shows a straight wire carrying acurrent i in a uniform magnetic field. An arrowindicates the magnetic force F on the wire. Of thefollowing possibilities, the direction of the magneticfield must be A out of the page into the page to the right

up the plane of thepage

down the plane ofthe page Use RHR–flat

22.magnetostatics.PNG

23 magnetostatics

For the four identical current-carrying wires shown (with conventionalcurrent coming out of the plane of the page), the wire on the right islabeled P. What is the direction of the magnetic force on the wire labeledP from the other wires? A To the left To the right

Up the plane of thepage

Down the plane ofthe page There is no force.

We first need to determine the directionof the B field at P due to the other wiresusing RHRcurl.The top wire creates a B field pointingup&right, the bottom wire creates a Bfield pointingup&left. The left and right parts of thesecancel out making a field only up fromthese twowires. The wire on the left alsoproduces a field only up so the net Bfield points up atlocation P. Now using RHRflat for theright wire, the force is left.

23.magnetostatics.PNG

24 magnetostatics

A wire has a conventional current I directed to the right. At the instant shownin the figure, anelectron has a velocity directed to the left. The magnetic force on the electronat this instant is E zero.

directed out of theplane of the page.

directed into theplane of the page.

directed toward thetop of the page.

directed toward thebottom of thepage.

First determine the B field directioncreated by the current wire at thelocation above the wireusing RHRcurl. This gives B out ofpage. Then use LHRflat for thenegative charge to getforce acting down.

24.magnetostatics.PNG

25 magnetostatics

An electron moves in the plane of the page through tworegions of space along the dotted-line trajectory shown inthe figure. There is a uniform electric field in Region Idirected into the plane of the page (as shown). There is noelectric field in Region II. What is a necessary direction ofthe magnetic field in regions I and II? Ignore gravitationalforces. C A B C D E

In region I, the electric field pushes thenegative electron with a force oppositethe direction ofthe E field (out of the page). For thecharge to not be pushed out, themagnetic field mustcreate a force into the page to resistthis. Based on LHRflat the B field mustpoint up. Thenin region II based on how the chargegets pushed, its magnetic force is upinitially. UsingLHRflat again in region II gives B fielddirection out of the page.

25.magnetostatics.png

26 magnetostatics

A proton moves straight up the plane of this page into a region that has amagnetic field directedto the right. If the particle is undeflected as it passes through this region, inwhat direction mustthere be a component of electric field? Ignore gravity. C To the left Into the page Out of the page Down the page To the right

Based on RHR–flat the magnetic forceis directed into the page. To beundeflected, the E fieldmust create a force out of the page toresist this, and since it’s a + charge theE field pointsout.

27 magnetostatics

For the figure shown, the variable resistance in the circuit is increased at aconstant rate. What is the direction of the magnetic field at the point P at thecenter of the circuit A A B C D E

This is a loop. Current flows clockwisearound the loop. Using the RHR–solenoid for the singleloop the B field in the center is pointinginto the page.

27.magnetostatics.png

28 magnetostatics

Which of the paths represents the path of an electron travelingwithout any loss of energy through a uniform magnetic field directedinto the page? D A B C D E

Charges moving without energy losshave to maintain a constant radiuscircle. For the circle todecrease in radius, energy would beradiated out from it. Since its anelectron we useLHRflat to get a force pointing downmaking it follow path D.

28.magnetostatics.PNG

29 magnetostatics

A wire in the plane of the page carries a current directed toward thetop of the page as shown. If the wire is located in a uniformmagnetic field B directed out of the page, the force on the wireresulting from the magnetic field is C

directed into thepage

directed out of thepage

directed to theright directed to the left zero Use RHRflat

29.magnetostatics.PNG

30 magnetostaticsThe direction of the magnetic field at point R caused by the current I inthe wire shown is E to the left to the right toward the wire into the page out of the page Use RHRcurl

30.magnetostatics.PNG

31 magnetostatics

Two long, parallel wires are separated by a distance d, as shown. One wirecarries a steady current I into theplane of the page while the other wirecarries a steady current I out of the page.At what points in the plane of the page andoutside the wires, besides points at infinity,is the magnetic field due to the currentszero?(A) Only E (A) Only at point P

(B) At all points onthe line SS' two wires

(D) At all points ona circle of radius2d centered onpoint P (E) At no points

Using RHRcurl we find the direction ofthe magnetic field from each wire. Tothe right of theleftmost wire, its field points down alongthe axis with a decreasing magnitudeas you moveaway from it. For the rightmost wire itsfield also points down when you moveleft of it.Since both fields point down betweenthe wires, they will add and cannotcancel. On the farright side of the arrangement, theleftmost wire makes a field down andthe rightmost wiremakes a field up but since thedistances to any location are differentfrom each wire themagnitude of the fields would bedifferent so no way to cancel. The samewould happen onthe far left of the wires.

31.magnetostatics.PNG

32 magnetostatics

An electron is in a uniform magnetic field B that is directed out of theplane of the page, as shown. When the electron is moving in the plane ofthe page in the direction indicated by the arrow, the force on the electron isdirected A A) toward the right B) out of the page C) into the page

(D) toward the topof the page

E) toward thebottom of the page Use LHRflat

32.magnetostatics.PNG

33 magnetostatics

A metal spring has its ends attached so that it forms acircle. It is placed in a uniform magnetic field, asshown. Which of the following will not cause a currentto be induced in the spring? D

A) Changing themagnitude of themagnetic field

B) Increasing thediameter of thecircle bystrenching thespring

C) Rotating thespring about adiameter

D) Moving thespring parallel tothe magnetic field

E) Moving thespring in and out ofthe magnetic field

To induce a current, the flux throughthe spring loop must change. Whenmoving the springparallel to the magnetic field, the sameB field and the same area is enclosedin the loop sothe flux stays constant and there is noinduced current.

33.magnetostatics.PNG

34 magnetostaticsOf the following, which is the best estimate of the work done by the magneticfield on the protons during one complete orbit of the circle? A 0 J 10^-22 J 10^-5 J 10^2 J 10^20 J

When moving in a circle at constantvelocity, no work is done as explainedin previous answers.

35 magnetostaticsOf the following, which is the best estimate of the speed of a proton in thebeam as it moves in the circle? C 10^-2 m/s 10^3 m/s 10^6 m/s 10^8 m/s 10^15 m/s

Choose 1 proton moving in the circle.For this proton. Fnet(C) = mv2/r Fb =mv2/rqvB = mv2/r v = qBr/m = 1.6x10–19(0.1)(0.1) / (1.67x10–27) ~ 10–21 / 10–27

36 magnetostaticsTwo parallel wires, each carrying a current I, repel each other with a force F.If both currents are doubled, the force of repulsion is C 2F 2√2 F 4F 4√2 F 8F

As described in question 17, the forceon either wire is Fb = (μoIa / 2πR) IbAL. So doubling bothI’s in the equation gives 4x the force.

37 magnetostatics

An electron e and a proton p are simultaneously released fromrest in a uniform electric field E, as shown. Assume that theparticles are sufficiently far apart so that the only force actingon each particle after it is released is that due to the electricfield. At a later time when the particles are still in the field,the electron and the proton will have the same E direction of motion Speed Displacement Magnitude of Accel

magnitude of forceacting on them

Not a magnetism question, but letsreview. Since the charge magnitude isthe same, they willexperience the same forces based onFe=Eq, but move in opposite directions.Since themasses are different, the same forceswill affect each object differently so thatthe smallermass electron accelerates more, thusgains more speed and covers moredistance in equaltime periods. So only the force is thesame.

37.magnetostatics.PNG

38 magnetostatics

As shown, a positively charged particlemoves to the right without deflectionthrough a pair of charged plates. Betweenthe plates are a uniform electric field E ofmagnitude 6.0 N/C and a uniformmagnetic field B of magnitude 2.0 T,directed as shown in the figure. The speedof the particle is most nearly C 0.33 m/s 0.66 m/s 3.0 m/s 12 m/s 18 m/s

To be undeflected, the electric andmagnetic forces must balance.Fe = Fb Eq = qvB v = E / B = 6 / 2

38.magnetostatics.PNG

39 magnetostatics

Two long, parallel wires, fixed in space, carry currents I1 and I2. The force of attraction has magnitude F. Whatcurrents will give an attractive force of magnitude 4F? D ½I2 & 2I I1 and ¼I2 ½I1 and ½I2 2I1 and 2I2 4I1 and 4I2

the force on either wire is Fb = (μoIa /2πR) Ib

1 induction The rate of change of flux has which of the following units Farads Joules Volts m/s Webers

Since the particle is moving parallel tothe field it does not cut across lines andhas no force.

2 induction

For the solenoids shown in the diagram (which are assumed to be close toeach other), the resistance of the left-hand circuit is slowly increased. Inwhich direction does the ammeter needle (indicating the direction ofconventional current) in the right-hand circuit deflect in response to thischange? A

The needledeflects to the left

The needledeflects to the right

The needleoscillates back andforth

The needle rotatesincounterclockwisecircles

The needle nevermoves

We first need to determine the directionof the B field at P due to the other wiresusing RHRcurl. The top wire creates aB field pointing up&right, the bottomwire creates a B field pointing up&left.The left and right parts of these cancelout making a field only up from thesetwo wires. The wire on the left alsoproduces a field only up so the net Bfield points up at location P. Now usingRHRflat for the right wire, the force isleft. 2.induction.png

3 induction

A strong bar magnet is held very close to the opening of a solenoid as shownin the diagram. As the magnet is moved away from the solenoid at constantspeed, what is the direction of conventional current through the resistorshown and what is the direction of the force on the magnet because of theinduced current? A A B C D E

A complex problem. On the leftdiagram, the battery shows how +current flows. Based on this it flows leftthrough the resistor and then down onthe front side wires of the solenoid.Using the RHR–solenoid, the right sideof the solenoid is the North pole. Sofield lines from the left solenoid arepointing to the right plunging into thesolenoid core of the right side circuit. Asthe resistance in the left side increases,less current flows, which makes themagnetic field lines created decrease invalue. Based on Lenz law, the right sidesolenoid wants to preserve the fieldlines so current flows to generate fieldlines to the right in order to maintain theflux. Using the RHR–solenoid for theright hand solenoid, current has to flowdown on the front side wires to createthe required B field. Based on this,current would then flow down theresistor and to the left through theammeter. 3.induction.png

4 inductionA magnet is dropped through a vertical copper pipe slightly larger than themagnet. Relative to the speed it would fall in air, the magnet in the pipe falls. C

more slowlybecause it isattracted by theinnate magneticfield of the pipe

more slowlybecause thecurrents induced inthe pipe producean opposingmagnetic field at the same rate

more quicklybecause it isattracted by theinnate magneticfield of the pipe

more quicklybecause thecurrents induced inthe pipe producean opposingmagnetic field

Similar to the problem above. The fieldlines from the bar magnet are directedto the left through the solenoid. As themagnet is moved away, the magnitudeof the field lines directed left in thesolenoid decrease so by Lenz law thesolenoid makes additional leftward fieldto maintain the flux. Based on RHR–solenoid, the current would flow up thefront side wires of the solenoid and thento the right across the resistor. Thisalso means that the left side of thesolenoid is a N pole so it attracts the Spole of the nearby magnet.

5 induction

A 0.20 m long copper rod has constant velocity 0.30 m/s traveling through auniform magnetic field of 0.060 T. The rod, velocity, and magnetic field are allmutually perpendicular. What is the potential difference induced across therod’s length? B 0.0036 V 0.040 V 0.090 V 1.0 V 25 V

As the magnet falls down towards thepipe, which is a looped conductor, themagnetic field lines plunging into thatconductor increase in magnitude.Based on Lenz’s law, current flows inthe conductor to oppose the gain infield and maintain the flux. The copperloop will create a B field upwards tomaintain flux and this upwards B fieldwill be opposite from the magnets Bfield which will make it slow.

6 induction

When a wire moving through a magnetic field has a voltage induced betweenthe wire’s ends, that voltage isI. directly proportional to the strength of the magnetic fieldII. directly proportional to the velocity of the wireIII. directly proportional to the diameter of the wire A I only II only III only I and II only II and III only Plug into ε =BLv

7 inductionLenz’s law concerning the direction of an induced current in a conductor by amagnetic field could be a restatement of D Ampere’s law Ohm’s Law Tesla’s Law

The Law ofConservation ofEnergy none of these Based on ε =BLv

8 induction

A square loop is placed in a uniform magnetic field perpendicular to the planeof the loop as shown. The loop is 0.50 meters on a side and the magneticfield B has a strength of 2 T. If the loop is rotated through an angle of 90° in0.1 second what would be the average induced EMF in the loop? D 0.025 C 0.40 V 5 V 10 V 80 V

This is a fact. It is best thought aboutthrough example and thinking abouthow non–conservative forces are atplay. Lenz law says opposing fields areinduced for moving magnets, this slowsthem … if the opposite was true youwould get accelerated systems whereenergy would not be conserved 8.induction.png

9 induction

The figure shows a bar moving to the right on two conducting rails. To makean induced current i in the direction indicated, in what direction would themagnetic field be in the area contained within the conducting rails? C out of the page into the page to the right to the left It is impossible

Use ε = ∆Ф / tε = ( BAf – BAi ) / tε = (0–(2)(0.5x0.5))/0.1 9.induction.png

10 induction

There is a counterclockwise current I in a circular loop of wire situated in anexternal magnetic field directed out of the page as shown. The effect of theforces that act on this current is to make the loop B expand in size contract in size

rotate about anaxis perpendicularto the page

rotate about anaxis in the plane ofthe page

accelerate into thepage

The rail makes a loop of wire as shownby the current flow. Using Lenz law, asthe loop expands with the motion of thebar, it is gaining flux lines in whateverdirection the B field is and the loopcurrent flows in a direction to opposethat gain. Using RHR–solenoid for thesingle loop, the B field induced isdirected out of the page so it must beopposing the gain of B field that isalready there going into the page. 10.induction.png

11 induction

The figure shows a rectangular loop of wire of width l and resistance R. Oneend of the loop is in a uniform magnetic field of strength B at right angles tothe plane of the loop. The loop is pulled to the right at a constant speed v.What are the magnitude and direction of the induced current in the loop? A A B C D E

Take a small section of wire on the loopat the top, bottom, right and left handsides and find the forces on them. Forexample, the section of wire on the tophas current pointing left and B pointingout … using RHRflat for that piecegives a force pointing up. At all of thepositions, the force acts in a manner topull the loop outwards and expand it. 11.induction.png

12 induction

In each of the following situations, a bar magnet is aligned along the axis of aconducting loop. The magnet andthe loop move with the indicated velocities. In which situation will the barmagnet NOT induce a current in theconducting loop? C A B C D E

The induced emf occurs in the left sidevertical wire as that is where the chargeseparationhappens. Looking at that wire, theinduced emf is given by ε =BLv. Thisemf then causes acurrent I to flow in the loop based onV=IR, so I is given as BLv / R. Thedirection of thatcurrent is found with Lenz law as thereis a loss of flux into the page, RHR–solenoid showscurrent must flow CW to add back fluxinto the page and maintain it. 12.induction.png

13 induction

A square loop of copper wire is initially placed perpendicular to the lines of aconstant magnetic field of5 x 10-3 tesla. The area enclosed by the loop is 0.2 square meter. The loop isthen turned through an angle of90° so that the plane of the loop is parallel to the field lines. The turn takes0.1 second. The average emfinduced in the loop during the turn is E 1x10^-4 V 2.5x10^-3 V 0.01 V 100 V 400 V

As long as the flux inside the loop ischanging, there will be an inducedcurrent. Since choice Ehas both objects moving in the samedirection, the flux through the loopremains constant sono need to induce a current.

14 induction

Two circular coils are situated perpendicular to the z-axis as shown.There is a current in the primary coil. All of the following procedureswill induce a current in the secondary coil EXCEPT C

rotating thesecondary coilabout the z-axis

rotating thesecondary coilabout a diameter

moving thesecondary coilcloser to theprimary coil

varying the currentin the primary coil

decreasing thecross-sectionalarea of thesecondary coil

Same as question 35, differentnumbers 14.induction.png

15 induction

A magnetic field B that is decreasing with time is directed out of the pageand passes through a loop of wire in the plane of the page, as shown. Whichof the following is true of the induced current in the wire loop? A

It iscounterclockwisein direction.

It is clockwise indirection.

It is directed intothe page.

It is directed out ofthe page.

It is zero inmagnitude.

Looking at the primary coil, currentflows CCW around it so based onRHR–solenoid themagnetic field lines from that coil arepointing to the left and they extend intothe secondarycoil. To induce a current in thesecondary coil, the flux through thesecondary coil needs tobe changed so an induced current willflow based on Lenz law. Choice Ameans spinningthe coil in place like a hula–hoop or aspinning top and this will not cause achange in flux. 15.induction.png

16 induction

A wire of constant length is moving in a constant magnetic field, as shown.The wire and the velocity vector are perpendicular to each other and areboth perpendicular to the field. Which of the following graphs bestrepresents the potential difference E between the ends of the wire as afunction of velocity? A A B C D E

Based on Lenz law, as the flux pointingup decreases, current flows in the loopto add back thatlost flux and maintain it. Based onRHR–solenoid, current would have toflow CCW 16.induction.png

17 induction

A square loop of wire of resistance R and side a is oriented with its planeperpendicular to a magnetic field B, as shown. What must be the rate ofchange ofthe magnetic field in order to produce a current I in the loop? A IR/a2

Ia2/R Ia/R Ra/I IRa Based on ε =BLv, its a linear variation 17.induction.png

18 induction

A rectangular wire loop is at rest in a uniform magnetic field B ofmagnitude 2 T that is directed out of the page. The loop measures5 cm by 8 cm, and the plane of the loop is perpendicular to the field, asshown. The total magnetic flux through the loop is A zero 2 x 10-3 T-m2 8 x 10-3 T-m2 2 x 10-1 T-m 8 x 10-1 T-m

We are looking to find rate of change ofmagnetic field ∆B/t so we need toarrange equations tofind that quantity. Using induced emf fora loop we have. ε = ∆Ф / t = ∆BA/t, andsubstituting V=IR, and area = a2 wehave … IR = ∆B (a2) / t … isolate ∆B/tto get answer 18.induction.png

19 induction

A single circular loop of wire in the plane of the page is perpendicular toa uniform magnetic field B directed out of the page, as shown. If themagnitude of the magnetic field is decreasing, then the induced current in C

directed out of thepaper

directed into thepaper

clockwise aroundthe loop

counterclockwisearound the loop

zero (no current isinduced) Ф = BA = (2)(0.05)(0.08) 19.induction.png

20 induction

A uniform magnetic field B that is perpendicular to the plane of the pagenow passes through the loops, as shown. The field is confined to a regionof radius a, where a < b, and is changing at a constant rate. The inducedemf in the wire loop of radius b is ε. What is the induced emf in thewire loop of radius 2b ? D Zero ε/2 ε 2ε 4ε

From Lenz law, as the flux decreasesthe loop induces current to add backthat declining field.Based on RHR–solenoid, current flowsCCW to add field coming out of page. 20.induction.png

21 induction

Two conducting wire loops move near a verylong, straight conducting wire that carries acurrent I. When the loops are in the positionsshown, they are moving in the direction shownwith the same constant speed v. Assume thatthe loops are far enough apart that they do notaffect each other. Which of the following istrue about the induced electric currents, if any,in the loops C A B C D E

Since both loops contain the samevalue of BA and it is changing the samefor both of them, thequantity ∆BA/t is the same for both soboth have the same induced emf. 21.induction.png

22 induction

A wire loop is rotated in a uniform magnetic field about an axis perpendicularto the field, as shown. How many times is the induced current in the loopreversed if the loop makes 3 complete revolutions from the position shown? C One Two Three Six Twelve

Above the wire is a B field which isdirected into the page based onRHRcurl. That B field has a decreasingmagnitude as you move away from thewire. Loop 1 is pulled up and thereforeisloosing flux lines into the page. By LenzLaw current flows to maintain thoselines into thepage and by RHR–solenoid currentwould have to flow CW to add lines intothe page andmaintain the flux. Loop 2 is moving in adirection so that the magnitude of fluxlines is not changing and thereforethere is no induced current 22.induction.png

23 inductionIf the bar is pushed northward on the rails, the electromotive force induced inthe bar as a result of the magnetic field will D

Be directedupwards Be zero

Produce awestward current

Produce aneastward current

Stop the motion ofthe bar

This is best done holding a smallcircular object like a small plate androtating it towards you keeping track ofthe current flow. Grab the top of theplate and pull it towards you out of thepage and move down at the same timeto rotate it. This will increase the fluxlines into theloop as you rotate and cause a currentto flow to fight the increase until itbecomes flat andyou have moved 90 degrees inrelations to the rotation you are making.Then as you pass this point and beginpushing the part of the loop you areholding down and into the page awayfrom you, you start to lose field linesand current will flow the other way to tryand maintain the flux lines until yourhand has moved what was once the topof the loop all the way to the bottom. Atthis point you are 180 degrees throughthe rotation and have changed directiononce. As you pass through 180, you willnotice that the current flows the sameway to maintain the zero flux you get atthe 180 location (even though youmight think there should be a changehere, this is where the physical objecthelps). Then as you move up the backand do the same thing on the reverseside to return the part of the loop youare holding to the top you will undergoanother direction change at 270degrees so you have 2 directionchanges total in one revolution. Do ittwo more times and you get 6reversals. 23.induction.png

24 inductionA battery is connected between the rails and causes the electrons in the barto drift to the east. The resulting magnetic force on the bar is directed B North South East West Vertically

Since the bar is not cutting across fieldlines and has no component in aperpendicular direction to the field linethere will be no induced emf.

25 induction

A battery is connected between the rails and causes the electrons in the barto drift to the east. The resulting magnetic force on the bar is directedvelocityv to the right through a region of spacewhere there is a uniform magnetic field Bdirected into the page, as shown. The inducedcurrent is as follows D

Directed CW bothentering andleavingREGION II

Directed CCWboth entering andleavingREGION II

Directed CWentering REGIONII andCCW leavingREGION II

Directed CCWentering REGIONII andCW leavingREGION II zero at all times

As you enter region II, flux into the pageis gained. To counteract that, currentflows to create a field out of the page tomaintain flux. Based on RHR–solenoid,that current is CCW. Whenleaving the region, the flux into thepage is decreasing so current flows toadd to that fieldwhich gives CW. 25.induction.png

26 induction

A square loop of wire of side 0.5 meter and resistance 10-2 ohm is located ina uniform magnetic field of intensity 0.4 tesla directed out of the page asshown. The magnitude of the field is decreased to zero at a constant rate in 2seconds. As the field is decreased, what are the magnitude and direction ofthe current in the loop? B Zero

5 A,counterclockwise 5 A, clockwise

20 A,counterclockwise 20 A, clockwise

Firstuseε=∆Ф/t ε=(BAf–BAi)/t ε=(0–(0.4)(0.5x0.5))/2 ε=0.05V Then use V=IR0.05V = I(.01) I = 5ADirection is found with Lenz law. As thefield out decreases, the current flows toaddoutward field to maintain flux. Based onRHR–solenoid, current flows CCW. 26.induction.png

27 induction After the switch S is closed, the initial current through resistor R2 is Afrom point X topoint Y

from point Y topoint X zero at all times

Oscillatingbetween point Xand Y

Impossible todetermine itsdirection

Loop 2 initially has zero flux. When thecircuit is turned on, current flowsthrough loop 1 in a CW direction, andusing RHR–solenoid it generates a Bfield down towards loop 2. As thefield lines begin to enter loop 2, loop 2has current begin to flow based on lenzlaw to try and maintain the initial zeroflux so it makes a field upwards. Basedon RHR–solenoid forloop 2, current would have to flow CCWaround that loop which makes it gofrom X to Y. 27.induction.png

28 inductionAfter the switch S has been closed for a very long time, the currents in thetwo circuits are C

zero in bothcircuits

zero in circuit 1and V/R2 in circuit2

V/R1 in circuit 1and zero in circuit2

V/R1 in circuit Iand V/R2 in circuit2

oscillating withconstant amplitudein both circuits

After a long time, the flux in loop 2becomes constant and no emf isinduced so no current flows. In circuit 1,the loop simply acts as a wire and thecurrent is set by the resistance andV=IR 27.induction.png

29 induction

In the figure, the north pole of the magnet is first moved down toward the loopof wire, then withdrawn upward. As viewed from above, the induced current inthe loop is E

always clockwisewith increasingmagnitude

always clockwisewith decreasingmagnitude

alwayscounterclockwisewith increasingmagnitude

alwayscounterclockwisewith decreasingmagnitude

firstcounterclockwise,then clockwise

As the magnet moves down, fluxincrease in the down direction. Basedon Lenz law, current in the loop wouldflow to create a field upwards to cancelthe increasing downwards field.Using RHR–solenoid, the current wouldflow CCW. Then, when the magnet ispulledupwards, you have downward flux linesthat are decreasing in magnitude socurrent flows toadd more downward field to maintainflux. Using RHR–solenoid you now getCW. 29.induction.png

30 induction

A vertical length of copper wire moves to the right with a steady velocity v inthe direction of a constant horizontal magnetic field B as shown. Which of thefollowing describes the induced charges on the ends of the wire? E

Top End: PosBottom End: Neg

Top End: NegBottom End: Pos

Top End: NegBottom End: Zero

Top End: ZeroBottom End: Neg

Top End: ZeroBottom End: Zero

Since the wire is not cutting across thefield lines, there is no force and nocharge separation 30.induction.png

31 induction

A conducting loop of wire that is initially around a magnet is pulled away fromthe magnet to the right, as indicated in the figure, inducing a current in theloop. What is the direction of the force on the magnet and the direction of themagnetic field at the center of the loop due to the induced current? A A B C D E

As the loop is pulled to the right, it losesflux lines right so current is generatedby Lenz law to add more flux lines right.This newly created field to the rightfrom the loop is in the samedirection as the magnetic field somakes an attractive force pulling themagnet right also. 31.induction.png

32 induction

A uniform magnetic field B is directed out of the page, as shown above.A loop of wire of area 0.40 m^2 is in the plane of the page. At a certaininstant the field has a magnitude of 3.0 T and is decreasing at the rateof 0.50 T/s. The magnitude of the induced emf in the wire loop at thisinstant is most nearly A 0.2 V 0.6 V 1.2 V 1.5 V 2.8 V

Use a 1 second time period, the fieldwould decrease to 2.5 T in that time.Then apply ε = ΔФ / tε = ( BAf – BAi ) / t … ε = A (Bf – Bi) …ε = (0.4)(3 – 2.5) / 1

1 Quantum

Light of a single frequency falls on a photoelectric material but no electronsare emitted. Electrons may beemitted if the B

frequency of lightis decreased

frequency of lightis increased

intensity of light isdecreased

intensity of light isincreased

velocity of light isincreased

Standard photoelectric effect question.If the frequency does not causeemission, it is below thethreshold and will not be able to causeemission. The only way to causeemission is the increasethe frequency above the threshold.

2 QuantumWhich of the following types of electromagnetic radiation has the least energyper photon C gamma infrared radio visible x-rays

E=hf. Energy is directly related tofrequency. The higher frequency meansmore energy.

3 Quantum

An atomic particle of mass m moving at speed v is found to have wavelengthλ. What is the wavelength of asecond particle with a speed 3v and the same mass B (1/9) λ (1/3) λ λ 3 λ 9 λ

de Broglie wavelength is given by, p = h/ λ … mv = h / λ … λ = h / mv … 3x m =1/3 λ

4 Quantum

A student performs the photoelectric effect experiment and obtains the datadepicted in the accompanying graphof Ekm (max kinetic energy) of photoelectrons vs the frequency of thephotons. What is the approximate workfunction of this material? A 1.5 eV 2.0 eV 2.7 eV 4.0 eV 6.0 eV

From K = hf – ϕ … y = mx + b … thework function is the y intercept, extendthe line. 4.quantum.png

5 Quantum

According to the Bohr theory of the hydrogen atom, electrons starting in the4th energy level and eventuallyending up in the ground state, could produce a total of how many lines in thehydrogen spectra? B 7 6 5 4 3

4–3,3–2,2–1 … or 4–2, 2–1 … or 4–3,3–1 … or 4–1 … this is a total of 6different transitions.

6 Quantum

In Rutherfords famous gold foil scattering experiment, he found that mostalpha particles would pass through thefoil undeflected. Which of the following nuclear properties can be inferredfrom this observation. D

The nucleus musthave a positivecharge

Most of the massof an atom is in thenucleus

The nucleuscontains bothprotons andneutrons

The diameter ofthe nucleus issmall compared tothe diameter of theatom none of the above.

While Rutherford’s experiment did showmost of these, looking at the single factprovided (thatmost particles pass straight through)only meant that most of the atom wasempty space and thatthe nucleus must be small.

7 Quantum Which of the following is best explained only by the wave theory of light Eblackbodyradiation the Compton effect

the photoelectriceffect pair–production diffraction Diffraction is a unique wave effect.

8 Quantum

In the photoelectric effect experiment, a stopping potential of Vstop is neededwhen light of frequency f shines onthe electron-emitting metal surface. If the metal surface on which the lightshines is replaced with a newmaterial that has half the work function, what is the new stopping potential,Vnew for light of frequency shiningon it? E Vnew > 2Vstop Vnew = 2 Vstop

Vstop < Vnew <2Vstop Vnew = Vstop

It is indeterminatewith the giveninformation

Stopping potential is given by.K=Vstopq ... combined with K = hf – ϕ ,we see the stoppingpotential is related to the incoming lightenergy minus the work function.However, none of thechoices give a proper result. Theanswer depends on what that actualincoming energy hf andwork function are. Here is an example.Lets say hf was 3eV and the ϕ was 2eV initially. FromVq=hf– ϕ … the stopping potential foran electron (1e) would be equal to 1eV.Now if we wereto half the work function, the newstopping potential would be 3eV – 1eV= 2 eV so it appearsthat the stopping potential doubled. Butthat result only works for those samplenumbers. Letsassume instead that hf = 10eV and ϕ =2eV. Now initially the Vstop = 8eV.Then we again halfthe work function … 10eV – 1 eV andwe get a stopping potential of 9V .. notnearly doubledthis time. The results depend on theactual numbers used because of theminus sign in theequation and not a simple multipliereffect.

9 Quantum

The diagram to the right shows the lowest four energy levels for an electron ina hypothetical atom. The electron is excited to the −1 eV level of the atomandtransitions to the lowest energy state by emitting only two photons. Which ofthe following energies could not belong to either of the photons? B 2 eV 4 eV 5 eV 6 eV 9 eV

To transition to the –12eV state withonly two photon emissions, the onlyoptions are for theelectron to make the followingtransitions: –1eV – 3eV –12eVgiving us photons of energy2eV and 9eV or –1eV – 7 eV –12eV giving photons of energy 6eV and5eV . This meansthat the 4 eV photon is not possible withonly two transitions. 9.quantum.png

10 Quantum

Monochromatic light falling on the surface of an active metal causes electronsto be ejected from the metallicsurface with a maximum kinetic energy of E. What would happen to themaximum energy of the ejectedelectrons if the frequency of the light were doubled? E

the maximumenergy of theelectrons would beless than ½ E

the maximumenergy of theelectrons would be½ E

the maximumenergy of theelectrons would be(√2) E

the maximumenergy of theelectrons would be2E

the maximumenergy of theelectrons would begreater than 2E

K = hf – ϕ … now double hf … Knew =2hf – ϕ…(now sub in the first equationrearranged for hf, into the secondequation) …Knew = 2(K+ ϕ) – ϕ = 2K + 2ϕ – ϕ …Knew = 2K + ϕSo the new energy is increased bydouble the old energy + the workfunction value

11 Quantum

If the electrons in an electron microscope are traveling with a velocity of 1.6x107 m/s, what would be theeffective wavelength of the electrons? C 1.2x10–8 m 6.6x10–9 m 4.5x10–11 m 2.6x10–11 m 8.6x10–17 m

p = h / λ … mv = h / λ … λ = h / mv =(6.63x10–4) / (9.11x10–1)(1.6x107) =4.5x10–1 m

12 Quantum

A very slow proton has its kinetic energy doubled. What happens to theprotons corresponding deBrogliewavelength A

the wavelength isdecreased by afactor of √2

the wavelength ishalved

there is no changein the wavelength

the wavelength isincreased by afactor of √2

the wavelength isdoubled.

From above λ = h / mv … Since K =½mv2 , 2x K means √2x v. So when weplug in the newvelocity of √2v, the wavelengthdecreases by this factor since wedivide.

13 Quantum

The diagram shows light being emitted due toa transition from the n=3 to the n=2 level of ahydrogen atom in the Bohr model. If thetransition were from the n=3 to the n=1 levelinstead, the light emitted would have E lower frequency less energy longer wavelength greater speed greater momentum

3 to 1 would be a higher energyemission. More energy means morefrequency, and less λ butthese are not choices. From p = h / λ,less λ means more momentum. 13.quantum.PNG

14 QuantumWhich color of light emitted from an atom would be associated with thegreatest change in energy of the atom? D Blue Green Red Violet Yellow

From E = hf, more frequency = moreenergy.

15 Quantum

Which graph best shows the maximum kinetic energy K of the photoelectronsas a function of the frequency ofincident light? A A B C D E

Below a threshold frequency, therewould be no emissions and thus zero Kfor everything belowthat point. Above that threshold, morefrequency means more K based on K =hf – ϕ, with h asthe constant slope. Graph A has allthese properties. 15.quantum.PNG

16 Quantum

Which graph best shows the maximum kinetic energy K of a photoelectron asa function of the intensity ofincident light? E A B C D E

Intensity has no effect on the energy ofa single given photoelectron. Eachphotoelectron’senergy is simply based on K = hf – ϕ.More intensity means a larger totalnumber ofphotoelectrons and would result inmore total energy, but the energy ofeach photoelectron is thesame for all levels of the overallintensity. 16.quantum.PNG

17 Quantum

Electrons that have been accelerated from rest through a potential differenceof 150 volts have a de Brogliewavelength of approximately 1 Angstrom (10–l0 meter). In order to obtainelectrons whose de Brogliewavelength is 0.5 Angstrom (5 x 10–lI meter), what accelerating potential isrequired? D 37.5 V 75 V 300 V 600 V 22,500 V

The following formulas apply. K = Vq …K = ½ mv2 … p = mv … p=h/ λTo get half the λ, the p must be doubled…To double the momentum, the velocitymust be doubled …When the velocity is doubled, theKinetic energy is 4x as much …To get 4x the K, we need 4x thepotential.

18 Quantum

According to the Bohr model of the atom, electrons orbit the nucleus indefinite orbits. According to the laws ofclassical physics, this model would be impossible because C

the positivelycharged nucleusattracts theelectrons

Coulomb's lawapplies

acceleratingelectrons radiateenergy

there is acentripetal force onthe electrons

angularmomentum isconserved

According to classical physics, whencharges accelerate in circles, theynecessarily radiate energyin the form of light. This would causethem to spiral into the nucleus as theyradiate continuousspectrums of color. This does nothappen though, which is a flaw in theRutherford model.

19 Quantum

The energy level diagram is for a hypothetical atom. Agas of these atoms initially in the ground state isirradiated with photons having a continuous range ofenergies between 7 and 10 electron volts. One wouldexpect photons of which of the following energies to beemitted from the gas? B 1, 2, and 3 eV only 4, 5, and 9 eV only

1, 3, 5, and 10 eVonly

1, 5, 7, and 10 eVonly

Since the originalphotons have arange of energies,one would expecta range of emittedphotons with noparticular energies.

The ground state is at –14eV. The nextexcited state is 4eV higher (at –10eV)which cant bereached since we are only putting in arange of 7–10. So we try the next jumpto the – 5eV state.This would require and input of 9 eVand this is possible since it falls in therange. The next state–3eV is not possible since it wouldrequire 11 eV input. So the only excitedstate we can bebrought to with this energy input is the –5eV state. From this state we will nowgo throughemissions as the electrons fall backdown to the ground state. This can bedone through threepossible jumps:–5eV–10eV, then –10eV–14eV or itcould go directly from –5eV–14eV.In these three scenarios, the emissionspossible are 5, 4 and 9. 19.quantum.PNG

20 Quantum All of the following are properties of x-rays EXCEPT: CThey penetratelight materials. They ionize gases.

They are deflectedby magnetic fields.

They dischargeelectrified bodies.

They are diffractedby crystals.

X–rays do not have a charge so wouldnot be deflected by a magnetic field. Allof the rest of thelisted properties are true however. a) xrays clearly pass through light materialsas evidencedfrom their use in the medical field. b)From Bohr’s energy level diagram forhydrogren we canconclude this is true. The differencesbetween levels on the diagramrepresent energies needed tojump levels, and these energiescorrespond to visible and UV lightenergies. The energy listedfor each level is the ionization energy,which is the energy needed to removean electron. Anyenergy larger than or equal to theionization energy for a level will do.Since X–rays have suchhigh energy, they clearly will be able toionize any level in hydrogen gas c) nottrue. d) TheCompton effect shows this ability tostrip electrons. e) An x ray is an EMwave and like all wavesshould diffract. Since the wavelength isso small, they would have to bediffracted by very smallopenings such as crystal structures inatoms.v

21 Quantum

Which of the following graphs best represents the de Broglie wavelength λ ofa particle as a function of thelinear momentum p of the particle? D A B C D E From p=h/ λ, they are inverses. 21.Quantum.PNG

22 Quantum

The scattering of alpha particles by a thin gold foil was measured by Geigerand Marsden. The Rutherford model of the atom was proposed in order toexplain why B

more particlesscattered throughangles greaterthan 90° thanthrough anglesless than 90°

the fraction ofparticles scatteredthrough largeangles was toolarge to beexplained byprevious models ofthe atom

no particlespassed throughthe foil undeflected

the most commonscattering anglewas about 90°

the most commonscattering anglewas about 180°

A) Not true. When particles came nearthe nucleus, most of them weredeflected up or downthrough angles less than 90. A few ofthem, were deflected back at angleslarger than 90.B) TRUE – Previous models could notaccounts for the particles that gotscattered through largeangles. These large angle scatteringevents prompted Rutherford toconclude a concentrated +nucleus to produce this result.

23 Quantum

Which of the following photon energies could NOT befound in the emission spectra of this atom after it has beenexcited to the n = 4 state? D 1 eV 2 eV 3 eV 4 eV 5 eV

Electron jumps could happen as follows4–3,3–2,2–1 … or 4–2, 2–1 … or 4–3,3–1 … or 4–1.In these emissions from the differencesin the energy level graph, we can makeall of the energydifference choices except 4 eV. 23.Quantum.PNG

24 QuantumWhich of the following transitions will produce the photon with the longestwavelength? E n = 2 to n = 1 n = 3 to n = 1 n = 3 to n = 2 n = 4 to n = 1 n = 4 to n = 3

Big λ means the least energy based onE=hc/ λ. The least energy correspondsto the smallestenergy level jump which is 4–. 24.Quantum.PNG

25 QuantumOf the following phenomena, which provides the best evidence that light canhave particle properties? C

Interference oflight in thin films

Electromagneticradiation Photoelectric effect Electron diffraction X-ray diffraction

The photoelectric effect is the mainproof of lights particle nature. All of theother choices arerelated to the proof of wave natures.

26 QuantumOf the following phenomena, which provides the best evidence that particlescan have wave properties? C

The absorption ofphotons byelectrons in anatom

The alpha-decayof radioactivenuclei

The interferencepattern producedby neutronsincident on acrystal

The production ofx-rays by electronsstriking a metaltarget

The scattering ofphotons byelectrons at rest

The Davisson–Germer experimentinvolves the diffraction of electronparticles through a nickelcrystal. Since these particles diffracted,this demonstrated the wave nature ofparticles.

27 Quantum

In the photoelectric effect, the maximum speed of the electrons emitted by ametal surface when it is illuminatedby light depends on which of the following?I. Intensity of the lightII. Frequency of the lightIII. Nature of the photoelectric surface D I only III only I and II only II and III only I, II, and III

This is explained in question 16. K isbased on the work function (which isbased on the natureof the surface) and K is also based onthe frequency of the incoming light.

28 Quantum

In the Bohr model of the atom, the postulate stating that the orbital angularmomentum of the electron isquantized can be interpreted in which of the following ways? A

An integral numberof electronwavelengths mustfit into theelectron's circularorbit.

Only one electroncan exist in eachpossible electronstate.

An electron has aspin of 1/2.

The atom iscomposed of asmall, positivelycharged nucleusorbited byelectrons.

An incident photonis completelyabsorbed when itcauses an electronto move to ahigher energystate.

The quantization of energy levels isfrom de Broglie and the relationship ofmomentum towavelength through matter–waves. deBroglie theorized that electrons havewavelike propertiesand must exist in whole numbermultiples of wavelengths around anorbit to so they interfereconstructively and do not get knockedout.

29 QuantumQuantum transitions that result in the characteristic sharp lines of the X-rayspectrum always involve A

the inner electronshells

electron energylevels that havethe same principalquantum number

emission of betaparticles from thenucleus

neutrons within thenucleus

protons within thenucleus

An obscure fact. Since the emission ofX–ray photons are high energy, theymust involve

30 Quantum

Which of the following experiments provided evidence that electrons exhibitwave properties?I. Millikan oil-drop experimentII. Davisson-Germer electron-diffraction experimentIII. J. J. Thomson's measurement of the charge-to-mass ratio of electrons B I only II only I and III only II and III only I, II, and III

The Davission–Germer experiment isdiscussed in question 26. The other twochoices havenothing to do with matter–waves.

31 QuantumIf the momentum of an electron doubles, its de Broglie wavelength ismultiplied by a factor of B 0.25 0.5 1 2 4

From p=h/ λ, 2x p means ½thewavelength.

32 Quantum Quantum concepts are critical in explaining all of the following EXCEPT A

Rutherford'sscatteringexperiments

Bohr's theory ofthe hydrogen atom

Comptonscattering

the blackbodyspectrum

the photoelectriceffect

Rutherford’s experiment was not aquantum concept; it was on the atomiclevel and led to amodel of the atom. All of the otherchoices involve a quantization effect orparticle nature oflight which are quantum concepts.

33 QuantumIf photons of light of frequency f have momentum p, photons of light offrequency 2f will have a momentum of A 2p (2)^1/2p p p/(2)^1/2 ½ p

From p=h/ λ, and c=f λ … p = hf/c.There is a direct relationship between pand f.

34 Quantum

In an experiment, light of a particular wavelength is incident on a metalsurface, and electrons are emitted fromthe surface as a result. To produce more electrons per unit time but with lesskinetic energy per electron, theexperimenter should do which of the following? B

Increase theintensity anddecrease thewavelength of thelight.

Increase theintensity and thewavelength of thelight.

Decrease theintensity and thewavelength of thelight.

Decrease theintensity andincrease thewavelength of thelight.

None of the abovewould produce thedesired result.

The K of each photoelectron is givenby. K = hf – ϕ. To reduce the energy ofeach photon, weneed less f (which means more λ) forthe incoming light. Since intensity isdirectly related to thenumber of photoelectrons emitted wewant to increase the intensity.

35 QuantumWhich of the following imposes a limit on the number of electrons in anenergy state of an atom? B

The Heisenberguncertaintyprinciple

The Pauliexclusion principle

The Bohr model ofthe hydrogen atom

The theory ofrelativity

The law ofconservation ofenergy(C)

A fact. The Pauli exclusion principleinvolves the filling of orbitals byelectrons and how manyelectrons fill each orbital. This is relatedto the quantum state of the electrons ineach level.

36 QuantumWhich graph shows the maximum kinetic energy of the emitted electronsversus the frequency of the light? A A B C D E Same as question 15. 36.quantum.png

37 Quantum

Which graph shows the total photoelectric current versus the intensity of thelight for a fixed frequency abovethe cutoff frequency? D A B C D E

The photoelectric current is directlyrelated to the number of photoelectronsemitted; the morephotoelectrons the more the current.Also, the # of photoelectrons is directlyrelated to theintensity. This means that photoelectriccurrent and intensity also have a directrelationship.When we are above the thresholdfrequency, 0 intensity would correspondto 0 current, but asintensity increases, the currentincreases proportionally. 37.quantum.png

38 Quantum

A 50,000 W radio station transmits waves of wavelength 4 m. Which of thefollowing is the best estimate of thenumber of photons it emits per second? C 10^8 10^22 10^30 10^40 10^56

We find the total energy produced in 1second and then use the energy of 1photon to determinehow many photons would be emitted.Total energy = W = Pt = 50000 (1 sec)= 50000 J = 5x10^4Energy of 1 photon E = hc / λ = 2x10^-25/ 4 = 0.5x10^-25 = 5x10^-26Total Energy / Energy of 1 photon = #photons released.5x10^4 / 5x10^-26 = 1030

39 Quantum

The work function for a metal is ϕ. What is the threshold frequency of incidentlight required for the emission ofphotoelectrons from a cathode made of that metal? A ϕ / h h / ϕ ϕh ϕ / hc hc / ϕ From the equation. ϕ = hfo … f = ϕ/h

40 Quantum

Two monochromatic light beams, one red and one green, have the sameintensity and the same cross sectionalarea. How does the energy of each photon and the number of photonscrossing a unit area per second in the redbeam compare with those of the green beam? E Same, same

Greater for red,less for red

Greater for red,greater for red

Less for red, lessfor red

Less for red,greater for red

Energy of a photon is related tofrequency. The red light has a lowerfrequency and thus less energy perphoton. Intensity is the total energy ofthe beam. To have the same intensity,there would need to be more of thelower energy red photons.

41 Quantum

In an x-ray tube, electrons striking a target are brought to rest, causing x-raysto be emitted. In a particular x-raytube, the maximum frequency of the emitted continuum x-ray spectrum isfo. If the voltage across the tube isdoubled, the maximum frequency is: E fo /2 fo /√2 fo √2fo 2fo

The energy of the electrons is thekinetic energy given by W = Vq = K.Doubling the voltage doubles theenergy of the electrons. The emitted x–ray energy coming from the electronenergyis given by E=hf and with double theenergy there should be doube thefrequency.

1 Nuclear An atomic mass unit is approximately equal to the mass of a(n): E alpha particle electron photon positron proton

1 u = 1.66x10 is 1/12 of carbon 12 andis approximately the same as a protonmass.

2 Nuclear A radioactive oxygen 15O8 nucleus emits a positron and becomes B 14N7 15N7 15O8 14F9 15F9

or a positron to be emitted, the oxygenmust have undergone beta+ decay,which is the opposite of beta– decay. Inbeta+ decay a proton turns into aneutron + the emitted beta particle. Themass number stays the same (P+N stillthe same), but the atomic number goesdown by 1 sincethere is 1 less proton.

3 nuclear A radon 220Rn86 nucleus emits an alpha particle becomes a: A 216Po84 220At85 220Rn86 220Fr87 224Ra88

An alpha particle is 4He2 so reduce theatomic mass by 4 and the atomicnumber by 2.

4 Nuclear A potassium 40K19 nucleus emits a B+ and becomes: E 36Cl17 44Sc21 40Ar18 40K19 40Ca20

In beta – decay, a neutron turns into aproton. Atomic mass same, massnumber +1.

5 nuclear A photon with frequency f behaves as if it had a mass equal to: B hfc2 hf/c2 c2 /hf fc2 /h h/fc2 Equate E=hf to E=mc2 ... m = hf/c2.

6 Nuclear What does the ? represent in the nuclear reaction 2H1 + 2H1 -> 3He2 D an alpha a beta a gamma a neutron a protonFor everything to add up properly, weneed ... 1/0... which is a neutron.

7 nuclear What does the ? represent in the nuclear reaction 6Li3 + ? ->7Li3 D an alpha particle a deuteron an electron a neutron a proton Same as above.

8 Nuclear An alpha particle is the same as: A a helium nucleus a positron an electrona high energyphoton a deuteron Definition of alpha particle.

9 nuclear The following equation is an example of what kind of nuclear reaction A Fission Fusion Alpha decay Beta decay Positron decayUranium split by a neutron is calledfission. 9.nuclear.png

10 Nuclear The following equation is an example of what kind of nuclear reaction B Fission Fusion Alpha decay Beta decay Positron decay

Merging together two elements (Heusually being one of them) is calledfusion. 10.nuclear.png

11 nuclear

During a particular kind of radioactive decay, a particle is emitted from thenucleus of an atom and the atom’s atomic number increases by one. Thisdecay necessarily involves the emission of _________ from the nucleus B An alpha particle A beta particle A gamma ray A proton A neutron This is the definition of Beta– decay.

12 Nuclear

A nucleus of U (atomic mass 235, atomic number 92) disintegrates to Pb(atomic mass 207, atomic number 82) in about a billion years by emitting 7alpha particles and x beta particles, where x is B 3 4 5 6 7

The mass number has changed by 28,the atomic number has changed by 10.7 alpha particles (4He2)*7 equates to aloss of 28 for atomic mass and 14 foratomic number. Ifonly the alpha particles were emitted, 4protons would be missing. Thoseprotons must havecome from the conversion of neutronsinto protons which would happen withthe release of 4beta particles.

13 nuclear The following nuclear reaction occurs: E A proton An electron A positron An alpha particle A neutron

To balance the nuclear reaction, thesum of the values across the “top” andacross the “bottom” must match... Thatis, we have 4 + 9 = 12 + A → A = 1 and2 + 4 = 6 + Z → Z = 0 . This gives usa particle with 1 nucleon, but 0 protons.This is a neutron. 13.nuclear.png

14 Nuclear

A scientist claims to have perfected a technique in which he canspontaneously convert an electron completely into energy in the laboratorywithout any other material required. What is the conclusion about this claimfrom our current understanding of physics? E

This is possiblebecause Einstein’sequation says thatmass and energyare equivalent... itis just verydifficult to achievewith electrons

This is possibleand it is done allthe time in thehigh-energyphysics labs.

The scientist isalmost correct...except that inconverting theelectron to energy,an electron’s anti-particleis produced in theprocess as well.

The scientist isalmost correct...except that inconverting theelectron to energy,a proton isproduced in theprocess as well.

This is not possiblebecause chargeconservationwould be violated.

Conservation of charge is required.Eliminating an electron by itself violatesthis. However, when and electron (–)meets a positron (+) the matter andantimatter can annihilate to produceenergy and the + and – charges canneutralize to conserve charge .. just asa side note.

15 nuclear

A new element, named Physonium (symbol Phys) is discovered to undergodouble alpha decay and beta decay simultaneously. Amazingly, this causesthe material to decay into an element called Awsomeonium (symbol Oo).What is the correct representation of the (Oo)? E A. B. C. D. E.

Simply balances the numbers acrossthe top and bottom arrives at choice E. 15.nuclear.png

16 Nuclear

The most common isotope of Uranium, U (atomic mass 238, atomic number92), radioactively decays into lead, Pb (atomic mass 206, atomic number 82),by a means of a series of alpha and beta particle emissions. How many ofeach particle must be emitted. D

32 alphas, 10betas

16 alphas, 16betas 16 alphas, 8 betas 8 alphas, 6 betas 4 alphas, 18 betas

This is the similar to problem 12. Betaparticles do not change the atomicmass number since there is simply aconversion between nucleons, so theonly way to reduce the mass number isbyemitting alpha particles. The massnumber goes down by 32 and eachalpha particle reduces it by4 so 8 alpha particles are needed. 8alpha particles by themselves wouldalso reduce the atomic #by 16, but it only ends up reduced by10 so there are 6 protons needed.These 6 protons come from the betadecay where 6 neutrons turn intoprotons and release 6 beta particles.

17 nuclear

Rutherford was the first person to artificially transmute one element intoanother (nitrogen to oxygen). A nuclear equation for his reaction could bewritten as follows (see image). The unknown particle in the above equation is A A proton A neutron An electron A gamma ray An alpha particle

For everything to add up properly, weneed ... 1 which is a proton. 17.nuclear.png

18 Nuclear When a radioactive nucleus emits a gamma ray the number of E

Protons increasesby one while thenumber ofneutronsdecreases by one.

Protons decreaseby one while thenumber ofneutrons increasesby one.

Protons andneutrons eachdecrease by two

Protons andneutrons eachincrease by two

Protons andneutrons remainunchanged

Gamma emission is pure energy so noparticles change.

19 nuclear

A nucleus of polonium–218 (atomic mass 218, atomic number 84) emits analpha particle (atomic mass 4, atomic number 2).The next two elements inradioactive decaychain each emit a beta particle (atomic mass 0, atomic number -1). Whatwould be the resulting nucleus after these three decays haveoccurred? B A B C D E

First in the alpha decay, the atomicmass goes down by 4 and the atomicnumber goes down by 2leaving X(atomic mass 214, atomicnumber 82) … then in the two betadecays, a neutron turns into a protoneach time increasing the atomicnumber by two leaving … X (atomicmass 214, atomic number 84). 19.nuclear.png

20 Nuclear The additional product of the nuclear fission reaction shown above is A A B C D ESimply make sure everything adds upto get the missing piece. 20.nuclear.png

21 nuclear

The nuclide 214 Pb 82 emits an electron and becomes nuclide X. Which ofthe following gives the mass numberand atomic number of nuclide X? E A B C D E

Pb (atomic mass 214, atomic number82) → X + e (atomic mass 0, atomicnumber -1) … For everything to add up,we need X (atomic mass 214, atomicnumber 83) 21.nuclear.png

22 Nuclear

The nuclear reaction X → Y + Z occurs spontaneously. If M(x), M(y), and M(z) are the masses of the threeparticles. which of the following relationships is true? C A B C D E

In a nuclear reaction, the total massbefore must be larger than the totalmass after since some ofthe mass will be ‘missing’ afterwards(mass defect) in the form of releasedenergy. 22.nuclear.png

23 nuclear The equation above is an illustration of E

artificiallyproducedradioactive decay

naturally occurringradioactive decay

nucleardisintegration nuclear fission nuclear fusion

In this reaction, two light elements arefusing together and producing a heavierelement. This isfusion. 23.nuclear.png

24 Nuclear

A proton collides with a nucleus of N (atomic mass 14, atomic number 7). Ifthis collision produces a nucleus of C (atomic mass 11, atomic number 6) andone other particle,that particle is D a proton a neutron a deuteron an α particle a β particle

The reaction is as follows p (atomicmass 1, atomic number 1) + N (atomicmass 14, atomic number 7) → C(atomic mass 11, atomic number 6)+ X … to make it all add up X must bean alpha.

25 nuclear

A nucleus of tritium contains 2 neutrons and 1 proton. If the nucleusundergoes beta decay, emitting an electron,the nucleus is transmuted into A

the nucleus of anisotope of helium

the nucleus of anisotope of lithium an alpha particle a triton a deuteron

We start with 2 neutrons and 1 proton.In beta decay with the emission of anelectron, the process involves a neutronturning into a proton. The resultingnucleus would have 1 neutron and 2protons. An atomic number of 2 isdefined as He. It is He (atomic mass 3,atomic number 2) which is an isotope ofHe (atomic mass 4, atomic number 2).

26 Nuclear Which of the following statements is true of a beta particle? E

A. Its speed in avacuum is 3 x 10^8m/s.

B. It has a chargeequal and oppositeto that of an alphaparticle.

C. It is morepenetrating than agamma ray of thesame energy.

D. It has a mass ofabout 1,840 timesthat of a proton

E. It can exhibitwave properties.

A beta particle, like all matter, canexhibit wave properties. Since theparticle is so small, it canmore readily show these waveproperties than normal size matter.

27 nuclear

An electron and a positron, each of mass 9.1 x 10^(–31) kilogram, are in thesame general vicinity and have very smallinitial speeds. They then annihilate each other, producing two photons. Whatis the approximate energy of each emerging photon? A . 0.51 MeV 2.0 MeV 4.0 MeV 6.6 MeV

it cannot bedetermined unlessthe frequency ofthe photon isknown.

Using E=mc^2 with twice the masssince two particles are destroyed =(2*9.1x10^(–31))(3x10^8)^2 = 1.64x10^(–13) J … 2.63x10^(–13) J * (1 eV / 1.6x10^(–19) J) = 1.02x10^6 eV. This isthe total energy released, and sincethere are two photons we split it in half.

28 Nuclear

An electron and a positron, each of mass 9.1 x 10^(–31) kilogram, are in thesame general vicinity and have very smallinitial speeds. They then annihilate each other, producing two photons. Whatis the angle between the paths of the emerging photons? E 0° 30º 45° 90° 180°

To conserve momentum, the photonsmust move in opposite directions.

29 nuclear The total number of free neutrons in the products of this reaction is B 2 3 4 5 6For everything to add up properly, 3neutrons are needed.

30 NuclearWhich of the following statements is always true for neutron-induced fissionreactions involving Uranium (atomic mass=235, atomic number 92)? A A B C D E

I. is Not True, for the following reason:In fission, and U–235 nucleus is brokeninto fragments that make smallerelements + neutrons+ energy. The fragments created arenot always the same and there is astatistical probabilityof which fragments can be created. Thereaction provided in this problem is themost probablebut other elements can be formed suchas the following U–235 fission reaction:U-235 + n Zr-94 + Te-139 + 3n +energy. There are actually manycombinations offragments that can be released. Smallamounts of mass are missing asreleased energy butadding the whole numbers of thereaction will always balance theequation for a given reaction.II. is TRUE. As explained above, assmall amount of the mass will bemissing in the form ofenergy after the reaction completes.This is necessary to produce theenergy from the reaction.III. is Not True. Again as explained inthe first paragraph. There will be asmall amount of massmissing but adding the whole numbersbefore and after will always result in thesame numbersof particles for a fission reaction. 30.nuclear.PNG

31 nuclear

Forces between two objects which are inversely proportional to the square ofthe distance between the objectsinclude which of the following?I. Gravitational force between two celestial bodiesII. Electrostatic force between two electronsIII. Nuclear force between two neutrons C I only III only I and II only II and III only I, II, and III

Fg=Gmm/r2… Fe= kqq/r2… The electric and gravitational forcesare inverse squared asshown from the equations here.Nuclear is not. This is fact and we don’tknow why. It was oneof Einstein’s last puzzles and heconsidered it a great failure of his to notsolve this. It is calledgrand unification theory that attempts tocombine all of the four fundamentalforces into oneunified force. It is a hot topic in modernphysics that is as of yet unsolved.

32 Nuclear Atoms of isotopes of the same element contain the same number of A

protons but adifferent number ofneutrons

electrons but adifferent number ofprotons

neutrons but adifferent number ofprotons

neutrons aselectrons

protons asneutrons

This is the definition of an isotope.Same atomic number so same numberof protons. Differentnumbers of neutrons make it anisotope. Also a baseball team on TheSimpsons.

33 nuclear

Quantities that are conserved in all nuclear reactions include which of thefollowing?I. Electric chargeII. Number of nucleiIII. Number of protons A I only II only I and III only II and III only I, II, and III

Some reactions conserve all of these,others do not. Clearly the numbers ofprotons is notconserved as evidenced by beta decay.The “number” of nuclei is more oftenconserved but insome reactions such as annihilation thenuclei are disintegrated and convertedinto energy. Thisagrees with the law of conservation ofmatter and energy, but when looking atthe total numbersof particles before and the totalnumbers of particles after, you wouldsay that number is notconserved. Charge is a fundamentalconservation law and it alwaysconserved. Even in theannihilation example, the net chargebefore was zero and is zero after.

34 Nuclear

A negative beta particle and a gamma ray are emitted during the radioactivedecay of a nucleus of Pb (atomic mass=214, atomic number=82). Which ofthe following is the resulting nucleus? D

Hg (atomicmass=210, atomicnumber=80)

Tl (atomicmass=214, atomicnumber=81)

Bi (atomicmass=213, atomicnumber=83)

Bi (atomicmass=214, atomicnumber=83)

Po (atomicmass=218, atomicnumber=84)

35 nuclearWhich of the following statements about the number of protons Z and thenumber of neutrons N in stable nuclei is true? A

All stable nucleihave Z = N

Only heavy stablenuclei have Z = N

Heavy stablenuclei tend to haveZ < N.

All light stablenuclei have Z< N

All light stablenuclei have Z > N.

36 Nuclear

When B (atomic mass=10) is bombarded by neutrons, a neutron can beabsorbed and an alpha particle (He (atomic mass=4)) emitted. If the B(atomic mass=10)target is stationary, the kinetic energy of the reaction products is equal to the. C

kinetic energy ofthe incidentneutron

total energy of theincident neutron

energy equivalentof the massdecrease in thereaction

energy equivalentof the massdecrease in thereaction, minus thekinetic energy ofthe incidentneutron

energy equivalentof the massdecrease in thereaction, plus thekinetic energy ofthe incidentneutron

This is a mass defect question. Theenergy released in the reaction is equalthe equivalence ofthe missing mass comparing theproducts and reactants.

37 nuclearRa (atomic mass=286, aatomic number=88) decays into Rn (atomicmass=222, atomic number=86) plus D a proton a neutron an electron

a helium nucleus(He(atomicmass=4, atomicnumber=2))

a deuteron ( H(atomic mass=2,atomic number=1))

For everything to add up we need ahelium nucleus (alpha particle).

38 Nuclear

Correct statements about the binding energy of a nucleus include which ofthe following?I. It is the energy needed to separate the nucleus into its individual protonsand neutrons.II. It is the energy liberated when the nucleus isformed from the originalnucleons.III. It is the energy equivalent of the apparent loss of mass of its nucleonconstituents. E I only III only I and II only II and III only I, II, and III

These are all true statements aboutbinding energy.

1Waves andSound

Which of the following statements about the speed of waves on a string aretrue?I. The speed depends on the tension in the stringII. The speed depends on the frequencyIII. The speed depends on the mass per unit length of the string. C II only I and II only I and III only II and III only I, II and III Based on the formula v = (F/(m/L))^.5

2Waves andSound

A string is firmly attached at both ends. When a frequency of60 Hz is applied, the string vibrates in the standing wave pattern shown.Assume the tension in the string and its mass per unit length do not change.Which of the following frequencies could NOT also produce a standing wavepattern in the string? A 30 Hz 40 Hz 80 Hz 100 Hz 180 Hz

The given diagram is the 3rd harmonicat 60 Hz. That means the fundamentalis 20Hz. The other A possible standingwaves should be multiples of 20

2.wavesandsound.png

3Waves andSound Which is not associated with a sound wave? C Amplitude Period Polarization Velocity Wavelength

A fact, sound cannot be polarized sinceits longitudinal

4Waves andSound A wave has a frequency of 50 Hz. The period of the wave is: E .01 s .2 s 7 s 20 s .02 s UseT=1/f

5Waves andSound If the frequency of sound is doubled, the wavelength: A

halves and thespeed remainsunchanged

doubles and thespeed remainsunchanged

is unchanged andthe speed doubles

is unchanged andthe speed halves

halves and thespeed halves

Frequency and wavelength areinverses

6Waves andSound

The standing wave pattern diagrammed to the right is produced in a stringfixed at both ends. The speed of waves in the string is 2 m/s. What is thefrequency of the standing wave pattern? D .25 Hz 1 Hz 2 Hz 4 Hz 8 Hz

From diagram, wavelength = 0.5 m.Find the frequency with v = f λ

6.wavesandsound.png

7Waves andSound

Two waves pulses approach each other as seen in the figure. The wavepulses overlap at point P. Which diagram best represents the appearance ofthe wave pulses as they leave point P? B A B C D E

After waves interfere they move alongas if they never met

7.wavesandsound.png

8Waves andSound

If the speed of sound in air is 340 m/s, the length of the organ pipe, open atboth ends, that can resonate at the fundamental frequency of 136 Hz, wouldbe: C .625 m .75 m 1.25 m 2.5 m 3.75 m

For an open–open pipe the harmonicfrequency is given by f=nv/(2L) with n=1

9Waves andSound

String L and string H have the same tension and length. String L has mass mand string H has mass 4m. If the speed of the waves in string L is v, thespeed of the waves in string H is A V/2 V 1.4v 2v 4v

Based on v = (F/(m/L))^.5. 4x the massgives 1⁄2 the velocity

10Waves andSound

An observer hears a sound with frequency 400 Hz. Its wavelength isapproximately A .85 m 1.2 m 2.75 m 13.6 m 44 m Speed of sound is 340,use v=fλ

11Waves andSound As sound travels from steel into air, both its speed and its: B

wavelengthincrease

wavelengthdecrease frequency increase

frequencydecrease

frequency remainunchanged

When sound travels into less densemedium, its speed decreases (unlikelight) … however, likeall waves when traveling between twomediums, the frequency remainsconstant. Based onv = f λ, if the speed decreases and thefrequency is constant then the λ mustdecrease also.

12Waves andSound

When a train is at rest, both a passenger on the train and a ticket seller at thestation agree that the trains whistleproduces sound at a frequency of 120 Hz. When the train is moving awayfrom the station at 15 m/s, thepassenger hears a frequency of ___ Hz and the ticket seller hears afrequency of ____ Hz. E 120, 125 115, 120 120, 120 115, 115 120, 115

Doppler effect. Since the passenger ison the train moving with the sound, thefrequency isunaltered, but since the sound ismoving away from the station, people atthe station should heara lower frequency.

13Waves andSound

A pipe that is closed at one end and open at the other resonates at afundamental frequency of 240 Hz. The nextlowest/highest frequency it resonates at is most nearly. E 60 Hz 80 Hz 120 Hz 480 Hz 720 Hz

Open–closed pipes only have oddmultiples of harmonic so next f is 3x f1

14Waves andSound

Assume that waves are propagating in a uniform medium. If the frequency ofthe wave source doubles then D

The speed of thewaves doubles

the wavelength dothe waves doubles

the speed of thewaves halves

the wavelength ofthe waves halves none of the above

For a given medium, speed is constant.Doubling the frequency halves thewavelength

15Waves andSound

A natural horn (trumpet with no valves) is similar to a pipe open at both ends.A musician plansto create a fundamental frequency of 256 Hz (middle C) using the horn. Ifsound travels at 350 m/s, what must be the length of this horn? B 0.34 m 0.68 m 0.78 m 1.36 m 1.46 m

UsingLf nv n 2= with n = 1, solve for L

16Waves andSound

A natural horn (trumpet with no valves) is similar to a pipe open at both ends.A musician plansto create a fundamental frequency of 256 Hz (middle C) using the horn. Atalented musician can produce a number of overtones on this natural horn.What would be the frequency ofthe fourth overtone produce when the musician is playing a middle Cfundamental? D 512 Hz 768 Hz 1024 Hz 1280 Hz 1536 Hz

The fourth overtone is the fifthharmonic, 5 x the fundamental.

17Waves andSound

One stereo loudspeaker produces a sound with a wavelength of 0.68 meterswhile the other speaker producessound with a wavelength of 0.65 m. What would be the resulting beatfrequency? B 3 Hz 23 Hz 66.5 Hz 500 Hz 11333 Hz

Determine each separate frequencyusing the speed of sound as 340 and v= f λ. Then subtractthe two frequencies to get the beatfrequency.

18Waves andSound

The diagram shows two transverse pulses moving along a string. One pulseis moving to the right and thesecond is moving to the left.Both pulses reach point x at thesame instant. What would bethe resulting motion of point xas the two pulses pass eachother? C up then down down then up up, down, up down, up, down

there would be nomotion, the pulsescancel one another

Step the two pulses through each othera little bit at a time and usesuperposition to see how theamplitudes add. At first the amplitudejumps up rapidly, then the amplitudemoves down as therightmost negative pulse continues topropagate. At the very end of theirpassing the amplitudewould be all the wave down and thenonce they pass the point will jump backup to equilibrium

18.wavesandsound.png

19Waves andSound

The diagrams below represent 5 different standing sound waves set up insideof a set of organ pipes 1 m long. What is the length of the longest wavelengthshown? E 0.5 m 0.75 m 1 m 2 m 4m

Cx is only ¼ of a wavelength. To makea full wavelength you would need 4xthe current length

19.wavesandsound.png

20Waves andSound

The diagrams below represent 5 different standing sound waves set up insideof a set of organ pipes 1 m long. Which organ pipe(s) shows a standing wavewhich has twice the frequency of one of the other waves shown? D Cy Cz Ox Oy Cy , Cz, Ox, Oy

Wavelengths of each are (dist/cycle) …4L, 4/3 L, 4/5 L, L, 2/3 L …Frequencies are f = v/ λ.v/4L, 3v/4L, 5v/4L, v/L, 3v/2L … Oy is2x Cy

20.wavesandsound.png

21Waves andSound The frequency of the tuning fork is (approximately) E 0.0039s 0.020s 2.55Hz 50Hz 256Hz f = cycles / seconds

21.wavesandsound.png

22Waves andSound

In order to calculate the speed of sound from the graph, you would also needto know D Pitch Volume Frequency Wavelength Length of tube To use v = f λ, you also need the λ

21.wavesandsound.png

23Waves andSound

A metal bar is vibrating with a frequency of 200 Hz. The resulting period ofoscillation would be E 200s 141s 0.007s 0.002s None of the above T = 1/f

21.wavesandsound.png

24Waves andSound

A tube is open at both ends with the air oscillating in the 4th harmonic. Howmany displacement nodes are located within the tube? C 2 3 4 5 6

To produce pipe harmonics, the endsare always antinodes. The first(fundamental) harmonic iswhen there are two antinodes on theend and one node in-between. To moveto each nextharmonic, add another node in themiddle and fill in the necessaryantinodes. (ex, 2nd harmonicis ANANA … So the 4thCharmonic would be ANANANANA andhave four nodes. Alternativesolution … if you know what theharmonics look like you can draw themand manually count thenodes.

25Waves andSound

Two separate strings of the same thickness are stretched so that theyexperience the same tension. String B is twice as dense as String A. String A,of length L, is vibrated at the fundamental frequency. How long is String B if ithas the same fundamental frequency as String A? B 1/2 L L/(sqrt(2)) L (Sqrt(2))*L 2L

The Fundamental is given byLnv fn2= (n=1), and the velocity is given byv=sqrt(Ft/(m/t))

26Waves andSound

A resonance occurs with a tuning fork and an air column of size 39 cm. Thenext highest resonance occurs with an air column of 65 cm. What is thefrequency of the tuning fork? Assume that the speed of sound is 343 m/s. C 329.8Hz 527.7Hz 659.6Hz 879.5Hz 1319Hz

This is an open–closed pipe. Look atthe harmonics shown below. Since thesame tuning fork isused in each case, the frequency for allof them is the same, and since they alltravel at the samespeed with equal frequencies, thewavelength of each wave is also thesame (though each has adifferent number of wavelengths fittingin the tube, the ‘wavelength’ of each issame). But, thelengths of the tubes vary using thewater to make each successiveharmonic and fit the necessarynumbers of wavelengths in each tube.Looking at the diagrams, we can seethat eachharmonic is ½ a wavelength longer thanthe next,regardless of which ones we arelooking at. Wedon’t have to know which harmonics wearelooking at if we know the differencebetween anytwo of them because each harmonichas the samedifference of ½ λ. So the difference inlengthbetween any two consecutiveharmonics is equal to½ the wavelength of the wave. ∆L = ½λ. Usingthis relationship, we have:(65 cm – 39 cm) = ½ λλ = 52 cm

26.wavesandsound.png

27Waves andSound A place of zero displacement on a standing wave is called B an antinode a node the amplitude the wavenumber the harmonic Definition of a node

28Waves andSound

A person vibrates the end of a string sending transverse waves down thestring. If the person then doubles the rate at which he vibrates the string whilemaintaining the same tension , the speed of the waves E

doubles and thewavelength isunchanged

doubles and thewavelengthdoubled

doubles while thewavelength ishalved

is unchanged whilethe wavelength isdoubled

is unchanged whilethe wavelength ishalved

Since the medium stays the same thespeed remains constant. Based on v = fλ, for constantspeed, f and λ change as inverses

29Waves andSound

A tube of length L1 is open at both ends. A second tube of length L2 is closedat one end and open at the other end. This second tube resonates at thesame fundamental frequency as the first tube. What is the value of L2 ? D 4L1 2L1 L1 1/2L1 1/4L1

Similar to problem 26, we should lookat the harmonic shapes open–open vsopen–closed. Comparing thefundamental harmonic of the open–open pipe to theclosed–open pipe. The closed–openpipe should be half as long astheopen–open pipe in order to fit theproper number of wavelengths of thesame waveform to produce the givenharmonic in each.

29.wavesandsound.png

30Waves andSound

For a standing wave mode on a string fixed at both ends, adjacent antinodesare separated by a distance of 20cm. Waves travel on this string at a speedof 1200 cm/s. At what frequency is the string vibrated to produce this standingwave? D 120Hz 60Hz 40Hz 30Hz 20Hz

Two antinodes by definition will be ½ λapart. So 20 cm = ½ λ, and the λ = 40cm. Then using

31Waves andSound

What would be the wavelength of the fundamental and first two overtonesproduced by an organ pipe of length L that is closed at one end and open atthe other? E L, ½ L, ¼ L ½ L, ¼ L, 1/6 L 2L, L, ½ L 4L, 2L, L 4L, 4/3 L, 4/5 L v = f λ we have 1200 = f (40)

32Waves andSound

A small vibrating object S moves across the surface of a ripple tank producingthe wave fronts shown above.The wave fronts move with speed v. The object is traveling in what directionand with what speed relative tothe speed of the wave fronts produced? B (A) (B) (C) (D) (E) Doppler effect

32.waves_and_sound.png

33Waves andSound

A cord of fixed length and uniform density, when held between two fixedpoints under tension T, vibrates witha fundamental frequency f. If the tension is doubled, the fundamentalfrequency is B 2f √(2f) f f/√(2) f/2

Doubling the tension, changes thespeed to √2 v comparatively, andmakes the frequency increase by thesame amount.

34Waves andSound

A vibrating tuning fork sends sound waves into the air surrounding it. Duringthe time in which the tuning forkmakes one complete vibration, the emitted wave travels A one wavelength about 340 meters

a distance directlyproportional to thefrequency of thevibration

a distance directlyproportional to thesquare root of theair density

a distanceinverselyproportional to thesquare root of thepressure

The time to make 1 cycle, is also thetime it takes the wave to travel 1 λ

35Waves andSound

Two wave pulses, each of wavelength λ, are traveling toward each otheralong a rope as shown. When both pulses are in the region between points Xand Y, which are a distance λ apart, the shape of the rope is B (A) (B) (C) (D) (E)

Superpose the two waves on top ofeach other to get the answer

35.waves_and_sound.png

36Waves andSound

A train whistle has a frequency of 100 hertz as heard by the engineer on thetrain. Assume that the velocity ofsound in air is 330 meters per second. If the train is approaching a stationarylistener on a windless day at avelocity of 30 meters per second, the whistle frequency that the listener hearsis most nearly B 90 Hz 110 Hz 120 Hz 240 Hz 300 Hz Doppler equation

37Waves andSound

Two sinusoidal functions of time are combined to obtain the result shown inthe figure above. Which of thefollowing can best be explained by using this figure? A Beats Doppler Effect Diffraction Polarization

Simple harmonicmotion

This diagram is associated with beats.The increasing and decreasingamplitude caused by interferenceoscillates the volume up and downwhich createsthe beat sound.

37.waves_and_sound.png

38Waves andSound The speed at which waves propagate on the string is D 0.4 m/s 2.5 m/s 5 m/s 10 m/s 20 m/s v = f λ

38.waves_and_sound.png

39Waves andSound The fundamental frequency of vibration of the string is B 1 Hz 2.5 Hz 5 Hz 7.5 Hz 10 Hz

The diagram shows the secondharmonic in the string. Since harmonicsare multiples, the first harmonic wouldbe half of this.

39.waves_and_sound.png

40Waves andSound Sound in air can best be described as which of the following types of waves? A Longitudinal Transverse Torsional Electromagnetic Polarized Fact

41Waves andSound

In the Doppler effect for sound waves, factors that affect the frequency thatthe observer hears include which of the following? C I only III only I and II only II and III only I, II, and III

A fact about the Doppler effect. Canalso be seen from the Dopplerequation.

41.waves_and_sound.png

42Waves andSound

The figure above shows two wave pulses that are approaching each other.Which of the following best shows the shape of the resultant pulse when thecenters of the pulses, points P and Q coincide? A (A) (B) (C) (D) (E)

Use superposition and overlap thewaves to see the resultant.

42.waves_and_sound.png

43Waves andSound

One end of a horizontal string is fixed to a wall. A transverse wave pulse isgenerated at the other end, moves toward the wall as shown and is reflectedat the wall. Properties of the reflected pulse include which of the following? B I only III only I and II only II and III only I, II, and III

When hitting a fixed boundary, some ofthe wave is absorbed, some is reflectedinverted. The reflected wave has lessamplitude since some of the wave isabsorbed, but since the string has notchanged its properties the speed of thewave should remain unchanged.

43.waves_and_sound.png

44Waves andSound

A small vibrating object on the surface of a ripple tank is the source of wavesof frequency 20 Hz and speed 60 cm/s. If the source S is moving to theright, as shown, with speed 20 cm/s, at which of the labeled points will thefrequency measured by a stationary observer be greatest? C A B C D

It will be the sameat all four points.

Clearly at point C the waves arecompressed so are more frequent.

44.waves_and_sound.png

45Waves andSound

The frequencies of the first two overtones (second and third harmonics) of avibrating string are f and 3f/2 .What is the fundamental frequency of thisstring? B f/3 f/2 f 2f 3f

Harmonics are multiples of thefundamental so the fundamental mustbe f/2.

46Waves andSound

Two fire trucks have sirens that emit waves of the same frequency. As the firetrucks approach a person, the person hears a higher frequency from truck Xthan from truck Y. Which of the following statements about truck X can becorrectly inferred from this information: A I only III only I and II only II and III only I, II, and III

Based on the Doppler effect, onlyspeed matters. The faster a vehicle ismoving, the closer together the soundwaves get compressed and the higherthe frequency. Take the case of a veryfast vehicle traveling at the speed ofsound; the compressions are all righton top of each other. So faster speedmeans closer compressions and higherfrequencies. Choice I must be truebecause X is a higher frequency somust be going faster. Distance to theperson affects the volume but not thepitch so choice II is wrong. III seemscorrect but its not. It doesn’t matterwhether you are speeding up or slowingdown, it only matters who is goingfaster. For example, suppose truck Xwas going 5 mph and speeding upwhile truck Y was going 50 mph andslowing down, this is an example ofchoice III but would not meet therequirement that X has a higherfrequency because only actual speedmatters, not what is happening to thatspeed.

46.waves_and_sound.png

47Waves andSound What is the amplitude of the wave? A 4 cm 5 cm 8 cm 10 cm 16 cm By inspection.

47.waves_and_sound.png

48Waves andSound What is the speed of the wave? C 4 cm/s 25 cm/s 50 cm/s 100 cm/s 200 cm/s

By inspection, the λ is 10 cm. f = 1 / T= 5, Then use v = f λ.

47.waves_and_sound.png

49Waves andSound

A standing wave pattern is created on a guitar string as a person tunes theguitar by changing the tension in the string. Which of the following propertiesof the waves on the string will change as a result of adjusting only the tensionin the string? I. Speed of the traveling wave that creates the pattern II.Frequency of the standing wave III. Wavelength of the standing wave C I only II only I and II only II and III only I, II, and III

Based on v = √(Ftension/(m/l)), thetension changes the speed. Thenbased on f = nv/2L, this resulting speedchange will effect the frequency also.But since the frequency increases indirect proportion to the speed, and v = fλ, the λ should remain unchanged.

49.waves_and_sound.png

50Waves andSound

A tuning fork is used to create standing waves in a tube open at the top andpartially filled with water. A resonance is heard when the water level is at acertain height. The next resonance is heard when the water level has beenlowered by 0.5 m. If the speed of sound is equal to 340 m/s, the frequency ofthe tuning fork is C 170 Hz 226 Hz 340 Hz 680 Hz 2450 Hz

This is the same as question 26. Thelength change corresponds to a ½ λincrease in length. ∆L = ½ λ ... 0.5 = ½λ ... λ = 1 ... then use v = f λ andsolve for f.

1PhysicalOptics

In Young’s double slit experiment, the second order bright band of one lightsource overlaps the third orderband of another light source. If the first light source has a wavelength of 660nm, what is the wavelength of thesecond light source? D 1320 nm 990 nm 495 nm 440 nm 330 nm

Using m λ = d sin θ, the value of sin θ isthe same for both sources since thelocation of the spotis the same, but the first source is atm=2, and the second source is at m=3.Equating d sin θ foreach gives m1 λ1 = m2 λ2 … (2)(660) =3 (λ2) … λ2 = 440 nm.

2PhysicalOptics

A student performs an experiment similar to Young’s Double Slit Experiment.Coherent light passes throughtwo narrow slits and produces a pattern of alternating bright and dark lines ona screen. Which of the followingwould cause the bright lines on the screen to be further apart?I. Increasing the distance between the slitsII. Decreasing the distance between the slitsIII. Decreasing the wavelength of the light B I only II only III only I & III only II & III only

Based on m λ = dx / L we want toincrease x. Only II does this.

3PhysicalOptics

A diffraction grating of 1000 lines/cm has red light of wavelength 700 nm passthrough it. The distancebetween the first and third principal bright spots on a screen 2 m away is B 14 cm 28 cm 42 cm 140 cm 280 cm

1000 lines/cm gives a line spacing d =1/1000 cm/line = 1x10–5 m/line. λ =7x10–7m=1. m λ = d sin θ (1)(7x10m.With diffraction gratings, we usuallyassume the small angle approximationdoes not work, so wefind θ then use the geometry with tan θor another trig function to find Y. Do thisfor each spot.–7) = (1x10–5) sin θ θ = 4.01° … tan θ= o/a … Y1 = 0.14 mRepeat for m=3 … Y3 = 0.43 m.Subtract Y3 – Y1 to find the distancebetween = 0.29 mNote: Since the angle θ here actuallycame out to be small, the x/L smallangle approximationcould be used and the spacing xbetween spots could be assumed to beequal as well, so youcould simply find x for the first spot anddouble it to find the spacing 1 to 3.

4PhysicalOptics

Monochromatic light with a wavelength of 6x10–7 meters falls upon a singleslit. After passing through the slit,it forms a diffraction pattern on a screen 1 m away. The distance between thecenter maximum and the firstmaximum away from the center is 3 mm. What is the thickness of the slit? C 0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm

Single slit. With the given values, wecan see the angle is small so we canuse the small angleapproximation and apply m λ = dx / L.Recall for single slits, the first maximumoff center is atx=1.5 unlike double slits.

5PhysicalOptics

In a Young's double-slit experiment, the slit separation is doubled. Tomaintain the same fringe spacing on thescreen, the screen-to-slit distance D must be changed to D D/2 D/(2)^1/2 D(2)^1/2 2D 4D From mλ = dx / L, d x2 needs L x2 also.

6PhysicalOptics

Monochromatic light falls on a single slit 0.01 cm wide and develops a first–order minimum (dark band) 0.59cm from the center of the central bright band on a screen that is one meteraway. Determine the wavelength ofthe light. D 1.18 x10^(–2) cm 5.90 x10(–3) cm 1.18 x10(–4) cm 5.90 x10(–5) cm 1.18 x10(–6) cm

Single Slit. Again based on the givenvalues we can see the angle is small sowe can usemλ = dx / L … dark spot at m=1. Note:use L=100 cm to get an answer in cm.

7PhysicalOptics Which station broadcasts with 3.27 m radio waves? A 91.7 MHz 92.5 MHz 98.5 MHz 102.5 MHz 106.3 MHz

Radio wave is EM and travels at lightspeed. Use c = f λ and solve.

8PhysicalOptics

Pioneering radio station KFKA started broadcasting 78 years ago at 1310(1.31 MHz) on the AM dial. What isthe approximate length of its radio wave? B 23m 230 m 2300 m 23000 m 3x10^(8) m

Radio wave is EM and travels at lightspeed. Use c = f λ and solve.

9PhysicalOptics

The length of the most effective transmitting antenna is equal to one–fourththe wavelength of the broadcastwave. If a radio station has an antenna 4.5 meters long then what is thebroadcast frequency of the radio station? C 1.4 x 10^(–8) Hz 6.0 x 10^(–8) Hz 1.7 x 10(7) Hz 6.7 x 10(7) Hz 3.0 x 10^(8) Hz

λ = 4*4.5, Radio wave is EM andtravels at light speed. Use c = f λ andsolve.

10PhysicalOptics

A radio signal with a wavelength of 1.2 x 10^(-4)m is sent to a distanceasteroid, is reflected, and returns to Earth72 hours and 48 minutes later. How far from Earth is the asteroid? B 1.9 x 10^(10) 3.9 x 10^(10) km 7.9 x 10^(10) km 1.9 x 10^(11) km 5.4 x 1011 km

It travels at light speed and takes halfthe total time to travel the distance oneway. Use v=d/t.Convert the time to seconds, find thedistance in meters, then convert that tokm.

11PhysicalOptics

In the electromagnetic spectrum, rank the following electromagnetic waves interms of increasing wavelength. E A B C D E

λ changes the opposite of frequencies(high freq = low λ) … based on this andknowledge of theEM spectrum, the answer is E. 11.physicaloptcs.png

12PhysicalOptics

Two sources, in phase and a distance d apart, each emit a wave ofwavelength λ. See figure below. Which of thechoices for the path difference ΔL = L1 – L2 will always produce destructiveinterference at point P? D d sin θ x/L1 (x/L2)d λ/2 2 λ

By definition, when the path differenceequals ½ λ or any odd multiple of ½ λ’sfor sources ofthe same λ, there will be destructiveinterference. 12.physicaloptics.png

13PhysicalOptics

Waves are produced by two point sources S and S’ vibrating in phase. Seetheaccompanying diagram. X represents the location of the 2ndinterference minima.The path difference SX – S’X is 4.5 cm. The wavelength of the waves isapproximately D 1.5 cm 1.8 cm 2.3 cm 3.0 cm 4.5 cm

Using path diff = m λ, with m=1.5 for the2nd min, we have 4.5 cm = (1.5) λ. 13.physicaloptics.png

14PhysicalOptics

A transmission diffraction grating is ruled with 5000 lines per cm. Throughwhat angle will the first ordermaxima be deflected when light with a wavelength of 4.5 x 10–7 m strikes thegrating? C 5.2° 6.4° 13° 27° 34°

5000 lines/cm gives a line spacing d =1/5000 cm/line = 2x10–6 m/line.Then use m λ = d sin θ, with m = 1 forthe first max.

15PhysicalOptics

In an experiment to measure the wavelength of light using a double slitapparatus, it is found that the brightfringes are too close together to easily count them. To increase only thespacing between the bright fringes, onecould D

increase the slitwidth

decrease the slitwidth

increase the slitseparation

decrease the slitseparation none of these

Based on m λ = dx / L we want toincrease x. d is separation of slits andless d means more x

16PhysicalOptics

Two point sources in a ripple tank radiate waves in phase with a constantwavelength of 0.02 meter. Thefirst-order interference maximum appears at 6° (use sin 6° = 0.1). Theseparation of the sources is most nearly E 0.001 m 0.002 m 0.06 m 0.1 m 0.2 m Using mλ = d sin θ … (1)(0.02) = d (0.1)

17PhysicalOptics Which of the following is true of a single-slit diffraction pattern? B

It has equallyspaced fringes ofequal intensity.

It has a relativelystrong centralmaximum.

It can be producedonly if the slit widthis less than onewavelength.

It can be producedonly if the slit widthis exactly onewavelength.

It can be producedonly if the slit widthis an integralnumber ofwavelengths. Fact about single slits.

18PhysicalOptics

For the five types of electromagnetic radiation listed above, which of thefollowing correctly describes the wayin which wavelength, frequency and speed, change as one goes from the leftto right on the list? B

DecreasesDecreasesDecreases

DecreasesIncreasesRemains the same

IncreasesDecreasesRemains the same

IncreasesDecreasesIncreases

IncreasesIncreasesIncreases Known facts about the EM spectrum. 18.physicaloptics.png

19PhysicalOptics

A radar operates at a wavelength of 3 centimeters. The frequency of thesewaves is E 10^(–10) Hz 10^(6) Hz 10^(8) Hz 3 x 10^(8) Hz 10^(10) Hz

Radar wave is EM and travels at lightspeed. Use c = f λ and solve.

20PhysicalOptics

Plane sound waves of wavelength 0.12 m areincident on two narrow slits in a box withnonreflecting walls, as shown. At a distance of5.0 m from the center of the slits, a first-ordermaximum occurs at point P, which is 3.0 m fromthe central maximum. The distance between theslits is most nearly D 0.07 m 0.09 m 0.16 m 0.20 m 0.24 m

Since the slits are narrow, we can usem λ = d sin θ, but since θ is clearlylarge we cannot use thex/L small angle approximation. Fromthe given diagram, the geometry showssin θ = o/h = 3/5 ..rather than finding θ, we will just usethis value for sin θ and plug in …m λ =d sin θ … (1) (0.12) = d (3/5) 20.physicaloptics.png

21PhysicalOptics

A radio station broadcasts on a carrier frequency of 100 MHz. Thewavelength of this radio wave is most nearly C 3.0x10^-3m 1.0m 3.0m 3.3m 3.0x10^6m

Radio waves are EM and travels at lightspeed. Use c = f λ and solve.

22PhysicalOptics

If one of the two slits in a Young’s double-slit demonstration of theinterference of light is covered with a thin filter that transmits only half the lightintensity, which of the following occurs? E

The fringe patterndisappears.

The bright linesare brighter andthe dark lines aredarker.

The bright linesand the dark linesare all darker.

The bright linesand the dark linesare all brighter.

The dark lines arebrighter and thebright lines aredarker.

This is still a double slit pattern becausethere is still light making it through bothslits. One ofthe light sources has reduced itsamplitude; which means when it meetsthe second light source itwill cause less interference than itoriginally did. This means lessconstructive interference andless destructive interference also. Sobright spots become less bright, anddark spots becomebrighter.

23PhysicalOptics

A diffraction grating is illuminated by light of wavelength 600 nm. On a screen100 cm away is a series of bright spots spaced 10 cm apart. If the screen isnow placed 30 cm from the diffraction grating, the new spacingbetweenadjacent bright spots on the screen is most nearly C 10cm 3cm 1cm 3mm

From the first scenario given. We candetermine the angle of the first spotusing tan θ = o /a.tan θ = 10 / 100 = 5.71°. The problemsays the remaining spots are spacedequally, which is arough approximation. The angles arerelatively small, but if we wanted to getaccurate results weshould find each spacing with d sin θ,but, this is just an approximation for thefirst few spots.When the screen is moved closer, theangle of the light leaving the grating willnot change, butthe spacing on the screen willdecrease. Think about a diagram of thissetup and it is clear thatthis must be true. Based on tan θ = o /awith the same angle θ but the adjacentside changed to 30cm, we get a new location of the firstspot at 3 cm, so the other spots willalso approximately belocated 3 cm apart as well for relativelysmall angles.

1GeometricOptics

The critical angle of a material is the angle of incidence for which the angle ofrefraction is: D 0° 30° 45° 90° 180° Definition of critical angle.

2GeometricOptics

An object is located 0.20 meters from a converging lens which has a focallength of 0.15 meters. Relative to the object, the image formed by the lens willbe: C real, erect, smaller.

real, inverted,smaller.

real, inverted,larger.

virtual, erect,larger.

virtual, inverted,smaller.

Using the math, 1/f = 1/do + 1/di, and M= – di / do

3GeometricOptics A plane mirror produces an image that is E

real, inverted andlarger than theobject.

real, upright, andthe same size ofthe object.

real, upright, andsmaller than theobject.

virtual, inverted,and smaller thanthe object.

virtual, upright, andthe same size asthe object.

Plane mirrors always makes virtual,same size, upright images.

4GeometricOptics The principle underlying fiber optics is: E diffraction dispersion interference polarization

total internalreflection

Fiber optics involves reflecting light in afiber strand as the light carries thesignal along the fiber.

5GeometricOptics A diverging lens produces an image of a real object that is: E

real, inverted andlarger than theobject.

real, upright, andthe same size asthe object.

virtual, inverted,and smaller thanthe object.

virtual, upright, andlarger than theobject.

virtual, upright, andsmaller than theobject. Fact about diverging lens.

6GeometricOptics

Light that has a wavelength of 500nm in air has a wavelength 400nm in atransparent material. What is the index of refraction of the material? D 0.64 0.8 1 1.25 1.56 Use n1 λ1 = n2 λ2

7GeometricOptics

A beam of light passes from medium 1 to medium 2 to medium 3 as shown inthe accompanying figure. What is true about the respective indices ofrefraction (n1, n2, and n3) D n1 > n2 > n3 n1 > n3 > n2 n2 > n3 > n1 n2 > n1 > n3 n3 > n1 > n2

More–Less dense bend away, Less–More dense bend towards. The morethe bend, the bigger the difference inn's.

7.geometricoptics.png

8GeometricOptics

A laser is embedded in a material of index of refraction n. Thelaser beam emerges from the material and hits a target. See theaccompanying figure for the position parameters of the laser andtarget. The value of n is: B 1.4 1.5 2.1 3.5 5

If you look carefully you can see theseare both 3–4–5 triangles and are alsothe same triangleflipped. The hypotenuse of each is 1.5m. Using the sides of the triangles, wehavesin θ1 = o/h = 0.8/1.5 for the bottomtriangle, and sin θ2 = o/h = 1.2/1.5 forthe top triangle. Nowuse n1 sin θ1 = n2 sin θ2 … n1 (0.8/1.5) = (1) (1.2/1.5) … n1 = 1.2/0.8 = 3/2=1.5

8.geometricoptics.png

9GeometricOptics

A beam of light is directed toward point P on a boundary as shown to theright. Which segment best represents the refracted ray? D PA PB PC PD PE

Less–More bend towards. But it can’tbe E because that would only happen ifthe incomingangle was also 0.

9.geometricoptics.png

10GeometricOptics

Which of the following is NOT possible for the images formed by the lens intheaccompanying figure? E real and inverted

real and smaller insize

real and larger insize virtual and erect

virtual and smallerin size

The lens shown has thick in the centerand thin on the outside which makes aconverging lens. Inconverging lenses, all of the realimages are inverted and can be anysize, but the virtual imagesare formed in a magnifying lensscenario and are always larger andupright.

10.geometricoptics.png

11GeometricOptics

A narrow beam of monochromatic light enters a lens parallel tothe optic axis, as shown in the accompanying diagram. Whicharrow best represents the direction of the light after leaving thelens? E A B C D E

A horizontal beam approaching aconverging lens bends and convergesthrough the focal point.

11.geometricoptics.png

12GeometricOptics

The accompanying diagram shows the path that a light ray takes passingthrough three transparent materials. The indices of refraction in materials 1,2, and 3 are n1, n2, and n3, respectively. Which of the following bestdescribes the relation between the indices of refraction? E n1>n2>n3 n1>n3>n2 n2>n1>n3 n2 > n3 > n1 n3 > n1 > n2

More–Less dense bend away, Less–More dense bend towards. The morethe bend, the bigger thedifference in n’s.

12.geometricoptics.png

13GeometricOptics

Which diagram best represents what happens to a ray of light entering airfrom water? Air is at the top in alldiagrams. C

Assuming total internal reflection didn’thappen, More–Less dense bend away

13.geometricoptics.png

14GeometricOptics In order to produce and enlarged, upright image of an object, you could use a B

converging lensmore than onefocal length fromthe object.

converging lensless than one focallength from theobject

diverging lensmore than onefocal length fromthe object.

diverging lensexactly one focallength from theobject.

diverging lens lessthan one focallength from theobject

Need a magnifying glass which ischoice B.

15GeometricOptics

The critical angle in a transparent substance surrounded by air is 30°. Thespeed of light in the substance (inmultiples of 108 m/s) is most nearly B 1 1.5 2 3 6

Use ni sin θc = nr sin (90), nr=1 … ni =2, then n = c / v to find v.

16GeometricOptics

A beam of light traveling in glass (ng = 1.5) strikes a boundarywith air (na = 1.0) at point P. The angle of incidence is 60° asshown in the diagram. Which ray would best indicate the beam’spath after point P? E A B C D E

Generally when we go from more–lesswe should always check the criticalangle first rather thanassuming the ray will refract and bendaway. Choice D might be correct, butnot until we firstcheck the critical angle for total internalreflection. Use ni sin θc = nr sin (90),ni=1.5, nr=1θc = 41.8°. Since our incoming angle(60) is larger than the critical angle,total internal reflectionwill occur and you will get choice E.

16.geometricoptics.png

17GeometricOptics

A small light bulb is placed 20 cm to the right of a converging lens of focallength 10 cm. Which of thefollowing statements is NOT true about the image of the bulb formed by thelens? A It is virtual It is inverted

It is the same sizeas the bulb

It is 20 cm to theleft of the lens

It can be projectedon a screen

Using the math, 1/f = 1/do + 1/di, and M= – di / do … di +20 M = – 1 …

18GeometricOptics

An image is formed on a screen by a convergent lens. If the top half of thelens is then covered what willhappen to the image? A

the image isdimmer butotherwiseunchanged

the imagebecomes half asbig

only the top half ofthe image isproduced

only the bottomhalf of the image isproduced

the imagebecomes half asbig and is invertedfrom its originalposition.

When light from multiple locations passthrough a given part of a lens to forman image, only asmall portion of a lens is needed toform the image. The more of a lens, themore light rays thatcan be bent by it to each imagelocation. This simply makes the imagebrighter. By coveringhalf the lens, all of the incoming raysstill bend all the same ways but thereare less total raysbeing bent to given locations on theimage so it is dimmer. This can easilybe seen by looking ata lens that has only horizontal raysapproaching it. All of these raysconverge to the focal point;covering a portion of the lens stillfocuses the rays on the focal point, justless of them.

19GeometricOptics

A wave moves from one medium to as second medium with a different indexof refraction. Which of thefollowing wave properties would NEVER change? A frequency wavelength speed angle all will change Fact for refraction problems.

20GeometricOptics Specular reflection occurs whenever light is incident on A a smooth surface a rough surface

a boundarybetween highindex of refractionand low index ofrefraction materials

a boundarybetween low indexof refraction andhigh index ofrefraction materials

a boundarybetween any twotransparentsubstances,regardless of indexof refraction Fact about specular reflection.

21GeometricOptics

A beam of light passes from medium 1 to medium 2 tomedium 3 as shown in the diagram. What may beconcluded about the speed of light in each medium? A v3 > v1 > v2 v1 > v2 > v3 v1 > v3 < v2 v2 > v3 > v1 v2 > v1 > v3

More–Less dense bend away, Less–More dense bend towards. The morethe bend, the bigger thedifference in n’s … this shows that n2 >n1 > n3. More n means less speed sov3 > v1 > v2

21.geometricoptics.png

22GeometricOptics

After striking the lens shown in the diagram at right, thelight ray will most likely follow which path? C A B C D E

It’s a diverging lens so light bends awayfrom what the horizontal path would bewithout the lens.

22.geometricoptics.png

23GeometricOptics

An object is placed 10 cm in front of the center of a concave curved mirrorwith a radius of curvature of 10 cm.About how far from the mirror will the real image of the object be formed? C 0 cm 5 cm 10 cm 20 cm

No image isformed

The focal point is = R/2. Then use themath 1/f = 1/do + 1/di … and di = 10

24GeometricOptics

Light travels from material X with an index of refraction of n=1.5 to material Ywith an index of refraction ofn=2.0. If the speed of light in material Y is v, what is the speed of light inmaterial X? C 0.56 v 0.75 v 1.33 v 1.78 v 3.0 v

From n=c/v. n1 = c/v1 … 1.5 = c / vX …vXn= c / 1.52 = c/v2 … 2.0 = c / vY … vYThe problem defines v= c / 2Y = vSo v = c/2, c = 2v … then subbing thatinto the vx equation we have vX = (2v) /1.5 = 1.33 v

25GeometricOptics

A light ray is incident normal to a thin layer of glass. Giventhe figure, what is the minimum thickness of the glass thatgives the reflected light an orangish color(λ(air) orange light = 600nm) B 50 nm 100 nm 150 nm 200 nm 500 nm

First find the λ in the film. nair λair =nfilm λfilm … (1)(600) = (1.5) λglass …λglass = 400 nmAs the light travels through the twoboundaries, you get a ½λ phase shift(flip) at the firstboundary but no shift at the secondboundary. Therefore, you need to makeanother ½λ of phasedifference total by traveling in the filmthickness to produce constructiveinterference to reinforcethe orange wavelength. When the glassthickness is ¼ of the λ in the glass, thelight will travelup and down to make the extra ½λneeded. So ¼ of the λ in the glassgives you 100 nmthickness needed.

25.geometrioptics.png

26GeometricOptics

Two thin lenses each with a focallength of +10 cm are located 30 cmapart with their optical axes alignedas shown. An object is placed 35cm from the first lens. After thelight has passed through both lenses,at what distance from the secondlens will the final image be formed? C 65 cm 35 cm 27 cm 17 cm –14 cm

Do the math twice. For the first lens. 1/f= 1/do + 1/di … di = + 14 cm (real). Sothis first‘pre–image’ is formed 14 cm to the rightof the first lens, which means it is 16 cmfrom thesecond lens. Now redo the math usingthis ‘pre–image’ as the object located16 cm away fromthe second lens. 1/f = 1/do + 1/di … di= + 26.67 cm.

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27GeometricOptics

A jeweler can distinguish between a diamond and a piece of glass byobserving the critical angle of light in eachmaterial. Glass with an index of refraction of 1.52 has a critical angle of 41.1°while a diamond with an indexof refraction of 2.42 would have critical angle of: D 65.4° 38.9° 25.8° 24.4° 16.2°

Use ni sin θc = nr sin (90), diamond intoair, so nr=1 … (2.42) sin θc = (1) sin(90) … θc = 24.4°

28GeometricOptics What causes chromatic aberration in a glass lens B

A) Eachwavelength of lightreflects from thesurface of the lens

B) Eachwavelength of lightis refracted adifferent amountby the lens

C) White lightwaves interfereinside the lens

D) White lightwaves diffractaround the edge ofthe lens

E) Chromaticaberration occurswith mirrors, notlenses Fact about chromatic aberration.

29GeometricOptics

A converging lens forms a virtual image of a real object that is two times theobjects size. The converging lensis replaced with a diverging lens having the same size focal length. What isthe magnification of the imageformed by the diverging lens? C A) –1 B) –2/5 C) 2/3 D) 3/2 E) 5/2

The magnification is M=2. Using M = –di/ do… di= – 2do Lets assume a valueof do= 10, then di= – 20, and from 1/f =1/do + 1/di, the focal point is 20. Nowredo the math with the focal point forthe diverging lens being negative andthe new di= –6.67, giving a new M=0.67

30GeometricOptics

A beam of light travels through the air and strikes the surface ofwater at an angle of incidence of 45°. It continues through thewater and then strikes the bottom of a glass aquarium. Which ofthe following would be closest to the angle of refraction after thebeam enters the glass. The index of refraction of water is 1.3 andthat of glass is 1.5 E A) 55° B) 45° C) 38° D) 33° E) 28°.

Use ni sin θi = nr sin θr, air to water andfind θr. That θr is the θi for the secondwater to glass interface. Then do ni sinθi= nr sin θr, water to glass and find θr 30.geometricoptics

31GeometricOptics

Light shines from air into a clear material. When the light makes an angle ofincidence equal to 30°, the lightrefracts at an angle of 15°. If the light is shone from an angle of incidence of60°, what is the angle of refraction? B A) 19.5° B) 26.6° C) 30° D) 45° E) 60°

Use ni sin θi = nr sin θr, air to materialto find n of the material. Then redo theproblem with θr as the unknown andsolve for θr.

32GeometricOptics

An object is in front of a convex lens, at a distance less than the focal lengthfrom the lens. Its image is A

A) virtual andlarger than theobject.

B) real and smallerthan the object.

C) virtual andsmaller than theobject.

D) real and largerthan the object.

E) virtual and thesame size as theobject.

A convex lens is a converging lens.When the object is in front of the focalpoint, it acts as amagnifying glass.

33GeometricOptics

Light is incident normal to a thin layer of soap. Given the figure,what is the minimum thickness of the soap film that gives the soap abluish color (λair(blue) = 500 nm)? B A) 100 nm B) 200 nm C) 250 nm D) 400 nm E) 500 nm

Similar to question 25, except bothboundaries undergo phase shifts, so 1full extra wavelength isneeded using the soap thickness. Thisrequires the thickness to be ½ λsoapgiving the answer. 33.geometricoptics

34GeometricOptics If the frequency of a periodic wave is doubled, the period of the wave will be A A) halved B) quartered C) doubled D) quadrupled E) unchanged Frequency are period are inverses.

35GeometricOptics

For which of the following does one obtain an image of increased size from areal object? Take all focus andradius of curvature values as positive. D

(a) The object isplaced at aposition outsidethe radius ofcurvature for aconverging lens.

(b) The object isplaced at aposition outsidethe radius ofcurvature for adiverging lens.

(c) The object isplaced at aposition inside themagnitude of thefocus for aconcave lens.

(d) The object isplaced at aposition betweenthe focus andradius of curvaturefor a concavemirror.

(e) The object isplaced at aposition betweenthe focus and theradius of curvaturefor a convexmirror.

Draw ray diagrams for each, or makeup numbers and do the math for eachto see which works.

36GeometricOptics

A sound wave generated from a tuning fork of single frequency travels fromair (with speed of sound 340 m/s)into rock (with speed of sound 1500 m/s). Which statement is true about thewavelength and frequency of thesound as it passes from air to rock? D

A) The frequencyof the soundincreases and thewavelengthincreases.

B) The frequencyof the soundincreases and thewavelength isunchanged.

C) The frequencyof the sound isunchanged andthe wavelength isdecreased.

D) The frequencyof the sound isunchanged andthe wavelength isincreased

E) The frequencyof the sounddecreases and thewavelength isincreased.

When traveling between mediums,sound behaves opposite from light. Asgiven in the problemthe sound travels faster in the denserrock. When the sound speeds up, thewavelength increasesand the frequency stays the same.

37GeometricOptics

When a beam of white light passes through a prism, the exiting light is seenas a spectrum of visible colors. Thisphenomenon is known as B (A) diffraction (B) dispersion (C) interference (D) polarization (E) reflection This is a fact.

38GeometricOptics

Modern telescopes use mirrors, rather than lenses, to form images. Oneadvantage of mirrors over lenses is thatthe images formed by mirrors are not affected by: C

destructiveinterference

constructiveinterference

chromaticaberration

sphericalaberration

atmosphericrefraction

The defect in a lens is chromaticaberration.

39GeometricOptics A diverging lens produces an image of a real object. This image is B

virtual, larger thanthe object, andupright.

virtual, smallerthan the object,and upright.

virtual, smallerthan the object,and inverted.

real, smaller thanthe object, andinverted.

real, larger thanthe object, andinverted

Diverging lens always produces thesame object type no matter what.

40GeometricOptics

A light beam passes through the air and strikes the surface of a plastic block.Which pair of statements correctlydescribes the phase changes for the reflected wave and the transmittedwave? E A B C D E

The transmitted wave never has aphase change, but hitting the moredense block causes thereflection to flip 180 degrees

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41GeometricOptics

The diagram below shows the path taken by a monochromatic light raytraveling through three media. Thesymbols v1, λ1, and f1 represent the speed, wavelength, and frequency of thelight in Medium 1, respectively.Which of the following relationships for the light in the three media is true? E A B C D E

More–Less dense bend away, Less–More dense bend towards. The morethe bend, the bigger thedifference in n’s … this shows n2> n1> n3. More n means less speed, so v3> v1> v2 but thisis not a choice. Speed goes withwavelength, the larger the speed themore the λ, so λ3> λ1> λ2

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42GeometricOptics

A real object is located in front of a convex lens at a distance greater than thefocal length of the lens. What typeof image is formed and what is true of the image’s size compared to that ofthe object? B A B C D E

Based on various ray diagrams drawnwith the object behind the focal point,the image is alwaysreal but its size depends on where it isin location to the focal point

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43GeometricOptics

A thin film of thickness t and index of refraction 1.33 coats a glass with indexofrefraction 1.50 as shown to the right. Which of the following thicknesses t willnotreflect light with wavelength 640 nm in air? C 160 nm 240 nm 360 nm 480 nm 640 nm

First determine the λfilm. n1 λ1= nfilm λfilm … (1)(640) = (1.33) λfilm… λfilm = 481 nm.When the wave reaches each boundaryis undergoes a ½ λ phase shift at eachboundary so thisessentially cancels out the phase shift.To not reflect any light, we want to havedestructiveinterference. In order to get destructiveinterference we need to get a total of ½λ or 1 ½ λ or2 ½ λ … phase differences from movingin the film thickness. These phasedifferences require athickness equal to ¼λfilm , ¾ λfilm , 5/4λfilm … 360 nm thickness matches the¾λfilm possibility.

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44GeometricOptics

Which of the following wave properties cannot be demonstrated by all kindsof waves? A Polarization Diffraction Superposition Refraction Frequency Longitudinal waves cannot be polarized

45GeometricOptics

Lenses in fine quality cameras are coated to reduce the reflection from thelenses. If the coating material has anindex of refraction between that of air and glass, what thickness of coating willproduce the least reflection? A

one–quarter of thewavelength in thecoating

one–third of thewavelength in thecoating

one–half of thewavelength in thecoating

one wavelength inthe coating

the amount ofreflection isindependent of thethickness of thecoating.

For air–film–glass of progressivelyincreasing index, to produce destructiveinterference we need¼ of a wavelength in the coating. Seequestion 43 for the reason.

46GeometricOptics

A beam of light from the air is incident on a transparent block of material. Theangle of incidence is 49° whilethe angle of refraction is 30°. What is the velocity of light in the transparentmaterial? B

1.8 x 108m/s 2.0 x 108 m/s

2.3 x 108m/s

3.0 x 108m/s

4.5 x 108m/s

First use nisin θi= nrsin θrTo find nr. Then use n = c / v to find v.

47GeometricOptics

Light with a wavelength of 500 nm in a vacuum enters a liquid with an indexof refraction of 1.25 at an angle ofincidence of 40°. What would be the wavelength of the light in the liquid? B 320 nm 400 nm 500 nm 625 nm 780 nm

Use n1 λ1= n2 λ2 (1)(500) = (1.25) λ2

48GeometricOptics

Light strikes three different thin films, which are in air, as shown. If t denotesthe film thickness and λ denotesthe wavelength of the light in the film, which films will produce constructiveinterference as seen by theobserver? A I only II only III only II and III only I and III only.

For all three diagrams, there is a ½ λphase shift when entering the film butno phase shift whenexiting. To produce constructiveinterference, a total extra phasedifferent of ½ λ from moving inthe film thickness is needed so oddmultiples of ¼ λ will produceconstructive interference

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49GeometricOptics

The critical angle for a transparent material in air is 30°. The index ofrefraction of the material is most nearly E 0.33 0.5 1 1.5 2

nisin θc= nrsin (90) nisin (30) = (1) ni= 2

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50GeometricOptics

An object is placed as shown in the figure above. The center of curvature Cand the focal point F of thereflecting surface are marked. As compared with the object, the image formedby the reflecting surface is E erect and larger

erect and thesame size erect and smaller inverted and larger

inverted andsmaller Draw a ray diagram

51GeometricOptics When one uses a magnifying glass to read fine print, one uses a A

converging lens toproduce a virtualimage of the print

converging lens toproduce a realimage of the print

mirror to produce avirtual image of theprint

diverging lens toproduce a realimage of the print

diverging lens toproduce a virtualimage of the print

A magnifying glass is a lens, and isproduced by a converging lens. It isvirtual.

52GeometricOptics Which color of light is associated with the highestspeed in a vacuum? E Blue Green Red Violet

They are all thesame

All light waves are EM and travel atlight speed

53GeometricOptics

An illuminated object is placed 0.30 meter from a lens whose focal length is–0.15 meter. The image is D

inverted, real, and0.30 meter fromthe lens on theopposite side fromthe object

upright, virtual, and0.30 meter fromthe lens on theopposite side fromthe object

upright, real, and0.10 meter fromthe lens on thesame side as theobject

upright, virtual, and0.10 meter fromthe lens on thesame side as theobject

Using the math, 1/f = 1/do+ 1/di, and M = – di/ do… di= – 0.10 m, M = +0.33

54GeometricOptics

Which of the following CANNOT be accomplished by a single converging lenswith spherical surfaces? D

Converting aspherical wavefront into a planewave front

Converting a planewave front into aspherical wavefront

Forming a virtualimage of a realobject

Forming a realupright image of areal upright object

Forming a realinverted image of areal upright object

Converging lenses make real imagesbut they are always inverted

55GeometricOptics

The image of the arrow is larger than the arrow itself in which of the followingcases? A I only II only I and III only II and III only I, II and III

When in front of the focal point of aconverging lens, it acts as a magnifyingglass. The otheroptical instruments can never makelarger images.

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56GeometricOptics

A postage stamp is placed 30 centimeters to the left of a converging lens offocal length 60 centimeters. Where is the image of the stamp located? A

60 cm to the left ofthe lens

20 cm to the left ofthe lens

20 cm to the rightof the lens

30 cm to the rightof the lens

(E) 60 cm to theright of the lens

Using the math, 1/f = 1/do+ 1/di, di= –60, since its virtual, the image is onthe same side asthe object which is why it is in the left.You would look through this lens fromthe right side

57GeometricOptics

Light leaves a source at X and travels to Y along the path shown above.Which of the following statements iscorrect? E

The index ofrefraction is thesame for the twomedia.

Light travels fasterin medium 2 thanin medium 1.

Snell's law breaksdown at theinterface.

Light would arriveat Y in less time bytaking a straightline path from X toY than it doestaking the pathshown above.

Light leaving asource at Y andtraveling to Xwould follow thesame path shownabove, but inreverse.

A fact about refraction problems, theangles going one way would be thesame as the anglesgoing to other way assuming totalinternal reflection does not occur.

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58GeometricOptics

Which three of the glass lenses above, when placed in air, will cause parallelrays of light to converge? B I, II, and III I, III, and V I, IV, and V II, III, and IV II, IV, and V

Converging lenses have centers thatare thick and top and bottom parts thatare thinner.

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59GeometricOptics

An object is placed near a plane mirror, as shown above. Which of thelabeled points is the position of the image? E A B C D E

In flat (plane) mirrors, the image issimply flipped to the other side of themirror.

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60GeometricOptics

Observations that indicate that visible light has a wavelength much shorterthan a centimeter include which ofthe following? C I only III only I and II only II and III only I, II, and III

Choice I. is true because a soap bubbleis a thin film. The colors produced aredue to the reinforcement of different λcolors due to variations in the thicknessof the soap bubble. In order to seethese interference results, the thicknessof the film must be similar in magnitudeto the wavelength of the light. Since thefilm is so small, this shows that light hasa very small wavelength. Choice II. alsoshows light has a very smallwavelength because a diffractiongrating has very tiny slits in it and toproduce the pattern seen thewavelength of the light has to be on asimilar scale as the size of theopenings. Choice III. is not truebecause all waves regardless of theirwavelength bend and it does not reflecton their wavelength size.

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61GeometricOptics

If the object distance for a converging thin lens is more than twice the focallength of the lens, the image is D virtual and erect

larger than theobject

located inside thefocal point

located at adistance between fand 2f from thelens

located at adistance more thanf from the lens

From practicing ray diagrams, thisshould be known. Or a sample could bedone to determine it. Mathematicallythis can be shown by using an extremeexample. Suppose do = 1000, and f =10. Using the lens equation, di = 10.1.Then decrease do down to 20 and di =20. So for the range of values of dolarger than 20, the image distance willfall between 10–20 which is between fand 2f.

62GeometricOptics

A concave mirror with a radius of curvature of 1.0 m is used to collect lightfrom a distant star. The distance between the mirror and the image of the staris most nearly B 0.25 m 0.50 m 0.75 m 1.0 m 2.0 m

Light from a distantstar is assumed tobe all horizontal. Horizontal light hittinga concave mirror will all converge at thefocal point to form an image of the stardirectly on the focal point. With a radiusof curvature = 1m, the focal point is 0.5m.

63GeometricOptics

When light passes from air into water, the frequency of the light remains thesame. What happens to the speed and the wavelength of light as it crossesthe boundary in going from air into water? E A B C D E

When light goes in higher indices ofrefraction, itslows down. Since v = f λand f remains constant, when vdecreases λ decrease with it.

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64GeometricOptics

A physics student places an object 6.0 cm from a converging lens of focallength 9.0 cm. What is the magnitude of the magnification of the imageproduced? D 0.6 1.5 2 3 3.6

Using the math, 1/f = 1/do + 1/di, di =–18 … then M = – di / do … M = 3

65GeometricOptics

An object is placed at a distance of 1.5f from a converging lens of focal lengthf, as shown. What type of image is formed and what is its size relative to theobject? D A B C D E

Draw the ray diagram, or makeup somenumbers and do the math

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66GeometricOptics

A light ray passes through substances 1, 2, and 3, as shown. The indices ofrefraction for these three substances are n1, n2, and n3, respectively. Raysegments in 1 and in 3 are parallel. From the directions of the ray, one canconclude that A

n3 must be thesame as n1

n2 must be lessthan n1

n2 must be lessthan n3

n1 must be equalto 1.00

all three indicesmust be the same

If the angle in equals the angle out in a3 tier medium arrangement, then thesubstances on the outsides must be thesame.

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67GeometricOptics

A beam of white light is incident on a triangular glass prism with an index ofrefraction of about 1.5 for visible light, producing a spectrum. Initially, theprism is in a glass aquarium filled with air, as shown above. If the aquarium isfilled with water with an index of refraction of 1.3, which of the following istrue? E

No spectrum isproduced.

A spectrum isproduced, but thedeviation of thebeam is oppositeto that in air.

The positions ofred and violet arereversed in thespectrum.

The spectrumproduced hasgreater separationbetween red andviolet than thatproduced in air.

The spectrumproduced has lessseparationbetween red andviolet than thatproduced in air.

The larger the difference between n’sthe more the rays bend. When thewater is added, the difference betweenn’s is less so the amount of bending isless.

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68GeometricOptics

An object, slanted at an angle of 45°, is placed in front of a vertical planemirror, as shown above. Which of the following shows the apparent positionand orientation of the object's image? D A B C D E

In a flat mirror, the image can be foundby flipping the object to the other side,basically folding it over the mirror ontothe other side.

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69GeometricOptics

The spherical mirror shown has a center of curvature at point c. Which pointis nearest to the focal point? B A B C D E

The focal point is half the center ofcurvature.

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70GeometricOptics

An object is placed in front of a converging thin lens at a distance from thecenter of the lens equal to half the focal length. Compared to the object, theimage is A upright and larger upright and smaller inverted and larger

inverted andsmaller

inverted and thesame size

When an object is placed in front of thefocal point of a converging lens, thelens acts as a magnifying glass.

71GeometricOptics Which of the following is characteristic of both sound and light waves? E

They arelongitudinal waves.

They aretransverse waves.

They travel withthe same velocity.

They can be easilypolarized

They give rise tointerference effects All waves demonstrate interference.

72GeometricOptics

A thin film with index of refraction n1separates two materials, each of which hasan index of refraction less than nf. Amonochromatic beam of light is incidentnormally on the film, as shown above. If thelight has wavelength λ within the film,maximum constructive interference betweenthe incident beam and the reflected beamoccurs for which of the following filmthicknesses? E 3λ 2λ λ λ/2 λ/4

The film has a higher n compared toboth sides, such as soap surrounded byair. So as the light ray hits the firstboundary it makes a ½ λ phase flip, butdoes not make the flip at the secondboundary. To be constructive, we needto cover a total of ½ λ extra phase shiftdue to traveling in the film thickness. Sothe thickness should be ¼ λ.

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73GeometricOptics

A light ray R in medium I strikes a sphere of medium II with angle of incidenceθ, as shown above. The figure shows five possible subsequent paths for thelight ray. Which path is possible if medium I is air and medium II is glass? E A B C D E

Medium I (air) is surrounding thesphere on both sides. As it enters thesphere, it goes less–more so bendstowards the normal line (leaving D or Eas the possibly answers). When the rayreaches the far edge of the sphere, itgoes from more–less so should bendaway from the normal line.

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74GeometricOptics

A light ray R in medium I strikes a sphere of medium II with angle of incidenceθ, as shown above. The figure shows five possible subsequent paths for thelight ray. Which path is possible if medium I is glass and medium II is air? A A B C D E

This should be the opposite of thescenario in the last question.

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75GeometricOptics

An object is placed on the axis of a converging thin lens of focal length 2 cm,at a distance of 8 cm from the lens.The distance between the image and thelens is most nearly E 0.4 cm 0.8 cm 1.6 cm 2.0 cm 2.7 cm

Using the math, 1/f = 1/do + 1/di, di =2.67.

76GeometricOptics

A large lens is used to focus an image of an object onto a screen. If the lefthalf of the lens is covered with a dark card, which of the following occurs D

The left half of theimage disappears

The right half ofthe imagedisappears

The imagebecomes blurred

The imagebecomes dimmer

No image isformed

When light from multiple locations passthrough a given part of a lens to forman image, only a small portion of a lensis needed to form the image. The moreof a lens, the more light rays that canbe bent by it to each image location.This simply makes the image brighter.By covering half the lens, all of theincoming rays still bend all the sameways but there are less total rays beingbent to given locations on the image soit is dimmer. This can easily be seen bylooking at a lens that has onlyhorizontal rays approaching it. All ofthese rays converge to the focal point;covering a portion of the lens stillfocuses the rays on the focal point, justless of them.

77GeometricOptics

Which of the following statements are true for both sound waves andelectromagnetic waves? E A B C D E

All waves demonstrate the listedchoices.

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78GeometricOptics

As shown, a beam of white light is separated into separatecolors when it passes through a glass prism. Red light isrefracted through a smaller angle than violet light becausered light has a B

slower speed inglass than violetlight

faster speed inglass than violetlight

slower speed inthe incident beamthan violet light

faster speed in theincident beam thanviolet light

greater intensitythan violet light

Bending of a wave (refraction) is due tothe speed change at an angle. Themore the speedchange, the more the bending. Hence,the violet bends more so must have alarger speed change(more slowing), so the red is faster.Additionally, we can note that since theviolet slows andbends more, the index of refraction inglass for a violet light is higher than theindex for a redlight.

78.geometricoptics.png

79GeometricOptics

A ray of light in glass that is incident on an interface with ice,as shown, is partially reflected and partially refracted. Theindex of refraction n for each of the two media is given inthe figure. How do the angle of reflection and the angle ofrefraction compare with the angle of incidence θ ? A A B C D E

Based on the law of reflection, theangle of reflection must be the same asthe incoming angle.When the light enters the ice it is goingmore–less so bends away from thenormal. This meansthat θr is larger than θi.

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80GeometricOptics

If the focal length of the lens is 0.40 m and point P is0.30 m to the left of the lens, where is the image of theobject located? A

1.2 m to the left ofthe lens

0.17 m to the leftof the lens At the lens

0.17 m to the rightof the lens

1.2 m to the rightof the lens

Using the math, 1/f = 1/do+ 1/di, di= –1.2. Its virtual so its on the sameside as the object,which puts the image on the left side ofthe lens.

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81GeometricOptics

Which of the following characterizes the image when the object is in theposition shown? D

Real, inverted, andsmaller than theobject

Real, upright, andlarger than theobject

Real, inverted, andlarger than theobject

Virtual, upright,and larger than theobject

Virtual, upright,and smaller thanthe object

This is a magnifying glass, which canbe memorized or the math can be doneto prove theanswer.

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82GeometricOptics

On a day when the speed of sound is 340 m/s, a ship sounds its whistle. Theecho of the sound from the shore isheard at the ship 6.0 s later. How far is the ship from the shore? C 56.7 m 113 m 1020 m 2040 m 4080 m

The time for the sound to travel the oneway distance to the shore is half of thetotal time(6/2 =3 sec). Then use v= d /t todetermine the distance.

83GeometricOptics

A ray of light in air is incident on a 30-°60°-90° prism,perpendicular to face ab, as shown in the diagram. The ray entersthe prism and strikes face ac at the critical angle. What is theindex of refraction of the prism? C 1/2/2013 sqrt(3/2) (2sqrt3)/3 2 3

From the diagram, the angle at thebottom of the small top triangle is 30°so when we draw thenormal line on that slanted interface,the angle of incidence there is 60°. Weare told this is thecritical angle which means the angle ofrefraction of the scenario is 90°. Nowwe usenisin θc= nrsin (90) … nisin(60) = (1)(1) … ni= 1/ sin 60 … ni1/ (root3 / 2) Rationalizing gives us the answer.

83.geometricoptics.png

1 Kinematics

A car travels 30 miles at an average speed of 60 miles per hour and then 30miles at an average speed of 30miles per hour. The average speed the car over the 60 miles is B 35 m.p.h. 40 m.p.h. 45 m.p.h. 10 m.p.h. 53 m.p.h.

Total distance = 60 miles, total time =1.5 hours; average speed = totaldistance/total time

2 Kinematics Which particle is farthest from the origin at t = 2 seconds B A B

they are in thesame location at t= 2 seconds

They are the samedistance from theorigin, but inopposite directions

It is not possible todetermine

Area bounded by the curve is thedisplacement By inspection of particle Athe positive areabetween 0 and 1s will be countered byan equal negative area between 1 and2s. 2-4.kinematics.png

3 Kinematics Which particle moves with constant non-zero acceleration? D A B both A and B neither A nor BIt is not possible todetermine

Constant non-zero acceleration wouldbe a straight line with a non-zero slope 2-4.kinematics.png

4 Kinematics Which particle is in its initial position at t = 2 seconds? A A B both A and B neither A nor B It is not possibleto determine

Area bounded by the curve is thedisplacement By inspection of particle Athe positive areabetween 0 and 1s will be countered byan equal negative area between 1 and2s. 2-4.kinematics.png

5 Kinematics

The graph above shows the velocity versus time for an object moving in astraight line. At what time after t = 0 does the object again pass through itsinitial position? C

Between 0 and 1 s

1 s Between 1 and 2 s 2 s

Between 2 and 3 s

Area bounded by the curve is thedisplacement By inspection thenegative area between 0 and 1swill be countered by an equal negativearea sometime between 1 and 2s. 5.kinematics.png

6 Kinematics

A body moving in the positive x direction passes the origin at time t =0. Between t = 0 and t = 1 second, the body has a constant speed of 24meters per second. At t = 1 second, the body is given a constantacceleration of 6 meters per second squared in the negative x direction.The position x of the body at t = 11 seconds is C #ERROR!:parse #ERROR!:parse – 36 m – 75 m – 99 m

Between 0 and 1 s; d1= vt; from 1 to 11seconds; d2= v0t + ½ at2; d = d1+ d2

7 KinematicsThe displacement, x, of an object moving along the x-axis is shown above asa function of time, t. The acceleration of this object must be A zero

constant but notzero increasing decreasing equal to g

Since the slope is positive andconstant, so is the velocity, thereforethe acceleration must be zero 7.kinematics.png

8 Kinematics

A 2-kilogram block rests at the edge of a platform that is 10 meters abovelevel ground. The block is launched horizontally from the edge of the platformwith an initial speed of 3 meters per second. Air resistance is negligible. Thetime it will take for the block to reach the ground is most nearly C 0.3 s 1.0 s 1.4 s 2.0 s 3.0 s

For a horizontal projectile, the initialspeed does not affect the time in theair. Use v0y = 0 with10 m = ½ gt^2

9 Kinematics

A diver initially moving horizontally with speed v dives off the edge of avertical cliff and lands in the water adistance d from the base of the cliff. How far from the base of the cliff wouldthe diver have landed if the diverinitially had been moving horizontally with speed 2v? C d (2d)^1/2 2d 4d

can’t bedetermined withoutknowing the heightof the cliff

The time in the air for a horizontalprojectile is dependent on the heightand independent of theinitial speed. Since the time in the air isthe same at speed v and at speed 2v,the distance (d = vt)will be twice as much at a speed of 2v

10 Kinematics

. A truck traveled 400 meters north in 80 seconds, and then it traveled 300meters east in 70 seconds. Themagnitude of the average velocity of the truck was most nearly B 1.2 m/s 3.3 m/s 4.6 m/s 6.6 m/s 9.3 m/s

Average velocity = totaldisplacement/total time; magnitude oftotal displacement = 500 m (3-4-5triangle) and total time = 150 seconds 10.kinematics.png

11 Kinematics

A projectile is fired with initial velocity v at an angle θ with the horizontal andfollows the trajectory shownabove. Which of the following pairs of graphs best represents the verticalcomponents of the velocity andacceleration, v and a, respectively, of the projectile as functions of time t? D (A) (B) (C) (D) (E)

The acceleration is constant andnegative which means the slope of thevelocity time graph must have aconstant negative slope. (Only onechoice has the correct accelerationanyway) 11.kinematics.png

12 Kinematics

An object is released from rest on a planet that has no atmosphere. Theobject falls freely for 3.0 meters in thefirst second. What is the magnitude of the acceleration due to gravity on theplanet? C 1.5 m/s2 3.0 m/s2 6.0 m/s2 10.0 m/s2 12.0 m/s2 From rest, h = ½ gt^2

13 Kinematics How do the speeds of the ball at the three points compare? D (A) (B) (C) (D) (E)

At the top of its path, the verticalcomponent of the velocity is zero, whichmakes the speed at the top a minimum.With symmetry, the projectile has thesame speed when at the same height,whether moving up or down. 13.kinematics.png

14 KinematicsWhich of the following diagrams best shows the direction of the accelerationof the ball at point P? E (A) (B) (C) (D) (E)

g points down in projectile motion.Always. 14.kinematics.png

15 Kinematics

A rock of mass m is thrown horizontally off a building from a height h, asshown above. The speed of the rock as it leaves the thrower’s hand at theedge of the building is v0. How much time does it take the rock to travel fromthe edge of the building to the ground? E (A) (B) (C) (D) (E)

For a horizontal projectile; h = ½ gt2E(initial vertical component of velocity iszero) 15.kinematics.png

16 KinematicsA ball is thrown straight up in the air. When the ball reaches its highest point,which of the following is true? E It is in equilibrium.

It has zeroacceleration.

It has maximummomentum

It has maximumkinetic energy. None of the above

At every point of a projectiles free-fall,the acceleration is the acceleration dueto gravity

17 Kinematics

The graph above represents position x versus time t for an object being actedon by a constant force. The average speed during the interval between 1 sand 2 s is most nearly D 2 m/s 4 m/s 5 m/s 6 m/s 8 m/s

Average speed = total distance/totaltime = (8 m – 2 m)/(1 second) 17.kinematics.png

18 Kinematics

An object slides off a roof 10 meters above the ground with an initialhorizontal speed of 5 meters per second as shown above. The time betweenthe object's leaving the roof and hitting the ground is most nearly C (A)

(B) (C) (D) (E)

For a horizontal projectile; h = ½ gt2C(initial vertical component of velocity iszero) 18.kinematics.png

19 Kinematics Which of the following is true at time t = 20 seconds? ACar Y is behind carX.

Car Y is passingcar X.

Car Y is in front ofcar X.

Both cars have thesame acceleration.

Car X isaccelerating fasterthan car Y.

The area under the curve is thedisplacement. There is more areaunder the curve for Car X. 19.kinematics.png

20 KinematicsFrom time t = 0 to time t = 40 seconds, the areas under both curves areequal. Therefore, which of the following is true at time t = 40 seconds? B

Car Y is behind carX.

Car Y is passingcar X.

Car Y is in front ofcar X.

Both cars have thesame acceleration.

Car X isaccelerating fasterthan car Y.

Area under the curve is thedisplacement. Car Y is moving fasteras they reach the same point. 20.kinematics.png

21 KinematicsWhich of the following pairs of graphs shows the distance traveled versustime and the speed versus time for an object uniformly accelerated from rest? E (A) (B) (C) (D) (E)

Uniformly accelerated means thespeed-time graph should be a strightline with non-zero slope. Thecorresponding distance-time graphshould have an increasing slope (curveupward) 21.kinematics.png

22 Kinematics

An object released from rest at time t = 0 slides down a frictionless incline adistance of 1 meter during the first second. The distance traveled by theobject during the time interval from t = 1 second to t = 2 seconds is C 1 m 2 m 3 m 4 m 5 m

From the equation d = ½ at2C ,displacement is proportional to timesquared. Traveling from rest for twicethe time gives 4 times the displacement(or 4 m). Since the object alreadytravelled 1 m in the first second, duringthe time interval from 1 s to 2 s theobject travelled the remaining 3 m

23 Kinematics

Two people are in a boat that is capable of a maximum speed of 5 kilometersper hour in still water, and wish to cross a river 1 kilometer wide to a pointdirectly across from their starting point. If the speed of the water in the riveris 5 kilometers per hour, how much time is required for the crossing? E 0.05 hr 0.1 hr 1 hr 10 hr

The point directlyacross from thestarting pointcannot be reachedunder theseconditions.

To travel straight across the river, theupstream component of the boat’svelocity must cancel the current. Sincethe speed of the current is the same asthe speed of the boat, the boat musthead directly upstream to cancel thecurrent, which leaves no componentacross the river

24 Kinematics

A projectile is fired from the surface of the Earth with a speed of 200 metersper second at an angle of 30° above the horizontal. If the ground is level,what is the maximum height reached by the projectile? C 5 m 10 m 500 m 1,000 m 2,000 m

viy = 200 m/s sin 30º = 100 m/s. Atmaximum height vy = 0. Use vy2 =viy2C + 2gh

25 Kinematics

Vectors V1 and V2 shown above have equal magnitudes. The vectorsrepresent the velocities of an object attimes t1, and t2, respectively. The average acceleration of the object betweentime t1 and t2 E (A) zero (B) directed north (C) directed west

(D) directed northof east

(E) directed northof westwas

Acceleration is proportional to Δv. Δv =v2 – v1 = v2 + (– v1) 25.kinematics.png

26 Kinematics

A rock is dropped from the top of a 45-meter tower, and at the same time aball is thrown from the top of thetower in a horizontal direction. Air resistance is negligible. The ball and therock hit the level ground adistance of 30 meters apart. The horizontal velocity of the ball thrown wasmost nearly B (A) 5 m/s (B) 10 m/s (C) 14.1 m/s (D) 20 m/s (E) 28.3 m/s

From a height of 45 m (= ½ gt2) it takes3 seconds to strike the ground. In thattime, the ball thrown traveled 30 m. v =d/t

27 Kinematics

In the absence of air friction, an object dropped near the surface of the Earthexperiences a constant accelerationof about 9.8 m/s2 This means that the A

(A) speed of theobject increases9.8 m/s duringeach second

(B) speed of theobject as it falls is9.8 m/s.

(C) object falls 9.8meters duringeach second

(D) object falls 9.8meters during thefirst second only

(E) rate of changeof thedisplacement withrespect to time forthe object equals9.8 m/s2

9.8 m/s2 can be thought of as a changein speed of 9.8 m/s per second.

28 Kinematics

A 500-kilogram sports car accelerates uniformly from rest, reaching a speedof 30 meters per second in 6seconds. During the 6 seconds, the car has traveled a distance of D 15 m 30 m 60 m 90 m 180 m

vi = 0 m/s; vf = 30 m/s; t = 6 s; v = (vi +vf)/2 = d/t

29 Kinematics

At a particular instant, a stationary observer on the ground sees a packagefalling with speed v1 at an angle tothe vertical. To a pilot flying horizontally at constant speed relative to theground, the package appears to befalling vertically with a speed v2 at that instant. What is the speed of the pilotrelative to the ground? D (A) v1 + v2 ( B) v1 – v2 (C) v2 – v1

(D) (v1^2 −v2^2)^1/2

(E)( v1^2 +v2^2)^1/2

velocity of package relative to observeron ground vpg = v1 =velocity of package relative to pilot vpp= v2 =velocity of pilot relative to ground vpo =Putting these together into a righttriangle yields vpg^2 + v2^2 = v1^2

30 Kinematics

An object is shot vertically upward into the air with a positive initial velocity.Which of the following correctlydescribes the velocity and acceleration of the object at its maximumelevation? D A B C D E

While the object momentarily stops atits peak, it never stops acceleratingdownward. 30.kinematics.png

31 Kinematics

A spring-loaded gun can fire a projectile to a height h if it is fired straight up. Ifthe same gun is pointed at anangle of 45° from the vertical, what maximum height can now be reached bythe projectile? C h/4 h/(2*2^1/2) h/2 h/(2^1/2) h

Maximum height of a projectile is foundfrom vy = 0 at max height and vy^2 =viy^2 + 2gh and gives hmax = viy^2/2g= (vi sin)^2/2g. Fired straight up, theangle = 90 and we have vi = (2gh)^1/2.Plugging this initial velocity into theequation for a 45º angle (sin 45 = 1/(2^1/2)) gives hnew = ( (2gh)^1/2 * 1/(2^1/2) )^2 /2g = h/2

32 Kinematics

A ball is thrown and follows a parabolic path, as shown above. Air friction isnegligible. Point Q is the highestpoint on the path. Which of the following best indicates the direction of theacceleration, if any, of the ball atpoint Q? C A B C D E

g points down in projectile motion.Always. 32.kinematics.png

33 Kinematics

The velocity of a projectile at launch has a horizontal component vh and avertical component vv. Air resistanceis negligible. When the projectile is at the highest point of its trajectory, whichof the following shows thevertical and horizontal components of its velocity and the vertical componentof its acceleration? E A B C D E

horizontal velocity vx remains the samethorughout the flight. g remains thesame as well. 33.kinematics.png

34 Kinematics

The graph above shows the velocity v as a function of time t for an objectmoving in a straight line. Which ofthe following graphs shows the corresponding displacement x as a function oftime t for the same time interval? D A B C D E 34.kinematics..png

35 Kinematics

An object is dropped from rest from the top of a 400 m cliff on Earth. If airresistance is negligible, what is thedistance the object travels during the first 6 s of its fall? D 30 m 60 m 120 m 180 m 360 m For a dropped object: d = ½ gt2

36 Kinematics

A target T lies flat on the ground 3 m from the side of a building that is 10 mtall, as shown above. A studentrolls a ball off the horizontal roof of the building in the direction of the target.Air resistance is negligible. Thehorizontal speed with which the ball must leave the roof if it is to strike thetarget is most nearly C 3/10 m/s √2 m/s 3/√2 m/s 3 m/s 10 √(5/3) m/s

For a horizontal projectile, the initialspeed does not affect the time in theair. Use v0y = 0 with 10 m = ½ gt2 toget 2t = For the horzontal part of themotion; v = d/t 36.kinematics.png

37 Kinematics

The graph above shows velocity v versus time t for an object in linear motion.Which of the following is apossible graph of position x versus time t for this object? A A B C D E

A velocity-time graph represents theslope of the displacement-time graph.Analyzing the v-t graph shows aconstant slope, then a decreasing slopeto zero, becoming negative andincreasing, then a constant slope. Notethis is an analysis of the values of v, notthe slope of the graph itself 37.kinematics.png

38 Kinematics

A student is testing the kinematic equations for uniformly accelerated motionby measuring the time it takes forlight-weight plastic balls to fall to the floor from a height of 3 m in the lab. Thestudent predicts the time to fallusing g as 9.80 m/s2 but finds the measured time to be 35% greater. Whichof the following is the most likelycause of the large percent error? D

The accelerationdue to gravity is70% greater than9.80 m/s2 at thislocation.

The accelerationdue to gravity is70% less than 9.80m/s2 at thislocation.

Air resistanceincreases thedownwardacceleration.

The acceleration ofthe plastic balls isnot uniform.

The plastic ballsare not trulyspherical.

By process of elimination (A and B areunrealistic; C is wrong, air resistanceshould decrease the acceleration; E isirrelevant)

39 Kinematics

An object is thrown with velocity v from the edge of a cliff above level ground.Neglect air resistance. In orderfor the object to travel a maximum horizontal distance from the cliff beforehitting the ground, the throw shouldbe at an angle θ with respect to the horizontal of C

greater than 60°above thehorizontal

greater than 45°but less than 60°above thehorizontal

greater than zerobut less than 45°above thehorizontal zero

greater than zerobut less than 45°below thehorizontal

The 45° angle gives the maximumhorizontal travel to the originalelevation, but the smaller angle causesthe projectile to have a greaterhorizontal component of velocity, sogiven the additional time of travel allowssuch a trajectory to advance a greaterhorizontal distance. In other wordsgiven enough time the smaller angle oflaunch gives a parabola which willeventual cross the parabola of the 45°launch. 39.kinematics.png

40 Kinematics

Starting from rest at time t = 0, a car moves in a straight line with anacceleration given by the accompanyinggraph. What is the speed of the car at t = 3 s? D 1.0 m/s 2.0 m/s 6.0 m/s 10.5 m/s 12.5 m/s

The area under the curve of anacceleration-time graph is the changein speed. 40.kinematics.png

41 Kinematics

A flare is dropped from a plane flying over level ground at a velocity of 70 m/sin the horizontal direction. At the instant the flare is released, the plane beginsto accelerate horizontally at 0.75 m/s2. The flare takes 4.0 s to reach theground. Assume air resistance is negligible. Relative to a spot directly underthe flare at release, the flare lands D

directly on thespot.

6.0 m in front ofthe spot.

274 m in front ofthe spot.

280 m in front ofthe spot.

286 m in front ofthe spot

In the 4 seconds to reach the ground,the flare travelled 70 m/s × 4 s = 280 mhorizontally.

42 KinematicsAs seen by the pilot of the plane (in question #41) and measured relative to aspot directly under the plane when the flare lands, the flare lands B

286 m behind theplane.

6.0 m behind theplane.

directly under theplane.

12 m in front of theplane.

274 m in front ofthe plane

In the 4 seconds to reach the ground,the flare travelled 70 m/s × 4 s = 280 mhorizontally. The plane travelled d = vit+ ½ at2 = (70 m/s)(4 s) + (0.5)(0.75m/s2)(4 s)2B = 280 m + 6 m, or 6 mahead of the flare.

43 KinematicsThe graph above is a plot of position versus time. For which labeled region isthe velocity positive and the acceleration negative? E A B C D E

Positive velocity = positive slope.Negative acceleration = decreasingslope (or downward curvature 43.kinematics.png

44 Kinematics

A child left her home and started walking at a constant velocity. After a timeshe stopped for a while and then continued on with a velocity greater thanshe originally had. All of a sudden she turned around and walked very quicklyback home. Which of the following graphs best represents the distanceversus time graph for her walk? B A B C D E

The slope of the line represents hervelocity. Beginning positive andconstant, going to zero, then positiveand larger than the initial, then negativewhile the line returns to the time axis 44.kinematics.PNG

45 Kinematics

In a rescue attempt, a hovering helicopter drops a life preserver to a swimmerbeing swept downstream by ariver current of constant velocity v. The helicopter is at a height of 9.8 m. Theswimmer is 6.0 m upstream froma point directly under the helicopter when the life preserver isreleased. Itlands 2.0 m in front of the swimmer.How fast is the current flowing? Neglect air resistance. D 13.7 m/s 9.8 m/s 6.3 m/s 2.8 m/s 2.4 m/s

Dropped from a height of 9.8 m, the lifepreserver takes (9.8 m = ½ gt2); t = 1.4 seconds to reach the water. Inthat 1.4 seconds the swimmer covered(6.0 m – 2.0 m) = 4.0 m meaning thewaterspeed is (4.0 m)/(1.4 s)

46 Kinematics

A child tosses a ball directly upward. Its total time in the air is T. Its maximumheight is H. What is its heightafter it has been in the air a time T/4? Neglect air resistance. E H/4 H/3 H/2 2H/3

3H/4

The ball takes time T/2 to reach heightH. Using vy= 0 at maximum height andd/t gives the initial speed as 4H/T. Inaddition from the top H = ½ g(T/2)2=gT2/8. Plugging in a time T/4 gives d=(4H/T)(T/4) + ½ (–g)(T/4)2= H – ¼(gT2/8) = ¾ H

47 Kinematics

A whiffle ball is tossed straight up, reaches a highest point, and falls backdown. Air resistance is not negligible.Which of the following statements are true? A I only II only I & II only I & III only I, II, & III

While the object momentarily stops atits peak, it never stops acceleratingdownward. Withoutair resistance, symmetry dictates timeup = time down. With air resistanceconsidered, the ballwill have a larger average velocity onthe way up and a lower averagevelocity on the way downsince it will land with a smaller speedthan it was thrown, meaning the balltakes longer to fall. 47.kinematics.PNG

48 Kinematics

A truck driver travels three-fourths the distance of his run at one velocity (v)and then completes his run at onehalf his original velocity (½v). What was the trucker’s average speed for thetrip? B 0.85v 0.80v 0.75v 0.70v 0.65v

Total distance = d. Time for first ¾ d ist1= (¾d)/v = 3d/4v. Time for second partis t2= (¼ d)/(½ v) = 2d/4v. Total time is thent1+ t2= 5d/4v. Average speed = d/(5d/4v) 48.kinematics.PNG

49 Kinematics

Above is a graph of the distance vs. time for car moving along a road.According the graph, at which of thefollowing times would the automobile have been accelerating positively? C

0, 20, 38, & 60min.

5, 12, 29, & 35min. 5, 29, & 57 min. 12, 35, & 41 min.

at all times from 0to 60 min

Positive acceleration is an increasingslope (including negative slopeincreasing toward zero) orupward curvature

50 Kinematics

A large beach ball is dropped from the ceiling of a school gymnasium to thefloor about 10 meters below.Which of the following graphs would best represent its velocity as a functionoftime? (do not neglect airresistance) D A B C D E

With air resistance, the acceleration(the slope of the curve) will decreasetoward zero as the ballreached terminal velocity. Note: withoutair resistance, choice (A) would becorrect 50.kinematics.PNG

51 Kinematics At what time would the car be moving with the greatest velocity? C 0 sec 2 sec 4 sec 6 sec 8 sec

Since for the first 4 seconds, the car isaccelerating positively the entire time,the car will bemoving fastest just beofre slowing downafter t = 4 seconds. 51.kinematics.PNG

52 Kinematics At what time would the car be farthest from its original starting position? E 0 sec 2 sec 4 sec 6 sec 8 sec

The area under the curve representsthe change in velocity. The car beginsfrom rest with anincreasing positive velocity, after 4seconds the car begins to slow and thearea under the curvefrom 4 to 8 seconds couters theincrease in velocity form 0 to 4seconds, bringing the car to rest.However, the car never changeddirection and was moving away from itsoriginal startingposition the entire time. 52.kinematics.PNG

53 Kinematics

A ball is dropped 1.0 m to the floor. If the speed of the ball as it reboundsfrom the floor is 75% of the speed atwhich it struck the floor, how high will the ball rise? C 0.28 m 0.35 m 0.56 m 0.75 m 0.84 m

The ball will land with a speed given bythe equaion v2= vi2+ 2gH or v = 2gH.Rebounding with ¾ the speed gives anew height of vf= 0 = ( ¾ 2gH )2+ 2(–g)hnew

54 Kinematics

. Which of the following sets of graphs might be the corresponding graphs ofPosition, Velocity, andAcceleration vs. Time for a moving particle? C A B C D E

The velocity-time graph shouldrepresent the slope of the position-timegraph and theacceleration-time graph shouldrepresent the slope of the velocity-timegraph 54.kinematics.PNG

55 Kinematics

An object is thrown with a fixed initial speed v0 at various angles α relative tothe horizon. At some constant height h above the launch point the speed v ofthe object is measured as a function of the initial angle α. Which of thefollowing best describes the dependence of v on α? (Assume that the heighth is achieved, and assume that there is no air resistance.) C

v will increasemonotonically withα.

v will increase tosome critical valuevmax and thendecrease.

v will remainconstant,independent of α.

v will decrease tosome critical valuevmin and thenincrease. None of the above.

It’s a surprising result, but while boththe horizontal and vertical componentschange at a givenheight with varying launch angle, thespeed (vx2 + vy2)1/2 will beindependent of α (try it!)

56 Kinematics

A bird is flying in a straight line initially at 10 m/s. It uniformly increases itsspeed to 15 m/s while covering a distance of 25 m. What is the magnitude ofthe acceleration of the bird? B 5.0 m/s2 2.5 m/s2 2.0 m/s2 0.5 m/s2 0.2 m/s2 vf2=vi2+2ad

57 Kinematics

A person standing on the edge of a fire escape simultaneously launches twoapples, one straight up with a speed of 7 m/s and the other straight down atthe same speed. How far apart are the two apples 2 seconds after they werethrown, assuming that neither has hit the ground? C 14 m 20 m 28 m 34 m 56 m

d1 = (+7 m/s)(2 s) + 1⁄2 (–10 m/s2)(2 s)2; d1 = (–7 m/s)(2 s) + 1⁄2 (–10 m/s2)(2s)2

58 Kinematics

A certain football quarterback can throw a football a maximum range of 80meters on level ground. What is the highest point reached by the football ifthrown this maximum range? Ignore air friction. B 10m 20m 30m 40m 50m

Range of a projectile R = (vi2 sin 2θ)/gand maximum range occurs at θ = 45o,which gives vi = Rg . Maximum heightof a projectile is found from vy = 0 atmax height and vy2 = viy2 + 2ghand gives hmax = viy2/2g = (vi sin θ)2/2g. Maximum range occurs at 45o,which gives h = (Rg)(sin 45)2/2g

59 Kinematics

A bird flying in a straight line, initially at 10 m/s, uniformly increases its speedto 18 m/s while covering a distance of 40 m. What is the magnitude of theacceleration of the bird? D 0.1 m/s2 0.2 m/s2 2.0 m/s2 2.8 m/s2 5.6 m/s2 vf2=vi2+2ad

60 Kinematics

A cockroach is crawling along the walls inside a cubical room that has anedge length of 3 m. If the cockroach starts from the back lower left handcorner of the cube and finishes in the front upper right hand corner, what isthe magnitude of the displacement of the cockroach? A 3√3 m 3(2^3/2) m √3 m 3m 9m

The diagonal of a face of the cube is 32 m. The diagonal across the cube itselfis the hypoteneuse of this facediagonal and a cube edge

61 KinematicsThe position vs. time graph for an object moving in a straight line is shownbelow. What is the instantaneous velocity at t = 2 s? A – 2 m/s 1⁄2 m/s 0 m/s 2 m/s 4 m/s

Instantaneous velocity is the slope ofthe line at that point 61.kinematics

62 KinematicsShown below is the velocity vs. time graph for a toy car moving along astraight line. What is the maximum displacement from start for the toy car? D 3m 5m 6.5m 7m 7.5m

Displacement is the area under thecurve. Maximum displacement is justbefore the car turns D around at 2.5seconds. 62.kinematics

63 Kinematics

A cannon fires projectiles on a flat range at a fixed speed but with variableangle. The maximum range of the cannon is L. What is the range of thecannon when it fires at an angle π/6 above the horizontal? Ignore air. A √3/2 L 1/√2 L 1/√3 L 1/2 L 1/3 L

Range of a projectile R = (vi2 sin 2θ)/gand maximum range occurs at θ = 45o,which gives vi = A Rg .Usingθ=30ogivesRnew =Rsin60o

64 Kinematics

Every time it rebounds, it loses a proportion of the magnitude of its velocitydue to the inelastic nature of the collision, such that if the speed just beforehitting the ground on a bounce is v, then the speed just after the bounce is rv,where r < 1 is a constant. Calculate the total length of time that the ballremains bouncing, assuming that any time associated with the actual contactof the ball with the ground is negligible. A A B C D E

advanced question!) The time for onebounce is found from –v = v + (–g)twhich gives t = 2v/g. A We aresumming the time for all bounces, whilethe velocity (and hence the time)converge in a geometric series with theratio vn+1/vn = r <1 to 1 1−r 64.kinematics

65 KinematicsThe graph shows velocity as a function of time for a car. What was theacceleration at time t = 90 seconds? B 0.22 m/s2 0.33 m/s2 1.0 m/s2 9.8 m/s2 30 m/s2

The acceleration is the slope of thecurve at 90 seconds. 65.kinematics

66 KinematicsAn object is released from rest and falls a distance h during the first second oftime. How far will it fall during the next second of time? C h 2h 3h 4h h2

From the equation d = 1⁄2 at2,displacement is proportional to timesquared. Traveling from rest for twicethe time gives 4 times the displacement(or 4 h). Since the object alreadytravelled h inthe first second, during the time intervalfrom 1 s to 2 s the object travelled theremaining 3h

67 Kinematics

A stone is thrown straight downward with a speed of 20 m/s from the top of atall building. If the stone strikes the ground 3.0 s later, about how tall is thebuilding? Assume air resistance is negligible. D 45m 60m 90m 105m 120m d=vit+1⁄2gt2

68 Kinematics

A coyote can run at a speed of 20 m/s while a prairie dog can manage only5.5 m/s. If a prairie dog is 45 m in front of a coyote, what is the maximum timeit has to reach its hole without being caught? B 2.3 s 3.1 s 5.4 s 5.9 s 8.2 s

The relative speed between the coyoteand the prairie dog is 14.5 m/s. Tocover the 45 m B distance betweenthem will take t = d/v = (45 m)/(14.5m/s)

69 Kinematics

A model rocket accelerates from rest upwards at 50 m/s2 for 2.0 s before itsengine burns out. The rocket then coasts upward. What is the maximumheight that the rocket reaches? You may assume air resistance is negligible. C 100 m 510 m 610 m 1020 m 1220 m

Forthefirstpartofthetrip(thethrust):d1=vit+1⁄2at2 =0m+1⁄2(50m/s2)(2s)2=100m For the second part, we first findthe velocity after the thrust v = at = 100m/s and at the maximumheightvf =0,sotofindd2 weusevf2 =vi2 +2ad2whichgivesd2 =510m

70 Kinematics

A hunter in a forest walks 800 m west. He then turns south and walks 400 mbefore turning west again and walking a final 300 m. At the end of the walk,what is the magnitude of the hunter's displacement from the beginning? C 640 m 890 m 1170 m 1390 m 1500 m

Total displacement west = 1100 m; totaldisplacement south = 400 m. Use thePythagorean theorem

71 Kinematics

Robin Hood aims his longbow horizontally at a target's bull's eye 30 m away.If the arrow strikes the target exactly 1.0 m below the bull's eye, how fast didthe arrow move as it was shot from the bow? Assume air resistance isnegligible. D 6 m/s 13 m/s 33 m/s 67 m/s 150 m/s

For a horizontal projectile (viy = 0 m/s)to fall 1 m takes (using 1 m = 1⁄2 gt2)0.45 seconds. To travel 30 m in thistime requires a speed of d/t = (30 m)/(0.45 s)

72 Kinematics

A baseball is thrown vertically into the air with a velocity v, and reaches amaximum height h. At what height was the baseball moving with one-half itsoriginal velocity? Assume air resistance is negligible. E .25 h .33 h .50 h .67 h .75 h

Maximum height of a projectile is foundfrom vy = 0 m/s at max height and (0m/s)2 = v2 + 2gh and gives h = v2/2g 22Theheightatwhichtheprojectileismovingwithhalfthespeedisfoundfrom(1⁄2v)=v +2(–g)d which gives d = 3v2/8g = 0.75 h

73 Kinematics

Two identical bowling balls A and B are each dropped from rest from the topof a tall tower as shown in thediagram below. Ball A is dropped 1.0 s before ball B is dropped but both ballsfall for some time before ball Astrikes the ground. Air resistance can be considered negligible during the fall.After ball B is dropped but beforeball A strikes the ground, which of the following is true? E

The distancebetween the twoballs decreases.

The velocity of ballA increases withrespect to ball (B)

The velocity of ballA decreases withrespect to ball (B)

The distancebetween the twoballs remainsconstant.

The distancebetween the twoballs increases.

Looking at choices A, D and Eeliminates the possibility of choices Band C (each ball increasesits speed by 9.8 m/s each second,negating those choices anyway). Sinceball A is moving fasterthan ball B at all times, it will continue topull away from ball B (the relativespeed between theballs separates them). 73.kinematics

74 Kinematics

The diagram below shows four cannons firing shells with different masses atdifferent angles of elevation. Thehorizontal component of the shell's velocity is the same in all four cases. Inwhich case will the shell have thegreatest range if air resistance is neglected? D cannon A cannon B only cannon C only cannon D

Both cannons Band C have thegreatest range

Since they all have the same horizontalcomponent of the shell’s velocity, theshell that spendsthe longest time in the air will travel thefarthest. That is the shell launched atthe largest angle(mass is irrelevant). 74.kinematics

75 Kinematics

Relief supplies are being dropped to flood victims from an airplane flyinghorizontally at a speed v. If theairplane is at an altitude of h above the ground, what distance d in front of thelanding site should the suppliesbe dropped? E 2v^1/2(h/g) 2vh/g 2^1/2(vh/h) 2vh^2/g^2 v^1/2(2h/g)

This is merely asking for the horizontalrange of a horizontal projectile. Thetime in the air isfound from the height using h = ½ gt^2which gives t =^1/2(2h/g) . The range isfound using d = vt

76 Kinematics

An airliner flies at a speed of 500 km/hr with respect to the air. The jet streamblows from west to east with aspeed of 100 km/hr. What is the minimum time in which the airliner could fly3000 km due west and then backto its original starting position? C 10hr 12hr 12.5hr 13.5hr 15hr

Flying into the wind the airliners speedrelative to the ground is 500 km/h – 100km/h = 400 km/hand a 3000 km trip will take t = d/v = 7.5hours. Flying with the wind the airlinersspeed relativeto the ground is 500 km/h + 100 km/h =600 km/h and a 3000 km trip will take t= d/v = 5 hoursmaking the total time 12.5 hours.

77 Kinematics

A punter in a football game kicks the ball with an initial speed of 28.3 m/s atan angle of 60° with respect to theground. The ball is in the air for a total of 5.00 s before hitting the ground. Ifwe assume that air resistance isnegligible, what would be the ball's horizontal displacement? D 0m 14.2m 24.5m 70.8m 122.5m

The horizontal component of thevelocity is 28.3 m/s cos 60º = 14.15m/s. If the ball is in the airfor 5 seconds the horizontaldisplacement is x = vxt

78 Kinematics

Starting from rest, object 1 falls freely for 4.0 seconds, and object 2 falls freelyfor 8.0 seconds. Compared toobject 1, object 2 falls: D half as far twice as far three times as far four times as far

sixteen times asfar

since (from rest) d = ½ gt^2, distance isproportional to time squared. An objectfalling for twicethe time will fall four times the distance.

79 Kinematics

A car starts from rest and uniformly accelerates to a final speed of 20.0 m/s ina time of 15.0 s. How far does thecar travel during this time? A 150m 300m 450m 600m 800m v=(vi+vf)/2=d/t

80 Kinematics

A ball is thrown off a high cliff with no horizontal velocity. It lands 6.0 s laterwith a velocity of 40 m/s. Whatwas the initial velocity of the ball? B 100 m/s up 20 m/s up 0 20 m/s down 100 m/s down

vf = –40 m/s (negative since it ismoving down when landing). Use vf = vi+ (–g)t

81 Kinematics

An arrow is aimed horizontally, directly at the center of a target 20 m away.The arrow hits 0.050 m below thecenter of the target. Neglecting air resistance, what was the initial speed ofthe arrow? D 20 m/s 40 m/s 100 m/s 200 m/s 400 m/s

For a horizontal projectile (viy = 0 m/s)to fall 0.05 m takes (using 0.05 m = ½gt^2) 0.1 seconds.To travel 20 m in this time requires aspeed of d/t = (20 m)/(0.1 s)

82 Kinematics

A freely falling body is found to be moving downwards at 27 m/s at oneinstant. If it continues to fall, onesecond later the object would be moving with a downward velocity closest to: B 270 m/s 37 m/s 27 m/s 17 m/s 10 m/s

9.8 m/s^2 means the speed changes by9.8 m/s each second

83 Kinematics

A rocket near the surface of the earth is accelerating vertically upward at 10m/s2. The rocket releases aninstrument package. Immediately after release the acceleration of theinstrument package is: D 20 m/s^2 up 10 m/s^2 up 0 10 m/s^2 down 20 m/s^2 down

Once released, the package is in free-fall (subject to gravity only)

84 Kinematics

A car starts from rest and accelerates at 0.80 m/s2 for 10 s. It then continuesat constant velocity. Twentyseconds (20 s) after it began to move, the car has a C

velocity of 8m/sand has traveled40m

velocity of 8m/sand has traveled80m

velocity of 8m/sand has traveled120m

velocity of 16m/sand has traveled160m

velocityof 16m/sand has traveled320m

For the first part v = at = 8.0 m/s and d= ½ at2 = 40 m. In the second part ofthe trip, the speedremains at 8 m/s, and travels anadditional d = vt = 80 m

85 Kinematics

A solid metallic sphere of radius R has charge Q uniformly distributed on itsouter surface. A graph of electric potential V as a function of position r isshown above. Which of the following graphs best represents the magnitude ofthe electric field E as a function of position r for this sphere? C A B C D E

Since E = ∆V/d, E represents theslope of the line on the graphwhich could be choice C or D.since V ∝ 1/r the slope isproportional to ∆V/r = (1/r)/r =1/r2C which is choice C 85.kinematics.png

86 Kinematics What is the magnitude of the resultant electric field at the center of the circle? A A B C D E by symmetry, all the vectors cancel 86.kinematics.png

87 Kinematics

With the six particles held fixed, how much work would be required to bring aseventh particle of charge + Q from very far away and place it at the center ofthe circle? D A B C D E

W = q∆V = +Q(Vcenter – V∞) =+QVcenter where VcenterD = ΣV =ΣkQ/r = 6kQ/R 87.kinematics.png

88 Kinematics Which vector best describes the direction of the electric field at point A ? A A B C D E

E points from high potential to lowpotential, perpendicular to equipotentiallines (the direction of the force on apositive charge) 88.kinematics.png

89 Kinematics At which point does the electric field have the greatest magnitude? B A B C D E

E is greatest in magnitude where Vchanges most rapidly with position (thelargest gradient) which is where thelines are closest together. 89.kinematics.png

90 KinematicsHow much net work must be done by an external force to move a –1 μC pointcharge from rest at point C to rest at point E ? B -20 micro joules -10 micro joules 10 micro joules 20 micro joules 30 micro joules

∆VCE = VE – VCB = 10 V. Theamount of work, W = q∆V = 1 μC × 10V = 10 μC. Since the external forcemust push against the negative chargeto keep it from accelerating and bring itto rest at point E, the work done by theexternal force must be negative 90.kinematics.png

91 Kinematics

The plates of a parallel–plate capacitor of cross sectional area A areseparated by a distance d, as shown above. Between the plates is a dielectricmaterial of constant K. The plates are connected in series with a variableresistance R and a power supply of potential difference V. The capacitance Cof this capacitor will increase if which of the following is decreased? D A R K d V

C = Kε0D A/d. Only changes in thegeometry of the capacitor will changethe capacitance, not changes to thebattery or resistor 91.kinematics.png

92 KinematicsA physics problem starts: "A solid sphere has charge distributed uniformlythroughout. . . " It may be correctly concluded that the E

electric field is zeroeverywhere insidethe sphere

electric field insidethe sphere is thesame as theelectric fieldoutside

electric potentialon the surface ofthe sphere is notconstant

electric potential inthe center of thesphere is zero

sphere is not madeof metal

For charge to be distributed throughouta material, it must be non-conducting

93 Kinematics

A uniform spherical charge distribution has radius R.. Which of the followingis true of the electric field strength due to this charge distribution at a distancer from the center of the charge? D

It is greatest whenr = 0.

It is greatest whenr = R/2.

It is directlyproportional to rwhen r > R.

It is directlyproportional to rwhen r < R.

It is directlyproportional to r2

Advanced question (not exactly in the Bcurriculum, but interesting). Like gravityinside a uniform sphere of mass, thefield is directly proportional to r wheninside the sphere (and proportional to1/r2D when outside)

94 Kinematics

When a negatively charged rod is brought near, but does not touch, theinitially uncharged electroscope shown above, the leaves spring apart (I).When the electroscope is then touched with a finger, the leaves collapse (II).When next the finger and finally the rod are removed, the leaves spring aparta second time (III). The charge on the leaves is D

positive in both Iand III

negative in both Iand III

positive in I,negative in III

negative in I,positive in III

impossible todetermine in eitherI or III

In I, charge separation occurs (negativecharges repel to the leaves). Thewhole process describes charging byinduction, where the electrons leave theelectroscope to ground (the finger) andonce contact with ground is broken, theelectroscope is left with a positivecharge (III) 94.kinematics.png

95 Kinematics

An ideal elastic rubber ball is dropped from aheight of about 2 meters, hits the floor and rebounds to its original height.Which of the following graphs would best represent the distance above thefloor versus time for the abovebouncing ball? C (A) (B) (C) (D) (E)

One could analyze the graphs based onslope, but more simply, the graph ofposition versus timeshould represent the actual pathfollowed by the ball as seen on aplatform moving past you atconstant speed. 95.kinematics.png

96 Kinematics

An ideal elastic rubber ball is dropped from aheight of about 2 meters, hits the floor and rebounds to its original height.Which of the following graphs would best represent acceleration versus timefor the bouncing ball? B (A) (B) (C) (D) (E)

Other than the falling portions (a = –9.8m/s2) the ball should have a “spike” in theacceleration Bwhen it bounces due to the rapidchange of velocity from downward toupward. 96.kinematics.png

97 KinematicsDuring which time interval would cars #2 and #3 be moving at the sameaverage speed? C t0 to t1 t1 to t2 t2 to t3 t3 to t4 t4 to t5

The same average speed would beindicated by the same distancetravelled in the time interval 97.kinematics.png

98 Kinematics About what position after t0 would car #1 and car #2 have been side by side? D 0 m 15 m 26 m 37 m 39 m

At t3, car #1 is ahead of car #2 and att4, car #1 is behind car #2. They werein the same position somewhere inbetween 98.kinematics.png

99 KinematicsWhich of the three cars had the greatest average speed during these 5seconds? B car #1

car #2 and car #3had the sameaverage speed car #2

all three cars hadthe same averagespeed car #3

Average speed = (total distance)/(totaltime). Cars #2 and #3 travelled thesame distance. 99.kinematics.png

100 KinematicsIf car #3 continues to constantly accelerate at the same rate what will be itsposition at the end of 6 seconds? C 22 m 68 m 72 m 78 m 94 m

If you look at the distance covered ineach time interval you should nitce apattern: 2 m, 6 m, 10m, 14 m, 18 m; making the distance inthe next second 22 m. 100.kinematics.png

101 Kinematics

The graph represents the relationship between distance and time for anobject that is moving along a straightline. What is the instantaneous speed of the object at t = 5.0 seconds? B 0.0 m/s 0.8 m/s 2.5 m/s 4.0 m/s 6.8 m/s

Instantaneous speed is the slope of theline at that point. 101.kinematics.png

102 Kinematics Between what times did the object have a non-zero acceleration? E 0 s only 0 s to 8 s 0 s to 5 s

the object was notaccelerating at anytime 5 s to 8 s

A non-zero accleeration is inidcated bya curve in the line 102.kinematics.png

103 Kinematics

An airplane takes off and flies 300 miles at an angle of 30º north of east. Itthen changes direction and flies 600miles due west before landing. In what direction is the plane’s landing pointfrom its starting point? C 14.2º north of west 66.2º north of west 23.8º north of west 75.9º north of west 37.4º north of west

Net displacement north = 300 miles sin30º = 150 milesNet displacement east = (300 miles cos30º – 600 miles) = – 340 miles, or 340miles west.Angle north of west

104 Kinematics

If a ball is thrown directly upwards with twice the initial speed of another, howmuch higher will it be at itsapex? C 8 times 2 times 4 times 2 times 2√2 times

Maximum height of a projectile is foundfrom vy= 0 m/s at max height and (0m/s)2= v2+ 2gh and gives h = v2/2g. Attwice the initial speed, the height will be4 times as much

105 KinematicsWhat was the average speed of the cart between 0.1 seconds and 0.3seconds? E 0.6 m/s 4.8 m/s 1.9 m/s 60 m/s 2.4 m/s

Average speed = total distance dividedby total time = (0.48 m)/(0.2 s)

105-107.kinematics.png

106 Kinematics What was the acceleration of the cart during the first 0.4 seconds? E 6.0 m/s^2 25 m/s^2 9.8 m/s^2 50 m/s^2 12 m/s^2 d = ½ at^2 (use any point)105-107.kinematics.png

107 KinematicsWhat was the instantaneous velocity of the cart at 96 centimeters from thestart? B 0.6 m/s 4.8 m/s 1.9 m/s 60 m/s 2.4 m/s v = viB + at

105-107.kinematics.png

108 Kinematics What would be the acceleration of the clown at 5s? C 1.6 m/s^2 8.0 m/s^2 2.0 m/s^2 none of the above 3.4 m/s^2Acceleration is the slope of the linesegment

108-109.kinematics.png

109 Kinematics After 12 seconds, how far is the clown from her original starting point? E 0 m 10 m 34 m 47 m 74 m Displacement is the area under the line108-109.kinematics.png

110 Kinematics

A box falls to the ground from a delivery truck traveling at 30 m/s. After hittingthe road, it slides 45 meters to rest. How long does it take the box to come torest? D 0.67 s 1.5 s 2.0 s 3.0 s 6.0 s vi=30m, vf=0, d=45m; v=(vi+vf)/2=d/t

111 Kinematics When an object falls freely in a vacuum near the surface of the earth Ethe velocity cannotexceed 10 m/s

the terminalvelocity will begreater than whendropped in air

the velocity willincrease but theacceleration will bezero

the accelerationwill constantlyincrease

the accelerationwill remainconstant

Ina vaccum, there is no air resistanceand henve no terminal velocity. It willcontinue to accelerate.

112 Kinematics

Two arrows are launched at the same time with the same speed. Arrow A atan angle greater than 45 degrees, and arrow B at an angle less than 45degrees. Both land at the same spot on the ground. Which arrow arrives first? B

arrow A arrivesfirst

arrow B arrivesfirst

they both arrivetogether

it depends on theelecation wherethe arrows arelaunched

it depends on theelevation wherethe arrows land

A projectile launched at a smaller angeldoes not go as high and will fall to theground first.

113 Kinematics

A ball is thrown into the air at an angle θ as measured from the horizontalwith a velocity v. The horizontal velocity of the ball will be directly proportionalto which of the following C the angle θ

the sine of theangle θ

the cosine of theangle θ

the tangent of theangle θ

the value of thegravitationalacceleration vx=vicosθ

114 Kinematics For which time interval(s) did the marble have a negative velocity? Dfrom t=8.0s tot=10.0s only

from t=6.9s to 10.0s only

from t=3.8s tot=10s only

from t=4.8s to t=6.2s and from t=6.9sto t=10s only

from t=3.2s to t=3.6s, from t=4.8 tot=5s, and from t=6.8s to t=7.2s only velocity is the slope of the line 114.kinematics.png

115 Kinematics For which time interval(s) did the marble have a positive acceleration? Dfrom t = 0.0 s to t =8.0 s only

from t = 0.0 s to t =3.6 only

from t = 3.8 s to t =4.8 s and t = 6.2 sto t = 6.8 s only

from t = 2.0 s to t =2.5 s, from t = 5.8s to t = 6.2 s, andfrom t = 8.4 s to t =8.8 s only

from t = 3.3 s to t =3.7 s, from t = 4.8s to t = 5.0 s, andfrom t = 6.8 s to t =7.2 s only

Positive acceleration is an upwardcurvature 114.kinematics.png

116 Kinematics What is the marbles average acceleration between t = 3.1 s and t = 3.8 s? E –2.0 m/s2 2.0 m/s2 0.0 m/s2 3.0 m/s2 0.8 m/s2 Average acceleration = Δv/Δt 114.kinematics.png

117 KinematicsA car accelerates uniformly from rest for a time of 2.00 s through a distanceof 4.00 m. What was the acceleration of the car? E 0.50 m/s2 0.71 m/s2 1.00 m/s2 1.41 m/s2 2.00 m/s2 d = ½ at2

118 Kinematics What is the acceleration of the toy car at t = 4 s? C –1 m/s2 0 m/s2 1 m/s2 2 m/s2 4 m/s2Acceleration is the slope of the linesegment 118.kinematics. png

119 KinematicsWhat was the total displacement of the toy car for the entire 10 secondinterval shown? B 0 meters 6.5 meters 9 meters 10 meters 11.5 meters

Displacement is the area between theline and the t-axis. Area is negativewhen the line is below the t-axis. 118.kinematics.png

120 Kinematics

An object is thrown upwards with a velocity of 30 m/s near the surface of theearth. After two seconds what would be the direction of the displacement,velocity and acceleration? B up; up; up up; up; down up; down; down up; down; up down; down; down

After two seconds, the object would beabove it’s original position, still movingupward, but the acceleration due togravity is always pointing down. 118.kinematics.png

121 KinematicsWhich of the following graphs could correctly represent the motion of anobject moving with a constant speed in a straight line? D Graph I only

Graphs II and Vonly Graph II only

Graphs I and IVonly

All of the abovegraphs representconstant velocity

Constant speed is a constant slope ona position-time graph, a horizontal lineon a velocity timegraph or a zero value on anacceleration-time graph 121.kinematics.png

122 Kinematics What is the average speed of the ball between 3 and 4 seconds? B 3.0 cm/s 7.0 cm/s 3.5 cm/s 12.5 cm/s 4.0 cm/sAverage speed = total distance dividedby total time = (7 cm)/(1 s) 122.kinematics.png

123 Kinematics Which of the following is closest to the acceleration of the ball? C 1 cm/s2 4 cm/s2 2 cm/s2 5 cm/s2 3 cm/s2 d = ½ at2 (use any point) 122.kinematics.png

124 Kinematics

Three stones of different mass (1 m, 2m & 3m) are thrown vertically upwardwith different velocities (l v, 2v &3v respectively). The diagram indicates the mass and velocity of each stone.Rank from high to low themaximum height of each stone. Assume air resistance is negligible. C I, II, III II, I, III III, II, I I, III, II

all reach the sameheight

Maximum height of a projectile is foundfrom vy = 0 m/s at max height and (0m/s)2 = v2 + 2ghand gives h = v2C/2g. Mass is irrelevant. Largest initialspeed = highest.

125 Kinematics

A rubber ball bounces on the ground as shown. After each bounce, the ballreaches one-half the height of thebounce before it. If the time the ball was in the air between the first andsecond bounce was 1 second. Whatwould be the time between the second and third bounce? B. 0.50 sec 0.71 sec 1.0 sec 1.4 sec 2.0 sec

Using d=1/2at^2 shows the height isproportional to the time squared. 1/2the maximum height is 1/sq root of 2times the time. 125.kinematics.png

126 Kinematics

The driver of a car makes an emergency stop by slamming on the car'sbrakes and skidding to a stop. How farwould the car have skidded if it had been traveling twice as fast? A 4 times as far the same distance 2 times as far

square root of 2times as far

the mass of the carmust be known

Stopping distance is found usingVt=0=vi^2+2ad which gives d=vi/2awhere stopping distance is proportionalto initial speed squared.

127 Kinematics

A pebble is dropped from a high vertical cliff. The collision of the pebble withthe ground below is seen 1.50seconds after the pebble is dropped. With what speed did the pebble hit theground? Ignore air resistance. B. 10 m/s 15 m/s 48.6 m/s 100.4 m/s 343 m/s Vt=Vi+gt

128 Kinematics

A snail is moving along a straight line. Its initial position is x0= –5 meters andit is moving away from theorigin and slowing down. In this coordinate system, the signs of the initialposition, initial velocity andacceleration, respectively, are B. A B C D E

Moving away from the origin willmaintain a negative position andvelocity. Slowing downindicates the acceleration is opposite indirection to the velocity. 128.kinematics.png

129 Kinematics

An arrow is shot horizontally toward a target 20 m away. In traveling the first 5m horizontally, the arrow falls0.2 m. In traveling the next 5 m horizontally, it will fall an additional A 0.6 m 0.4 m 0.3 m 0.2 m 0.1 m

The arrow travels equal horizontaldistances in equal amounts of time. Thedistance fallen isproportional to time squared. The arrowwill have fallen a total of 0.8 m in thenext 5 mhorizontally, or an additional 0.6 m.

130 KinematicsHow tall is a tree if the sun is at a 53º angle above the horizon and theshadow is 8.0 meters long? B. 4.8 m 10.6 m 6.0 m 13.3 m 8.0 m Tan 53 degrees=h/(8m)

131 Kinematics

Three students were arguing about the height of a parking garage. Onestudent suggested that to determine theheight of the garage, they simply had to drop tennis balls from the top andtime the fall of the tennis balls. If thetime for the ball to fall was 1.4 seconds, approximately how tall is the parkinggarage? C 4.9 m 7.0 m 9.8 m 13.8 m 19.6 m d=1/2at^2

132 Kinematics

An arrow is shot from a bow at an angle of 40º from the horizontal at a speedof 24.0 m/s. Ignoring airresistance, what is the arrow’s maximum height above its launch point? B. 5.9 m 11.9 m 16.9 m 23.8 m 28.8 m

Maximum height of a projectile is foundfrom vy = 0 at max height and vy2 = viy 2 + 2gh and gives hmax = viy2/2g = (vi sin θ)2 B/2g

133 Kinematics

A car has the velocity versus time curve shown above. Which of the followingstatements regarding its motionis INCORRECT? D

The car is movingfastest at 2.0 s

The car is at restat approximately5.2 s.

The car isspeeding up from t= 0 to t = 2.0 s

The car hasnegativeacceleration at t =4.5 s.

The car has noacceleration at theinstant t = 2 s.24 Acceleration is the slope of the line

134 Kinematics

A rock is dropped from the top of a tall tower. Half a second later anotherrock, twice as massive as the first, isdropped. Ignoring air resistance, A

the distancebetween the rocksincreases whileboth are falling.

the acceleration isgreater for themore massiverock.

the speed of bothrocks is constantwhile they fall.

they strike theground more thanhalf a secondapart.

they strike theground with thesame kineticenergy.

Since the first rock is always travelingfaster, the relative distance betweenthem is alwaysincreasing.

135 Kinematics

A cart is initially moving at 0.5 m/s along a track. The cart comes to rest aftertraveling 1 m. The experiment is repeated on the same track, but now the cartis initially moving at 1 m/s. How far does the cart travel before coming to rest? B 1m 2m 3m 4m 8m

Stopping distance is found using vf= 0 = vi^2+ 2ad which gives d = vi^2/2awhere stopping Bdistance is proportional to initial speedsquared.

136 Kinematics

During an interval of time, a tennis ball is moved so that the angle betweenthe velocity and the acceleration of the ball is kept at a constant 120o. Whichstatement is true about the tennis ball during this interval of time? B

Its speedincreases and it ischanging itsdirection of travel.

Its speeddecreases and it ischanging itsdirection of travel.

Its speed remainsconstant, but it ischanging itsdirection of travel.

Its speed remainsconstant and it isnot changing itsdirection of travel.

Its speeddecreases and it isnot changing itsdirection of travel.

At an angle of 120º, there is acomponent of the accelerationperpendicular to the velocitycausing the direction to change and acomponent in the opposite direction ofthe velocity, causingit to slow down.

137 Kinematics

A dog starts from rest and runs in a straight line with a constant accelerationof 2.5 m/s2. How much time does it take for the dog to run a distance of 10.0m? C 8.0 s 4.0 s 2.8s 2.0 s 1.4 s d = ½a^2

138 Kinematics What is the direction of the average velocity during this time interval? B → ← ↑ ↓The averagevelocity is zero.

The displacement is directly to the left.The average velocity is proportional tothe displacement 138.kinematics.png

139 Kinematics What is the direction of the average acceleration during this time interval? D → ← ↑ ↓

The averageacceleration iszero.

The velocity is initially pointing up, thefinal velocity points down. Theacceleration is in thesame direction as ∆v = vf+ (–vi) 138.kinematics.png

140 Kinematics At which time is the car the greatest distance from the origin? C t = 10 s t = 6 s t = 5 s t = 3 s t = 0 s

The car is the greatest distance justbefore it reverses direction at 5seconds 140.kinematics.png

141 Kinematics What is the average speed of the car for the 10 second interval? D 1.20 m/s 1.40 m/s 3.30 m/s 5.00 m/s 5.40 m/s

Average speed = (total distance)/(totaltime), the total distance is themagnitude of the area underthe line (the area below the t-axis isconsidered positive) 140.kinematics.png

142 KinematicsConsider the motion of an object given by the position vs. time graph shown.For what time(s) is the speed of the object greatest? C

At all times from=0.0s→t=2.0s At time t=3.0s At time t=4.0s

At all times from t= 5.0 s → t = 7.0 s At time t = 8.5 s Speed is the slope of the line. 142.kinematics.png

143 Kinematics

The free fall trajectory of an object thrown horizontally from the top of abuilding is shown as the dashed line in the figure. Which sets of arrows bestcorrespond to the directions of the velocity and of the acceleration for theobject at the point labeled P on the trajectory? A

velocity is pointing tangent to the path,acceleration (gravity) is downward. 143.kinematics.png

144 Kinematics

A toy car moves 3.0 m to the North in one second. The car then moves at 9.0m/s due South for two seconds. What is the average speed of the car for thisthree second trip? D 4.0 m/s 5.0 m/s 6.0 m/s 7.0 m/s 12 m/s

Average speed = (total distance)/(totaltime)

145 Kinematics

A projectile launched from the ground landed a horizontal distance of 120.0 mfrom its launch point. Theprojectile was in the air for a time of 4.00 seconds. If the projectile landed atthe same vertical position fromwhich it was launched, what was the launch speed of the projectile? Ignoreair resistance. c 22.4m/s 30.0m/s 36.1m/s 42.4m/s 50.0m/s

To travel 120 m horizontally in 4 s givesvx= 30 m/s. The time to reach maximumheight was 2seconds and vy= 0 at the maximum height which givesviy = 20 m/s. viSQRT(Vx^2+Viy^2)= v

146 Kinematics

Two automobiles are 150 kilometers apart and traveling toward each other.One automobile is moving at 60km/h and the other is moving at 40 km/h. In how many hours will they meet? a 1.5 1.75 2 2.5 3

The relative speed between the twocars is v1 – v2= (60 km/h) – (–40 km/h) = 100 km/h.Theywill meet in t = d/vrelativeA= 150 km/100 km/h

147 KinematicsA particle moves on the x-axis. When the particle’s acceleration is positiveand increasing E

its velocity must bepositive

its velocity must benegative

it must be slowingdown

it must bespeeding up

none of the abovemust be true.

Acceleration is independent of velocity(you can accelerate in any directionwhile traveling in any direction).

148 Kinematics What does one obtain by dividing the distance of 12 Mm by the time of 4 Ts? B 3 nm/s 3 µm/s 3mm/s 3km/s 3 Gm/s

12/4 =3, now the units: M = 106, T = 1012: M/T = 10–6= micro (µ)

149 Kinematics. Is it possible for an object’s velocity to increase while its accelerationdecreases? E

No, this isimpossiblebecause of theway in whichacceleration isdefined

No, because ifacceleration isdecreasing theobject will beslowing down

No, becausevelocity andacceleration mustalways be in thesame direction

Yes, an examplewould be a fallingobject near thesurface of themoon

Yes, an examplewould be a fallingobject in thepresence of airresistance

Acceleration is independent of velocity(you can accelerate in any directionwhile traveling in any direction). If the accleration is in thesame direction as the velocity, theobject is speeding up.

150 Kinematics

During a recent winter storm, bales of hay had to be dropped from an airplaneto a herd of cattle below. Assumethe airplane flew horizontally at an altitude of 180 m with a constant velocityof 50 m/s and dropped one bale ofhay every two seconds. It is reasonable to assume that air resistance will benegligible for this situation. As the bales are falling through the air, what willhappen to their distance of separation? A

the distance ofseparation willincrease

the distance ofseparation willdecrease

the distance ofseparation willremain constant

the distance ofseparation willdepend on themass of the bales

none of the aboveare always true

As the first bales dropped will alwaysbe traveling faster than the later bales,their relativevelocity will cause their separation toalways iincrease.

151 Kinematics

During a recent winter storm, bales of hay had to be dropped from an airplaneto a herd of cattle below. Assumethe airplane flew horizontally at an altitude of 180 m with a constant velocityof 50 m/s and dropped one bale ofhay every two seconds. It is reasonable to assume that air resistance will benegligible for this situation. About how far apart from each other will the balesland on the ground? D 9000m 300m 180m 100m 5m

Horizontally, the bales will all travel atthe speed of the plane, as gravity willnot affect theirhorizontal motion. D = vt = (50 m/s)(2seconds apart)

152 Kinematics

If a boat can travel with a speed of v in still water, which of the following tripswill take the least amount oftime. A

traveling adistance of 2d instill water

traveling adistance of 2dacross(perpendicular to)the current in astream

traveling adistance ddownstream andreturning adistance dupstream

traveling adistance dupstream andreturning adistance ddownstream

all of the above willtake equal times

Traveling in still water will take a time t= d/v = 2d/v. Traveling perpendicularlyacross thestream requires the boat to head at anangle into the current, causing therelative velocity of theboat to the shore to be less than whenin still water and therefore take a longertime. Since thiseliminates choice E and choices D andC are identical, that leaves A as theonly single option.

153 Kinematics

Suppose two cars are racing on a circular track one kilometer incircumference. The first car can circle thetrack in 15 seconds at top speed while the second car can circle the track in12 seconds at top speed. How muchlead does the first car need starting the last lap of the race not to lose? A atleast 250m atleast 83m atleast 200m atleast 67m atleast 104m

When the first car starts the last lap, itwill finish the race in 15 seconds fromthat point. In 15seconds, the second car will travel (1km/12 s) × 15 s = 1250 m so the firstcar must be at least250 m ahead when starting the last lapto win the race.

1 Dynamics

A ball of mass m is suspended from two strings of unequal length as shownabove. The magnitudes of thetensions T1 and T2 in the strings must satisfy which of the followingrelations? C T1=T2 T1> T2 T1< T2 Tl+ T2= mg T1 – T2= mg

As T2 is more vertical, it is supportingmore of the weight of the ball. Thehorizontalcomponents of T1 and T2 are equal 1.dynamics.png

2 Dynamics

Which of the following diagrams best represents the gravitational force W. thefrictional force f, and the normalforce N that act on the block? E A B C D E

Normal force is perpendicular to theincline, friction acts up, parallel to theincline (opposite themotion of the block), gravity actsstraight down. 2.dynamics.png

3 Dynamics The magnitude of the frictional force along the plane is most nearly C 2.5 N 5 N 6 N 10 N 16 N ΣF = ma; mgsinθ – f = ma 3.dynamics.png

4 Dynamics

When the frictionless system shown above is accelerated by an applied forceof magnitude the tension in thestring between the blocks is E 2 F F 2/3 F 1/2 F 1/3 F

The “diluted” force between objects isthe applied force times the ratio of themass behind therope to the total mass being pulled.This can be derived from a = F/m(total)and FT = m(behind therope)a 4.dynamics.png

5 Dynamics

A ball falls straight down through the air under the influence of gravity. Thereis a retarding force F on the ballwith magnitude given by F = bv, where v is the speed of the ball and b is apositive constant. The magnitude ofthe acceleration, a of the ball at any time is equal to which of the following? B g-b g – bv/m g + bv/m g/b bv/m ΣF = ma; mg – bv = ma

6 Dynamics

A push broom of mass m is pushed across a rough horizontal floor by a forceof magnitude T directed at angle θas shown above. The coefficient of friction between the broom and the floor isµ. The frictional force on thebroom has magnitude A µ(mg + Tsinθ) µ(mg – Tsinθ) µ(mg + Tcosθ) µ(mg – Tcosθ) µmg

Ff= µF(N) where F(N) is found fromΣFy= 0 = (F(N) – mg – Tsinθ) 6.dynamics.png

7 Dynamics

A block of weight W is pulled along a horizontal surface at constant speed vby a force F, which acts at an angleof θ with the horizontal, as shown above. The normal force exerted on theblock by the surface has magnitude B W – F cos θ W – F sin θ W W + F sin θ W + F cos θ ΣFy= 0 = Fsinθ + F(N) – W 7.dynamics.png

8 Dynamics

A uniform rope of weight 50 newtons hangs from a hook as shown above. Abox of weight 100 newtons hangsfrom the rope. What is the tension in the rope? E

50 N throughoutthe rope

75 N throughoutthe rope

100 N throughoutthe rope

150 N throughoutthe rope

It varies from 100N at the bottom ofthe rope to 150 Nat the top.

The bottom of the rope supports thebox, while the top of the rope mustsupport the rope itselfand the box. 8.dynamics.png

9 Dynamics

When an object of weight W is suspended from the center of a masslessstring as shown above, the tension atany point in the string is D 2Wcosθ ½Wcosθ Wcosθ W/(2cosθ) W/(cosθ)

The vertical components of the tensionin the rope are two equal upwardcomponents of Tcosθ,which support the weight. ΣFy= 0 =2Tcosθ – W

10 Dynamics

An ideal spring obeys Hooke's law, F = –kx. A mass of 0.50 kilogram hungvertically from this springstretches the spring 0.075 meter. The value of the force constant for thespring is most nearly E 0.33 N/m 0.66 N/m 6.6 N/m 33 N/m 66 N/m

F = mg = kx (the negative sign merelyindicates the direction of the springforce relative to thedisplacement)

11 Dynamics

A block of mass 3m can move without friction on a horizontal table. This blockis attached to another block ofmass m by a cord that passes over a frictionless pulley, as shown above. Ifthe masses of the cord and the pulleyare negligible, what is the magnitude of the acceleration of the descendingblock? B Zero g/4 g/3 2g/3 g

ΣF(external) = m(total)a;mg is the only force acting from outsidethe system of masses so we have mg =(4m)a 11.dynamics.png

12 Dynamics

A plane 5 meters in length is inclined at an angle of 37°, as shown above. Ablock of weight 20 newtons isplaced at the top of the plane and allowed to slide down. The mass of theblock is most nearly: D 1.0 kg 1.2 kg 1.6 kg 2.0 kg 2.5 kg W = mg 12.dynamics.png

13 Dynamics

A plane 5 meters in length is inclined at an angle of 37°, as shown above. Ablock of weight 20 newtons isplaced at the top of the plane and allowed to slide down. The magnitude ofthe normal force exerted on the block by the plane is most nearly: C 10 N 12 N 16 N 20 N 33 N

F(N) = mgcosθ, cosθ =adjacent/hypotenuse = 4/5 13.dynamics.png

14 Dynamics

The forces act on an object. If the object is in translational equilibrium, whichof the following must be true? I. The vector sum of the three forces mustequal zero. II. The magnitudes of the three forces must be equal. III. All threeforces must be parallel. A I only II only I and III only II and III only I, II, and III

Three vectors add to zero if they formthe sides of a triangle, there is norequirement they beequal or parallel, though it is possible.

15 Dynamics

Three objects can only move along a straight, level path. The graphs aboveshow the position d of each of theobjects plotted as a function of time t. The sum of the forces on the object iszero in which of the cases? C II only III only I and II only I and III only I, II, and III

Any curvature of the line in a d-t graphindicates a non-zero acceleration 15.dynamics.png

16 Dynamics

For which of the following motions of an object must the acceleration alwaysbe zero? I. Any motion in a straight line. II. Simple harmonic motion. III. Anymotion in a circle. E I only II only III only

Either I or III, butnot II

None of thesemotionsguarantees zeroaccleration.

Motion in a straight line does not meanthe speed is constant. Simple harmonicmotion is a constantly changing velocityand can only occur with anacceleration. Motion in a circle requirescentripetal acceleration.

17 Dynamics

A rope of negligible mass supports a block that weighs 30 N, as shownabove. The breaking strength of therope is 50 N. The largest acceleration that can be given to the block by pullingup on it with the rope withoutbreaking the rope is most nearly: B 6 m/s^2 6.7 m/s^2 10 m/s^2 15 m/s^2 16.7 m/s^2

ΣF = ma; FT – mg = ma; Let FT = 50 N(the maximum possible tension) amd m= W/g = 3 kg 17.dynamics.png

18 Dynamics

A horizontal, uniform board of weight 125 N and length 4 m is supported byvertical chains at each end. Aperson weighing 500 N is sitting on the board. The tension in the right chain is250 N. What is the tension in the left chain? B 250 N 375 N 500 N 625 N 875 N

The sum of the tensions in the chains(250 N + Tleft) must support the weightof the board and Bthe person (125 N + 500 N)

19 Dynamics

A horizontal, uniform board of weight 125 N and length 4 m is supported byvertical chains at each end. Aperson weighing 500 N is sitting on the board. The tension in the right chain is250 N. How far from the left end of the board is the person sitting? B 0.4 m 1.5 m 2 m 2.5 m 3 m

From symmetry, each chain supportshalf of the weight of the board (62.5 N),The weight of theperson is then split between the chainswith the left chain holding 375 N – 62.5N = 312.5 Nand the right chain supporting 250 N –62.5 N = 187.5 N or 3/5 of the tensionin the left chain.This means if the person sits a distancex from the left end, they sit a distance(5/3)x from theright end. This gives x + (5/3)x = 4 m

20 Dynamics

The cart of mass 10 kg shown above moves without frictional loss on a leveltable. A 10 N force pulls on thecart horizontally to the right. At the same time, a 30 N force at an angle of 60°above the horizontal pulls on the cart to the left. What is the magnitude of thehorizontal acceleration of the cart? A 0.5 m/s^2 1.6 m/s^2 2.0 m/s^2 2.5 m/s^2 2.6 m/s^2

ΣF = ma; 10 N – (30 N cos60º) = (10kg)a 20.dynamics.png

21 Dynamics

An object of mass m is initially at rest and free to move without friction in anydirection in the xy-plane. Aconstant net force of magnitude F directed in the +x direction acts on theobject for 1 s. Immediately thereaftera constant net force of the same magnitude F directed in the +y direction actson the object for 1 s. After this, noforces act on the object. Which of the following vectors could represent thevelocity of the object at the end of3 s, assuming the scales on the x and y axes are equal? C

Since the same force acts for the sametime in each direction, the velocity ineach direction isthe same. The vector should then pointat a 45º angle in the first quadrant. 21.dynamics.png

22 Dynamics

Two people are pulling on the ends of a rope. Each person pulls with a forceof 100 N. The tension in the ropeis: C 0 N 50 N 100 N 141 N 200 N

Consider that no part of the system is inmotion, this means at each end of therope, a personpulling with 100 N offorce is reacted towith a tension in the rope of 100 N.

23 Dynamics

The parabola above is a graph of speed v as a function of time t for an object.Which of the following graphsbest represents the magnitude F of the net force exerted on the object as afunction of time t? E A B C D E

As v is proportional to t2and a is proportional to ∆v/t, this meansa should be proportional to t 23.dynamics.png

24 DynamicsA 100-newton weight is suspended by two cords as shown above. Thetension in the slanted cord is D 50 N 100 N 150 N 200 N 250 N ΣFy= 0 = Tsin 30º – mg 24.dynamics.png

25 Dynamics

Two blocks are pushed along a horizontal frictionless surface by a force of 20newtons to the right, as shownabove. The force that the 2-kilogram block exerts on the 3-kilogram block is A

8 newtons to theleft

8 newtons to theright

10 newtons to theleft

12 newtons to theright

20 newtons to theleft

F = ma gives 20 N = (5 kg)a or anacceleration of 4 m/s2. The 2 kg blockis accelerating due to the contact forcefrom the 3 kg block Fcontact = ma = (2kg)(4 m/s2) = 8 N. The 2 kg pushesback on the 3 kg block with a forceequal in magnitude and opposite indirection. 25.dynamics.png

26 Dynamics

A ball initially moves horizontally with velocity vi, as shown above. It is then struck by a stick. After leavingthe stick, the ball moves vertically with a velocity vf, which is smaller in magnitude than vi. Which of thefollowing vectors best represents the direction of the average force that thestick exerts on the ball? B A B C D E

The direction of the force is the sameas the direction of the acceleration,which is proportional to ∆v = vf+ (–vi) 26.dynamics.png

27 Dynamics

Two 0.60-kilogram objects are connected by a thread that passes over a light,frictionless pulley, as shownabove. The objects are initially held at rest. If a third object with a mass of0.30 kilogram is added on top of oneof the 0.60-kilogram objects as shown and the objects are released, themagnitude of the acceleration of the0.30-kilogram object is most nearly D 10.0 m/s2 6.0 m/s2 3.0 m/s2 2.0 m/s2 1.0 m/s2

ΣFexternal = mtotala gives (0.90 kg ×10m/s2) – (0.60 kg × 10 m/s2) = (1.5kg)a 27.dynamics.png

28 Dynamics

Two identical massless springs are hung from a horizontal support. A block ofmass 1.2 kilograms is suspendedfrom the pair of springs, as shown above. When the block is in equilibrium,each spring is stretched anadditional 0.15 meter. The force constant of each spring is most nearly A 40 N/m 48 N/m 60 N/m 80 N/m 96 N/m

Each spring supports half of the weight,or 6 N. F = kx 28.dynamics.png

29 Dynamics

A ball is thrown and follows a parabolic path, as shown above. Air friction isnegligible. Point Q is the highestpoint on the path. Which of the following best indicates the direction of the netforce on the ball at point P ? D A B C D E gravity acts downward 29.dynamics.png

30 Dynamics

A block of mass 5 kilograms lies on an inclined plane, as shown above. Thehorizontal and vertical supportsfor the plane have lengths of 4 meters and 3 meters, respectively. Thecoefficient of friction between the planeand the block is 0.3. The magnitude of the force F necessary to pull the blockup the plane with constant speedis most nearly B 30 N 42 N 49 N 50 N 58 N

At constant speed ΣF = 0; The forcesacting parallel to the incline are F (up),Ff(down) and mgsinθ (down), which givesF – Ff– mgsinθ = 0, where Ff= µFN =µmgcosθ and cosθ = 4/5 30.dynamics.png

31 Dynamics What is the acceleration of the block? D F/m (Fcosφ)/m (F–f)/m (Fcosφ–f)/m (Fsinφ–mg)/m ΣF = ma = Fcosφ – f 31.dynamics.png

32 Dynamics What is the coefficient of friction between the block and the surface? E f/mg mg/f (mg–Fcosφ)/f f/(mg–Fcosφ) f/(mg–Fsinφ)f = µFN where FN = mg – Fsinθ 32.dynamics.png

33 Dynamics

Three blocks of masses 3m, 2m, ands are connected to strings A, B, and Casshown above. The blocks arepulled along a rough surface by a force of magnitude F exerted by string C.The coefficient of friction betweeneach block and the surface is the same. Which string must be the strongest inorder not to break? C A B C

They must all bethe same strength.

It is impossible todetermine withoutknowing thecoefficient offriction.

The string pulling all three masses (total6m) must have the largest tension.String A is onlypulling the block of mass 3m and stringB is pulling a total mass of 5m. 33.dynamics.png

34 Dynamics

A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontalsurface with a force shown as afunction of time t by the graph above. The acceleration of the block at t = 2 sis B 3/4 m/s^2 4/3 m/s^2 2 m/s^2 8 m/s^2 12 m/s^2 At t = 2 s the force is 4 N. F = ma 34.dynamics.png

35 Dynamics

An object weighing 300 N is suspended by means of two cords, as shownabove. The tension in the horizontalcord is... D 0 N 150 N 210 N 300 N 400 N

The upward component of the slantedcord is 300 N to balance the weight ofthe object. Sincethe slanted cord is at an angle of 45º, ithas an equal horizontal component.The horizontalcomponent of the slanted cord is equalto the tension in the horizontal cord

36 Dynamics

A small box is on a ramp tilted at an angle θ above the horizontal. The boxmay be subject to the followingforces: frictional (f ) ,gravitational (mg), pulling or pushing (FP) and normal (I).In the following free-bodydiagrams for the box, the lengths of the vectors are proportional to themagnitudes of the forces. Which figure best represents the free-body diagramfor the box if it is accelerating up the ramp? E Figure A Figure B Figure C Figure D Figure E

The normal force must pointperpendicular to the surface and theweight must point down. Inorder to accelerate up the ramp, theremust be an applied force up the ramp. Ifthe box isaccelerating up the ramp, friction actsdown the ramp, opposite the motion 36.dynamics.png

37 Dynamics

A small box is on a ramp tilted at an angle θ above the horizontal. The boxmay be subject to the followingforces: frictional (f ) ,gravitational (mg), pulling or pushing (FP) and normal (I).In the following free-bodydiagrams for the box, the lengths of the vectors are proportional to themagnitudes of the forces. Which figure best represents the free-body diagramfor the box if it is at rest on the ramp? C Figure A Figure B Figure C Figure D Figure E

The normal force must pointperpendicular to the surface and theweight must point down. Ifthe box is at rest on the ramp, frictionacts up the ramp, opposing thetendency to slide down 36.dynamics.png

38 Dynamics

A small box is on a ramp tilted at an angle θ above the horizontal. The boxmay be subject to the followingforces: frictional (f ) ,gravitational (mg), pulling or pushing (FP) and normal (I).In the following free-bodydiagrams for the box, the lengths of the vectors are proportional to themagnitudes of the forces. C Figure A Figure B Figure C Figure D Figure E

The normal force must pointperpendicular to the surface and theweight must point down. Ifthe box is sliding down at constantspeed, friction acts up the ramp,opposing the motion 36.dynamics.png

39 Dynamics

Two blocks of masses M and m, with M > m, are connected by a light string.The string passes over africtionless pulley of negligible mass so that the blocks hang vertically. Theblocks are then released from rest.What is the acceleration of the block of mass M ? E g (M-m/M)g (M+m/M)g (M+m/M-m)g (M-m/M+m)g

ΣFexternal = m totala gives (Mg) – (mg)= (M + m)a

40 Dynamics

A horizontal force F pushes a block of mass m against a vertical wall. Thecoefficient of friction between theblock and the wall is μ. What value of F is necessary to keep the block fromslipping down the wall? C mg μ mg mg/μ mg(1 - μ) mg(1 + μ)

. To keep the box from slipping, frictionup the wall must balance the weight ofthe block, or Ff= mg, where Ff= µFN and FN= the applied force F. This gives µF =mg 40.dynamics.png

41 Dynamics

One end of a massless rope is attached to a mass m; the other end isattached to a mass of 1.00 kg. The rope ishung over a massless frictionless pulley asshown in the accompanying figure.Mass m accelerates downward at5.0 m/s2. What is m? A 3.0 kg 2.0 kg 1.5 kg 1.0 kg 0.5 kg

ΣFexternal = mtotala gives (mg) – (10N) = (m + 1 kg)(5 m/s^2) 41.dynamics.png

42 Dynamics

As shown in the accompanying figure, a force F is exerted at an angle of θ.The block of weight mg is initially moving the right with speed v. Thecoefficient of friction between the rough floor and the block is µ. The frictionalforce acting on the block is: E µmg to the left. µmg to the right.

µmg – F sin θ tothe left.

µ(mg – F cos θ) tothe right.

µ(mg + F sin θ) tothe left.

Friction opposes the motion of the blockand therefore points to the left. Thenormal force is found from ΣFy = 0 =FN – mg – Fsinθ and the force offriction Ff = µFN 42.dynamics.png

43 Dynamics The “reaction” force does not cancel the “action” force because: C

The action force isgreater than thereaction force.

The action force isless than thereaction force.

They act ondifferent bodies.

They are in thesame direction.

The reaction existsonly after theaction force isremoved.

When an object exerts a force on asecond object, the second object exertsan equal and opposite force back onthe first object.

44 Dynamics

A student pulls a wooden box along a rough horizontal floor at constantspeed by means of a force P as shown to the right. Which of the followingmust be true? A P > f and N < W. P > f and N = W. P = f and N > W. P = f and N = W. P < f and N = W.

Since P is at an upward angle, thenormal force is decreased as Psupports some of the weight. Since acomponent of P balances the frictionalforce, P itself must be larger than f. 44.dynamics.png

45 DynamicsA block with initial velocity 4.0 m/s slides 8.0 m across a rough horizontal floorbefore coming to rest. The coefficient of friction is: D 0.8 0.4 0.2 0.1 0.05

Newton’s 2nd law applied to an objectsliding to rest gives ΣF = –Ff = –µFN =ma. On a horizontal surface, FN = mgand we have –µmg = ma, or a = –µg.Use this acceleration with vf^2 = vi^2 +2ad.

46 DynamicsA car whose mass is 1500 kg is accelerated uniformly from rest to a speed of20 m/s in 10 s. The magnitude of the net force accelerating the car is: C 1000 N 2000 N 3000 N 20000 N 30000 N F = ma = m∆v/t

47 DynamicsAn 800-kg elevator accelerates downward at 2.0 m/s^2. The force exerted bythe cable on the elevator is: C 1.6 kN down 1.6 kN up 6.4 kN up 8.0 kN down 9.6 kN down

ΣF = ma; Fcable – mg = ma = m(–2m/s^2)

48 Dynamics

The 10.0 kg box shown in the figure to the right is sliding to the right along thefloor. A horizontal force of 10.0 N is being applied to the right. The coefficientof kinetic friction between the box and the floor is 0.20. The box is movingwith: A

acceleration to theleft.

centripetalacceleration.

acceleration to theright.

constant speedand constantvelocity.

constant speed butnot constantvelocity.

The force of friction = µFN = 0.2 × 10kg × 9.8 m/s^2 = 19.6 N, which isgreater than the applied force, whichmeans the object is accelerating to theleft, or slowing down 48.dynamics.png

49 Dynamics

Two blocks X and Y are in contact on a horizontal frictionless surface. A 36 Nconstant force is applied to X as shown to the right. The force exerted by X onY is: D 1.5 N 6.0 N 29 N 30 N 36 N

F = ma gives 36 N = (24 kg)a or anacceleration of 1.5 m/s^2. The 20 kgblock is accelerating due to the contactforce from the 4 kg block Fcontact = ma= (20 kg)(1.5 m/s^2) = 30 N. 49.dynamics.png

50 Dynamics

Assume the objects in the following diagrams have equal mass and thestrings holding them in place are identical. In which case would the string bemost likely to break? B A B C D E

The upward component of the tensionis Tup = Tsinθ, where θ is the angle tothe horizontal. This gives T = Tup/sinθ.Since the upward components are allequal to one half the weight, the rope atthe smallest angle (and the smallestvalue of sinθ) will have the greatesttension, and most likely break 50.dynamics.png

51 Dynamics

A string with masses of 1.5 kg and 3.0 kg on its ends is hung over africtionless, massless pulley as shown to theright. What is the approximate magnitude of the acceleration of the masses? C 1.5 m/s^2 3.0 m/s^2 3.3 m/s^2 6.7 m/s^2 10 m/s^2

ΣFexternal = mtotal•a gives (3.0 kg ×10 m/s^2) – (1.5 kg × 10 m/s^2) = (4.5kg)a 51.dynamics.png

52 Dynamics

Two blocks of mass 1.0 kg and 3.0 kg are connected by a string which has atension of 2.0 N. A force F acts inthe direction shown to the right. Assuming friction is negligible, what is thevalue of F? E 1.0 N 2.0 N 4.0 N 6.0 N 8.0 N

From the 1 kg block: F = ma giving a =2 m/s2. For the system: F = (4 kg)(2m/s2) 52.dynamics

53 DynamicsAn object in equilibrium has three forces, F1 of 30 N, F2 of 50 N, and F3 of 70N, acting on it. The magnitude of the resultant of F1 and F2 is D 10 N 20 N 40 N 70 N 80 N

For three forces in equilibrium, any oneof the forces is equal and opposite tothe resultant of the other two forces.

54 Dynamics

A 50-kg student stands on a scale in an elevator. At the instant the elevatorhas a downward acceleration of 1.0m/s2 and an upward velocity of 3.0 m/s, the scale reads approximately B 350 N 450 N 500 N 550 N 650 N

Elevator physics: FN represents thescale reading. ΣF = ma; FN – mg = ma,or FN = m(g + a). The velocity of theelevator is irrelevant.

55 Dynamics

If the net force on an object were doubled while at the same time the mass ofthe object was halved, then theacceleration of the object is D 1/4 as great. 1/2 as great. 2 times greater. 4 times greater. unchanged

F = ma, if F is doubled, a is doubled. Ifm is halved, a will be doubled

56 Dynamics

A tractor-trailer truck is traveling down the road. The mass of the trailer is 4times the mass of the tractor. If thetractor accelerates forward, the force that the trailer applies on the tractor is C

4 times greaterthan the force ofthe tractor on thetrailer.

2 times greaterthan the force ofthe tractor on thetrailer.

equal to the forceof the tractor onthe trailer.

¼ the force of thetractor on thetrailer

zero since thetractor is pullingthe trailer forward. Newton’s third law 56.dynamics

57 Dynamics

Two boxes are accelerated to the right on a frictionless horizontal surface asshown. The larger box has a massof 9 kilograms and the smaller box has a mass of 3 kilograms. If a 24 newtonhorizontal force pulls on the largerbox, with what force does the larger box pull on the smaller box? B 3 N 6 N 8 N 18 N 24 N

F = ma gives 24 N = (12 kg)a or anacceleration of 2 m/s2. The 3 kg blockis accelerating due to the tension in therope FT = ma = (3 kg)(2 m/s2) = 6 N. 57.dynamics

58 Dynamics What happens to the inertia of an object when its velocity is doubled? E

the object’s inertiabecomes 2 timesgreater

the object’s inertiabecomes 2 timesgreater

the object’s inertiabecomes 4 timesgreater

the object’s inertiabecomes 8 timesgreater

the object’s inertiais unchanged Inertia is mass

59 Dynamics

A wooden box is first pulled across a horizontal steel plate as shown in thediagram A. The box is then pulledacross the same steel plate while the plate is inclined as shown in diagram B.How does the force required toovercome friction in the inclined case (B) compare to the horizontal case (A)? C

the frictional forceis the same in bothcases

the inclined casehas a greaterfrictional force

the inclined casehas less frictionalforce

the frictional forceincreases withangle until theangle is 90º, thendrops to zero

more information isrequired

The normal force is mgcosθ. For ahorizontal surface, FN = mg. At anyangle FN < mg and Ff is proportional toFN

60 DynamicsAn object near the surface of the earth with a weight of 100 newtons isaccelerated at 4 m/s2. What is the netforce on the object? B 25 N 40 N 250 N 400 N 2500 N F = ma, where m = W/g = 10 kg

61 Dynamics

A car of mass m slides across a patch of ice at a speed v with its brakeslocked. It then hits dry pavement and skids to a stop in a distance d. Thecoefficient of kinetic friction between the tires and the dry road is μ. If the carhad a mass of 2m, it would have skidded a distance of B 0.5 d d 1.41 d 2 d 4 d

Newton’s 2nd law applied to an objectsliding to rest gives ΣF = –Ff = –μFN =ma. On ahorizontal surface, FN = mg and wehave –μmg = ma, or a = –μg. Using thisacceleration withvf2 = vi2 + 2ad gives d = vi2/2μg. Thereis no dependence on mass.

62 Dynamics

Shown below is the velocity vs. time graph for a toy car moving along astraight line. What is the maximumdisplacement from start for the toy car? D 3 m 5 m 6.5 m 7 m 7.5 m

Displacement is the area under thecurve. Maximum displacement is justbefore the car turnsaround at 2.5 seconds. 62.dynamics.png

63 Dynamics

A cannon fires projectiles on a flat range at a fixed speed but with variableangle. The maximum range of thecannon is L. What is the range of the cannon when it fires at an angle π/6above the horizontal? Ignore airresistance. A √3/2 L 1/√2 L 1/√3 L 1/2 L 1/3 L

Range of a projectile R = (vi^2 sin 2θ)/gand maximum range occurs at θ = 45º,which gives vi√Rg. Using θ = 30º givesRnew= R sin 60º

64 Dynamics

A ball is launched upward from the ground at an initial vertical speed of v0and begins bouncing vertically.Every time it rebounds, it loses a proportion of the magnitude of its velocitydue to the inelastic nature of thecollision, such that if the speed just before hitting the ground on a bounce is v,then the speed just after thebounce is rv, where r < 1 is a constant. Calculate the total length of time thatthe ball remains bouncing,assuming that any time associated with the actual contact of the ball with theground is negligible. A (2vo/g)*(1/1−r) (vo/g)*(r/1−r) (2vo/g)*(1−r/r) (2vo/g)*(1/1−r^2)

(2vo/g)*(1/1+(1-r)^2)

(advanced question!) The time for onebounce is found from –v = v + (–g)twhich gives t = 2v/g.We are summing the time for allbounces, while the velocity (and hencethe time) converge in ageometric series with the ratiovn+1/vn = r<1 to (1/1 − r)

65 DynamicsThe graph shows velocity as a function of time for a car. What was theacceleration at time t = 90 seconds? B 0.22 m/s^2 0.33 m/s^2 1.0 m/s^2 9.8 m/s^2 30 m/s^2

The acceleration is the slope of thecurve at 90 seconds. 65.dynamics.png

66 Dynamics

An object is released from rest and falls a distance h during the first second oftime. How far will it fall duringthe next second of time? C h 2h 3h 4h h^2

From the equation d = ½ at^2,displacement is proportional to timesquared. Traveling from restfor twice the time gives 4 times thedisplacement (or 4 h). Since the objectalready travelled h inthe first second, during the time intervalfrom 1 s to 2 s the object travelled theremaining 3h

67 Dynamics

A stone is thrown straight downward with a speed of 20 m/s from the top of atall building. If the stone strikesthe ground 3.0 s later, about how tall is the building? Assume air resistance isnegligible. D 45 m 60 m 90 m 105 m 120 m d = vit + ½ gt^2

68 Dynamics

A coyote can run at a speed of 20 m/s while a prairie dog can manage only5.5 m/s. If a prairie dog is 45 m infront of a coyote, what is the maximum time it has to reach its hole withoutbeing caught? B 2.3 s 3.1 s 5.4 s 5.9 s 8.2 s

The relative speed between the coyoteand the prairie dog is 14.5 m/s. Tocover the 45 mdistance between them will take t = d/v= (45 m)/(14.5 m/s)

69 Dynamics

A model rocket accelerates from rest upwards at 50 m/s2for 2.0 s before its engine burns out. The rocket thencoasts upward. What is the maximum height that the rocket reaches? Youmay assume air resistance isnegligible. C 100 m 510 m 610 m 1020 m 1220 m

For the first part of the trip (the thrust):d1 = vit + ½ at^2 = 0 m + ½ (50 m/s^2)(2 s)^2For the second part, we first find thevelocity after the thrust v = at = 100 m/sand at themaximum height v= 100 mf = 0, so to find d2 we use vf^2 = vi^2 +2ad2 which gives d2= 510 m

70 Dynamics

A hunter in a forest walks 800 m west. He then turns south and walks 400 mbefore turning west again andwalking a final 300 m. At the end of the walk, what is the magnitude of thehunter's displacement from thebeginning? C 640 m 890 m 1170 m 1390 m 1500 m

Total displacement west = 1100 m; totaldisplacement south = 400 m. Use thePythagoreantheorem.

71 Dynamics

Robin Hood aims his longbow horizontally at a target's bull's eye 30 m away.If the arrow strikes the targetexactly 1.0 m below the bull's eye, how fast did the arrow move as it was shotfrom the bow? Assume airresistance is negligible. D 6.0 m/s 13 m/s 33 m/s 67 m/s 150 m/s

For a horizontal projectile (viy = 0 m/s)to fall 1 m takes (using 1 m = ½ gt^2)0.45 seconds. Totravel 30 m in this time requires aspeed of d/t = (30 m)/(0.45 s)

72 Dynamics

A 2 kg mass and a 4 kg mass on a horizontal frictionless surface areconnected by a massless string A. They arepulled horizontally across the surface by a second string B with a constantacceleration of 12 m/s2. What is the magnitude of the force of string B on the2 kg mass? A 72 N 48 N 24 N 6 N 3 N

String B is pulling both masses so FB =(6 kg)(12 m/s2) 72.dynamics.png

73 Dynamics

A 2 kg mass and a 4 kg mass on a horizontal frictionless surface areconnected by a massless string A. They arepulled horizontally across the surface by a second string B with a constantacceleration of 12 m/s2. What is the magnitude of the force of string A on the4 kg mass? B 72 N 48 N 24 N 6 N 3 N

String A is only pulling the 4 kg mass soFA = (4kg)(12 m/s2) 72.dynamics.png

74 Dynamics

A 2 kg mass and a 4 kg mass on a horizontal frictionless surface areconnected by a massless string A. They arepulled horizontally across the surface by a second string B with a constantacceleration of 12 m/s2. What is the magnitude of the net force on the 2 kgmass? C 72 N 48 N 24 N 6 N 3 N Fnet = ma 72.dynamics.png

75 Dynamics

A mass is suspended from the roof of a lift (elevator) by means of a springbalance. The lift (elevator) is movingupwards and the readings of the spring balance are noted as follows:Speeding up: RUConstant speed: RCSlowing down: RDWhich of the following is a correct relationship between the readings? A RU > RC RU = RD RC = RD RC < RD RU < RD

Elevator physics: R represents thescale reading. ΣF = ma; R – mg = ma,or R = m(g + a). Thisranks the value of R from largest tosmallest as accelerating upward,constant speed,accelerating downward

76 Dynamics

A small box of mass m is placed on top of a larger box of mass 2m as shownin the diagram at right. When aforce F is applied to the large box, both boxes accelerate to the right with thesame acceleration. If thecoefficient of friction between all surfaces is μ, what would be the forceaccelerating the smaller mass? A A B C D E

ΣF = ma for the whole system gives F –µ(3m)g = (3m)a and solving for a givesa = (F – 3µmg)/3m. For the top block,Fm= ma = m[(F – 3µmg)/3m] 76.dynamics.png

77 Dynamics

The S.I. unit of force is named the newton in honor of Sir Isaac Newton'scontributions to physics. Which ofthe following combination of units is the equivalent of a newton? D A B C D E m × a = kg × m/s^2 77.dynamics.png

78 Dynamics

A 6.0 kg block initially at rest is pushed against a wall by a 100 N force asshown. Thecoefficient of kinetic friction is 0.30 while the coefficient of static friction is0.50. What istrue of the friction acting on the block after a time of 1 second? D

Static friction actsupward on theblock.

Kinetic friction actsupward on theblock

No friction acts onthe block

Kinetic friction actsdownward on theblock

Static friction actsdownward on theblock.

The normal force comes from theperpendicular component of the appliedforce which is Fcosθ= 50 N. The maximum value of staticfriction is then µFN = 25 N. The upward component ofthe applied force is Fsinθ = 87 N. ΣFy= Fup – mg = 87 N– 60 N > 25 N. Sincethe net force onthe block is great than static friction canhold, the block will begin moving up thewall. Since itis in motion, kinetic friction is actingopposite the direction of the block’smotion 78.dynamics.png

79 Dynamics

A homeowner pushes a lawn mower across a horizontal patch of grass with aconstant speed by applying aforce P. The arrows in the diagram correctly indicate the directions but notnecessarily the magnitudes of thevarious forces on the lawn mower. Which of the following relations among thevarious force magnitudes, W, f, N, Pis CORRECT? A P > f and N> W P < f and N = W P > f and N< W P = f and N > W none of the above

Since P is at a downward angle, thenormal force is increased. Since acomponent of P balancesthe frictional force, P itself must belarger than f. 79.dynamics.png

80 Dynamics

A mass, M, is at rest on a frictionless surface, connected to an idealhorizontal spring that is unstretched. Aperson extends the spring 30 cm from equilibrium and holds it at this locationby applying a 10 N force. Thespring is brought back to equilibrium and the mass connected to it is nowdoubled to 2M. If the spring isextended back 30 cm from equilibrium, what is the necessary force applied bythe person to hold the massstationary there? C 20.0 N 14.1 N 10.0 N 7.07 N 5.00 N

Since the force is applied horizontally,the mass has no effect.

81 Dynamics

A baseball is thrown by a pitcher with a speed of 35 m/s. The batter swingsand hits the ball. The magnitude ofthe force that the ball exerts on the bat is always E

zero as it is onlythe bat that exertsa force on the ball.

equal to thegravitational forceacting on the ball.

larger than theforce the batexerts on the ball.

smaller than theforce the batexerts on the ball.

equal to the forcethat the bat exertson the ball. Newton’s third law

82 DynamicsA book leans against a crate on a table. Neither is moving. Which of thefollowing statements concerning this situation is CORRECT? C

The force of thebook on the crateis less than that ofcrate on the book.

Although there isno friction actingon the crate, theremust be frictionacting on the bookor else it will fall.

The net forceacting on the bookis zero.

The direction ofthe frictional forceacting on the bookis in the samedirection as thefrictional forceactingon the crate.

The Newton’sThird Law reactionforce to the weightof the book is thenormal force fromthe table

If they are not moving, the net forcemust be zero. While the book and crateare pushing each other apart, there isfriction from the table pointing inwardagainst each object on the table to keepthem at rest. 82.dynamics.png

83 Dynamics

A crate of toys remains at rest on a sleigh as the sleigh is pulled up a hill withan increasing speed. The crate is not fastened down to the sleigh. What forceis responsible for the crate’s increase in speed up the hill? B

the contact force(normal force) ofthe ground on thesleigh

the force of staticfriction of thesleigh on the crate

the contact force(normal force) ofthe sleigh on thecrate

the gravitationalforce acting on thesleigh no force is needed

The only force in the direction of thecrate’s acceleration is the force offriction from the sleigh

84 DynamicsA student weighing 500 N stands on a bathroom scale in the school’selevator. When the scale reads 520 N, the elevator must be A

acceleratingupward.

acceleratingdownward.

moving upward ata constant speed.

moving downwardat a constantspeed. at rest.

Elevator physics: FN represents thescale reading. ΣF = ma; FN – mg = ma,or FN = m(g + a). When FN > mg, theelevator is accelerating upward (a ispositive)

85 DynamicsIn which one of the following situations is the net force constantly zero on theobject? E

A mass attachedto a string andswinging like apendulum.

A stone fallingfreely in agravitational field.

An astronautfloating in theInternationalSpace Station.

A snowboarderriding down asteep hill.

A skydiver whohas reachedterminal velocity.

Changing direction (choices A and C(the astronaut is still orbiting the earth!))cannot occurwith a zero net force. Choices B and Drepresent accelerated motion.

86 Dynamics

A box slides to the right across a horizontal floor. A person called Ted exertsa force T to the right on the box. A person called Mario exerts a force M to theleft, which is half as large as the force T. Given that there is friction f and thebox accelerates to the right, rank the sizes of these three forces exerted onthe box A f < M < T M < f < T M < T < f f = M < T

It cannot bedetermined.

Given that the box accelerates towardTed, Ted’s force must be greater thanMario’s force plus the force of friction.Since Mario’s force is ½ of Ted’s force,the force of frction must be less thanhalf of Ted’s force.

87 Dynamics

You hold a rubber ball in your hand. The Newton's third law companion forceto the force of gravity on the ball is the force exerted by which object ontowhat other object? C ball on the hand Earth on the ball ball on the Earth Earth on your hand hand on the ball

For a Newton’s third law pair, justswitch the nouns

88 Dynamics

An object on an inclined plane has a gravitational force of magnitude 10 Nacting on it from the Earth. Which of the following gives the correctcomponents of this gravitational force for the coordinate axes shown in thefigure? The y-axis is perpendicular to the incline’s surface while the x-axis isparallel to the inclined surface. A

X-component-positive 6 N Y-component-negative 8 N

X-component-positive 8 N Y-component-negative 6 N

X-component-negative 6 N Y-component-positive 8 N

X-component-negative 8 N Y-component-positive 6 N

X-component- 0 NY-component-positive 10 N

The component of gravity acting downthe incline (+x) is mgsinθ and thecomponentperpendicularly intothe incline (–y) ismgcosθ. 36.9º indicates a 3-4-5triangle. 88.dynamics.png

89 Dynamics

A spaceman of mass 80 kg is sitting in a spacecraft near the surface of theEarth. The spacecraft is accelerating upward at five times the accelerationdue to gravity. What is the force of the spaceman on the spacecraft? A 4800 N 4000 N 3200 N 800 N 400 N ΣF = ma; F – mg = m(5g) or F = 6mg

90 Dynamics

. A 22.0 kg suitcase is dragged in a straight line at a constant speed of 1.10m/s across a level airport floor by a student on the way to Mexico. Theindividual pulls with a 1.0 × 102 N force along a handle which makes anupward angle of 30.0 degrees with respect to the horizontal. What is thecoefficient of kinetic friction between the suitcase and the floor? C μk = 0.013 μk = 0.394 μk= 0.509 μk= 0.866 μk= 1.055

ΣFy= Fsinθ + FN – mg = 0, which givesFN = 170 N. The force of friction isequal to the horizontal component ofthe force applied by the student whichis Fcosθ = 86.6N. Ff= µFN

91 Dynamics

A person pushes a block of mass M = 6.0kg with a constant speed of 5.0 m/sstraight up a flat surface inclined30.0° above the horizontal. The coefficient of kinetic friction between theblock and the surface is μ = 0.40.What is the net force acting on the block? A 0 N 21 N 30 N 51 N 76 N constant speed means F(net) = 0 N 91.dynamics.png

92 Dynamics

In the figure above, a box moves with speed 5.0 m/s at the bottom of a rough,fixed inclined plane. The boxslides with constant acceleration to the top of the incline as it is being pusheddirectly to the left with a constantforce of F = 240 N. The box, of mass m = 20.0 kg, has a speed of 2.50 m/swhen it reaches the top of theincline. What is the magnitude of the acceleration of the box as it slides upthe incline? E 12.0 m/s^2 10.0 m/s^2 5.88 m/s^2 1.88 m/s^2 0.938 m/s2

As the initial and final velocities and thedisplacement are given, as well as anindication that the acceleration isconstant, this is merely a kinematicsproblem. vf2 = vi2 + 2ad 92.dynamics.png

93 Dynamics

A 20.0 kg box remains at rest on a horizontal surface while a person pushesdirectly to the right on the box witha force of 60 N. The coefficient of kinetic friction between the box and thesurface is μk = 0.20. The coefficientof static friction between the box and the surface is μs= 0.60. What is themagnitude of the force of frictionacting on the box during the push? C 200 N 120 N 60 N 40 N 0 N

The maximum value of static friction inthis case is μsFN = 120 N. Since theperson is pushing with only 60 N offorce, the box remains at rest.

94 Dynamics

Two identical blocks of weight W are placed one on top of the other as shownin the diagram above. The upperblock is tied to the wall. The lower block is pulled to the right with a force F.The coefficient of static frictionbetween all surfaces in contact is μ. What is the largest force F that can beexerted before the lower block startsto slip? E μW 3μW/2 2μW 5μW/2 3μW

Between the lower block and thetabletop, there is a force of friction tothe left of maximummagnitude μ(2W) as both blocks arepushing down on the tabletop. There isalso a force offriction acting to the left on the uppersurface of the lower block due to theupper block ofmaximum magnitude μW. The totalmaximum static frictional force holdingthe lower block inplace is therefore μ(2W) + μW 94.dynamics.png

95 Dynamics

A force F is used to hold a block of mass m on an incline as shown in thediagram (see above). The plane makesan angle of θ with the horizontal and F is perpendicular to the plane. Thecoefficient of friction between theplane and the block is μ. What is the minimum force, F, necessary to keepthe block at rest? E μmg mgcosθ mgsinθ mgsinθ/μ mg(sinθ – μcosθ)/μ

The normal force on the block can befound from ΣFy = 0 = FN – mgcosθ – F.The force offriction necessary to hold the block inplace is mgsinθ. Setting the force offriction equal tomgsinθ gives μFN = mgsinθ = μ(F +mgcosθ) 95.dynamics.png

96 Dynamics

A mass m is resting at equilibrium suspended from a vertical spring of naturallength L and spring constant kinside a box as shown. The box begins accelerating upward with accelerationa. How much closer does the equilibrium position of themass move to the bottom of the box? C (aL)/g (gL)/a (m(g+a))/k (m(g-a))/k (ma)/k

In equilibrium, mg = kx and theequilibrium position x = mg/k. In anaccelerating elevator, wecan just adjust gravity to its effectivevalue g(eff) = g + a, thus making thenew equilibriumposition mg(eff)/k 96.dynamics.png

97 Dynamics

When the speed of a rear-drive car is increasing on a horizontal road, what isthe direction of the frictional forceon the tires? A

backward on thefront tires andforward on the reartires

forward on thefront tires andbackward on therear tires. forward on all tires

backward on alltires zero

This is a tricky one. In order to movethe car forward, the rear tires roll backagainst theground, the force of friction pushingforward on the rear tires. The front tires,however, are nottrying to roll on their own, rather theybegin rolling due to the friction actingbackward,increasing their rate of rotation

98 Dynamics

A ball of mass m is launched into the air. Ignore air resistance, but assumethat there is a wind that exerts aconstant force Fo in the –x direction. In terms of Fo and the acceleration dueto gravity g, at what angle abovethe positive x-axis must the ball be launched in order to come back to thepoint from which it was launched? B tan-1(Fo/mg) tan-1(mg/Fo) sin-1(Fo/mg)

the angle dependson the launchspeed

no such angle ispossible

Gravity is still the only force actingvertically so we can find the total time inthe air fromkinematics: vy = 0 at the top = vosinθ –gt giving t (to the top) = v0sinθ/g andthe total time istwice the time to the top, or 2vosinθ/g.In this time, the ball is also acceleratinghorizontally(think of it as a “sideways” gravity) andin this time, should return to its startinglocation.Using x = 0 = (vocosθ)t + ½ at2, wherea = Fo/m and t is found above, we cansolve for θ

99 Dynamics

Given the three masses as shown in the diagram above, if the coefficient ofkinetic friction between the largemass (m2) and the table is μ, what would be the upward acceleration of thesmall mass (m3)? The mass andfriction of the cords and pulleys are small enough to produce a negligibleeffect on the system. E

m1g/(m1 + m2 +m3)

g(m1 + m2μ)/(m1+ m2 + m3)

gμ(m1 + m2 + m3)/(m1 – m2 – m3)

gμ(m1 – m2 – m3)/(m1 + m2 + m3)

g(m1 – μm2 – m3)/(m1 + m2 + m3)

The external forces acting on thesystem of masses are the weights ofblock 1 (pulling thesystem to the left), the weight of block 3(pulling the system to the right) and theforce offriction on block 2 (pulling the system tothe left with a magnitude μFN = μm2g)ΣF(external) = m(total)a gives (m1g –μm2g – m3g) = (m1 + m2 + m3)a 99.dynamics.png

100 Dynamics

Two masses 5.0 and 7.0 kg are originally at rest on a frictionless surface. Themasses are connected by a lightcord. A second cord is attached to the 7.0 kg mass and pulled with ahorizontal force of 30 N. What is thetension in the cord that connects the two masses? C 5 N 7 N 12.5 N 17.5 N 30 N

F = ma gives 30 N = (12 kg)a or anacceleration of 2.5 m/s2. The 5 kg blockis accelerating dueto the tension in the rope FT = ma = (5kg)(2.5 m/s2) = 12.5 N. 100.dynamics.png

101 Dynamics

Two masses are connected by a light cord which is looped over a lightfrictionless pulley. If one mass is 3.0 kgand the second mass is 5.0 kg, what is the downward acceleration of theheavier mass? Assume air resistance isnegligible. E 9.8 m/s^2 8.4 m/s^2 6.3 m/s^2 3.8 m/s^2 2.5 m/s^2

ΣF(external) = m(total)a gives (5.0 kg ×10 m/s2) –(3 kg × 10 m/s2) = (8 kg)a 101.dynamics.png

102 Dynamics

Three identical laboratory carts A, B, and C are each subject to a constantforce FA, FB, and FC, respectively.One or more of these forces may be zero. The diagram below shows theposition of each cart at each second ofan 8.0 second interval. Which car has the greatestaverage velocity during the interval? D A B C

all three averagevelocities areequal

not enoughinformation isprovided

As they are all at the same positionafter 8 seconds, they all have the sameaverage velocity 104.dynamics.png

103 Dynamics

Three identical laboratory carts A, B, and C are each subject to a constantforce FA, FB, and FC, respectively.One or more of these forces may be zero. The diagram below shows theposition of each cart at each second ofan 8.0 second interval. How does the magnitude of theforce acting on each car compare? B FA > FB > FC FA = FC > FB FA > FC = FB FA = FB > FC

not enoughinformation

Car A decelerates with the samemagnitude that C accelerates. Car B ismoving at constantspeed, which means FBB= 0. 104.dynamics.png

104 Dynamics

A skydiver is falling at terminal velocity before opening her parachute. Afteropening her parachute, she falls ata much smaller terminal velocity. How does the total upward force before sheopens her parachute compare tothe total upward force after she opens her parachute? E

The ratio of theforces is equal tothe ratio of thevelocities

The ratio of theforces is equal tothe ratio of thevelocities

the upward forcewith the parachutewill depend on thesize of theparachute

The upward forcebefore theparachute will begreater because ofthe greatervelocity.

The upward forcein both cases mustbe the same.

When falling with terminal velocity, theforce of air resistance equals yourweight, regardless ofthe speed.

105 Dynamics

Each of the diagrams below represents two weights connected by a masslessstring which passes over amassless, frictionless pulley. In which diagram will the magnitude of theacceleration be the largest? A

For each case, ΣFexternal = mtotal*agives Mg – mg = (M + m)a or a=[(M-m)/(M+m)]g 105.dynamics.png

106 Dynamics

A simple Atwood's machine is shown in the diagram above. It is composed ofa frictionless lightweight pulleywith two cubes connected by a light string. If cube A has a mass of 4.0 kg andcube B has a mass of 6.0 kg, thesystem will move such that cube B accelerates downwards. What would bethe tension in the two parts of thestring between the pulley and the cubes? B

TA = 47 N ; TB =71 N

TA = 47 N ; TB =47 N

TA = 47 N ; TB =42 N

TA = 39 N ; TB =59 N

TA = 39 N ; TB =39 N

The two ends of the light string musthave the same tension, eliminatingchoices A, C and D. Ifchoice E was correct, both masseswould be accelerating downward andTA must be greater than the weight ofblock A. 106.dynamics.png

107 Dynamics

If a net force F applied to an object of mass m will produce an acceleration ofa, what is the mass of a secondobject which accelerates at 5a when acted upon by a net force of 2F? A (2/5)m 2m (5/2)m 5m 10m

If F = ma, then m = F/a. For the secondobject m′ = 2F/5a = 2/5(F/a) = (2/5)m 107.dynamics.png

108 Dynamics

A simple Atwood's machine remains motionless when equal masses M areplaced on each end of the chord.When a small mass m is added to one side, the masses have an accelerationa. What is M? You may neglectfriction and the mass of the cord and pulley. A

ΣFexternal = mtotala gives (M + m)g –Mg = (2M + m)a 108.dynamics.png

109 Dynamics

Block 1 is stacked on top of block 2. Block 2 is connected by a light cord toblock 3, which is pulled along africtionless surface with a force F as shown in the diagram. Block 1 isaccelerated at the same rate as block 2because of the frictional forces between the two blocks. If all three blockshave the same mass m, what is theminimum coefficient of static friction between block 1 and block 2? E 2F/mg 2F/3mg F/mg 3F/2mg F/3mg

As the entire system moves as one, F =(3m)a, or a = F/(3m). The force offriction acting onblock 1 is the force moving block 1 andwe have μmg = m(F/(3m))

110 Dynamics

An object originally traveling at a velocity, v0, is accelerated to a velocity, v, ina time, t, by a constant force, F.What would be the mass of the object? B F = ma = mΔv/t 110.dynamics.png

111 Dynamics

A frictionless air puck of mass m is placed on a plane surface inclined at anangle of 60° with respect to thehorizontal. A string of length l is attached to the puck at one end and theupper edge of the inclined plane at theother to constrain the movement of the puck. What would be the magnitude ofthe normal force from the planeacting on the puck? E mg(sin 60°) mg(cos 30°) mg(tan 30°) mg/(tan 60) None of these

This is really no different than any otherincline problem. The normal force on anincline withno other forces acting into the incline ismgcosθ 11.dynamics.png

112 Dynamics

Three blocks (m1, m2, and m3) are sliding at a constant velocity across arough surface as shown in thediagram above. The coefficient of kinetic friction between each block and thesurface is μ. What would be theforce of m1 on m2? A (m2 + m3)gμ F – (m2 – m3)gμ (m1+ m2+ m3)gμ F m1gμ – (m2+ 3)gμ

Since the system is moving at constantvelocity, m1 is pushing m2 and m3with a force equal tothe force of frictionacting on those two blocks, which is µ(FN2 + FN3) 112.dynamics.png

113 Dynamics

Two 5 kg masses are attached to opposite ends of a long massless cordwhich passes tautly over a masslessfrictionless pulley. The upper mass is initially held at rest on a table 50 cmfrom the pulley. The coefficient ofkinetic friction between this mass and the table is 0.2. When the system isreleased, its resulting acceleration isclosest to which of the following? D 9.8 m/s^2 7.8 m/s^2 4.9 m/s^2 3.9 m/s^2 1.9 m/s^2

ΣFexternal = mtotala gives (5 kg × 9.8m/s2) – Ff= (10 kg)a, where Ffis the force of friction actingon the 5 kg block on the table: µmg =0.2 × 5 kg × 9.8 m/s2D= 9.8 N 113.dynamics.png

1 Circular

When a person stands on a rotating merry-go-round, the frictional forceexerted on the person by themerry-go-round is B

greater inmagnitude thanthe frictional forceexerted on theperson by themerry-go-round

opposite indirection to thefrictional forceexerted on themerry-go-round bythe person

directed away fromthe center of themerry-go-round

zero if the rate ofrotation is constant

independent of theperson's mass Newton’s third law

2 Circular

A ball attached to a string is whirled around in a horizontal circle having aradius r. If the radius of the circle ischanged to 4r and the same centripetal force is applied by the string, the newspeed of the ball is which of thefollowing? D

One-quarter theoriginal speed

One-half theoriginal speed

The same as theoriginal speed

Twice the originalspeed

Four times theoriginal speed

F = mv^2/r ; v=sqrt((Fr)/m) all othervariables being constant, if r isquadrupled, v is doubled

3 Circular

A racing car is moving around the circular track of radius 300 meters shownabove. At the instant when the car'svelocity is directed due east, its acceleration is directed due south and has amagnitude of 3 meters per secondsquared. When viewed from above, the car is moving A

clockwise at 30m/s

clockwise at 10m/s

counterclockwiseat 30 m/s

counterclockwiseat 10 m/s

with constantvelocity

With acceleration south the car is at thetop (north side) of the track as theacceleration points toward the center ofthe circular track. Moving east indicatesthe car is travelling clockwise. Themagnitude of the acceleration is foundfrom a = v2/r 3.circular.png

4 Circular

The horizontal turntable shown above rotates at a constant rate. As viewedfrom above, a coin on the turntablemoves counterclockwise in a circle as shown. Which of the following vectorsbest represents the direction of thefrictional force exerted on the coin by the turntable when the coin is in theposition shown? D A B C D E

The frictional force acts as thecentripetal force (toward the center) 4.circular.png

5 Circular

In which of the following situations would an object be accelerated?I. It moves in a straight line at constant speed.II. It moves with uniform circular motion.III. It travels as a projectile in a gravitational field with negligible air resistance. D I only III only I and II only II and III only I, II, and III.

Acceleration occurs when an object ischanging speed and/or direction

6 Circular

An automobile moves at constant speed down one hill and up another hillalong the smoothly curved surfaceshown above. Which of the following diagrams best represents the directionsofthe velocity and theacceleration of the automobile at the instant that it is at the lowest position. asshown? B A B C D E

Velocity is tangential, accelerationpoints toward the center of the circularpath 6.circular.png

7 Circular

A car initially travels north and then turns to the left along a circular curve.This causes a package on the seat ofthe car to slide toward the right side of the car. Which of the following is trueof the net force on the packagewhile it is sliding? E

The force isdirected away fromthe center of thecircle

The force isdirected north.

There is notenough forcedirected north tokeep the packagefrom sliding.

There is notenough forcetangential to thecar's path to keepthe package fromsliding.

There is notenough forcedirected toward thecenter of the circleto keep thepackage fromsliding.

To move in a circle, a force directedtoward the center of the circle isrequired. While thepackage slides to the right in the car, itis actually moving in its original straightline path whilethe car turns from under it.

8 Circular

A child has a toy tied to the end of a string and whirls the toy at constantspeed in a horizontal circular path ofradius R. The toy completes each revolution of its motion in a time period T.What is the magnitude of theacceleration of the toy? B Zero (4 pi^2 R)/T^2 (pi R)/T^2 g 2*pi*g

a = v^2/r and v = 2×(pi r)/T giving a = (6pi^2 r)/T^2

9 Circular10 Circular11 Circular12 Circular13 Circular14 Circular15 Circular16 Circular17 Circular18 Circular

19 Circular

A child whirls a ball at the end of a rope, in a uniform circular motion. Whichof the following statements isNOT true? B

The speed of theball is constant

The velocity of theball is consant

The radius isconstant

The magnitude ofthe ball'sacceleration isconstant

The acceleration ofthe ball is directedradially inwardstowards the center

While speed may be constant, thechanging direction means velocitycannot be constant asvelocity is a vector

20 Circular

An astronaut in an orbiting space craft attaches a mass m to a string andwhirls it around in uniform circularmotion. The radius of the circle is r, the speed of the mass is v, and thetension in the string is F. If the mass,radius, and speed were all to double the tension required to maintain uniformcircular motion would be D F/2 F 2F 4F 8F

F = mv2/r. Fnew = (2m)(2v)2/(2r) = 4(mv2/r) = 4F

21 Circular

Assume the roller coaster cart rolls frictionlessly alongthe curved track from point A to point C under theinfluence of gravity. What would be the direction of thecart's acceleration at point B? A Upward Downward Forward Backward No acceleration

Assuming the track is circular at thebottom, the acceleration points towardthe center of thecircular path 21.circular.png

22 Circular Which car has had the lowest average speed during the race so far? C Car A Car B Car C

All three cars havehad the sameaverage speed

Cannot bedetermined withinformationprovided

Average speed = (total distance)/(totaltime). Lowest average speed is the carthat covered the least distance 22.circular.png

23 CircularWhich car at the moment of the snapshot MUST have a net force acting onit? D Car A Car B Car C

All three cars havenet forces actingon them

Cannot bedetermined withinformationprovided

As all the cars are changing direction,there must be a net force to change thedirection of theirvelocity vectors 22.circular.png

24 Circular

A centripetal force of 5.0 newtons is applied to a rubber stopper moving at aconstant speed in a horizontalcircle. If the same force is applied, but the radius is made smaller, whathappens to the speed, v, and thefrequency, f, of the stopper? D

v increases and fincreases

v decreases and fdecreases

v increases and fdecreases

v decreases and fincreases neither changes

F = mv2/r; v2 = rF/m, if r decreases, vwill decrease with the same appliedforce. Also, v = 2πrfso 4π2r2f = rF/m, or f = F/(4π2rm) andas r decreases, f increases.

25 Circular

What is the centripetal acceleration of an object (mass = 50 g) on the end ofan 80-cm string rotating at aconstant rate of 4 times a second? D 25 m/s^2 32 m/s^2 100 m/s^2 500 m/s^2 2500 m/s^2 f = 4 rev/sec. a = v2/r and v = 2πrf

26 Circular

What net force is necessary to keep a 1.0 kg puck moving in a circle of radius0.5 m on a horizontal frictionlesssurface with a speed of 2.0 m/s? D O N 2.0 N 4.0 N 8.0 N 16 N F = mv2/r

27 Circular

Astronauts on the Moon perform an experiment with a simple pendulum thatis released from the horizontalposition at rest. At the moment shown in the diagram with 0° <θ < 90°, thetotal acceleration of the mass maybe directed in which of the following ways? A Straight to the right Straight to the left Straight upward Straight downward

Straight along theconnecting stringtoward point P (thepivot)

There is a force acting downward(gravity) and a centripetal force actingtoward the center ofthe circle (up and to the right). Addingthese vectors cannot produceresultants in the directionsof B, C, D or E. 27.circular.png

28 Circular

A 4.0 kg mass is attached to one end of a rope 2 m long. If the mass is swungin a vertical circle from the freeend of the rope, what is the tension in the rope when the mass is at itshighest point if it is moving with a speedof 5 m/s? B 5.4 N 10.8 N 21.6 N 50 N 65.4 N

ΣF = ma; mg + FT = mv2/r giving FT =mv2/r –mg

29 Circular30 Circular31 Circular

1 Torque2 Torque3 Torque4 Torque5 Torque6 Torque7 Torque

8 Torque

To weigh a fish, a person hangs a tackle box of mass 3.5 kilograms and acooler of mass 5 kilograms from the ends of a uniform rigid pole that issuspended by a rope attached to its center. The system balances when thefish hangs at a point 1/4 of the rod’s length from the tackle box. What is themass of the fish? C 1.5 kg 2 kg 3 kg 6 kg 6.5 kg

Apply rotational equilibrium using therope as the pivot point. (3.5)(9.8)(L/2)+ m(9.8)(L/4) – (5)(9.8)(L/2) = 0therefore m=3 kg 8.torque.png

9 Torque

Two objects, of masses 6 and 8 kilograms, are hung from the ends of a stickthat is 70 cm long and has marks every 10 cm, as shown. If the mass of thestick is negligible, at which of the points indicated should a cord be attached ifthe stick is to remain horizontal when suspended from the cord? D A B C D E

To balance the torques on each side,we obviously need to be closer to theheavier mass. Trying point D as a pivotpoint we have:(m1g) • r1 ?=? (m2g) • r2(6kg) (40 cm) ?=? (8kg) (30 cm) and wesee it works 9.torque.png

10 Torque

A wheel of radius R and negligible mass is mounted on a horizontalfrictionless axle so that the wheel is in a vertical plane. Three small objectshaving masses m, M, and 2M, respectively, are mounted on the rim of thewheel, as shown. If the system is in static equilibrium, what is the value of min terms of M? C M/2 M 3M/2 2M 5M/2

Applying rotational equilibrium at thecenter pivot we get: +mg(R) + Mg(Rcos60°) – 2Mg(R) = 0.Using cos60° = 1⁄2 we arrive at theanswer 3M/2 10.torque.png

11 Torque

A rod on a horizontal tabletop is pivoted at one end and is free to rotatewithout friction about a vertical axis, as shown. A force F is applied at theother end, at an angle θ to the rod. If F were to be applied perpendicular tothe rod, at what distance from the axis should it be applied in order toproduce the same torque? A Lsinθ Lcosθ L Ltanθ 2^(1/2) L

Finding the torque in the currentconfiguration we have: (Fsinθ)(L) = FLsin θ.To get the same torque with F appliedperpendicular we would have to changethe L to get F (Lsinθ) 11.torque.png

12 Torque

A horizontal, uniform board of weight 125 N and length 4 m is supported byvertical chains at each end. A person weighing 500 N is sitting on the board.The tension in the right chain is 250 N.What is the tension in the left chain? B 250 N 375 N 500 N 625 N 875 N

Simple Fnet(y) = 0T – 500 + 250 – 125 = 0

13 Torque

A horizontal, uniform board of weight 125 N and length 4 m is supported byvertical chains at each end. A person weighing 500 N is sitting on the board.The tension in the right chain is 250 N.How far from the left end of the boardis the person sitting? B .4 m 1.5 m 2 m 2.5 m 3 m

Apply rotational equilibrium using leftend as pivot:Same Diagram+ (250)(4) – (125)(2) – (500)(r) = 0therefore r =1.5m

14 Torque Torque is the rotational analogue of D kinetic energy linear momentum acceleration force mass Definition of torque

15 Torque

A square piece of plywood on a horizontal tabletop is subjected to the twohorizontal forces shown. Where should a third force of magnitude 5 newtonsbe applied to put the piece of plywood into equilibrium? A A B C D E

To balance the forces (Fnet=0) theanswer must be A or D, to preventrotation, obviously A would be needed 15.torque.png

16 Torque

A uniform rigid bar of weight W is supported in a horizontal orientation asshown by a rope that makes a 30° angle with the horizontal. The forceexerted on the bar at point O, where it is pivoted, is best represented by avector whose direction is which of the following? B A B C D E

Since the rope is a tan angle it has xand y B components of force.Therefore, H would have to exist tocounteract Tx. Based on Ʈnet = 0requirement, V also would have to existto balance W if we were to chose apivotpoint at the right end of the bar 16.torque.png

17 Torque

In which of the following diagrams is the torque about point O equal inmagnitude to the torque about point X in the diagram? (All forces lie in theplane of the paper.) C A B C D E

In the given diagram the torque is = FL.Finding the torque of all the choicesreveals C as correct. (2Fsin60°) (L) =2F 1⁄2 L = FL 17.torque.png

18 Torque

A rod of length L and of negligible mass is pivoted at a point that is off-centerwith lengths shown in the figurebelow. The figures show two cases in which masses are suspended from theends of the rod. In each case theunknown mass m is balanced by a known mass, M1 or M2, so that the rodremains horizontal. What is the valueof m in terms of the known masses? E Ml + M2 ½(Ml + M2) Ml M2 ½M1M2 √M1M2

Applying rotational equilibrium to eachdiagram givesDIAGRAM 1: (mg)(L1) = (M1g)(L2), L1= M1(L2) /m. (sub this L1) into theDiagram 2 eqn, and solve. DIAGRAM2: (M2g)(L1) = mg(L2), M2 (L1) = m(L2) 18.torque.png

19 Torque

A system of two wheels fixed to each other is free to rotate about africtionless axis through the common center of the wheels andperpendicular to the page. Four forces are exerted tangentially to therims of the wheels, as shown. The magnitude of the net torque onthe system about the axis is C zero FR 2FR 5FR 14FR

Find the torques of each using propersigns and add up. + (1) – (2) + (3) + (4)+F(3R) – (2F)(3R) + F(2R) +F(3R) =2FR 19.torque.png

20 Torque

For the wheel-and-axle system shown, which of the followingexpresses the condition required for the system to be in staticequilibrium? B m1 = m2 am1 = bm2 am2 = bm1 a^2m1 = b^2m^2 b^2m1 = a^2m2

Simply apply rotational equilibrium(m1g) • r1 = (m2g) • r2m1a = m2b 20.torque.png

21 Torque

A meterstick of negligible mass is placed on a fulcrum at the 0.60 m mark,with a 2.0 kg mass hung at the 0 mmark and a 1.0 kg mass hung at the 1.0 m mark. The meterstick is releasedfrom rest in a horizontal position.Immediately after release, the magnitude of the net torque on the meterstickabout the fulcrum is most nearly B 2.0 N•m 8.0 N•m 10 N•m 14 N•m 16 N•m

Question says meterstick has no mass,so ignore that force.Pivot placed at 0.60 m. Based on theapplied masses, thismeterstick would have a net torque androtate. Find the netTorque as followsƮnet = + (m1g) • r1 – (m2g) • r2+ (2)(10 m/s2)(0.6 m) – (1)(10 m/s2)(0.4 m)

1 WorkPowerEnergy

A mass m attached to a horizontal massless spring with spring constant k, issetinto simple harmonic motion. Its maximum displacement from its equilibriumposition is A. What is the masses speed as it passes through its equilibriumposition? B 0 A√k/m A√m/k (1/A)√k/m (1/A)√m/k

Conservation of Energy, Usp = K, ½kA2 = ½ mv2 solve for v

1.workpowerenergy.png

2 WorkPowerEnergy

A force F at an angle θ above the horizontal is used to pull a heavy suitcaseof weight mg a distance d along alevel floor at constant velocity. The coefficient of friction between the floor andthe suitcase is μ. The workdone by the frictional force is: A –Fd cos θ mgh – Fd cos θ – μ Fd cos θ -μmgd -μ mgd cos θ

Constant velocity ---> Fnet=0, fk = Fx =Fcos θ Wfk = – fkd = – Fcos θ d

3 WorkPowerEnergyIf the unit for force is F, the unit for velocity V, and the unit for time T, then theunit for energy is: A FVT F/T FV/T F/T^2 FV^2/T^2

Try out the choices with the properunits for each quantity.Choice A … FVT = (N) (m/s) (s) = Nmwhich is work in joules same as energy.

4 WorkPowerEnergy

A force of 10 N stretches a spring that has a spring constant of 20 N/m. Thepotential energy stored in thespring is: A 2.5 J 5.0 J 10 J 40 J 200 J

Two step problem. Do F = kΔx, solvefor Δx then sub in the Usp = ½ kΔx2

5 WorkPowerEnergy

A 2 kg ball is attached to a 0.80 m string and whirled in a horizontal circle at aconstant speed of 6 m/s. Thework done on the ball during each revolution is: E 450 J 90 J 72 J 16 J zero

In a circle moving at a constant speed,the work done is zero since the Force isalwaysperpendicular to the distance moved asyou move incrementally around thecircle

6 WorkPowerEnergy

A pendulum bob of mass m on a cord of length L is pulled sideways until thecord makes an angle θ with the vertical as shown in the figure to the right.Thechange in potential energy of the bob during the displacement is: A mgL (1–cos θ) mgL (1–sin θ) mgL sin θ mgL cos θ 2mgL (1–sin θ)

The potential energy at the first positionwill be the amount “lost” as the ball fallsand this will be the change in potential.U=mgh = mg(L–Lcos θ)

6.workpowerenergy.png

7 WorkPowerEnergy

A force F directed at an angle θ above the horizontal is used to pull a crate adistance D across a level floor.The work done by the force F is B FD FD cos θ FD sin θ mg sin θ mgD cos θ

A force directed above the horizontallooks like this θ To find the work doneby thisforce we use the parallel component ofthe force (Fx) x distance. = (Fcos θ) d

8 WorkPowerEnergyA compressed spring has 16 J of potential energy. What is the maximumspeed it can impart to a 2 kg object? B mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

The maximum speed would occur if allof the potential energy was convertedto kineticU = K 16 = ½ mv216 = ½ (2) v2

9 WorkPowerEnergy

A softball player catches a ball of mass m, which is moving towards her withhorizontal speed V. While bringing the ball to rest, her hand moved back adistance d. Assuming constant deceleration, the horizontal force exerted onthe ball by the hand is A mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

The work done by the stopping forceequals the loss of kinetic energy. –W=∆K– Fd = ½ mvf2– ½ mvi2vf = 0 F = mv2/2d

10 WorkPowerEnergy

A 3 kg block with initial speed 4 m/s slides across a rough horizontal floorbefore coming to rest. The frictional force acting on the block is 3 N. How fardoes the block slide before coming to rest? D mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

The work done by friction equals theloss of kinetic energy– fk d = ½ mvf2– ½ mvi2vf = 0, plug in values to get answer

11 WorkPowerEnergy

A construction laborer holds a 20 kg sheet of wallboard 3 m above the floorfor 4 seconds. During these 4 seconds how much power was expended onthe wallboard? E mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

P = Fd / t. Since there is no distancemoved, the power is zero

12 WorkPowerEnergy

A pendulum is pulled to one side and released. It swings freely to theopposite side and stops. Which of thefollowing might best represent graphs ofkinetic energy (Ek), potential energy (Ep) and total mechanical energy (ET) C mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

This is a conservative situation so thetotal energy should stay same thewhole time. It should also start with maxpotential and min kinetic, which onlyoccurs in choice C

13 WorkPowerEnergy

Problems 13 and 14 refer to the following situation: A car of mass m slidesacross a patch of ice at a speed v with its brakes locked. It the hits drypavement and skids to a stop in a distance d. The coefficient of kinetic frictionbetween the tires and the dry road isμ. B mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

Stopping distance is a work-energyrelationship. Work done by friction tostop = loss of kinetic– fk d = – ½ mvi2µkmg = ½ mvi2The mass cancelsin the relationshipabove so changing mass doesn’tchange the distance

14 WorkPowerEnergy

Problems 13 and 14 refer to the following situation: A car of mass m slidesacross a patch of ice at a speed v withits brakes locked. It the hits dry pavement and skids to a stop in a distance d.The coefficient of kinetic frictionbetween the tires and the dry road isμ. E mgD cos θ mgD cos θ mgD cos θ v mgD cos θ

Same relationship as above … doublethe v gives 4x the distance

15 WorkPowerEnergy

A ball is thrown vertically upwards with a velocity v and an initial kineticenergy Ek. When half way to the top of its flight, it has a velocity and kineticenergy respectively of B mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

Half way up you have gained half of theheight so you gained ½ of potentialenergy. Thereforeyou must have lost ½ of the initialkinetic energy so E2= (Ek/2).Subbing into this relationship

16 WorkPowerEnergy

A football is kicked off the ground a distance of 50 yards downfield.Neglecting air resistance, which of thefollowing statements would be INCORRECT when the football reaches thehighest point? A mgD cos θ mgD cos θ mgD cos θ mgD cos θ mgD cos θ

At the top, the ball is still moving (vx) sowould still possess some kinetic energy

17 WorkPowerEnergy

A mass m is attached to a spring with a spring constant k. If the mass is setinto motion by a displacement d from its equilibrium position, what would bethe speed, v, of the mass when it returns to equilibrium position? E v=(kd/m)^1/2 v2=kd/m v=kd/mg v2=mgd/k v=d*(k/m)^1/2 Conservation of energy

18 WorkPowerEnergyIf M represents units of mass, L represents units of length, and T representsunits of time, the dimensions of power would be: C ML/T2 ML2/T2 ML2/T3 ML/T ML2/T

P = F d / t = (ma)d / t = (kg)(m/s2)(m) / (s) = kg m2/ s3

19 WorkPowerEnergy

An automobile engine delivers 24000 watts of power to a car’s driving wheels.If the car maintains a constant speed of 30 m/s, what is the magnitude of theretarding force acting on the car? A 800 N 960 N 1950 N 720000 N 1560000 N

P = Fv, plug in to get the pushing forceF and since its constant speed, Fpush= fk

20 WorkPowerEnergyA fan blows the air and gives it kinetic energy. An hour after the fan has beenturned off, what has happened to the kinetic energy of the air? C it disapears

it turns intopotential energy

it turns into thermalenegy

it turns into soundenergy

it turns intoelectrical energy

Total energy is always conserved so asthe air molecules slow and lose theirkinetic energy, thereis a heat flow which increases internal(or thermal) energy

21 WorkPowerEnergy

A box of old textbooks is on the middle shelf in the bookroom 1.3 m from thefloor. If the janitor relocates thebox to a shelf that is 2.6 m from the floor, how much work does he do on thebox? The box has a mass of 10 kg. D 13 J 26 J 52 J 130 J 260 J

The work done must equal the increasein the potential energy mgh = (10)(10)(1.3)

22 WorkPowerEnergy

A mass, M, is at rest on a frictionless surface, connected to an idealhorizontal spring that is unstretched. A person extends the spring 30 cm fromequilibrium and holds it by applying a 10 N force. The spring is brought backto equilibrium and the mass connected to it is now doubled to 2M. If thespring is extended back 30 cm from equilibrium, what is the necessary forceapplied by the person to hold the mass stationary there? C 20 N 14.1 N 10 N 7.07 N 5 N

Based on F = k ∆x. The mass attachedto the spring does not change thespring constant so thesame resistive spring force will exist, sothe same stretching force would berequired

23 WorkPowerEnergy

A deliveryman moves 10 cartons from the sidewalk, along a 10-meter ramp toa loading dock, which is 1.5 meters above the sidewalk. If each carton has amass of 25 kg, what is the total work done by the deliveryman on the cartonsto move them to the loading dock? B 2500 J 3750 J 10000 J 25000 J 37500 J

The work done must equal the totalgain in potential energy10 boxes * mgh (25)(10)(1.5) of each

24 WorkPowerEnergyA rock is dropped from the top of a tall tower. Half a second later anotherrock, twice as massive as the first, is dropped. Ignoring air resistance, A

the distancebetween the rocksincreases whileboth are falling.

the acceleration isgreater for themore massiverock.

the speed of bothrocks is constantwhile they fall.

they strike theground more thanhalf a secondapart.

they strike theground with thesame kineticenergy

Eliminating obviously wrong choicesonly leaves A as an option. The answeris A because sincethe first ball has a head start on thesecond ball it is moving at a faster rateof speed at alltimes. When both are moving in the airtogether for equal time periods the firstfaster rockwill gain more distance than the slowerone which will widen the gap betweenthem.

25 WorkPowerEnergy

A 60.0-kg ball of clay is tossed vertically in the air with an initial speed of 4.60m/s. Ignoring air resistance, what is the change in its potential energy when itreaches its highest point? D 0 J 45 J 280 J 635 J 2700 J

All of the K = ½ m v2is converted to U. Simply plug in thevalues

26 WorkPowerEnergyWhich of the following is true for a system consisting of a mass oscillating onthe end of an ideal spring? D

The kinetic andpotential energiesare equal to eachother at all times.

The kinetic andpotential energiesare both constant

The maximumpotential energy isachieved when themass passesthrough itsequilibriumposition.

The maximumkinetic energy andmaximum potentialenergy are equal,but occur atdifferent times

The maximumkinetic energyoccurs atmaximumdisplacement ofthe mass from itsequilibriumposition

For a mass on a spring, the max Uoccurs when the mass stops and hasno K while the max Koccurs when the mass is moving fastand has no U. Since energy isconserved it istransferred from one to the other soboth maximums are equal

27 WorkPowerEnergy28 WorkPowerEnergy29 WorkPowerEnergy30 WorkPowerEnergy31 WorkPowerEnergy32 WorkPowerEnergy33 WorkPowerEnergy34 WorkPowerEnergy35 WorkPowerEnergy36 WorkPowerEnergy

37 WorkPowerEnergy

A block of mass m slides on a horizontal frictionless table with an initial speedvo. It then compresses a springof force constant k and is brought to rest. How much is the springcompressed from its natural length? D Vo^2/2g mg/k Vo m/k Vo m/k Vo ^(1/2) k/m Vo ^(1/2)

Simple energy conservation K=Usp ½mvo^2= ½ k ∆x2 solve for ∆x

38 WorkPowerEnergy

A plane 5 meters in length is inclined at an angle of 37°, as shown. A blockof weight 20 newtons is placed at the top of the plane and allowed to slidedown. The mass of the block is most nearly D 1.0 kg 1.2 kg 1.6 kg 2.0 kg 2.5 kg Simple application of Fg=mg 38.powerenergy.png

39 WorkPowerEnergyThe magnitude of the normal force exerted on the block by the plane ismost nearly C 10 N 12 N 16 N 20 N 33 N

Fn= Fgy = mg cos θ. Since you aregiven the incline with sides listed, cos θcan be found byusing the dimensions of the incline …cos θ = adj / hyp = 4/5 to make mathsimple. This isa good trick to learn for physicsproblems 38.powerenergy.png

40 WorkPowerEnergyThe work done on the block by the gravitational force during the 5-meter slidedown the plane is most nearly B 20 J 60 J 80 J 100 J 130 J

As the box slides down the incline, thegravity force is parallel to the height ofthe incline thewhole time so when finding the work orgravity you use the gravity force for Fand theheight of the incline as the paralleldistance. Work = (Fg)(d) = (20)(3) 38.powerenergy.png

41 WorkPowerEnergy

A student weighing 700 N climbs at constant speed to the top of an 8 mvertical rope in 10 s. The averagepower expended by the student to overcome gravity is most nearly C 1.1 W 87.5 W 560 W 875 W 5600 W

The student must exert an averageforce equal to their weight (Fg) in orderto lift themselves sothe lifting force F=mg. The power isthen found with P = Fd / t = (Fg)d / t

42 WorkPowerEnergy

The graph shown represents the potential energy U as a function ofdisplacement x for an object on the end of a spring moving back andforth with amplitude x0. Which of the following graphs representsthe kinetic energy Kof the object as a function of displacement x ? D A B C D E

As the object oscillates its totalmechanical energy is conserved andtransfers from U to K backand forth. The only graph that makessense to have an equal switchthroughout is D

42.workpowerenergy.png

43 WorkPowerEnergy

A child pushes horizontally on a box of mass m which moves with constantspeed v across a horizontal floor.The coefficient of friction between the box and the floor is µ. At what ratedoes the child do work on the box? A µmgv mgv µmg/v µm^2g/v^2 µmv^2

To push the box at a constant speed,the child would need to use a forceequal to friction soF=fk=µmg. The rate of work (W/t) is thepower. Power is given by P=Fv µmgv

44 WorkPowerEnergy

A block of mass 3.0 kg is hung from a spring, causing it tostretch 12 cm at equilibrium, as shown. The 3.0 kg block is thenreplaced by a 4.0 kg block, and the new block is released fromthe position shown, at which the spring is unstretched. How farwill the 4.0 kg block fall before its direction is reversed? D 9 cm 18 cm 24 cm 32 cm 48 cm

Two steps. I) use hookes law in the firstsituation with the 3 kg mass to find thespring constant(k). Fsp=k∆x, mg=k∆x, k = 30/.12 =250. II) Now do energy conservationwith the secondscenario (note that the initial height ofdrop will be the same as the stretch∆x).U top = Usp bottom, mgh = ½ k ∆x^2,(4)(10)(∆x) = ½ (250) (∆x^2)

44.workpowerenergy.png

45 WorkPowerEnergyWhat is the kinetic energy of a satellite of mass m that orbits the Earth, ofmass M, in a circular orbit of radius R? B Zero

1/2 GMm/R

1/4 GMm/R 1/2 GMm/R^2 GMm/R^2

In a circular orbit, the velocity of asatellite is given byV= (GMe/r)^(1/2) with Me = M. Kineticenergy of the satellite is given by K = ½m v^2. Plug in v from above to get answer

46 WorkPowerEnergy

A rock of mass m is thrown horizontally off a building from a height h, asshown above. The speed of the rock as itleaves the thrower’s hand at the edge of the building is v0. How much time does it take the rock to travel from the edge of the buildingto the ground? E hvo^(1/2) h/v0 hVo/g 2h/g 2h/g^(1/2)

Projectile. Vx doesn’t matter Viy = 0.Using d = viyt + ½ at^2we get the answer

46.workpowerenergy.png

47 WorkPowerEnergyWhat is the kinetic energy of the rock just before it hits the ground? D mgh ½ mv^2 ½ mv^2 - mgh ½ mv^2+mgh mgh- ½ mv^2

Energy conservation Etop = Ebot,Kt+Ut = Kb. Plug in for K top and U topto get answer

47.workpowerenergy.png

48 WorkPowerEnergyWhich of the following is true for both spheres? A

The maximumkinetic energy isattained as thesphere passesthrough itsequilibriumposition.

The maximumkinetic energy isattained as thesphere reaches itspoint of release.

The minimumgravitationalpotential energy isattained as thesphere passesthrough itsequilibriumposition.

The maximumgravitationalpotential energy isattained when thesphere reaches itspoint of release.

The maximum totalenergy is attainedonly as the spherepasses through itsequilibriumposition.

A is true; both will be moving the fastestwhen they move through equilibrium.

48.workpowerenergy.png

49 WorkPowerEnergy

An object of mass m is initially at rest and free to move without friction in anydirection in the xy-plane. Aconstant net force of magnitude F directed in the+x direction acts on the object for 1 s. Immediately there after a constant netforce of the same magnitude F directed in the +y direction acts on the objectfor 1 s. After this, no forces act on the objectWhich of the following vectorscould represent the velocity of the object at the end of 3 s, assuming thescaleson the x and y axes are equal? C A B C D E

X and Y directions are independent andboth start with the same velocity of zeroin eachdirection. The same force is applied ineach direction for the same amount oftime so eachshould gain the same velocity in eachrespective direction.

49.workpowerenergy.png

50 WorkPowerEnergy

An object of mass m is initially at rest and free to move without friction in anydirection in the xy-plane. Aconstant net force of magnitude F directed in the+x direction acts on the object for 1 s. Immediately there after a constant netforce of the same magnitude F directed in the +y direction acts on the objectfor 1 s. After this, noforces act on the objectWhich of the following graphsbest represents the kinetic energy K of the object as a function of time? B A B C D E

Kinetic energy is not a vector and thetotal resultant velocity should be usedto determine the KE.For the 1st second the object gainsspeed at a uniform rate in the xdirection and since KE isproportional to v2 we should get aparabola. However, when the 2ndsecond starts the newgains in velocity occur only in the ydirection and are at smaller values sothe gainsessentially start over their parabolictrend as shown in graph B

50.workpowerenergy.png

51 WorkPowerEnergy

A constant force of 900 N pushes a100 kg mass up the inclined planeshown at a uniform speed of 4 m/s.The power developed by the 900 Nforce is most nearly E 400W 900W 800W 1000W 3600W Simple P = Fv

51.workpowerenergy.png

52 WorkPowerEnergyAn object of mass m is lifted at constant velocity a vertical distance H in timeT. The power supplied by the lifting force is B mgHT mgH/T mg/HT mgT/H Zero

The force needed to lift something at aconstant speed is equal to the objectweight F=mg. Thepower is then found by P = Fd / t = mgh/ t

53 WorkPowerEnergy

A system consists of two objects having masses ml and m2 (ml < m2). Theobjects areconnected by a massless string, hung over a pulley as shown, and thenreleased.When the object of mass m2has descended a distance h, the potential energy of thesystem has decreased by A (m2-m1)gh M2gh (M1+M2)gh ½(ml + m2)gh 0

As the system moves, m2 loses energyover distance h and m1 gains energyover the samedistance h but some of this energy isconverted to KE so there is a net loss ofU. Simplysubtract the U2 – U1 to find this loss

53.workpowerenergy.png

54 WorkPowerEnergy

The following graphs, all drawn to the same scale, represent the net force Fas a function of displacement x foran object that moves along a straight line. Which graph represents the forcethat will cause the greatest changein the kinetic energy of the object from x = 0 to x = x1?151 E sqrt(gl) sqrt(2gl) .5gl gl 2gl

In a force vs. displacement graph, thearea under the line gives the work doneby the force andthe work done will be the change in theK so the largest area is the most Kchange

54.workpowerenergy.png

55 WorkPowerEnergy

From the top of a 70-meter-high building, a l-kilogram ball is thrown directlydownward with an initial speed of10 meters per second. If the ball reaches the ground with a speed of 30meters per second, the energy lost tofriction is most nearly C 0J 100J 300J 400J 700J

Compare the U+K ( mgh + ½ mv2 ) atthe top, to the K ( ½ mv2 ) at the bottomand subtract themto get the loss.

56 WorkPowerEnergy

A pendulum consists of a ball of mass m suspended at the end of amassless cord of length L as shown. The pendulum is drawn asidethrough an angle of 60° with the vertical and released. At the low pointof its swing, the speed of the pendulum ball is A sqrt(gl) sqrt(2gl) .5gl gl 2gl

Use energy conservation, U top = Kbottom. As in problem #6 (in thisdocument), the initialheight is given by L – Lcos θ, with cos60 = .5 so the initial height is ½ L.

56.workpowerenergy.png

57 WorkPowerEnergy

A rock is lifted for a certain time by a force F that is greater in magnitude thanthe rock's weight W. The changein kinetic energy of the rock during this time is equal to the A

work done by thenet force (F - W)

work done by Falone

work done by Walone

difference inthe momentum ofthe rock beforeand after this time.

difference in thepotential energy ofthe rock beforeand after this time.

Use application of the net work energytheorem which says … Wnet = ΔK. Thenet work is thework done by the net force which givesyou the answer

58 WorkPowerEnergy

A ball is thrown upward. At a height of 10 meters above the ground, the ballhas a potential energy of 50 joules(with the potential energy equal to zero at ground level) and is moving upwardwith a kinetic energy of 50joules. Air friction is negligible. The maximum height reached by the ball ismost nearly B 10 m 20 m 30 m 40 m 50 m

First use the given location (h=10m)and the U there (50J) to find the mass.U=mgh, 50=m(10)(10), so m = 0.5 kg.The total mechanical energy is given inthe problemas U+K = 100 J. The max height isachieved when all of this energy ispotential. So set100J = mgh and solve for h

59 WorkPowerEnergy

A block on a horizontal frictionless plane isattached to a spring, as shown. The blockoscillates along the x-axis with amplitude A.Which of the following statements aboutenergy is correct? A

The potentialenergy of thespring is at aminimum at x = 0.

The potentialenergy of thespring is at aminimum at x = A.

The kinetic energyof the block is at aminimum at x =0.

The kinetic energyof the block is at amaximum at x = A.

The kinetic energyof the block isalways equal tothe potentialenergy of thespring.

There is no Usp at position x=0 sincethere is no Δx here so this is theminimum U location

59.workpowerenergy.png

60 WorkPowerEnergy

During a certain time interval, a constant force delivers an average power of 4watts to an object. If the objecthas an average speed of 2 meters per second and the force acts in thedirection of motion of the object, themagnitude of the force is E 16 N 8 N 6 N 4 N 2 N P = Fv

61 WorkPowerEnergy

A spring-loaded gun can fire a projectile to a height h if it is fired straight up. Ifthe same gun is pointed at anangle of 45° from the vertical, what maximum height can now be reached bythe projectile? C h/4 h/2(2^1/2) h/2 h/(2^1/2) h

Using energy conservation in the firstsituation presented K=U gives the initialvelocity asv = (2gh)^1/2 . The gun will fire at thisvelocity regardless of the angle. In thesecondscenario, the ball starts with the sameinitial energy but at the top will haveboth KE and PEso will be at a lower height. The velocityat the top will be equal to the vxvx = vcosθ = ((2gh)^1/2) cos45 = (2gh)^1/2 ((2^1/2)/2) = (gh^1/2)at the beginning. Now sub into the full energyconservation problem for situation 2and solve for h2. Kbottom = Utop +Ktop. 1/2m ((2gh^1/2)^2)= mgh + 1/2m((gh^1/2)^2)

62 WorkPowerEnergy

A force F is exerted by a broom handle on the head of the broom, which hasamass m. The handle is at an angle θ to the horizontal, as shown. The workdone by the force on the head of the broom as it moves a distance d across ahorizontal floor is B Fd sin θ Fd cosθ Fm cosθ Fm tanθ Fmd sin θ

To find work we use the parallelcomponent of the force to the distance,this gives Fcos θ d

62.workpowerenergy.png

63 WorkPowerEnergy

A spring has a force constant of 100 N/m and an unstretched length of 0.07m. Oneend is attached to a post that is free to rotate in the center of a smooth table,asshown in the top view. The other end is attached to a 1 kg disc moving inuniform circular motion on the table, which stretches the spring by 0.03 m.Friction is negligible. What is the centripetal force on the disc? B .3 N 3 N 10 N 300 N 1000 N

The centripetal force is the forceallowing the circular motion which inthis case is the springforce Fsp=kΔx=(100)(.03)

63-64.workpowerenergy.png

64 WorkPowerEnergy

A spring has a force constant of 100 N/m and an unstretched length of 0.07m. Oneend is attached to a post that is free to rotate in the center of a smooth table,asshown in the top view. The other end is attached to a 1 kg disc moving inuniform circular motion on the table, which stretches the spring by 0.03 m.Friction is negligible. What is the work done on the disc by the spring duringone full circle? A 0 J 94 J 186 J 314 J 628 J

In a circle at constant speed, the workdone is zero since the Force is alwaysperpendicular to thedistance moved as you moveincrementally around the circle

63-64.workpowerenergy.png

65 WorkPowerEnergy

A frictionless pendulum of length 3 m swings with an amplitude of 10°. At itsmaximum displacement, thepotential energy of the pendulum is 10 J. What is the kinetic energy of thependulum when its potential energyis 5 J ? B 3.3 J 5 J 6.7 J 10 J 15 J

At the maximum displacement the K=0so the 10J of potential energy at thisspot is equal to thetotal amount of mechanical energy forthe problem. Since energy is conservedin thissituation, the situation listed must haveU+K add up to 10J.

66 WorkPowerEnergy

A descending elevator of mass 1,000 kg is uniformly decelerated to restover a distance of 8 m by a cable in which the tension is 11,000 N. Thespeed vi of the elevator at the beginning of the 8 m descent is mostnearly A 4 m/s 10 m/s 13 m/s 16 m/s 21 m/s

Using the work-energy theorem. Wnc =Δ ME,WFt = ΔU+ΔK,– Fd = (mghf – mghi) + ( ½mvf^2 – ½mvi^2),– (11000)(8) = (0 – (1000)(10)(8)) + (0– ½ (1000)(vi^2) … solve for vi

66.workpowerenergy.png

67 WorkPowerEnergy68 WorkPowerEnergy69 WorkPowerEnergy70 WorkPowerEnergy71 WorkPowerEnergy72 WorkPowerEnergy73 WorkPowerEnergy74 WorkPowerEnergy75 WorkPowerEnergy76 WorkPowerEnergy

1 momentum

A car of mass m, traveling at speed v, stops in time t when maximum brakingforce is applied. Assuming thebraking force is independent of mass, what time would be required to stop acar of mass 2m traveling at speed v? D t/2 t 2^1/2 t 2t 4t

Based on Ft = mΔv, doubling the masswould require twice the time for samemomentum change

2 momentum

A block of mass M is initially at rest on a frictionless floor. The block, attachedto a massless spring with springconstant k, is initially at its equilibrium position. An arrow with mass m andvelocity v is shot into the block.The arrow sticks in the block. What is the maximum compression of thespring? E v(m/k)^(1/2) v(k/m)^(1/2) v((m+M)/k)^(1//2) (m+M)v/(mk)^1/2 mv/((m+M)k)^1/2

Two step problem.I) find velocity after collision with arrow.mvi = (ma+mb) vf vf = mv / (m+M) II)now use energy conservation Ki=U½ (m+M)vf2 = ½ k X2, sub in vffrom I

3 momentumHow long must a 100 N net force act to produce a change in momentum of200 kg·m/s? D .25s .5s 1.0s 2.0s 4.0s Use J=p Ft=p (100)t=200 t=2

4 momentum Which is a vector quantity C energy mass impulse power workDefinition. Impulse, just like momentum,needs a direction and is a vector

5 momentum When the velocity of a moving object is doubled, its _____ is also doubled D acceleration kinetic energy mass momentum potential energySince p=mv, by doubling v you alsodouble p

6 momentumTwo objects, P and Q, have the same momentum. Q can have more kineticenergy than P if it has: C More mass than P

The same mass asP More speed thanP

The same speedat P

Q can not havemore kineticenergy than P

Since the momentum is the same, thatmeans the quantity m1v1 = m2v2. Thismeans that themass and velocity changeproportionally to each other so if youdouble m1 you would haveto double m2 or v2 on the other side aswell to maintain the same momentum.Now weconsider the energy formula KE= ½mv2 since the v is squared, it is themore important termto increase in order to make moreenergy. So if you double the mass of 1,then double thevelocity of 2, you have the samemomentum but the velocity of 2 whensquared will make agreater energy, hence we want morevelocity in object 2 to have moreenergy.

7 momentum

A spring is compressed between two objects with unequal masses, m and M,and held together. The objects areinitially at rest on a horizontal frictionless surface. When released, which ofthe following is true? E

Kinetic energy isthe same asbefore beginreleased.

The total finalkinetic energy iszero.

The two objectshave equal kineticenergy.

The speed of oneobject is equal tothe speed of theother.

The total finalmomentum of thetwo objects is zero.

Due to momentum conservation, thetotal before is zero therefore the totalafter must also be zero

8 momentum Net Impulse is best related to B momentumchange inmomentum kinetic energy

change in kineticenergy none of the above Definition. Jnet = p

9 momentum

Two football players with mass 75 kg and 100 kg run directly toward eachother with speeds of 6 m/s and 8 m/srespectively. If they grab each other as they collide, the combined speed ofthe two players just after thecollision would be: A 2 m/s 3.4 m/s 4.6 m/s 7.1 m/s 8 m/s

Perfect inelastic collision. m1v1i +m2v2i = mtot(vf) … (75)(6) + (100)(–8)= (175) vf

10 momentum

A 30 kg child who is running at 4 m/s jumps onto a stationary 10 kgskateboard. The speed of the child and theskateboard is approximately: A 3m/s 4m/s 5m/s 6m/s 7m/s

Perfect inelastic collision. m1v1i = mtot(vf) … (30)(4) = (40)vf

11 momentum

A 5000 kg freight car moving at 4 km/hr collides and couples with an 8000 kgfreight car which is initially atrest. The approximate common final speed of these two cars is C 1 km/h 1.3 km/h 1.5 km/h 2.5 km/h 4 km/h

Perfect inelastic collision. m1v1i = mtot(vf) ... (5000)(4) = (13000)vf

12 momentum

A rubber ball is held motionless a height ho above a hard floor and released.Assuming that the collision withthe floor is elastic, which one of the following graphs best shows therelationship between the total energy E ofthe ball and its height h above the surface. E A B C D E

Energy is conserved during fall andsince the collision is elastic, energy isalso conserved during the collision andalways has the same total valuethroughout. 12.momentum.png

13 momentum

Two carts are held together. Cart 1 is more massive than Cart 2. As they areforced apart by a compressedspring between them, which of the following will have the same magnitude forboth carts. C acceleration change of velocity force speed velocity

To conserve momentum, the change inmomentum of each mass must be thesame so each must receive the sameimpulse. Since the spring is in contactwith each mass for the sameexpansion time, the applied force mustbe the same to produce the sameimpulse.

14 momentumIf the unit for force is F, the unit for velocity is v and the unit for time t, thenthe unit for momentum is A Ft Ftv Ft2v Ft / v Fv / t

Momentum is equivalent to impulsewhich is Ft

15 momentum

A ball with a mass of 0.50 kg and a speed of 6 m/s collides perpendicularlywith a wall and bounces off with aspeed of 4 m/s in the opposite direction. What is the magnitude of the impulseacting on the ball? C 13 J 1 Ns 5 Ns 2 m/s 10 m/s

Use J=∆p J = mvf – mvi J = (0.5)(– 4) –(0.5)(6)

16 momentum

A cart with mass 2m has a velocity v before it strikes another cart of mass 3mat rest. The two carts couple andmove off together with a velocity of B v/5 2v/5 3v/5 2v/3 (2/5)1/2 v

Perfect inelastic collision. m1v1i = mtot(vf) ... (2m)(v) = (5m) vf

17 momentum Which of the above statements would be correct? E I only II only III only I and II only I and III only

First of all, if the kinetic energies are thesame, then when brought to rest, thenon conservative work done on eachwould have to be the same based onwork-energy principle. Also, sinceboth have the same kinetic energies wehave 1⁄2 m1v12 = 1⁄2 m2v22 ... sincethe velocity issquared an increase in mass wouldneed a proportionally smaller decreasein velocity to keepthe terms the same and thus make thequantity mv be higher for the largermass. This can be seen throughexample: If mass m1 was double massm2 its velocity would be v / √2 times incomparison to mass m2’s velocity. Soyou get double the mass but less thanhalf of the velocity which makes alarger mv term. 17.momentum.png

18 momentum

A mass m has speed v. It then collides with a stationary object of mass 2m. Ifboth objects stick together in aperfectly inelastic collision, what is the final speed of the newly formedobject? A v / 3 v / 2 2v / 3 v 3v / 2

Perfect inelastic collision. m1v1i = mtot(vf) ... (m)(v) = (3m) vf

19 momentum

A Freight car is moving freely along a railroad track at 7 m/s and collides witha tanker car that is at rest. After the collision, the two cars stick together andcontinue to move down the track. What is the magnitude of the final velocityof the cars if the freight car has a mass of 1200 kg and the tanker car has amass of 1600 kg? C 0 m/s 1 m/s 3 m/s 4 m/s 6 m/s

Perfect inelastic collision. m1v1i = mtot(vf) ... (1200)(7) = (2800)vf

20 momentum

A 50 kg skater at rest on a frictionless rink throws a 2 kg ball, giving the ball avelocity of 10 m/s. Which statement describes the skater’s subsequentmotion? B

0.4 m/s in thesame direction asthe ball.

0.4 m/s in theopposite directionof the ball

2 m/s in the samedirection as theball

4 m/s in the samedirection as theball

4 m/s in theopposite directionof the ball

Explosion. pbefore = 0 = pafter ... 0 =m1v1f + m2v2f ... 0 = (50)(v1f) + (2)(10)

21 momentumA certain particle undergoes erratic motion. At every point in its motion, thedirection of the particles momentum is ALWAYS A

the same as thedirection of itsvelocity

the same as thedirection of itsacceleration

the same as thedirection of the netforce

the same as thedirection of thekinetic energyvector none of the above

Since p=mv and both p and v arevectors, they must share the samedirection

22 momentum

A student initially at rest on a frictionless frozen pond throws a 1 kg hammerin one direction. After the throw,the hammer moves off in one direction while the student moves off in theother direction. Which of thefollowing correctly describes the above situation? C

The hammer willhave themomentum withthe greatermagnitude

The student willhave themomentum withthe greatermagnitude

The hammer willhave the greaterkinetic energy

The student willhave the greaterkinetic energy

The student andthe hammer willhave equal butopposite amountsof kinetic energy

Explosion, momentum before is zeroand after must also be zero. To haveequal momentum theheavier student must have a muchsmaller velocity and since that smallervelocity is squaredit has the effect of making the heavierobject have less energy than thesmaller one

23 momentum

The net force on a rocket with a weight of 1.5 x 104 N is 2.4 x 104 N. Howmuch time is needed to increase therockets speed from 12 m/s to 36 m/s near the surface of the Earth at takeoff? C 0.62 s 0.78 s 1.5 s 3.8 s 15 s

Use J=Δp Ft = mvf – mvi Ft = m(vf – vi)… note: since m is not given we willplug inFg / g with g as 10 to be used in theimpulse equation.(24000)(t) = (15000 / 10m/s2 ) (36–12)

24 momentum

A 50 kg gymnast falls freely from a height of 4 meters on to a trampoline. Thetrampoline then bounces herback upward with a speed equal to the speed at which she first struck thetrampoline. What is the average forcethe trampoline applies to the gymnast. E 50 N 200 N 500 N 2000 N

More information isrequired

This is a rather involved question. Firstfind speed of impact using free fall orenergy. Define upas positive and Let v1 = trampolineimpact velocity and v2 be trampolinerebound velocity.With that v1 = √80 and v2 = – √80. Nowanalyze the impact with the pad usingJnet =ΔpFnet t = mv2 – mv1 At this point werealize we need the time in order to findthe Fnet andtherefore cannot continue. If the timewas given, you could find the Fnet andthen useFnet = Fpad – mg to find Fpad.

25 momentum

Two toy cars with different masses originally at rest are pushed apart by aspring between them. Which of thefollowing statements would NOT be true? B

both toy cars willacquire equal butopposite momenta

both toy cars willacquire equalkinetic energies

the more massivetoy car will acquirethe least speed

the smaller toy carwill experience anacceleration of thegreatestmagnitude

Based on momentum conservation bothcarts have the same magnitude ofmomentum “mv” butbased on K = ½ m v2 the one with thelarger mass would have a directlyproportional smallervelocity that then gets squared. So bysquaring the smaller velocity term it hasthe effect ofmaking the bigger mass have lessenergy. This can be shown with anexample of one objectof mass m and speed v compared to asecond object of mass 2m and speedv/2. The largermass ends up with less energy eventhrough the momenta are the same.

26 momentum

A bat striking a 0.125 kg baseball is in contact with the ball for a time of 0.03seconds. The ball travels in astraight line as it approaches and then leaves the bat. If the ball arrives at thebat with a speed of 4.5 m/s andleaves with a speed of 6.5 m/s in the opposite direction, what is themagnitude of the average force acting on theball? D 8.33 N 18.75 N 27.08 N 45.83 N 458 N

Use J=Δp Ft = mvf – mvi Ft = m(vf – vi)F (0.03) = (0.125)( – 6.5 – 4.5)

27 momentum

An arrow is shot through an apple. If the 0.1 kg arrow changes speed by 10m/s during the collision (from 30m/s to 20 m/s) and the apple goes from rest to a speed of 2 m/s during thecollisions, then the mass of the applemust be B 0.2 kg 0.5 kg 0.8 kg 1 kg 2 kg

Momentum conservation. pbefore =pafter m1v1i = m1v1f + m2v2f (0.1)(30)= (0.1)(20)+(ma)(2)

28 momentum

A railroad flatcar of mass 2,000 kilograms rolls to the right at 10 meters persecond and collides with a flatcar ofmass 3,000 kilograms that is rolling to the left at 5 meters per second. Theflatcars couple together. Their speedafter the collision is A 1 m/s 2.5 m/ s 5 m/ s 7 m/ s 7.5 m/ s

Perfect inelastic collision. m1v1i +m2v2i = mtot(vf) … (2000)(10) + (3000)(–5) = (5000) vf

29 momentum Which of the following quantities is a scalar that is always positive or zero? C Power Work Kinetic energy Linear momentumAngularmomentum

Kinetic energy has no direction andbased on K = ½ m v2 must always be +

30 momentum

A tennis ball of mass m rebounds from a racquet with the same speed v as ithadinitially as shown. The magnitude of the momentum change of the ball is E 0 mv 2mv 2mv sinθ 2mv cosθ

A 2d collision must be looked at in bothx-y directions always. Since the angle isthe same andthe v is the same, vy is the same bothbefore and after therefore there is nomomentumchange in the y direction. All of themomentum change comes from the xdirection.vix = v cos θ and vfx = –v cos θ. Δp =mvfx – mvix … – mv cos θ – mv cos θ

31 momentum

Two bodies of masses 5 and 7 kilograms are initially at rest on a horizontalfrictionless surface. A light spring is compressed between the bodies, whichare held together by a thin thread. After the spring is released by burningthrough the thread, the 5 kilogram body has a speed of 0.2 m/s. The speed ofthe 7 kilogram body is (in m/s) B 1/12. 1/7. 1/sqrt(35) 1/5. 7/25.

Explosion. pbefore = 0 = pafter ... 0 =m1v1f + m2v2f ... 0 = (7)(v1f) + (5)(0.2)

32 momentum

A satellite of mass M moves in a circular orbit of radius R at a constant speedv. Which of the following must be true?I. The net force on the satellite is equal to MR and is directed toward thecenter of the orbit.II. The net work done on the satellite by gravity in one revolution is zero.III. The angular momentum of the satellite is a constant. D I only III only I and II only II and III only I, II, and III

In a circle at constant speed, work iszero since the force is parallel to theincremental distance moved duringrevolution. Angular momentum is givenby mvr and since none of thosequantities are changing it is constant.However the net force is NOT = MR, itsMv2/R

33 momentum

Two pucks are firmly attached by a stretched spring and are initially held atrest on a frictionless surface, as shown above. The pucks are then releasedsimultaneously. If puck I has three times the mass of puck II, which of thefollowing quantities is the same for both pucks as the spring pulls the twopucks toward each other? E Speed Velocity Acceleration Kinetic energy

Magnitude ofmomentum

Since the momentum before is zero,the momentum after must also be zero.Each mass must have equal andopposite momentum to maintain zerototal momentum. 33.momentum.png

34 momentum

Which of the following is true when an object of mass m moving on ahorizontal frictionless surface hits and sticks to an object of mass M > m,which is initially at rest on the surface? D

The collision iselastic.

All of the initialkinetic energy ofthe less massiveobject is lost.

The momentum ofthe objects that arestuck together hasa smallermagnitude thanthe initialmomentum of theless-massiveobject.

The speed of theobjects that arestuck together willbe less than theinitial speed of theless massiveobject.

The direction ofmotion of theobjects that arestuck togetherdepends onwhether the hit is ahead-on collision.

In a perfect inelastic collision with oneof the objects at rest, the speed afterwill always be less no matter what themasses. The ‘increase’ of mass in ‘mv’is offset by a decrease in velocity

35 momentum

Two objects having the same mass travel toward each other on a flat surfaceeach with a speed of 1.0 meter per second relative to the surface. Theobjects collide head-on and are reported to rebound after the collision, eachwith a speed of 2.0 meters per second relative to the surface. Which of thefollowing assessments of this report is most accurate? B

Momentum wasnot conservedtherefore thereport is false.

If potential energywas released tothe objects duringthe collision thereport could betrue.

If the objects haddifferent massesthe report could betrue.

If the surface wasinclined the reportcould be true.

If there was nofriction betweenthe objects and thesurface the reportcould be true.

Since the total momentum before andafter is zero, momentum conservationis not violated, however the objectsgain energy in the collision which is notpossible unless there was someenergy input which could come in theform of inputting stored potential energyin some way.

36 momentum

A solid metal ball and a hollow plastic ball of the same external radius arereleased from rest in a large vacuum chamber. When each has fallen 1m,they both have the same B Inertia Speed Momentum Kinetic energy

Change inpotential energy

The plastic ball is clearly lighter soanything involving mass is out, thisleaves speed which makes sensebased on free-fall

37 momentum

A railroad car of mass m is moving at speed v when it collides with a secondrailroad car of mass M which is at rest. The two cars lock togetherinstantaneously and move along the track. What is the speed of the carsimmediately after the collision? E v/2 mv/M Mv/m (m+M)v/m mv/(m+M)

Perfect inelastic collision. m1v1i = mtot(vf) ... (m)(v) = (m+M) vf

38 momentum

An open cart on a level surface is rolling without frictional loss through avertical downpour of rain, as shown above. As the cart rolls, an appreciableamount of rainwater accumulates in the cart. The speed of the cart will C

increase becauseof conservation ofmomentum

increase becauseof conservation ofmechanical energy

decrease becauseof conservation ofmomentum

decrease becauseof conservation ofmechanical energy

remain the samebecause theraindrops arefallingperpendicular tothe direction of thecart's motion

As the cart moves forward it gainsmass due to the rain but in the xdirection the rain does not provide anyimpulse to speed up the car so itsspeed must decrease to conservemomentum 38.momentum.png

39 momentum

A2kgobjectmovesinacircleofradius4mataconstantspeedof3m/s. Anetforceof4.5Nactson the object. What is the angular momentum of the object withrespect to an axis perpendicular to the circle and through its center? E 9Nm/kg 12m^2/s 13.5kgm^2/s^2 18Nm/kg 24kgm^2/s.

Angular momentum is given by theformula L = mvr = (2)(3)(4)

40 momentum

Two objects of mass 0.2 kg and 0.1 kg, respectively, move parallel to the x-axis, as shown above. The 0.2 kg object overtakes and collides with the 0.1kg object. Immediately after the collision, the y-component of the velocity ofthe 0.2 kg object is 1 m/s upward. What is the y-component of the velocity ofthe 0.1 kg object immediately after the collision'? A 2 m/s downward 0.5 m/s downward 0 m/s 0.5 m/s upward 2 m/s upward

2D collision. Analyze the y direction.Before py = 0 so after py must equal 0.0 = m1v1fy + m2v2fy 0 = (0.2)(1) +(0.1)(V2fy) 40.momentum.png

41 momentumThe magnitude of the momentum of the object is increasing in which of thecases? B IIonly IIIonly IandIIonly IandIIIonly I,II,andIII

Momentum increases if velocityincreases. In a d-t graph, III showsincreasing slope (velocity) 41.momentum.png

42 momentum The sum of the forces on the object is zero in which of the cases? C IIonly IIIonly IandIIonly IandIIIonly I,II,andIIIThe net force is zero if velocity (slope)does not change, this is graphs I and II 42.momentum.png

43 momentum

A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leavesthe kicker's foot with a speed of 5.0 m/s in a direction 60° above thehorizontal. The magnitude of the impulse imparted by the ball to the foot ismost nearly C 1 N s (3)^1/2 N s 2 N s 2/(3)^1/2 N s 4 N s

Since the impulse force is applied in thesame direction (60°) as the velocity, wedo not need to C use components butuse the 60° inclined axis for the impulsemomentum problem. In thatdirection. J=∆p J=mvf –mvi =m(vf –vi)=(0.4)(0–5)

44 momentum

Two people of unequal mass are initially standing on ice with neglibiblefriction. They then simultaneously push each other horizontally. Afterward,which of the following is true? C

The kineticenergies of the twopeople are equal.

the speeds of thetwo people areequal.

The momenta ofthe two people areequal.

The center ofmass of the two-person systemmoves in thedirection of theless massiveperson.

The less massiveperson has asmaller initialacceleration thanthe more massiveperson.

Initially, before the push, the two peopleare at rest and the total momentum iszero. After, the C total momentum mustalso be zero so each man must haveequal and opposite momenta.

45 momentum

A stationary object exploses, breaking into three pieces of masses m, m, and3m. The two pieces of mass m move off at right angles to each other with thesame magnitude of momentum mV, as shown in the diagram above. Whatare the magnitude and direction of the velocity of the piece having mass 3m? D A B C D E

Since the initial object was stationaryand the total momentum was zero itmust also have zero D total momentumafter. To cancel the momentum shownof the other two pieces, the 3mpiece would need an x component ofmomentum px = mV and a ycomponent of momentumpy = mV giving it a total momentum of√2 mV using Pythagorean theorem.Then set thistotal momentum equal to the mass *velocity of the 3rd particle. √2 mV =(3m) Vm3 and solve for Vm3 45.momentum.png

46 momentumA ball is thrown stright up in the air. When the ball reaches its highest point,which of the following is true? E It is in equilibrium.

It has zeroacceleration.

It has maximummomentum.

It has maximumkinetic energy.

None of these aretrue.

None of the statements are true. I) it isaccelerating so is not in equilibrium, II)Its acceleration is E –9.8 at all times, III)Its momentum is zero because itsvelocity is momentarily zero, IV) Itskinetic energy is also zero since itsvelocity is momentarily zero.

47 momentum

An empty sled of mass M moves without friction across a frozen pond atspeed vo. Two objects are dropped vertically into the sled one at a time: firstan object of mass m and then an object of mass 2m. Afterward the sledmoves with speed vf. What would be the final speed of the sled if the objectswere dropped into it in reverse order? C vf /3 vf /2 vf 2vf 3vf

Its does not matter what order tomasses are dropped in. Adding massreduces momentum C proportionally.All that matters is the total mass thatwas added. This can be provided byfinding the velocity after the first drop,then continuing to find the velocity afterthe seconddrop. Then repeating the problem inreverse to find the final velocity whichwill come outthe same

48 momentum The slope of the “best fit” straight line is most nearly A 5 N/s 6 N/s 7 N/s 8 N/s 10 N/s Stupid easy. Find slope of line 48.momentum.png

49 momentumThe increase in the momentum of the object between t=0 s and t=4 s is mostnearly C 40 N∙s 50 N∙s 60 N∙s 80 N∙s 100 N∙s

Increase in momentum is momentumchange which 49.momentum.png

50 momentumHow does an air mattress protect a stunt person landing on the ground after astunt? E

It reduces thekinetic energy lossof the stuntperson.

It reduces themomentumchange of the stuntperson.

It increases themomentumchange of the stuntperson.

It shortens thestopping time ofthe stunt personand increases theforce appliedduring the landing.

It lengthens thestopping time ofthe stunt personand reduces theforce appliedduring the landing.

Basic principle of impulse. Increasedtime lessens the force of impact.

51 momentum

Two objects, A and B, initially at rest, are "exploded" apart by the release of acoiled spring that was compressed between them. As they move apart, thevelocity of object A is 5 m/s and the velocity of object B is – 2 m/s. The ratioof the mass of object A to the mass object B, ma/mb is B 0.16 0.4 1 2.5 6.25

Explosion. pbefore = 0 = pafter … 0 =m1v1f + m2v2f … 0 = m1(5) + m2(–2)

52 momentum

The two blocks of masses M and 2M shown above initially travel at the samespeed v but in opposite directions. They collide and stick together. How muchmechanical energy is lost to other forms of energy during the collision? D Zero .5mv² .75mv² 1.3mv² 1.5mv²

Perfect inelastic collision. m1v1i +m2v2i = mtot*(vf) … Mv + (– 2Mv) =(3M)*vf gives vf = v/3.Then to find the energy loss subtractthe total energy before – the totalenergy after[ ½ Mv²+ ½ (2M)v²] – ½ (3M) (v/3)² =3/6 Mv²+ 6/6 Mv²– 1/6 Mv² 52.momentum.png

53 momentum

Two particles of equal mass mo, moving with equal speeds vo along pathsinclined at 60° to the x-axis as shown, collide and stick together. Theirvelocity after the collision has magnitude B v0/4 v0/2 (v0√2)/2 (v0√3)/2 v0

2D collision. The y momentums areequal and opposite and will cancel outleaving only the x momentums whichare also equal and will add together togive a total momentum equal to twicethe x component momentum beforehand. pbefore = pafter 2m0v0cos60= (2m0)*vf 53.momentum.png

54 momentum

A particle of mass m moves with a constant speed v along the dashed line y= a. When the x-coordinate of the particle is xo, the magnitude of the angularmomentum of the particle with respect to the origin of the system is B zero mva mvx0 mv√(x²+a²) mva/√(x²+a²)

Angular momentum is given by L = mvr= mva 54.momentum.png

55 momentum The final speed of the first 4-kilogram mass is C 0 m/s 2 m/s 3 m/s 4 m/s 6 m/sPerfect inelastic collision. m1v1i = mtot(vf) … (4)(6) = (8)vf 55.momentum.png

56 momentum The final speed of the two 4-kilogram masses that stick together is B 0 m/s 2 m/s 3 m/s 4 m/s 6 m/sPerfect inelastic collision. m1v1i = mtot(vf) … (8)(3) = (12)vf 55.momentum.png

57 momentum

A projectile of mass M1 is fired horizontally from a spring gun that is initially atrest on a frictionless surface. The combined mass of the gun and projectile isM2. If the kinetic energy of the projectile after firing is K, the gun will recoilwith a kinetic energy equal to D K M2*K/M1 [(M1/M2)^2]*K (M1*K)/(M2-M1) K*[M1/(M2-M1)]^.5

First use the given kinetic energy ofmass M1 to determine the projectilespeed after.K= ½M1v1f² … v1f = √(2K/M1) . Nowsolve the explosion problem withpbefore=0 = pafter. Note that the massof the gun is M2–M1 since M2 wasgiven as the total mass. 0 = M1v1f +(M2–M1)v2f … now sub in from abovefor v1f. M1(√(2K/M1)) = – (M2–M1) v2fand find v2f … v2f = – M1(√(2K/M1)) /(M2–M1) .Now sub this into K2 = ½ (M2–M1) v2f²and simplify.

58 momentum

Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10meters per second, as shown in Figure I above. It then collides elastically withidentical ball Y which is initially at rest. After the collision, ball X moves at 6meters per second along a path at 53° to its original direction, as shown inFigure II above. Which of the following diagrams best represents the motionof ball Y after the collision? D A B C D E

Since there is no y momentum before,there cannot be any net y momentumafter. The balls have equal masses soyou need the y velocities of each ball tobe equal after to cancel out themomenta. By inspection, looking at thegiven velocities and angles and withoutdoing any math, the only one that couldpossibly make equal y velocities ischoice D

58.momentum.png &58.momentumm.png

59 momentumIf one knows only the constant resultant force acting on an object and thetime during which this force acts, one can determine the A

change inmomentum of theobject

change in velocityof the object

change in kineticenergy of theobject mass of the object

acceleration of theobject Definition. Jnet = ∆p. Fnet*t = ∆p

60 momentum

An object of mass m is moving with speed vo to the right on a horizontalfrictionless surface, as shown above,when it explodes into two pieces. Subsequently, one piece of mass 2/5 mmoves with a speed vo/2 to the left.The speed of the other piece of the object is E vo / 2 vo / 3 7vo / 5 3vo / 2 2vo

Explosion with initial momentum.pbefore = pafter mvo = mavaf + mbvbfmvo = (2/5 m)(– vo / 2) + (3/5 m)(vbf)… solve for vbf 60.momentum.png

61 momentum62 momentum63 momentum64 momentum65 momentum66 momentum67 momentum68 momentum69 momentum70 momentum

71 momentum

A 2 kg object initially moving with a constant velocity is subjectedto a force of magnitude F in the direction of motion. A graph of Fas a function of time t is shown. What is the increase, if any, in thevelocity of the object during the time the force is applied? C 0 m/s 2.0 m/s 3.0 m/s 4.0 m/s 6.0 m/s

The area under the F-t graph will givethe impulse which is equal to themomentum change.With the momentum change we canfind the velocity change.J = area = 6 Then J = Δp = mΔv 6 = (2)Δv Δv = 3 m/s 71.momentum.png

72 momentum

A disk slides to the right on a horizontal, frictionless air table and collides withanother disk that was initiallystationary. The figures below show a top view of the initial path I of the slidingdisk and a hypothetical path Hfor each disk after the collision. Which figure shows an impossible situation? B A B C D E

This is a 2D collision. Before thecollision, there is no y momentum, so inthe after condition they momenta of each disk must cancelout. In choice B, both particles wouldhave Ymomentum downwards making a net Ymomentum after which is impossible. 72.momentum.png

73 momentum

A ball of mass m with speed v strikes a wall at an angle θ with the normal, asshown. It then rebounds with the same speed and at the same angle. Theimpulse delivered by the ball to the wall is E zero mv sin θ mv cos θ 2mv sin θ 2mv cos θ

This is the same as question 30 exceptoriented vertically instead ofhorizontally. 73.momentum.png

1 gravitation

Each of five satellites makes a circular orbit about an object that is muchmore massive than any of thesatellites. The mass and orbital radius of each satellite are given below.Which satellite has the greatest speed? B ½m R m ½R m R m 2R 2m R

Orbital speed is found from setting(GMm)/(r2) which gives v=(GM/r)1/2 where M is theobject being orbited. Notice thatsatellite mass does not affect orbitalspeed. The smallest radiusof orbit will be the fastest satellite.

2 gravitation

An asteroid moves in an elliptic orbit with the Sun at one focus as shownabove. Which of the following quantities increases as the asteroid movesfrom point P in its orbit to point Q? E Speed

Angularmomentum Total energy Kinetic energy Potential energy

As a satellite moves farther away, itslows down, also decreasing its angularmomentum andkinetic energy. The total energyremains the same in the absence ofresistive or thrust forces.The potential energy becomes lessnegative, which is an increase. 2.gravitation.png

3 gravitation

Two planets have the same size, but different masses, and no atmospheres.Which of the following would be the same for objects with equal mass on thesurfaces of the two planets? D A B C D E

With different masses, g would have adifferent value, but the physicalcharacteristics of theobjects would not be affected. 3.gravitation.png

4 gravitation

A person weighing 800 newtons on Earth travels to another planet with twicethe mass and twice the radius ofEarth. The person's weight on this other planet is most nearly A 400 N 800/√2 N 800 N 800√2 1,600 N

g = GM / r2 so the acceleration due togravity (and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M × 2 = g × 2 and r × 2 = g ÷4, so the net effect is the person’sweight is divided by 2

5 gravitation

Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. Theacceleration of a falling body near thesurface of Mars is most nearly D 0.25 m/s2 0.5 m/s2 2 m/s2 4 m/s2 25 m/s2

g = GM / r2 so the acceleration due togravity (and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M ÷ 10 = g ÷ 10 and r ÷ 2 = g× 4, so the net effect is g × 4/10

6 gravitation

A satellite of mass M moves in a circular orbit of radius R at a constant speedv. Which of the following mustbe true? E A B C D E

Circular orbit = constant r, combinedwith constant speed gives constantangular momentum(mvr). As it is a circular orbit, the forceis centripetal, points toward the centerand is alwaysperpendicular to the displacement ofthe satellite therefore does no work. 6.gravitation.png

7 gravitation

If Spacecraft X has twice the mass of Spacecraft Y, then true statementsabout X and Y include which of thefollowing? C A B C D E

The gravitational force on an object isthe weight, and is proportional to themass. In the samecircular orbit, it is only the mass of thebody being orbited and the radius of theorbit thatcontributes to the orbital speed andacceleration. 7.gravitation.png

8 gravitation

. The two spheres pictured above have equal densities and are subject onlyto their mutual gravitational attraction. Which of the following quantities musthave the same magnitude for both spheres? E (A) Acceleration (B) Velocity (C) Kinetic energy

(D) Displacementfrom the center ofmass

(E) Gravitationalforce Newton’s third law 8.gravitation.png

9 gravitation

The planet Mars has mass 6.4 × 1023 kilograms and radius 3.4 × 106 meters.The acceleration of an object in free-fall near the surface of Mars is mostnearly D (A) zero (B) 1.0 m/s2 (C) 1.9 m/s2 (D) 3.7 m/s2 (E) 9.8 m/s2 g = GM/r^2

10 gravitation

An object has a weight W when it is on the surface of a planet of radius R.What will be the gravitational force on the object after it has been moved to adistance of 4R from the center of the planet? E (A) 16W (B)4W (C)W (D)4 (E)1/16W

Force is inversely proportional todistance between the centers squared.R × 4 = F ÷ 16

11 gravitation

A new planet is discovered that has twice the Earth's mass and twice theEarth's radius. On the surface of this new planet, a person who weighs 500 Non Earth would experience a gravitational force of B (A) 125N (B) 250N (C) 500N (D) 1000N (E) 2000N

g = GM/r^2 so the acceleration due togravity (and the weight of an object) isproportional to the mass of the planetand inversely proportional to thedistance from the center of the planetsquared. M × 2 = g × 2 and r × 2 = g ÷4, so the net effect is the person’sweight is divided by 2

12 gravitation

A simple pendulum and a mass hanging on a spring both have a period of 1 swhen set into small oscillatory motion on Earth. They are taken to Planet X,which has the same diameter as Earth but twice the mass. Which of thefollowing statements is true about the periods of the two objects on Planet Xcompared to their periods on E

(A) Both areshorter.

(B) Both are thesame.

(C) Both arelonger.

(D) The period ofthe mass on thespring is shorter,that of thependulum is thesame.

(E) The period ofthe pendulum isshorter; that of themass on the springis the same.

A planet of the same size and twice themass of Earth will have twice theacceleration due to gravity. The periodof a mass on a spring has nodependence on g, while the period of apendulum is inversely proportional to g.

13 gravitationA satellite of mass m and speed v moves in a stable, circular orbit around aplanet of mass M. What is the radius of the satellite's orbit? C (A) GM/mv (B)Gv/mM (C)GM/v^2 (D)GmM/v (E)GmM/v^2

Orbital speed is found from settingrmvrGMm 22 = which givesrv = GM

14 gravitation

The mass of Planet X is one-tenth that of the Earth, and its diameter is one-half that of the Earth. The acceleration due to gravity at the surface of PlanetX is most nearly B (A) 2 m/s2 (B) 4 m/s2 (C) 5 m/s2 (D) 7 m/s2 (E) 10 m/s2

g = GM/r^2 so the acceleration due togravity (and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M ÷ 10 = g ÷ 10 and r ÷ 2 = g× 4, so the net effect is g × 4/10 14.gravitation.png

15 gravitation

.A satellite travels around the Sun in an elliptical orbit as shown above. As thesatellite travels from point X to point Y. which of the following is true about itsspeed and angular momentum? D (A) (B) (C) (D) (E)

Kepler’s second law (Law of areas) isbased on conservation of angularmomentum, whichremains constant. In order for angularmomentum to remain constant, as thesatellite approachesthe sun, its speed increases.

16 gravitation

16. A newly discovered planet, "Cosmo," has a mass that is 4 times the massof the Earth. The radius of the Earth isR . The gravitational field strength at the surface of Cosmo is equal to that atthe surface of the Earth if the eradius of Cosmo is equal to C (A) .5Re (B)Re (C)2Re (D) Sqrt Re (E) Re^2

g = GM/r^2 so the acceleration due togravity (and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M × 4 = g × 4 and if the neteffect is g = gEarth then r must be twicethat of Earth.

17 gravitation

The radius of the Earth is approximately 6,000 kilometers. The acceleration ofan astronaut in a perfectly circular orbit 300 kilometers above the Earth wouldbe most nearly D (A) 0 m/s2 (B) 0.05 m/s2 (C) 5 m/s2 (D) 9 m/s2 (E) 11 m/s2

g = GM/r^2 . 300 km above the surfaceof the Earth is only a 5% increase in thedistance (1.05times the distance). This will produceonly a small effect on g (÷1.052)

18 gravitation

Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radiiR1 and R2, respectively, as shown above. If R2 = 2R1, the accelerations a2and a1 of the two satellites are related by which of the following? E a2 =4a1 a2 =2a1 a2 =a1 a2 =a1/2 a2 =a1/4 a=g=GM ,if R =2R then a =1⁄4a1 18.Gravitation.png

19 gravitation

A satellite moves in a stable circular orbit with speed vo at a distance R fromthe center of a planet. For this satellite to move in a stable circular orbit adistance 2R from the center of the planet, the speed of the satellite must be B v/2 v/(2^1/2) vo (2v)^1/2 2vo

Orbital speed is found from settingGMm = mv 2 which gives v = GMwhere M is the Br2rr object being orbited. If r is doubled,v decreases by 2

20 gravitation

If F1 is the magnitude of the force exerted by the Earth on a satellite in orbitabout the Earth and F2 is the magnitude of the force exerted by the satelliteon the Earth, then which of the following is true? C

F1 is much greaterthan F2.

F1 is slightlygreater than F2. F1 is equal to F2.

F2 is slightlygreater than F1

F2 is much greaterthan F1 Newton’s third law

21 gravitation

A newly discovered planet has twice the mass of the Earth, but theacceleration due to gravity on the new planet's surface is exactly the same asthe acceleration due to gravity on the Earth's surface. The radius of the newplanet in terms of the radius R of Earth is C 1⁄2R ((2^1/2)*R)/2 (2^1/2)*R 2R

g = GM/(r^2) so the acceleration due togravity (and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M × 2 = g × 2 and if the neteffect is g = gEarth then r must be 2^(1/2) times that of Earth

22 gravitation

A satellite S is in an elliptical orbit around a planet P, as shown above, with r1and r2 being its closest and farthest distances, respectively, from the centerof the planet. If the satellite has a speed v1 at its closest distance, what is itsspeed at its farthest distance? A (r1*v1)/R2 (r2*v1)/R1 (r2−r2)v1 ((r1+r2)*v)/2 ((r2−r1)*v)/ (r2+r1)

From conservation of angularmomentum v1r1= v2r2 22.Gravitation.png

23 gravitation

A ball is tossed straight up from the surface of a small, spherical asteroid withno atmosphere. The ball rises to a height equal to the asteroid's radius andthen falls straight down toward the surface of the asteroid. What forces, ifany, act on the ball while it is on the way up? A

Only a decreasinggravitational forcethat actsdownward

Only an increasinggravitational forcethat actsdownward

Only a constantgravitational forcethat actsdownward

Both a constantgravitational forcethat actsdownward and adecreasing forcethat acts upward

No forces act onthe ball.

As the ball moves away, the force ofgravity decreases due to the increasingdistance

24 gravitation

A ball is tossed straight up from the surface of a small, spherical asteroid withno atmosphere. The ball rises to a height equal to the asteroid's radius andthen falls straight down toward the surface of the asteroid. The acceleration ofthe ball at the top of its path is: D

at its maximumvalue for the ball'sflight

equal to theacceleration at thesurface of theasteroid

equal to one-halfthe acceleration atthe surface of theasteroid

equal to one-fourththe acceleration atthe surface of theasteroid Zero

g = GM/(r^2) At the top of its path, ithas doubled its original distance fromthe center of theasteroid

25 gravitation

A satellite of mass M moves in a circular orbit of radius R with constant speedv. True statements about this satellite include which of the following?I. Its angular speed is v/R.II. Its tangential acceleration is zero.III. The magnitude of its centripetal acceleration is constant. E I only II only I and III only II and III only I, II, and III

Angular speed (in radians per second)is v/R. Since the satellite is notchanging speed, there isno tangential acceleration and v2/r isconstant.

26 gravitation

Two identical stars, a fixed distance D apart, revolve in a circle about theirmutual center of mass, as shown above. Each star has mass M and speed v.G is the universal gravitational constant. Which of the following is a correctrelationship among these quantities? B v^2 =GM/D v^2 =GM/2D v^2 =GM/D^2 v^2 =MGD v^2 =2GM^2/D

The radius of each orbit is ½ D, whilethe distance between them is D. Thisgives2/22DMvDGMM 26.Gravitation.png

27 gravitation

A spacecraft orbits Earth in a circular orbit of radius R, as shown above.When the spacecraft is at position P shown, a short burst of the ship'sengines results in a small increase in its speed. The new orbit is best shownby the solid curve in which of the following diagrams? D A) B) C) D) E)

An burst of the ships engine producesan increase in the satellite’s energy.Now the satellite ismoving at too large a speed for acircular orbit. The point at which theburst occurs must remainpart of the ship’s orbit, eliminatingchoices A and B. The Earth is no longerat the focus of theellipse in choice E.

27.Gravitation.pngand 27. Gravitation.png

28 gravitation

The escape speed for a rocket at Earth's surface is ve. What would be therocket's escape speed from the surface of a planet with twice Earth's massand the same radius as Earth? B 2ve (2)^½ ve ve ve/(2)^½ ½ ve

Escape speed with the speed at whichthe kinetic energy of the satellite isexactly equal to thenegative amount of potential energywithin the satellite/mass system. That isrGMmmv = −221which gives the escape speedrGM

29 gravitation

A hypothetical planet orbits a star with mass one-half the mass of our sun.The planet’s orbital radius is thesame as the Earth’s. Approximately how many Earth years does it take forthe planet to complete one orbit? D ½ 1/(2)^½ 1 2^½ 2

Orbital speed is found from settingrmvrGMm 22= which givesrGMv = where M is theobject being orbited. Also,vrT2π= . Since the mass is divided by 2, v isdivided by 2

30 gravitation

A hypothetical planet has seven times the mass of Earth and twice the radiusof Earth. The magnitude of thegravitational acceleration at the surface of this planet is most nearly C 2.9 m/s^2 5.7 m/s^2 17.5 m/s^2 35 m/s^2 122 m/s^2

g = so the acceleration due to gravity(and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M × 7 = g × 7 and r × 2 = g ÷4, so the net effect is g × 7/4

31 gravitation

Two artificial satellites, 1 and 2, are put into circular orbit at the same altitudeabove Earth’ssurface. The massof satellite 2 is twice the mass of satellite 1. If the period of satellite 1 is T,what is the period of satellite 2? C T/4 T/2 T 2T 4T

Orbital speed is found from settingrmvrGMm 22= which givesrGMv = where M is theobject being orbited. Notice thatsatellite mass does not affect orbitalspeed or period.

32 gravitation

A planet has a radius one-half that of Earth and a mass one-fifth the Earth’smass. The gravitational accelerationat the surface of the planet is most nearly B 4.0 m/s^2 8.0 m/s^2 12.5 m/s^2 25 m/s2 62.5 m/s2

g = so the acceleration due to gravity(and the weight of an object) isproportional to themass of the planet and inverselyproportional to the distance from thecenter of the planetsquared. M ÷ 5 = g ÷ 5 and r ÷ 2 = g ×4, so the net effect is g × 4/5

33 gravitation

In the following problem, the word “weight” refers to the force a scaleregisters. If the Earth were to stoprotating, but not change shape, A

the weight of anobject at theequator wouldincrease.

the weight of anobject at theequator woulddecrease.

the weight of anobject at the northpole wouldincrease.

the weight of anobject at the northpole woulddecrease.

all objects on Earthwould becomeweightless.

Part of the gravitational force acting onan object at the equator is providing thenecessarycentripetal force to move the object in acircle. If the rotation of the earth were tostop, this partof the gravitational force is no longerrequired and the “full” value of this forcewill hold theobject to the Earth.

34 gravitation

Assume that the Earth attracts John Glenn with a gravitational force F at thesurface of the Earth. When hemade his famous second flight in orbit, the gravitational force on John Glennwhile he was in orbit was closestto which of the following? A 0.95F 0.50F 0.25F 0.10F zero

Standard orbital altitudes are not alarge percentage of the radius of theEarth. The accelerationdue to gravity is only slightly smaller inorbit compared to the surface of theEarth.

35 gravitation

What happens to the force of gravitational attraction between two smallobjects if the mass of each object isdoubled and the distance between their centers is doubled? E It is doubled It is quadrupled It is halved

It is reducedfourfold

It remains thesame

F = . F is proportional to each mass andinversely proportional to the distancebetweentheir centers squared. If each mass isdoubled, F is quadrupled. If r is doubledF is quartered.

36 gravitation

One object at the surface of the Moon experiences the same gravitationalforce as a second object at the surfaceof the Earth. Which of the following would be a reasonable conclusion? B

both objects wouldfall at the sameacceleration

the object on theMoon has thegreater mass

the object on theEarth has thegreater mass

both objects haveidentical masses

the object on Earthhas a greatermass but the Earthhas a greater rateof rotation

Since the acceleration due to gravity isless on the surface of the moon, tohave the samegravitational force as a second objecton the Earth requires the object on theMoon to have alarger mass.

37 gravitation Astronauts in an orbiting space shuttle are “weightless” because E

of their extremedistance from theearth

the netgravitational forceon them is zero

there is noatmosphere inspace

the space shuttledoes not rotate

they are in a stateof free fall

Satellites in orbit are freely fallingobjects with enough horizontal speed tokeep from fellingcloser to the planet

38 gravitation

Consider an object that has a mass, m, and a weight, W, at the surface of themoon. If we assume the moon has anearly uniform density, which of the following would be closest to the object’smass and weight at a distancehalfway between Moon’s center and its surface? D ½ m & ½ W ¼ m & ¼ W 1 m & 1 W 1 m & ½ W 1 m & ¼ W

The mass of an object will not changebased on its location. As one digs into asphere of uniformdensity, the acceleration due to gravity(and the weight of the object) variesdirectly with distancefrom the center of the sphere.

39 gravitation

The mass of a planet can be calculated if it is orbited by a small satellite bysetting the gravitational force on thesatellite equal to the centripetal force on the satellite. Which of the followingwould NOT be required in thiscalculation? A

the mass of thesatellite

the radius of thesatellite's orbit

the period of thesatellite's orbit

Newton's universalgravitationalconstant

all of the above arerequired for thiscalculation

CombiningrmvrGMm 22 = withvT r2π = gives the equation correspondingto Kepler’s secondlaw. The mass of the satellite cancels inthese equations.

40 gravitation

As a rocket blasts away from the earth with a cargo for the internationalspace station, which of the followinggraphs would best represent the gravitational force on the cargo versusdistance from the surface of the Earth? E A B C D E

r 2GMmF = so F is proportional to 1/r2. Standard orbital altitudes are not alarge percentage ofthe radius of the Earth. Theacceleration due to gravity is onlyslightly smaller in orbit comparedto the surface of the Earth. 40.gravitation.png

41 gravitation

In chronological order (earliest to latest), place the following events:(1) Henry Cavendish's experiment(2) Newton's work leading towards the Law of Universal Gravitation(3) Tycho Brahe takes astronomical data(4) Nicolaus Copernicus proposes the heliocentric theory(5) Johannes Kepler's work on the orbit of Mars. A 43521 42135 43251 35421 42351

NO, this is not part of the curriculum,but interesting to know (and a bit ofcommon sense if youfollow the changing of the theories)

42 gravitation

A 20 kg boulder rests on the surface of the Earth. Assume the Earth hasmass 5.98 × 1024 kg and g = 10 m/s2What is the magnitude of the gravitational force that the boulder exerts on theEarth? E 5.98x10^25 N 5.98x10^24N 20N

The boulder exertsno force on theEarth 200 N

Gravitational force is also the weight.mg.

43 gravitation

An astronaut on the Moon simultaneously drops a feather and a hammer. Thefact that they reach the surface atthe same instant shows that E

no gravity forcesact on a body in avacuum.

the accelerationdue to gravity onthe Moon is lessthan theacceleration due togravity on theEarth

the gravitationalforce from theMoon on heavierobjects (thehammer) is equalto the gravitationalforce onlighter objects (thefeather).

a hammer andfeather have lessmass on the Moonthan on Earth.

in the absence ofair resistance allbodies at a givenlocation fall withthe sameacceleration.

g is the same for all bodies in theabsence of air resistance

44 gravitationA scientist in the International Space Station experiences "weightlessness"because C

there is nogravitational forcefrom the Earthacting on her.

the gravitationalpull of the Moonhas canceled thepull of the Earth onher.

she is in free fallalong with theSpace Station andits contents.

at an orbit of 200miles above theEarth, thegravitational forceof the Earth on heris 2% less than onitssurface.

in space she hasno mass.

Satellites in orbit are freely fallingobjects with enough horizontal speed tokeep from fellingcloser to the planet.

45 gravitation

A rocket is in a circular orbit with speed v and orbital radius R around a heavystationary mass. An externalimpulse is quickly applied to the rocket directly opposite to the velocity andthe rocket’s speed is slowed to v/2,putting the rocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new ellipticalorbit is E

= 14

= 12

= 71 1

= √ 83

= 47

The energy of a circular orbit is K+U=(1/2)mv^2 + (-Gmm/r)= (1/2)m((GMm/r)^1/2)^2 + (-GMm/r)= -GMm/2r. Theenergy ofan elliptical orbit is –(GMm/2a) where ais the semimajor axis. If the speed iscut in half we have K+U= (1/2)m(v/2)^2+ (-Gmm/r)=(1/2)m((1/2)(GM/r)^1/2))^2+(-Gmm/r) = -(7GMm/8r). Setting –(7GMm/8r)= (-GMm/2a) gives a= (4/7)r

46 gravitation

Kepler’s Second Law about “sweeping out equal areas in equal time” can bederived most directly from whichconservation law? C energy mechanical energy

angularmomentum mass linear momentum

Sweeping out equal areas in based onthe satellite moving faster as it movescloser to the body itis orbiting. This is a result ofconservation of angular momentum.

47 gravitation

Three equal mass satellites A, B, and C are in coplanar orbits around a planetas shown in the figure. Themagnitudes of the angular momenta of the satellites as measured about theplanet are LA, LB, and LC. Which ofthe following statements is correct? A LA > LB > LC LC > LB > LA LB > LC > LA LB > LA > LC

The relationshipbetween themagnitudes isdifferent at variousinstants in time.

The angular momentum of eachsatellite is conserved independently sowe can compare theorbits at any location. Looking at thecommon point between orbit A and Bshows that satelliteA is moving faster at that point thansatellite B, showing LA > LB. A similaranalysis at thecommon point between B and C showsLB > LC 47.gravitation.png

48 gravitation What is the value of the gravitational potential energy of the two star system? D

−2

3 2

−2

2

−3 2

−2

2

.rGMmU −= 48.gravitation.png

49 gravitation Determine the period of orbit for the star of mass 3M A

3

4

3

33

2

3

4

3

Since they are orbiting their center ofmass, the larger mass has a radius oforbit of d41. Thespeed can be found from42)3(2)3(dvMdMMG= which givesTddGMv)4 49.gravitation.png

50 gravitation

Two satellites are launched at a distance R from a planet of negligible radius.Both satellites are launched in thetangential direction. The first satellite launches correctly at a speed v0 and enters a circular orbit. The secondsatellite, however, is launched at a speed ½v0.What is the minimum distance between the second satellite andthe planet over the course of its orbit? E

1√2

12

13

14

17

The energy of a circular orbit isrGMmrGMmrGMmrGmmmvUK2)(221)(221=−+=+ −=−+

The energy of an elliptical orbit isaGMm2− where a is the semimajor axis. If thespeed is cut inhalf we haverGMmrGMmrGMmrvGmmmUK87)(22121)(22 21=+ =−+ −=−+

SettingaGMmrGMm8 27−=− gives a = (4/7)rThe distance to the planet from thispoint is r (the radius of the circular orbitand aphelion for theelliptical orbit). The opposite side of theellipse is 2a away, or 8r/7, making thedistance to theplanet at perihelion 8r/7 – r = r/7

50 gravitation

Two satellites are launched at a distance R from a planet of negligible radius.Both satellites are launched in thetangential direction. The first satellite launches correctly at a speed v0 and enters a circular orbit. The secondsatellite, however, is launched at a speed ½v0.What is the minimum distance between the second satellite andthe planet over the course of its orbit? E

1√2

12

13

14

17

The energy of a circular orbit isrGMmrGMmrGMmrGmmmvUK2)(221)(221=−+=+ −=−+

The energy of an elliptical orbit isaGMm2− where a is the semimajor axis. If thespeed is cut inhalf we haverGMmrGMmrGMmrvGmmmUK87)(22121)(22 21=+ =−+ −=−+

SettingaGMmrGMm8 27−=− gives a = (4/7)rThe distance to the planet from thispoint is r (the radius of the circular orbitand aphelion for theelliptical orbit). The opposite side of theellipse is 2a away, or 8r/7, making thedistance to theplanet at perihelion 8r/7 – r = r/7

51 gravitation

When two stars are very far apart, their gravitational potential energy is zero;when they are separated by adistance d, the gravitational potential energy of the system is U. What is thegravitational potential energy of thesystem if the stars are separated by a distance 2d? B U/4 U/2 U 2U 4U

.rGMmU −=

52 gravitation

The gravitational force on a textbook at the top of Pikes Peak (elevation14,100 ft) is 40 newtons. What wouldbe the approximate gravitational force on the same textbook if it were taken totwice the elevation? D 5 N 10 N 20 N 40 N 80 N

The top of Pikes Peak is a very smallfraction of the radius of the Earth.Moving to twice thiselevation will barely change the value ofg

53 gravitation

Assume the International Space Station has a mass m and is in a circularorbit of radius r about the center of theEarth. If the Earth has a mass of M, what would be the speed of the SpaceStation around the Earth? A

2

2

√

Orbital speed is found from settingrmvrGMm 22= which givesrGMv = where M is theobject being orbited.

54 gravitation

What would be the gravitational force of attraction between the proton in thenucleus and the electron in anorbit of radius 5.3 × 10–11 m in a simple hydrogen atom? B 2.0 × 10–57 N 3.7 × 10–47 N 6.1 × 10–28 N 8.2 × 10–8 N

the only force ofattraction would beelectrical

.2rGMmF = . The masses of the proton andelectron can be found in the table ofconstants (thesemasses do not need to be memorized)

55 gravitation

Two iron spheres separated by some distance have a minute gravitationalattraction, F. If the spheres are movedto one half their original separation and allowed to rust so that the mass ofeach sphere increases 41%, what would be the resulting gravitational force? D 2 F 4 F 6 F 8 F 10 F

2rGMmF = ; If r ÷ 2, F × 4. If each mass ismultiplied by 1.41, F is doubled (1.41×1.41)

56 gravitation

A ball which is thrown upward near the surface of the Earth with a velocity of50 m/s will come to rest about 5seconds later. If the ball were thrown up with the same velocity on Planet X,after 5 seconds it would be stillmoving upwards at nearly 31 m/s. The magnitude of the gravitational fieldnear the surface of Planet X is whatfraction of the gravitational field near the surface of the Earth? B 0.16 0.39 0.53 0.63 1.59

g = ∆v/t = (31 m/s – 50 m/s)/(5 s) = –3.8m/s B2

57 gravitation

An object placed on an equal arm balance requires 12 kg to balance it. Whenplaced on a spring scale, the scalereads 120 N. Everything (balance, scale, set of masses, and the object) isnow transported to the moon where thegravitational force is one-sixth that on Earth. What are the new readings ofthe balance and the spring scale(respectively)? A 12 kg, 20 N 1 kg, 120 N 12 kg, 720 N 2 kg, 20 N 2 kg, 120 N

mass is unchanged, weight is changeddue to a change in the acceleration dueto gravity

58 gravitation

Two artificial satellites I and II have circular orbits of radii R and 2R,respectively, about the same planet. Theorbital velocity of satellite I is v. What is the orbital velocity of satellite II? B .5v v/(sqrt(2)) v (sqrt(2))v 2v

Orbital speed is found from settingGMm/(r^2)=mv^2/r which gives v =(GM/r)^(1/2) where M is theobject being orbited.

59 gravitation

The gravitational acceleration on the surface of the moon is 1.6 m/s^2. Theradius of the moon is 1.7 × 10^6 m. What is the period of a satellite placed ina low circular orbit about the moon? B 1.0x10^3 s 6.5x10^3 s 1.1x10^6 s 5.0x10^6 s 7.1x10^12 s g = v^2/r and v = 2πr/T

1 oscillations

A mass m, attached to a horizontal massless spring with spring constant k, isset into simple harmonic motion.Its maximum displacement from its equilibrium position is A. What is themass’s speed as it passes through itsequilibrium position? B A B C D E

Energy conservation. Usp = K, so ½ kA^2 = ½ mv^2 1.oscillations.png

2 oscillations

The period of a spring-mass system undergoing simple harmonic motion is T.If the amplitude of the springmasssystem’s motion is doubled, the period will be: C .25T .5T T 2T 4T

The period of a mass-spring is onlyaffected by mass and k so its stays thesame

3 oscillations

A simple pendulum of mass m and length L has a period of oscillation T atangular amplitude θ = 5° measuredfrom its equilibrium position. If the amplitude is changed to 10° and everythingelse remains constant, the newperiod of the pendulum would be approximately. C 2T (sqrt(2))T T T/(sqrt(2)) .5T

The period of a pendulum is onlyaffected by length and “g” so it staysthe same

4 oscillations

A mass m is attached to a spring with a spring constant k. If the mass is setinto simple harmonic motion by adisplacement d from its equilibrium position, what would be the speed, v, ofthe mass when it returns to theequilibrium position? E A B C D E

Energy conservation. Usp = K, so ½ kd^2 = ½ mv^2 4.oscillations.png

5 oscillations

A mass on the end of a spring oscillates with the displacement vs.time graph shown. Which of the following statements about itsmotion is INCORRECT? A

The amplitude ofthe oscillation is0.08 m.

The frequency ofoscillation is 0.5Hz.

The massachieves amaximum in speedat 1 sec.

The period ofoscillation is 2 sec.

The massexperiences amaximum in thesize of theacceleration at t=1.5 sec

The amplitude from the graph is 0.04not 0.08, the rest are true 5.oscillations.png

6 oscillationsWhat is the period of a simple pendulum if the cord length is 67 cm and thependulum bob has a mass of 2.4 kg. B .259s 1.63s 3.86s 16.3s 24.3s

The mass is irrelevant, only the lengthmatters. T is found with 2π √(L/g)

7 oscillationsIf the mass of a simple pendulum is doubled but its length remains constant,its period is multiplied by a factor of C 0.5 1/(sqrt(2)) 1 (sqrt(2)) 2

Mass does not affect the period, onlythe length matters

8 oscillationsWhich of the following is true for a system consisting of a mass oscillating onthe end of an ideal spring? D

The kinetic andpotential energiesare equal to eachother at all times.

The kinetic andpotential energiesare both constant.

The maximumpotential energy isachieved when themass passesthrough itsequilibriumposition.

The maximumkinetic energy andmaximum potentialenergy are equal,but occur atdifferent times.

The maximumkinetic energyoccurs atmaximumdisplacement ofthe mass from itsequilibriumposition

Energy is conserved here and switchesbetween kinetic and potential whichhave maximums atdifferent locations

9 oscillationsThe length of a simple pendulum with a period on Earth of one second ismost nearly B 0.12m 0.25m 0.50m 1.0m 10.0m Sub into T = 2π √(L/g) and solve for L

10 oscillationsWhich graph can represent the total mechanical energy of the block-springsystem as a function of x ? E A B C D E

Only conservative forces are actingwhich means mechanical energy mustbe conserved so it stays constant asthe mass oscillates 10.oscillations.png

11 oscillations Which graph can represent the kinetic energy of the block as a function of x ? D A B C D E

The box momentarily stops at x(min)and x(max) so must have zero K atthese points. The box accelerates themost at the ends of the oscillation sincethe force is the greatest there. Thischanging acceleration means that thebox gains speed quickly at first but notas quickly as it approaches equilibrium.This means that the KE gain starts ofrapidly from the endpoints andgets less rapid as you approachequilibrium where there would be amaximum speed and maximum K, butzero force so less gain in speed. Thisresults in the curved graph. 11.oscillations.png

12 oscillations

An object swings on the end of a cord as a simple pendulum with period T.Another object oscillates up and down on the end of a vertical spring also withperiod T. If the masses of both objects are doubled, what are thenew values for the Periods? B A. B. C. D. E.

Pendulum is unaffected by mass.Mass-spring system has mass causingthe T to change proportional to √m sosince the mass is doubled the period ischanged by √2 12.oscillations.png

13 oscillations

An object is attached to a spring and oscillates with amplitude A and period T,as represented on the graph. The nature of the velocity v and acceleration aof the object at time T/4 is best represented by which of the following? D v > 0, a > 0 v > 0, a < 0 v > 0, a = 0 v = 0, a < 0 v = 0, a = 0

At T/4 the mass reaches maximum +displacement where the restoring forceis at a maximum and pulling in theopposite direction and hence creating anegative acceleration. Atmaximum displacement the mass stopsmomentarily and has zero velocity 13.oscillations.png

14 oscillations

When an object oscillating in simple harmonic motion is at its maximumdisplacement from the equilibrium position. Which of the following is true ofthe values of its speed and the magnitude of the restoring force? A A B C D E

At T/4 the mass reaches maximum +displacement where the restoring forceis at a maximum and pulling in theopposite direction and hence creating anegative acceleration. Atmaximum displacement the mass stopsmomentarily and has zero velocity 14.oscillations.png

15 oscillations

A particle oscillates up and down in simple harmonic motion. Its height y as afunction of time t is shown in the diagram. At what time t does the particleachieve its maximum positive acceleration? A 1 second 2 seconds 3 seconds 4 seconds

None of the above,because theacceleration isconstant

Positive Acceleration occurs when themass is at negative displacementssince the force will be acting A in theopposite direction of the displacementto restore equilibrium. Based on F=k∆xthemost force, and therefore the mostacceleration occurs where the mostdisplacement is 15.oscillations.png

16 oscillations

The graph shown represents the potential energy U as a function ofdisplacement x for an object on the end of a spring oscillating in simpleharmonic motion with amplitude xο. Which of the following graphs representsthe kinetic energy K of the object as a function of displacement x ? D A B C D E

As the object oscillates, its totalmechanical energy is conserved andtransfers from U to K back and forth.The only graph that makes sense tohave an equal switch throughout is D 16.oscillations.png

17 oscillations Which of the following is true for both spheres? A

The maximumkinetic energy isattained as thesphere passesthrough itsequilibriumposition

The maximumkinetic energy isattained as thesphere reaches itspoint of release.

The minimumgravitationalpotential energy isattained as thesphere passesthrough itsequilibriumposition.

The maximumgravitationalpotential energy isattained when thesphere reaches itspoint of release.

The maximum totalenergy is attainedonly as the spherepasses through itsequilibriumposition.

For the spring, equilibrium is shownwhere the maximum transfer of kineticenergy has occurred and likewise forthe pendulum the bottom equilibriumposition has the maximum transfer ofpotential energy into spring energy. 17.oscillations.png

18 oscillations

If both spheres have the same period of oscillation, which of the following isan expression for the springconstant E L / m1g g/m2L m1L/g m2L/g m1g/L

Set period formulas equal to each otherand rearrange for k 18.oscillations.png

19 oscillations

A block attached to the lower end of a vertical spring oscillates up and down.If the spring obeysHooke's law, the period of oscillation depends on which of the following?I. Mass of the blockII. Amplitude of the oscillationIII. Force constant of the spring E I only II only III only I and II I and III

In a mass-spring system, both massand spring constant (force constant)affect the period.

20 oscillations

A simple pendulum and a mass hanging on a spring both have a period of 1 swhen set into small oscillatorymotion on Earth. They are taken to Planet X, which has the same diameter asEarth but twice the mass. Which of thefollowing statements is true about the periods of the two objects on Planet Xcompared to their periods on Earth? E Both are shorter. Both are the same. Both are longer.

The period of themass on the springis shorter; that ofthe pendulum isthe same.

The period of thependulum isshorter; that of themass on the springis the same

The mass spring system in unaffectedbecause the attached mass and springconstant are thesame. Based on g = GMp / R^2 and thegiven values, g on planet X would begreater. Usingthe pendulum period formula, larger gmeans smaller period.

21 oscillations

A simple pendulum of length l, whose bob has mass m, oscillates with aperiod T. If the bob is replaced by oneof mass 4m, the period of oscillation is C T/4 T/2 T 2T 4T

Mass does not affect the period of apendulum

22 oscillationsWhat is the amplitude, in meters, of the resulting simple harmonic motion ofthe block? A m/40 m/20 m/4 m/2 m

At the current location all of the energyis gravitational potential. As the springstretches to itsmax location all of that gravitationalpotential will become spring potentialwhen it reachesits lowest position. When the boxoscillates back up it will return to itsoriginal locationconverting all of its energy back togravitational potential and will oscillateback and forthbetween these two positions. As suchthe maximum stretch bottom locationrepresents twicethe amplitude so simply halving thatmax Δx will give the amplitude. Findingthe maxstretch: The initial height of the box hand the stretch Δx have the same value(h=Δx)U = Usp mg(Δx1) = ½ kΔx12 mg = ½ k Δx1 Δx1 = .05 m.This is 2A, so the amplitude is 0.025 mor 1/40 m.Alternatively, we could simply find theequilibrium position measured from theinitial topposition based on the forces atequilibrium, and this equilibrium stretchmeasured from thetop will be the amplitude directly. To dothis:Fnet = 0 Fsp = mg kΔx2 = mg Δx2 =0.025 m, which is the amplitude 22.oscillations.png

23 oscillations What will the resulting period of oscillation be? C π/40s π/20s π/10s π/5s π/4ssPlug into period for mass-spring systemT = 2π √(m/k) 22.oscillations.png

24 oscillations

A ball is dropped from a height of 10 meters onto a hard surface so that thecollision at the surface may beassumed elastic. Under such conditions the motion of the ball is D

simple harmonicwith a period ofabout 1.4 s

simple harmonicwith a period ofabout 2.8 s

simple harmonicwith an amplitudeof 5 m

periodic with aperiod of about 2.8s but not simpleharmonic

motion withconstantmomentum

Based on free fall, the time to fall downwould be 1.4 seconds. Since thecollision with theground is elastic, all of the energy willbe returned to the ball and it will riseback up to itsinitial height completing 1 cycle in atotal time of 2.8 seconds. It will continuedoing thisoscillating up and down. However, thisis not simple harmonic because to besimpleharmonic the force should vary directlyproportional to the displacement butthat is not thecase in this situation

25 oscillations

Which of the following graphs shows the kinetic energy K of the particle as afunction of time t for one cycle ofmotion? B A B C D E

Energy will never be negative. The maxkinetic occurs at zero displacement andthe kineticenergy become zero when at themaximum displacement 25.oscillations.png

26 oscillationsWhich of the following graphs shows the kinetic energy K of the particle as afunction of its displacement x ? C A B C D E Same reasoning as above, it must be C 26.oscillations.png

27 oscillations

A mass m is attached to a vertical spring stretching it distance d. Then, themass is set oscillating on a springwith an amplitude of A, the period of oscillation is proportional to A A B C D E

First use the initial stretch to find thespring constant. Fsp = mg = kΔx k = mg/ dThen plug that into T = 2π √(m/k) 27.oscillations.png

28 oscillations

Two objects of equal mass hang from independent springs of unequal springconstant and oscillate up and down.The spring of greater spring constant must have the C

smaller amplitudeof oscillation

larger amplitude ofoscillation

shorter period ofoscillation

longer period ofoscillation

lower frequency ofoscillation

Based on T = 2π √(m/k) the largerspring constant makes a smaller period

29 oscillations30 oscillations31 oscillations32 oscillations33 oscillations34 oscillations35 oscillations36 oscillations37 oscillations38 oscillations

39 oscillations

An object of mass m hanging from a spring of spring constant k oscillates witha certain frequency. What is thelength of a simple pendulum that has the same frequency of oscillation? B mk/g mg/k kg/m k/mg g/mk

Since the frequencies are the same, theperiods are also the same. Set theperiod for themass-spring system equal to the periodfor the string pendulum and rearrangefor L.

40 oscillations

A platform of mass 2 kg is supported by a spring of negligible mass asshown.The platform oscillates with a period of 3 s when the platform is pushed downand released. What must be the mass of a block that when placed on theplatform doubles the period of oscillation to 6 s? D 1kg 2kg 4kg 6kg 8kg

Based on T = 2π √(m/k), in order todouble the period, the mass would haveto be increased by4x the original amount. Here is thetricky part … you are to increase themass to 4 x itsoriginal value by adding mass the to2kg tray. So to make the total masshave a value of8 kg, only 6 kg of extra mass wouldneed to be added to the tray. 40.oscillations.PNG

1 Fluids

A cork has weight mg and density 25% of water density. A string is tiedaround the cork and attached to the bottom of a water-filled container. Thecork is totally immersed. Express in terms of the cork weight mg, the tensionin the string D 0 mg 2mg 3mg 4mg

FBD has Ft pointing down Fb pointingup and weight (mg) down. Fnet = 0 Fb– FtThe buoyant force is given by theweight of the displaced water. Since thewaters displacedvolume is equal to the corks displacedvolume and the water weight for thesame volumewould be 4 times heavier (based on thegiven cork weight = 25% water weight)compared tothe cork, the buoyant force is equal to 4x the cork weight = 4mg. Using theforce equationcreated initially. F– mg = 0t = Fb – mg = 4mg – mg = 3mg 1.fluids.PNG

2 Fluids Which of the following is the best statement of Pascals Law? A

pressure on aconfined liquid istransmitted equallyin all directions

a numericalarrangementwhere eachnumber is the sumof the two numbersabove

two electronscannot occupy thethe same quantumstate at the sametime

the volume of agas is directlyreated to itstemperature

the farther away agalaxy is the fasterit is receding Definition of Pascal's principle

3 FluidsWhen submerged under water, the apparent mass of one cubic meter of puregold is 18300 kg. What would be its mass in air? D 16300kg 17300kg 18300kg 19300kg 20300kg

A 1 m3 volume cube under waterdisplaces 1m3 of water. This weight ofwater = pVg =1000(1)(10) = 10000 N which isequivalent to the buoyant force. Theapparent weight inwater is mappg = 18300(10) = 183000N. This apparent weight is lessened bythe buoyantforce pulling up with 10000 N of force.So outside of the water, this upwardsforce wouldnot exist and the actual weight wouldbe 193000 N which equal 19300 kg ofmass.

4 Fluids

An ideal fluid flows through a long horizontal circular pipe. In one region of thepipe, it has radius R. The pipethen widens to radius 2R. What is the ratio of the fluids speed in the region ofradius R to the speed of the fluidin region with radius 2R E 1/4. 1/2. 1 2 4

Using fluid continuity. A1v1 = A2v2πR2v1 = π(2R)2v2 v1 = 4 v2

5 Fluids

A fluid is forced through a pipe of changing cross section as shown. In whichsection would the pressure of thefluid be a minimum B I II III IV

all sections havesame pressure

This is based on two principles. 1 –Bernoulli’s principle says that whenspeed increasespressure drops. Second, continuitysays more area means less speedbased on A1v1 = A2v2So the smallest area would have thelargest speed and therefore mostpressure drop. 5.fluids.PNG

6 Fluids

Three fishing bobbers all float on top of water. They have the followingrelationships:-A,B: same mass, same density, different shapes-B,C: same size, same shape,mass & density C < mass & density BThree identical weights are tied to each bob, and each is pulled completelybeneath the water. Which bob willdisplace the greatest amount of water E A B C A and B

All displace thesame amount ofwater.

Since A and B have the same massand density, they have the samevolume. C has the samevolume as A and B since it’s the sameshape as B. So all three objects havethe samevolume. When submerged, they will alldisplace the same amount of water andtherefore allhave the same buoyant force acting onthem. Note: if the objects were floatinginstead ofsubmerged than the heavier oneswould have larger buoyant forces.

7 FluidsA hydraulic press allows large masses to be lifted with small forces as a resultof which principle? A Pascal's Bernoulli's Archimedes' Huygens' Newton's

Pascals principle of equal pressuretransfer in a fluid allows for hydrauliclifts to function.

8 Fluids

A 500 N weight sits on the small piston of a hydraulic machine. The smallpiston has an area of 2 cm2 . If thelarge piston has an area of 40 cm2, how much weight can the large pistonsupport? C 25N 500N 10000N 40000N

Pascals principle says P1 = P2 F1/A1 =F2/A2 F2 = F1A2 / A1 = 500(40)/(2)

9 FluidsAs a rock sinks deeper and deeper into water of constant density, whathappens to the buoyant force on it? B It increases.

It remainsconstant. It decreases.

It may increase ordecrease,depending on theshape of the rock.

Buoyant force is equal to weight ofdisplaced fluid. Since the density isconstant and the volumedisplaced is always the same, thebuoyant force stays constant

10 Fluids

50 cm^3 of wood is floating on water, and 50 cm^3 of iron is totallysubmerged. Which has the greater buoyantforce on it? B The wood. The iron.

Both have thesame buoyantforce.

Cannot bedetermined withoutknowing theirdensities.

The wood is floating and is only partiallysubmerged. It does not displace aweight of waterrelated to its entire volume. The ironhowever is totally submerged and doesdisplace aweight of water equal to its entirevolume. Since the iron displaces morewater, it has alarger buoyant force acting on it.

11 Fluids

Salt water is more dense than fresh water. A ship floats in both fresh waterand salt water. Compared to thefresh water, the amount of water displaced in the salt water is B more. less. the same.

Cannot bedetermined fromthe informationgiven.

For floating objects, the weight of thedisplaced fluid equals the weight of theobject. For a moredense fluid, less of that fluid needs tobe displaced to create a fluid weightequal to theweight of the object. Since the saltwater is more dense, it will not need asmuch displaced.

12 Fluids A liquid has a specific gravity of 0.357. What is its density? A 357 kg/m3 643 kg/m3 1000 kg/m3 3570 kg/m3Definition of specific gravity. s.g = ρx /ρH20

13 Fluids

Water flows through a pipe. The diameter of the pipe at point B is larger thanat point A. Where is the waterpressure greater? B Point A Point B

Same at both Aand B

Cannot bedetermined fromthe informationgiven.

This is based on two principles. 1 –Bernoulli’s principle says that whenspeed increasespressure drops. Second, continuitysays more area means less speedbased on A1v1 = A2v2So the smallest area would have thelargest speed and therefore mostpressure drop. Moving to more area ->less speed -> more pressure

14 Fluids

Liquid flows through a 4 cm diameter pipe at 1.0 m/s. There is a 2 cmdiameter restriction in the line. What isthe velocity in this restriction? D 0.25 m/s 0.50 m/s 2 m/s 4 m/s

Flow continuity. A1v1 = A2v2 π(0.02)^2(1) = π(0.01)^2(v2)

15 Fluids

A copper block is connected to a string and submerged in a container ofwater.Position 1: The copper is completely submerged, but just under the surface ofthe water.Position 2: The copper is completely submerged, mid-way between the watersurface and the bottom of thecontainer.Position 3: The copper is completely submerged, but just above the bottomsurface of the container.Assume that the water is incompressible. What is the ranking of the buoyantforces (B) acting on the copperblocks for these positions, from least to greater? C B1 < B2 < B3 B3 < B2 < B1 B1 = B2 = B3 B1 < B2 = B3 B3 < B1 = B2

Buoyant force is based on how muchweight of water is displaced. Since allthree are completelysubmerged they all displace the sameamount of water so have equal buoyantforces.

16 Fluids

Two objects labeled K and L have equal mass but densities 0.95Do and Do,respectively. Each of these objectsfloats after being thrown into a deep swimming pool. Which is true about thebuoyant forces acting on theseobjects? D

The buoyant forceis greater onObject K since ithas a lowerdensity anddisplaces morewater.

The buoyant forceis greater onObject K since ithas lower densityand lower densityobjects alwaysfloat“higher” in thefluid.

The buoyant forceis greater onObject L since it isdenser than K andtherefore “heavier.”

The buoyantforces are equalon the objectssince they haveequal mass.

Without knowingthe specific gravityof the objects,nothing can bedetermined.

For floating objects, the buoyant forceequals the weight of the objects. Sinceeach object has thesame weight, they must have the samebuoyant force to counteract that weightand makethem float. IF the equal mass objectssunk, then the one with the smallerdensity would havea larger volume and displace morewater so have a larger buoyant force.But that is not thecase here.

17 Fluids

A driveway is 22.0 m long and 5.0 m wide. If the atmospheric pressure is 1.0x 10^5 Pa, How much force doesthe atmosphere exert on the driveway? E 9.09 x 10^8 N 1.1 x 10^-3 N 909 N 4545 N 1.1 x 10^7 N P = F / A 1x10^5 = F / (22*5)

18 Fluids Which of the following could be a correct unit for pressure? D kg/m^2 kg/(ms) kg/s^2 kg/(ms^2) (ms)/kgP = F / A = ma / A = kg (m/s^2) / m^2 =kg / (m•s^2)

19 Fluids

A block is connected to a light string attached to the bottom of a largecontainer of water. The tension in the string is 3.0 N. The gravitationalforce from the earth on the block is 5.0 N. What is the block’s volume? 2.0×10^−4 m^3

3.0×10^-4 m^3 5.0×10^-4 m^3 8.0×10^−4 m^3 1.0×10^-3m^3 19.fluids.png

20 Fluids

A cube of unknown material and uniform density floats in a container of waterwith 60% of its volumesubmerged. If this same cube were placed in a container of oil with density800 kg/m,what portion of thecube’s volume would be submerged while floating? 33% 50% 58% 67% 75%

21 Fluids 21.fluids.png22 Fluids 22.fluids.png23 Fluids 23.fluids.png24 Fluids 24.fluids.png25 Fluids 25.fluids.png26 Fluids27 Fluids 27.fluids.png28 Fluids 28.fluids.png

29 Fluids

One cubic centimeter of iron (density ~7.8 g/cm and 1 cubic centimeter ofaluminum (density ~2.7 g/cm) are dropped into a pool. Which has the largestbuoyant force on it? C iron aluminum both are the same

neither has abouyant force on it

Both object are more dense than waterand will sink in the pool. Since bothhave the samevolume, they will displace the sameamount of water and will have the samebuoyant forces.

30 Fluids

One kilogram of iron (density ~7.8 g/cm3) and 1 kilogram of aluminum(density ~2.7 g/cm3 are dropped into apool. Which has the largest buoyant force on it? B iron aluminum both are the same

neither has abouyant force on it

Again both samples sink. Also, bothsamples have the same mass butdifferent densities. For thesame mass, a smaller density musthave a larger volume, and the largervolume displacesmore water making a larger buoyantforce. So the smaller density with thelarger volume hasa larger buoyant force.

31 Fluids

Find the approximate minimum mass needed for a spherical ball with a 40 cmradius to sink in a liquid ofdensity 1.4x103 kg/m B 37.5kg 375kg 3750kg 37500kg 357000kg

V of this ball is 4/3 π r3 = 4/3 π (0.4)3 =0.2681 m3. For the ball to just sink, it ison the verge offloating, meaning the weight of the ballequals the buoyant force of the fullysubmerged ball.mg = ρfl Vdisp g m (10) = 1400(0.2681) (10) m = 375 kg

32 Fluids

What vertical percentage of a 0.25 m deep sheet of ice, whose density is 0.95x103kg/m3, will be visible in an ocean whose density is 1.1x103 kg/m A 14% 34% 58% 71% 87%

This object will float, so mobjg = FbρobjVobj g = ρocean Vdisp g(0.95x103)(V)(10) = (1.1x103)(x% V)(10)Gives x% = 0.86 but that is the amountsubmerged, so the visible about wouldbe 1 – 0.86

33 Fluids

The idea that the velocity of a fluid is high when pressure is low and that thevelocity of a fluid is low when thepressure is high embodies a principle attributed to E Torricelli Pascal Galileo Archimedes Bernoulli

Statement associated with Bernoulli’sprinciple

34 Fluids The mass of a 1.3 m3 object with a specific gravity of 0.82 is D 630kg 730kg 820kg 1100kg 1600kg

s.g = ρobj / ρh20 0.82 = ρobj / 1000ρobj = 820 … then ρ = m/V 820 = m /1.3

35 FluidsThe apparent weight of a 600 kg object of volume 0.375 m3 submerged in aliquid of density 1.25x103 kg/m3 D 180N 250N 480N 1300N 4700N

The apparent weight is the air weight –the upwards buoyant force. Thebuoyant force is givenby Fb = ρfl Vdisp g = 1.25x103 (0.375)(10) = 4687.5 N.The apparent weight is then (600)(10) –4687.5 = 1312.5 N

36 Fluids

A conduit of radius 7R carries a uniformly dense liquid to a spigot of radius Rat the same height, where it has avelocity of V. What is its initial velocity A 0.02V 0.11V V 7V 49V

Using fluid continuity. A1v1 = A2v2 π(7R)2v1 = π(R)2V v1 = V / 49

37 Fluids

The pressure in a pipe carrying a liquid with a density of ρ and an initialvelocity v at the inlet is P, which is ymeters lower than its outlet, which has a velocity of 2v. In these terms, what isthe final pressure? B

The fluid flow is occurring in a situationsimilar to the diagram for question #27.Apply Bernoulli’s equation. P1 + ρgy1 +½ ρv12 = P2 + ρgy2 + ½ ρv22P + 0 + ½ ρv2 = P2 + ρgy + ½ ρ (2v)2P2 = P + ½ ρv2 – ½ 4ρv2 – ρgy = P –3/2 ρv2– ρgy 37.fluids.PNG

38 Fluids The units of specific gravity are E kg/m3 g/m3 m/s2 N/m none of the above s.g is density / density and has no units

39 Fluids

The buoyant force on an object is equal to the weight of the water displacedby a submerged object. This is aprinciple attributed to D Torricelli Pascal Galileo Archimedes Bernoulli Definition of Archimedes principle

40 FluidsIf the gauge pressure of a device reads 2.026x105 N/m2, the absolutepressure it is measuring is D 1.013x10^5 N/m2 2.052x10^5 N/m2 2.026x10^5 N/m2 3.039x10^5 N/m2 6.078x10^5 N/m2

Pabs = Pg + Po = 2.026x10^5 + 1.01x10^5 = 3.03x10^5 Pa

41 Fluids

A block of mass m, density ρB , and volume V is completely submerged in aliquid of density ρL. The density ofthe block is greater than the density of the liquid. The block C

floats, because ρB> ρL

experiences abuoyant forceequal to ρB gV.

experiences abuoyant forceequal to ρL gV.

experiences abuoyant forceequal to mB g

does notexperience anybuoyant force,because ρB> ρL Definition of buoyant force

42 Fluids

A river gradually deepens, from a depth of 4 m to a depth of 8 m as shown.The width, W, of the river does notchange. At the depth of 4 m, the river’s speed is 12 m/sec. Its velocity at the 8m depth is C 12 m/sec 24 m/sec 6 m/sec 8 m/sec 16 m/sec

Using fluid continuity with W as riverwidth. A1v1 = A2v2 4(W)(12) = (8)(W)v2 v2 = 6 m/s 42.fluids.png

43 Fluids

In the open manometer shown, water occupies a part of the left arm, from aheight of y1 to a height of y2remainder of the left arm, the bottom of the tube, and the right arm to a heightof y. The3 are filled with mercury. B

the pressure at aheight y3 is thesame in both arms.

the pressure at aheight y2 is thesame in both arms.

the pressure at thebottom of the rightarm is greater thanat the bottom ofthe left arm.

the pressure at aheight y3 is less inthe left arm than inthe right arm.

the pressure at aheight y1 is less inthe left arm than inthe right arm.

The relevant formula here is P = Po +ρghAnswer (a) is wrong, because at y1 onboth arms, the pressure is just theatmospheric pressure.The pressure in the right arm at y3 isstill just atmospheric, but on the left, it isatmospheric plusρg(y1– y3). That rules out (a). Thepressure at the bottom of the tube iseverywhere the same(Pascal’s principle), which rules out (c),and at the same time, tells us (b) isright. At y2, we cansay P = Pbottom – ρHggy2 on bothsides, so the pressure is equal. Answer(d) is wrong because aty3, the right arm is supporting only theatmosphere, while the left arm issupporting theatmosphere plus ρH20pressure.gh. Finally, (e) is silly because botharms at height y1 are at atmospheric 43.fluids.png

44 Fluids

Water flows in a pipe of uniform cross-sectional area A. The pipe changesheight from y1 = 2 meters to y2 = 3 meters. Since the areas are the same, wecan say v1 = v2. Which of the following is true? A

P1=P2 + ρg(y2–y1) P1=P2 P1=0 P2=0 ρ1>ρ2

Apply Bernoulli’s equation. P1 + ρgy1 +½ ρv1^2 = P2 + ρgy2 + ½ ρv2^2P1 =P2 + ρg(y2–y1) 44.fluids.png

45 Fluids

A vertical force of 30 N is applied uniformly to a flat button with a radius of 1cm that is lying on a table. Whichof the following is the best order of magnitude estimate for the pressureapplied to the button? E 10 Pa 10^2 Pa 10^3 Pa 10^4 Pa 10^5 Pa

P = F / A = 30 / π r2 … use 3 for πsince its an estimate … 30 / (3*(.01)^2)= 100000 Pa

46 Fluids

A ball that can float on water has mass 5.00 kg and volume 2.50 x 10^-2 m3.What is the magnitude of thedownward force that must be applied to the ball to hold it motionless andcompletely submerged in freshwaterof density 1.00 x 10^3 kg/m3? D 20.0 N 25.0 N 30.0 N 200 N 250 N

From a force standpoint, for the objectto be completely submerged therewould be three forcesacting. Fb up, mg down and Fpushdown. Fb = Fpush + mg Fpush = Fb –mgFpush = ph20 Vdisp g – mg= (1000)(2.5x10–2)(10) – (5)(10) = 200N

47 Fluids

Water flows through the pipe shown. At the larger end, the pipe has diameterD and the speed of the water is v1 . What is the speed of the water at thesmaller end, where the pipe has diameter d ? E v1 dv1/D Dv1/d d^2v1/D^2 D^2v1/d^2

Using fluid continuity. A1v1 = A2v2 π(D/2)^2v1 = π(d/2)^2v2 solve for v2 47.fluids.png

1 Thermo

The maximum efficiency of a heat engine that operates betweentemperatures of 1500 K in the firing chamberand 600 K in the exhaust chamber is most nearly C 33% 40% 60% 67% 100% ec=(TH-TC)/TH

2 Thermo

An ideal gas is made up of N diatomic molecules, each of mass M. All of thefollowing statements about thisgas are true EXCEPT: B

The temperature ofthe gas isproportional to theaveragetranslational kineticenergy of themolecules

All of themolecules havethe same speed.

The moleculesmake elasticcollisions with thewalls of thecontainer.

The moleculesmake elasticcollisions witheach other.

The averagenumber ofcollisions per unittime that themolecules makewith the walls ofthe containerdepends on thetemperature of thegas.

While all collisions are elastic andKavg ∝ T, the molecules move witha wide range of speedsrepresented by the Maxwelliandistribution.

3 Thermo For the process X→Y, ∆U is greater than zero and C Q < 0 and W = 0 Q < 0 and W > 0 Q > 0 and W < 0 Q > 0 and W = 0 Q > 0 and W > 0

For XY, the process is isobaric. Sincethe gas is expanding, W < 0 and sincethe temperature is increasing, ∆U > 0and ∆U = Q + W so Q > 0 (it is also truebecause process XY lies above anadiabatic expansion from point X) 3.thermo.png

4 Thermo For the process Y→Z, Q is greater than zero and C W < 0 & ∆U = 0 W = 0 & ∆U < 0 W = 0 & ∆U > 0 W > 0 & ∆U = 0 W > 0 & ∆U > 0

For YZ, the process is isochoric,which means no work is done (W = 0)and since the temperature isincreasing, ∆U > 0 4.thermo.png

5 Thermo

An ideal gas confined in a box initially has pressure p. If the absolutetemperature of the gas is doubled and thevolume of the box is quadrupled, the pressure is C p/8 p/4 p/2 p 2p

PV ∝ T, or P ∝ T/V and if T × 2 thenP × 2 and if V × 4 then P ÷ 4 sothe net effect is P×2÷4

6 Thermo James Joule did much to establish the value of the C

universalgravitationalconstant speed of light

mechanicalequivalent of heat

charge of anelectron

specific heatcapacity of helium

James Joule did experiments onchanging the temperature of waterthrough various means,including by doing work on it.

7 Thermo

An ideal gas in a closed container initially has volume V, pressure P. andKelvin temperature T. If thetemperature is changed to 3T, which of the following pairs of pressure andvolume values is possible? A 3P and V P and V P and V/3 P/3 and V 3P and 3V

PV ∝ T so to triple thetemperature, the product of P andV must be tripled

8 Thermo

If three identical samples of an ideal gas are taken from initial state I to finalstate F along the paths IAF, IF, andIBF as shown in the pV-diagram above, which of the following must be true? C

The work done bythe gas is thesame for all threepaths.

The heat absorbedby the gas is thesame for all threepaths.

The change ininternal energy ofthe gas is thesame for all threepaths.

The expansionalong path IF isadiabatic.

The expansionalong path IF isisothermal.

Changes in internal energy are pathindependent on a pV diagram as itdepends on the change intemperature, which is based on thebeginning and end points of the pathand not the path taken 8.thermo.png

9 Thermo

If the average kinetic energy of the molecules in an ideal gas at atemperature of 300 K is E, the average kineticenergy at a temperature of 600 K is D E/√(2) E √(2)E 2E 4E Kavg ∝ T

10 Thermo

A metal rod of length L and cross-sectional area A connects two thermalreservoirs of temperatures T1 and T2.The amount of heat transferred through the rod per unit time is directlyproportional to B A and L A and 1/L 1/A and L 1/A and 1/L √(A) and L^2 H = kA∆T/L

11 Thermo Which of the following is always a characteristic of an adiabatic process? D

The temperaturedoes not change(∆T = 0).

The pressure doesnot change (∆ P =0).

The internalenergy does notchange (∆U = 0).

No heat flows intoor out of thesystem (Q = 0)

No work is doneon or by thesystem (W = 0) By definition

12 Thermo During which process is no work done on or by the gas? A AB BC CD DE EA

No work is done in an isochoricprocess, or a process where ΔV = 0 (avertical line on the pv graph) 12.thermo.png

13 Thermo At which point is the gas at its highest temperature? C A B C D E

The temperature at any point isproportional to the product of P and V.Point A at temperature(T0) is at pressure × volume (p0)(V0).Point C is at 3(p0) × 3(V0) = 9(T0) andpoint D is at 2(p0) × 4(V0) =8(T0) 12.thermo.png

14 Thermo

Gas in a chamber passes through the cycle ABCA as shown in the diagramabove. In the process AB, 12 joules of heat is added to the gas. In theprocess BC, no heat is exchanged with the gas. For the complete cycleABCA, the work done by the gas is 8 joules. How much heat is added to orremoved from the gas during process CA? B 20 J is removed. 4 J is removed. 4 J is added. 20 J is added.

No heat is addedto or removed fromthe gas.

For the entire cycle, ΔU = 0 and W = –8J so Q = ΔU – W = +8 J (8 J added).This means Q(AB) + Q(BC) + Q(CA) =+8 J = +12 J + 0 J + Q(CAB) = +8 J 14.thermo.png

15 Thermo

If the gas in a container absorbs 275 joules of heat, has 125 joules of workdone on it, and then does 50 joules of work, what is the increase in theinternal energy of the gas? C 100 J 200 J 350 J 400 J 450 J

Q = +275 J; W = + 125 J + (– 50 J) =+75 J; ΔU = Q + W

16 Thermo

In each cycle of a certain Carnot engine, 100 joules of heat is absorbed fromthe high-temperature reservoir and 60 joules is exhausted to the low-temperature reservoir. What is the efficiency of the engine? A 40% 60% 67% 150% 167%

Q(H) = 100 J and Q(C) = 60 J; e=(W/Q(H))=((Q(H)-Q(C))/Q(H))

17 Thermo Which of the following is true of the mechanical work done on the gas? AIt is greatest forprocess 1.

It is greatest forprocess 3.

It is the same forprocesses I and 2and less forprocess 3.

It is the same forprocesses 2 and 3and less forprocess 1.

It is the same forall threeprocesses.

Work is the area under the curve, theline bounding the greatest areaindicates the most workdone 17.thermo.png

18 Thermo Which of the following is true of the final temperature of this gas? AIt is greatest forprocess 1.

It is greatest forprocess 2.

It is greatest forprocess 3.

It is the same forprocesses 1 and 2.

It is the same forprocesses 1 and 3.

Temperature rises as you travel up andto the right on a pV diagram. Sinceprocesses 1, 2 and 3are at the same volume, the highestpoint is at the highest temperature 17.thermo.png

19 Thermo

In a certain process, 400 J of heat is added to a system and the systemsimultaneously does 100 J of work. The change in internal energy of thesystem is C 500 J 400 J 300 J -100 J -300 J Q = +400 J; W = – 100 J; ΔU = Q + W

20 Thermo

An ideal gas is initially in a state that corresponds to point 1 on the graphabove, where it has pressure p1, volume V1, and temperature T1. The gasundergoes an isothermal process represented by the curve shown, whichtakes it to a final state 3 at temperature T3. If T2 and T4 are the temperaturesthe gas would have at points 2 and 4, respectively, which of the followingrelationships is true? B T(1)<T(3) T(1)<T(2) T(1) < T(4) T(1) = T(2) T(1) = T(4)

Isothermal means the temperature isconstant. Points to the right or aboveare at higher temperatures. 20.thermo.png

21 Thermo

The absolute temperature of a sample of monatomic ideal gas is doubled atconstant volume. What effect, if any, does this have on the pressure anddensity of the sample of gas? C A B C D E

P ∝ T at constant volume. If T × 2,then P × 2. Since the mass andvolume are unchanged, thedensity is unchanged as well 21.thermo.png

22 ThermoWhich of the following statements is NOT a correct assumption of theclassical model of an ideal gas? D

The molecules arein random motion.

The volume of themolecules isnegligiblecompared with thevolume occupiedby the gas.

The moleculesobey Newton'slaws of motion.

The collisionsbetweenmolecules areinelastic.

The onlyappreciable forceson the moleculesare those thatoccur duringcollisions.

If the collisions were inelastic, the gaswould change its temperature by virtueof the collisionswith no change in pressure or volume.

23 Thermo

A sample of an ideal gas is in a tank of constant volume. The sample absorbsheat energy so that its temperaturechanges from 300 K to 600 K. If v1 is the average speed of the gas moleculesbefore the absorption of heat andv2 is their average speed after the absorption of heat, what is the ratio v2/v1? C 0.5 1 square root of 2 2 4

related to average speed, v= (3RT/M)^(1/2)

24 Thermo

Two blocks of steel, the first of mass 1 kg and the second of mass 2 kg, are inthermal equilibrium with a thirdblock of aluminum of mass 2 kg that has a temperature of 400 K. What arethe respective temperatures of thefirst and second steel blocks? C 400 K and 200 K 200 K and 400 K 400 K and 400 K 800 K and 400 K None of the above

Being in thermal equilibrium means theobjects are at the same temperature.Mass is irrelevant.The question describes the zeroth lawof thermodynamics.

25 Thermo

An ideal gas may be taken from one state to another state with a differentpressure, volume, and temperaturealong several different paths. Quantities that will always be the same for thisprocess, regardless of which pathis taken, include which of the following?I. The change in internal energy of the gasII. The heat exchanged between the gas and its surroundingsIII. The work done by the gas A I only II only I and III only II and III only I, II, and III

Changes in internal energy are pathindependent on a pV diagram as itdepends on the change intemperature, which is based on thebeginning and end points of the pathand not the path taken.Different paths, with different areasunder them will do different amounts ofwork and hence,different amounts of heat exchanged.

26 Thermo

A square steel plate with sides of length 1.00 m has a hole in its center 0.100m in diameter. If the entire plate isheated to such a temperature that its sides become 1.01 m long, the diameterof the hole will be D 0.090 m 0.099 m 0.100 m 0.101 m 0.110 m

In linear expansion, every lineardimension of an object changes by thesame fraction whenheated or cooled.

27 Thermo

Which of the following will occur if the average speed of the gas molecules ina closed rigid container isincreased? C

The density of thegas will decrease.

The density of thegas will increase.

The pressure ofthe gas willincrease.

The pressure ofthe gas willdecrease.

The temperature ofthe gas willdecrease.

“rigid container” = constant volume. Ifthe speed increases, the temperaturewill increase, and ifthe temperature increases at constantvolume, the pressure will increase.

28 Thermo

In time t, an amount of heat Q flows through the solid door of area A andthickness d represented above. Thetemperatures on each side of the door are T2 and T1, respectively. Which ofthe following changes would becertain to decrease Q? D Increasing A only Decreasing d only

Increasing d andT2– T1 only

Decreasing A andT2 – T1 only

Increasing d, A,and T2 – T1 H= kA(Tf-Ti)/L 28.thermo.png

29 Thermo

A gas with a fixed number of molecules does 32 J of work on itssurroundings, and 16 J of heat are transferredfrom the gas to the surroundings. What happens to the internal energy of thegas? A

It decreases by 48J.

It decreases by 16J.

It remains thesame.

It increases by 16J.

It increases by 48J. Q = –16 J; W = –32 J; ∆U = Q + W

30 ThermoWhich of the following could NOT be used to indicate a temperature change?A change in: E

color of a metalrod.

length of a liquidcolumn.

pressure of a gasat constant volume

electricalresistance.

mass of one moleof gas at constantpressure.

Mass is independent of the state of agas. (“color” will be addressed in a latertopic, think about ayellow vs. blue flame or a “red hot”piece of metal)

31 Thermo

A mass m of helium gas is in a container of constant volume V. It is initially atpressure p and absolute (Kelvin)temperature T. Additional helium is added, bringing the total mass of heliumgas to 3m. After this addition, thetemperature is found to be 2T. What is the gas pressure? E 2/3 p 3/2 p 2 p 3 p 6 p

P ∝ nT/V; if n × 3 then P × 3 and ifT × 2 then P × 2, the net effect isP × 3 × 2

32 Thermo33 Thermo34 Thermo35 Thermo36 Thermo37 Thermo38 Thermo39 Thermo40 Thermo41 Thermo

42 Thermo

A 200 gram sample of copper is submerged in 100 grams of water until boththe copper and water are at the same temperature. Which of the followingstatements would be true? B

the molecules ofthe water andcopper would haveequal averagespeeds

the molecules ofthe water andcopper would haveequal averagemomenta

the molecules ofthe water andcopper would haveequal averagekinetic energies

the watermolecules wouldhave twice theaveragemomentum of thecopper molecules

the coppermolecules wouldhave twice theaverage speed ofthe watermolecules Kavg∝T 42.thermo.png

43 Thermo

A rectangular piece of metal 3 cm high by 6 cm wide has a hole cut in itscenter 1cm high by 4 cm wide as shown in the diagram at right. As the metalis warmed from 0oC to 1000C, what will happen to the dimensions of thehole? C

both height andwidth will increase

both height andwidth will decrease

both height andwidth will remainunchanged

height willdecrease whilewidth will increase

height will increasewhile width willdecrease

In linear expansion, every lineardimension of an object changes by thesame fraction when Aheated or cooled.

44 Thermo

A gas is enclosed in a cylindrical piston. When the gas is heated from 0oC to100oC, the piston is allowed to move to maintain a constant pressure.According to the Kinetic-Molecular Theory of Matter A

the mass of thegas will increase

the number ofmolecules of gasmust increase

the size of theindividualmolecules hasincreased

the average speedof the moleculeshas increased

the moleculescontinue to strikethe sides of thecontainer with thesame energy Kavg ∝ T 44.thermo.png

45 Thermo

Two containers are filled with gases at the same temperature. In thecontainer on the left is a gas of molar mass 2M, volume 2V, and number ofmoles 2n. In the container on the right is a gas of molar mass M, volume V,and moles n. Which is most nearly the ratio of the pressure of the gas on theleft to the pressure of the gas on the right? D 1:01:00 8:01:00 2:01:00 16:01:00 4:01:00 P ∝ n/V at constant temperature

46 Thermo

A thermally insulating container has a membrane separating the containerinto two equal parts. In one part is a vacuum. In the other part is an ideal gasof temperature T and internal energy U. The membrane is punctured and thegas rushes into the region which was a vacuum. After the system hasreturned to equilibrium, which of the following is NOT true for the gas? A

The temperature ofthe gas isunchanged.

No work is done bythe gas on thesurroundings.

There is no heatexchanged by thegas with thesurroundings.

There is noentropy change ofthe system.

The internalenergy of the gasis unchanged.

Since the container is insulated, noheat is exchanged (C is true), sincethere is no work done (noforce required to expand), choice B istrue. Since Q = 0 and W = 0, ΔU andΔT = 0 (A and E aretrue). While entropy change does havea heat component (and if Q = 0, thechange in entropymay be incorrectly regarded as zero) italso has a volume component (how“spread out” the gas is)

47 ThermoA fan blows the air and gives it kinetic energy. An hour after the fan has beenturned off, what has happened to the kinetic energy of the air? D it disappears

it turns into soundenergy

it turns intopotential energy

it turns intoelectrical energy

it turns into thermalenergy

This question is a bit of a paradox asthe energy form the fan giving the airkinetic energy istheoretically adding to the thermalenergy of the air, But as the air lowersin temperature, thisenergy will dissipate into the walls andother outside areas of the room asthermal energy as well.

48 ThermoAccording to the kinetic theory of gases, when the absolute temperature of anideal gas doubles, the average kinetic energy of the molecules of the gas E quadruples doubles stays the same is cut in half is quartered Kavg ∝ T

49 ThermoWhen gas escapes from a pressurized cylinder, the stream of gas feels cool.This is because B

work is being doneat the expense ofthermal energy

of the convectioninside the cylinder

pressurizedcylinders are goodthermal insulators

the gas inside thecylinder is actuallyfrozen

the moisture in theair condenses andcools

Gas escaping form a pressurizedcylinder is an example of an adiabaticprocess. While the gasrapidly does work (W < 0), ΔU isnegative since heat does not have timeto flow into the gas in arapid expansion.

50 Thermo

A monatomic ideal gas is used as the working substance for the Carnot cycleshown in the figure. Processes A → B and C → D are isothermal, whileprocesses B → C and D → A are adiabatic. During process A → B, there are400 J of work done by the gas on the surroundings. How much heat isexpelled by the gas during process C → D? A 1600 J 800 J 400 J 200 J 100 J

In a Carnot cycleQ = and in process AB, ΔU = 0 andsince WAB = –400 J, QAB = +400 Jand this is Qh 50.thermo.png

51 Thermo

Two completely identical samples of the same ideal gas are in equal volumecontainers with the same pressure and temperature in containers labeled Aand B. The gas in container A performs non-zero work W on the surroundingsduring an isobaric (constant pressure) process before the pressure is reducedisochorically (constant volume) to 1⁄2 its initial amount. The gas in container Bhas its pressure reduced isochorically (constant volume) to 1⁄2 its initial valueand then the gas performs non-zero work W on the surroundings during anisobaric (constant pressure) process.After the processes are performed on the gases in containers A and B, whichis at the higher temperature? E

The gas incontainer A

The gas incontainer B

The gases haveequal temperature

The value of thework W isnecessary toanswer thisquestion.

The value of thework W isnecessary, alongwith both the initialpressure andvolume, in order toanswer thequestion.

Since process A and B perform thesame amount of work, they must havethe same area undertheir respective lines. Since A does thework at a higher pressure, it does nothave to move as farto the right as process B, whichperforms the work at a lowertemperature. Since the end ofprocess B lies farther to the right, it is atthe higher temperature.

52 Thermo53 Thermo54 Thermo55 Thermo56 Thermo57 Thermo58 Thermo59 Thermo60 Thermo61 Thermo62 Thermo63 Thermo64 Thermo65 Thermo66 Thermo67 Thermo68 Thermo69 Thermo70 Thermo71 Thermo72 Thermo73 Thermo74 Thermo75 Thermo76 Thermo77 Thermo78 Thermo79 Thermo80 Thermo

81 Thermo82 Thermo83 Thermo

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