Name:

A

PHYSICS 1050 Final ExaminationUniversity of Wyoming

2 May 2006

This test is open-note and open-book. This means that any reference material ispermitted during the test. Calculators also are permitted. However, no collaboration,consultation, or communication with other people (other than the administrator) isallowed by any means, including but not limited to verbal, written, or electronic methods.

Please do not begin this test until everyone has received a booklet and the testadministrator has indicated for you to begin.

Physical Constants:

Gravitational const:G = 6.67 10 11 Nm2 kg2

Earth surface gravity: g = 9.8 m/s2= 9.8 N/kg

Boltzmann const: kB =1.3807 10 23 J/K

Speed of light:c = 2.9979 108m/sCoulomb const: k = 8.992 109Nm2/C2

Planck const: h = 6.626 10 34 JsProton charge: e =1.6021 10 19C

Formulas:

Instantaneous velocity:

r v = lim

t 0

r x t

Instantaneous acceleration:

r a = lim

t 0

r v t

Dist in const accel:

r x =

r v 0 t + 1

2

r a t( )

2

Acceleration from net force r F :

r a =

r F /m

Momentum: r p = m

r v

Work: w =r F

r x = E

Kinetic energy: KE = 12mv

2

Earth’s surface gravity: r F = m

r g

Universal gravitation: 2

21dmGmF =

gravitational PE: PE = mgh

Torque: r =

r r

r F

Centripetal acceleration: a = v 2 r

Hooke’s law spring: xkFrr

= ; 2

2

1 kxPE =

Pressure in a liquid: p = ghBuoyant force in a liquid: F = gVIdeal gas law: pV = NkBTHeat capacity: TQC =

Spring period: kmfT 21 ==

Pendulum period: gLfT 21 ==

Wave speed: u = T = fElectrostatic force: F = kq1q2 d2

Electromagnetic force: r F = q

r v

r B

Ohm’s law: I = RElectric power: P = ITransformer potentials: 1 2 = N1 N2

Electromagnetic wave energy: E = hfSnell’s law: n1 sin 1 = n2 sin 2

Uncertainty principle: p x h 4

Answer Key

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Part 1: Electricity–Nukes (Test 3, 100 Points)

Multiple choice10 questions, 8 points each.

Please circle the most correct answer from the choices given.

1. A speck of dust with a charge of 2.0 10–6 C is initially at rest. It is accelerated by anelectric potential of 5.0 106 V. No other forces act on it. What is its kinetic energywhen it is finished accelerating?

a. 1.0 10–6 J.b. 2.0 J.c. 5.0 106 J.d. 1.0 J.e. 10 J.

2. The circuit diagrams below show four different circuits made with three identicalresistors and identical potential sources . Through which of these circuits does themost current flow?

a. b.

c. d.

E = q = (5 106 V)(2.0 10–6 C) = 10 106–6 J = 10 J

A current of /R goes through each resistor, for a total of 3 /R.

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3. The four illustrations below show identical charged particles moving at identicalspeeds through magnetic fields depicted as field lines (gray arrows). The charges ofthe particles are not specified; they could be positive or negative, and they are all thesame, but they are not zero. Which one of the following statements about them istrue?

I. II.

III. IV.

a. The force on the particles in illustrations II and III are weaker than the forces on theparticles in illustrations I and IV.

b. The particles in illustrations I and III are accelerated either upward ( ) ordownward ( ) by the field.

c. The particles in illustrations I and III experience forces perpendicular to the plane ofthe paper, either toward you ( • ) or away from you ( ).

d. The particles in illustrations II and IV are either accelerated ( ) or decelerated ( )by the field.

e. The particles in illustrations II and III experience forces in opposite directions.f. The particles in illustrations I and IV experience forces in opposite directions.

4. A simple machine produces the same power on its output side as it receives on itsinput side, though it trades between force and velocity. In the same way, an electricaltransformer produces the same power on its output side as it receives on its inputside, thought it trades between

a. potential and current.b. force and current.c. current and resistance.d. potential and resistance.

The force on a charge moving through a magnetic field is perpendicularto both the velocity of the charge and the magnetic field. If thevelocity is parallel to the field, the force is zero.

Power = I is the same on both sides;the side with greater potential hasless current, and vice versa.

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5. A positive charge might be placed at one of two different locations in a region wherethere is a uniform electric field, as shown below. (The gray arrows represent electricfield lines.)

How would the electric forces on the charge at locations 1 and 2 compare?

a. The force on the charge at both locations is the same but not zero.b. The force on the charge at both locations is zero.c. The force on the charge is stronger at location 1.d. The force on the charge is stronger at location 2.e. The force on the charge at both locations has the same magnitude but opposite

directions.

6. A wave is an organized disturbance that repeats in space and time. What is disturbedand “waves” in an electromagnetic wave?

a. Charged particles.b. Electric currents.c. Magnets.d. Electric and magnetic fields.

7. Heisenberg’s Uncertainty principle states that the product of p , the uncertainty inand object’s momentum, and x , the uncertainty in its position, cannot be less thanthe constant h 4 = 5.273 10 35 Js, that is, p x h 4 . If the constant h were tosomehow become much larger than it is now, how would atomic sizes be affected?

a. Atoms would become larger than they are now (the average electron-nucleus distancewould increase).

b. Atoms would become smaller than they are now (the average electron-nucleusdistance would decrease).

c. The size of atoms would not change.

1 2

Increasing h would require increasing x, p, or both. Any way you doit, the electron would get farther from the nucleus!

The force on a charge in an electric field is (charge)(field strength) = qE. The directionof field lines shows the direction of the field, and how close together they are showsthe field strength. Here, the field strength and direction is the same in both locations.

Electromagnetic waves are electric andmagnetic fields oscillating in phase,perpendicular to each other and to thedirection of travel.

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8. Why cannot our eyes distinguish yellow light from a mixture of red and green light?

a. Red and green light interfere constructively to produce yellow light.b. The red and green color receptor cells in our eyes both also detect yellow light.c. Yellow light is the beat frequency between red and green light.d. Red light contains magenta + yellow and green light contains cyan + yellow, so we

see their yellow light in common.

9. The illustration below shows an object (black outline) in front of a convex lens. Theaxis of the lens is shown by the dashed line and the foci of the lens are shown byblack dots. Which of the filled gray shapes represents the object’s image in thislens?

a. Shape A. b. Shape B.b. Shape C. d. Shape D.c. Shape E. f. Shape F.

10. What particles or nuclei complete the series of nuclear reactions below?

54137Xe + 55

137Cs

55137Cs +

a. , 55137Cs

b. , 56137Ba

c. , 53133I

d. , 54137Xe

This one is physiology, not physics! Our brain cannot tell the differencebetween our red and green color receptors being excited equally by redand green light or by yellow light. A spectroscope would not be fooled.

Only beta decay increases atomic number whilekeeping the mass number the same.

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Calculation and Short Answer2 questions, 10 points each.

Please provide complete answers to each question. Provide units with all numericalanswers. Show all work so that partial credit can be assigned.

11. A 100-W light bulb dissipates 100 watts of power (that is, 100 joules per second)when powered by an electric potential of 120 V. What is the current through thebulb? (Don’t forget the units!)

12. The Heisenberg Uncertainty relation is p x = 5.273 10 35 Js. Show that the unitsin this expression work out, that is, that the units of length and the units ofmomentum, when multiplied together, give J s.

Power P = I, so

I = P/ = (100 W)/(120 V) = 0.83 A.

Units of length = m

Units of momentum = kg m/s

product = = Jskg m2

ss

s2

kg m2

=

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Extra Credit2 questions, 5 points each.

13. The liquid-crystal displays in digital watches contain two crossed polarizers, that is,polarizing filters whose axes are perpendicular to each other. Between the twopolarizing filters is a layer of liquid crystals, which can be electrically switchedbetween being polarizing or completely transparent. If the numbers in the LCDdisplay appear dark to the viewer, which part of the liquid crystal layer is polarizing:the numbers, or the background? Explain your answer.

14. If you rub a balloon on a wool sweater, it will stick to the wall. Why? (Justanswering “static electricity” is not good enough.)

The background must be polarizing: it must polarize the light alonga different axis than either of the crossed polarizers so that lightgets through. The numbers will appear dark if they don’t changethe light’s polarization.

The balloon picks up an electric charge, which attracts oppositecharges and repels like charges in the material of the wall. Sincethe electric force is greater at close distances, the closer oppositecharges attract the balloon more than the farther-away likecharges repel it, and the balloon is attracted to the wall.

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Part 2: Comprehensive (Test 4, 100 Points)

Multiple Choice10 questions, 8 points each.

1. A skydiver jumps out of anairplane, falls toward the ground,opens her parachute to slow herdescent, then “flares” theparachute (momentarily increasesits drag) to land. The thick grayline in the graph to the rightshows her height during the fall.Over which one of the labeledtime intervals is her accelerationalways zero?

a. Interval A.b. Interval B.c. Interval C.d. Interval D.e. Interval E.

2. A catapult throws an ewok horizontally with a kinetic energy of 8000 J. Before theewok leaves the basket of the catapult, the catapult carries it a distance of 2 m. Whatis the average force applied by the catapult while it launches the ewok ? Disregardany small change in the ewok’s potential energy.

a. 8000 N.b. 4000 N.c. 2 N.d. You need to know

the ewok’s mass tocalculate the force.

2 m

KE = work = F d, so F = KE/d = (8000 J)/(2 m) = 4000 N.

In a position-time graph, acceleration is the curvature of the plot.The only interval in which the curvature is always zero (the slopedoes not change) is interval C.

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3. A rubber balloon filled with air is held just below the surface of the sea. It is thenmoved to a depth of 100 m below the surface. How do the forces of weight andbuoyancy acting on the balloon differ at those two locations?

a. The balloon’s buoyancy force is greater at 100 m depth than at the surface.b. The balloon’s buoyancy force is less at 100 m depth than at the surface.c. The balloon’s weight is greater at 100 m depth than at the surface.d. The balloon’s weight is less at 100 m depth than at the surface.

4. The direction of the centripetal acceleration a of an object moving in a circular pathat a constant speed is

a. outward. b. inward.

c. to the right(into the page).

d. to the left(out of the page).

e. forward. f. backward.v

a

v a

v

a

va

v a v

a

The balloon compresses at the greater pressure at 100 m depth, reducing itsvolume. The buoyancy force = gV; V changes while and g do not, sobuoyancy force decreases. The balloon’s weight, however, does not change.

Always, always, always!

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5. An astronaut, floating motionless in outer space, throws a baseball. If the ball movesaway at a speed of 20 meters per second, how will the astronaut move?

a. She will move in the opposite direction at a speed of 20 m/s.b. She will move in the opposite direction faster than 20 m/s.c. She will move in the opposite direction slower than 20 m/s.d. She will not move as stated in any of the above choices.

6. If there is no air resistance, an object released from rest near the earth’s surface willaccelerate downward at 9.8 m/s2. If, instead of being released from rest, the object isthrown upward at a velocity of 5 m/s, how will it initially accelerate? Assume thatthere is no air resistance.

a. The object will initially accelerate upward.b. The object will initially accelerate downward at 9.8 m/s2.c. The object will initially accelerate downward at less than 9.8 m/s2.d. The object will initially accelerate downward at more than 9.8 m/s2.

7. The average distance from the sun to the earth is about 389 times the average distancefrom the moon to the earth. The mass of the sun is 2.71 107 times the mass of themoon. (The actual numbers are sun distance = 1.496 1011 m, moon distance =3.844 108 m, sun mass = 1.989 1030 kg, and moon mass = 7.350 1022 kg.)Which body exerts the stronger gravitational pull on the earth: the moon or the sun?

a. The moon and sun exert exactly the same gravitational pull on the earth.b. The moon exerts the stronger gravitational pull on the earth.c. The sun exerts the stronger gravitational pull on the earth.d. You cannot tell from the information given.

Newton’s third law: opposite direction. F = ma: Her mass is more than the baseball’s, soher acceleration is less. You can also reach the same conclusion using conservation ofmomentum. The total momentum before the throw was zero, so it is also zero after thethrow. The baseball and astronaut must then have the same magnitude of momentum inopposite directions. Since the astronaut’s mass is greater, her speed must be less.

The force of gravity follows F = G m1 m2/d2. In both cases, G isuniversal and m1 is the mass of the earth, so the quantities that varyare m2 and d. The sun is 389 times farther away than the moon but 30million times more massive. (389)2 151,000, which is less than 30million. So. the sun’s greater mass trumps its greater distance.

The only force acting is gravity, so the only acceleration will be theacceleration of gravity: g = 9.8 m/s2, straight downward.

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8. Sound waves generated by a loudspeaker travel to the right. As they travel, in whatdirection(s) do they cause the molecules of air they pass through to move?

a. Up and down ( ).b. Side to side ( • ).c. Left and right ( ).e. Some combination of up and down and/or side to side.

9. An electrical transformer with input of 120 V and 0.2 A produces 12 V output. Whatis its output current?

a. 0.2 A.b. 12 A.c. 0.02 A.d. 2.0 A.

10. When you see an object, its image is projected onto the retina of your eye. What typeof image is this?

a. A virtual inverted image.b. A real inverted image.c. A virtual upright image.d. A real upright image.

Sound waves are longitudinal, that is, they travel in the same directionas the medium. That means left and right as illustrated.

In a transformer, 1I1 = 2I2, so I2 = I1 1/ 2 = (0.2 A)(120 V)/(12 V) = 2.0 A. inEnglish, The potential is reduced tenfold, so the current increases tenfold tokeep power the same.

It has to be real, because only real images can be projected onto asurface. You can verify for yourself that it is inverted by lightlypressing a finger against your eyelid. The phosphene you see will beopposite where you press!

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Short Answer and Calculation2 questions, 10 points each.

Please provide complete answers to each question. Provide units with all numericalanswers. Show all work so that partial credit can be assigned.

11. The specific heat capacity of liquid water is 4184 J/(kg K).How much energy (as heat) is required to raise the temperature of 4 kg of water from30 °C to 35 °C? (Don’t forget the units!)

12. If you’re in a car at rest that gets hit from behind, you can suffer a serious neck injurycalled whiplash. Explain the physics of why this occurs, particularly what it has todo with Newton’s first law.

Heat capacity C = (specific heat capacity)(mass) = (4184 J/kg K)(4 kg).

Also, C = Q/ T, so Q, the heat required, = C T. The temperature changeT = 5 K (because Celsius and kelvin degrees are the same size).

So,

Q = (4184 J/kg K)(4 kg)(5 K) = (4184 20) J = 83680 J.

When your car gets hit from behind, it moves forward. It takes your bodywith it, because the seat, moving forward with the car, pushes on yourbody. However, your head does not move forward, because no force actson it initially. Your body leaves your head behind, and your neck, whichhopefully connects your head to your body, flexes and hyper-extends.

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Extra Credit2 questions, 5 points each.

13. What is wrong with the physics depicted in the movie clip shown?

14. In lecture, when I sang

Every fire that burns,Every leaf that turns,Every child that’s born,Every crystal formed,Every speedboat’s wake,Every growing tree,Every breath you take:They’re all enriching me!

what physical quantity was I portraying?

There are a number of things. Most glaring is that the attack ‘droidperches on the fighter’s wing as if held there by gravity; when it is“killed” by R2-D2, it falls over as if by gravity and sides off the wing asif by wind. But there’s no gravity or wind in space! Unless the fighterwere accelerating, the wrecked ‘droid would at most gently float away.

Also, there wouldn’t be any sound transmitted in space, which wasactually accurately portrayed by the audio difficulties I encounteredshowing the movie clip…

Entropy. It is the only physical quantity we discussedthat always increases.