Physics 220 - Final Exam Summer 2013

Physics 220 - Final Exam

Summer 2013

Version 81

Name:(Last) (First) (Middle)

1. Please fill out your name and your Purdue student ID on the scantron from.

2. Record ”81” as your two-digit exam version number on the scantron form in the field”TEST/QUIZ NUMBER”

3. Sign your name on the scantron form and write the class ”Physics 220”.

4. Write your name on this cover page. When you are finished, tear off this cover pageand hand it in. You may keep the exam.

5. There are 20 questions. Each question is worth 15 points for a total of 300 points.

Physics 220 - Final Exam - Summer 2013Version 81Page 1 of 9

1. A suction cup has an air pressure of 90.8 kPa inside the suction cup when it is attachedto a ceiling. The suction cup covers an area of 7.89 cm2, and a mass is hanging fromthe suction cup. What is the largest mass that the suction cup can hold before falling?

(a) 0.85 kg

(b) 1.43 kg

(c) 0.05 kg

(d) 7.31 kg

(e) 8.28 kg

2. A reversible heat engine has two reservoirs, one at a temperture of 389 K, and the otherat 741 K. If 5,460 J of heat is extracted from the hot reservoir, how much work is doneby the engine?

(a) 2,866 J

(b) 2,594 J

(c) 3,686 J

(d) 1,419 J

(e) 5,233 J

3. A source of sound waves of frequency 5,408 Hz is traveling through the air at a velocityof 174.7 m/s. What is the frequency of the sound recieved by a stationary observer ifthe source moves away from the observer?

(a) 3,583 Hz

(b) 5,583 Hz

(c) 11,021 Hz

(d) 1,409 Hz

(e) 2,654 Hz

Version 81 Physics 220 - Final Exam - Summer 2013 Page 2 of 9

4. 51 moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. Ifthe gas has a temperature is 15.3 ◦C and the pressure is 32.5 kPa, what is the volumeof the gas?

(a) 2.00 m3

(b) 5.00 m3

(c) 4.28 m3

(d) 3.76 m3

(e) 1.17 m3

5. The following wave is traveling on a string with a velocity of 28.2 m/s. What is thefrequency of the wave?

(a) 16.72 Hz

(b) 84.60 Hz

(c) 1.99 Hz

(d) 9.40 Hz

(e) 4.70 Hz

6. Two metal blocks are placed in a room and have the same initial temperature. Bothblocks have the same mass, but one block is made of aluminum while the other block ismade of steel. The steel block is heated by transfering an amount of heat (Q) while thealuminum block is heated by twice as much (2Q). Which of the following is true aboutthe change in temperatures of the blocks?

(a) ∆Tal = ∆Tsteel/2

(b) ∆Tal = 4 ∆Tsteel

(c) ∆Tal = ∆Tsteel/4

(d) ∆Tal = 2 ∆Tsteel

(e) ∆Tal = ∆Tsteel


7. What should be the length of an organ pipe, closed at one end, if the fundamental fre-quency is to be 678.7 Hz?

(a) 197.87 cm

(b) 12.63 cm

(c) 5.71 cm

(d) 18.99 cm

(e) 25.27 cm

8. An ideal gas is in a sealded container with volume (V). The container is then compressedso that the new volume is half of the original volume (V’=V/2). The number of parti-cles and temperature are kept constant. What happens to the pressure of the gas in thecontainer?

(a) the new pressure is four times the original pressure

(b) the new pressure is one fourth of the original pressure

(c) the new pressure is half of the original pressure

(d) the new pressure is twice the original pressure

(e) the new pressure is equal to the original pressure

9. A marble with a mass of 7.8 grams is rolling without slipping with a velocity of 3.41 m/s.The marble then rolls up a ramp at a 26◦ angle above the horizontal. How high abovethe ground will the marble be when it comes to a complete stop?

(a) 0.47 m

(b) 1.13 m

(c) 0.03 m

(d) 0.83 m

(e) 0.59 m


10. A Pitot-Static tube is used to measure pessure in orderto find an airplane’s velocity. The pressure at 1, wherethe velocity of air is zero, is 5.47 ×104 Pa, and thepressure at 2 is 3.17 ×104 Pa. The airplane is flyingat an altitude where the density of air is 0.58 kg/m3.What is the velocity of the airplane?

(a) 558.08 m/s

(b) 185.72 m/s

(c) 330.63 m/s

(d) 281.63 m/s

(e) 434.32 m/s

11. You want to use a steel cable to tow your car. Your car has a mass of 6,100 kg. Thecable is solid steel with a diameter of 1.3 cm and a length of 44.8 m. If you are pullingthe car such that its acceleration is 2.4 m/s2, how much will the cable stretch?(Steel has a Young’s Modulus of 2.0 ×1011 Pa, a Shear Modulus of 8.1 ×1010 Pa, a BulkModulus of 1.4 ×1011 Pa)

(a) 1.53 cm

(b) 4.81 cm

(c) 2.47 cm

(d) 0.88 cm

(e) 1.72 cm

12. A ball with a mass of 1.0 kg is thrown up at a 20.6◦ angle above the horizontal. Theball initially has a velocity of 18.5 m/s and starts approximately on the ground. Howlong is the ball in the air before it hits the ground?

(a) 0.94 s

(b) 1.33 s

(c) 0.66 s

(d) 1.77 s

(e) 2.36 s


Refer to the following P-V diagram for Problem 13 and Problem 14.

In the figure above, P1 = 33.5 kPa, P2 = 52.9 kPa, P3 = 73.9 kPa, V1 = 4.28 m3, andV2 = 6.26 m3.

13. A gas undergoes a two part process from A to C as shown in the P-V diagram above.The first part is from A to B and the second from B to C. What is the work done bythe gas during this process (all parts from A to C)?

(a) +66.33 kJ

(b) −146.32 kJ

(c) +104.74 kJ

(d) −56.25 kJ

(e) −282.77 kJ

14. After going through the two part process from A to C as explained in Problem 13, thegas undergoes another two part process. Part one is from C to D, and part two is from Dto A. The gas has now undergone one complete cycle and is back at A (where it started).What is the work done by the gas during the entire cycle (all four parts A-B-C-D-A)?

(a) −19.11 kJ

(b) −78.47 kJ

(c) −60.79 kJ

(d) +85.54 kJ

(e) +104.74 kJ


15. A large bucket is partially filled with water. After filling the bucket, a person noticedthat there is a hole in the side of the bucket at the very bottom. If the speed of thewater coming out of the hole is 0.82 m/s, what is the height of the water in the bucket?

(a) 4.62 cm

(b) 0.39 cm

(c) 4.18 cm

(d) 6.86 cm

(e) 3.43 cm

16. A guitar player notices that one of the guitar strings is a little out of tune. The frequencyof the note played is higher than it should be. Which of the following should the guitarplayer do in order to get the desired frequency?

(a) tighten the string

(b) increase the amplitude of the wave on the string

(c) decrease the amplitude of the wave on the string

(d) decrease the mass of the string

(e) loosen the string

17. A 40 kg boy is standing on the edge of a stationary 30 kg circular platform that is freeto rotate. The boy tries to walk around the platform in a counterclockwise direction.As he does:

(a) the platform rotates in a counterclockwise direction while the boy also goes aroundin a counterclockwise direction relative to the ground.

(b) the platform doesn’t rotate.

(c) the platform rotates in a clockwise direction just fast enough so that the boy remainsstationary relative to the ground.

(d) both go around with equal angular velocities and in the same direction.

(e) the platform rotates in a clockwise direction while the boy goes around in acounterclockwise direction relative to the ground.


18. A 6.2 kg piece of aluminum is warmed so that its temperature increases by 14.9 ◦C. Ifthe same amount of heat is used to melt ice, how many grams of ice would melt?

(a) 0.55 g

(b) 399.43 g

(c) 248.93 g

(d) 19.86 g

(e) 138.79 g

19. A certain grandfather clock uses a pendulum to keep time; however, the clock is runningfast so that the period of the pendulum needs to be increased. Which of the followingwould fix the clock so that it runs on time?

(a) decrease the mass

(b) decrease the length and increase the mass

(c) decrease the length

(d) increase the mass

(e) increase the length

20. A cart with a mass of 7.5 kg is pushed to the right with a velocity of 7.4 m/s. A secondcart with a mass of 1.3 kg is in front of the first cart and is moving to the right with avelocity of 4.3 m/s. The first cart collides with the back of the second cart so that thetwo carts stick together in a totally ineslastic collision. What is the final velocity of thetwo carts?

(a) 8.15 m/s

(b) 6.94 m/s

(c) 3.70 m/s

(d) 4.76 m/s

(e) 9.73 m/s


Motion

vav =∆x

∆t

aav =∆v

∆t

x = x0 + v0t+1

2at2

v = v0 + at

v2 = v20 + 2a(x− x0)

Forces

Σ~F = m~a

Fspring = −kxFfriction = µN

Fgrav =Gm1m2

r2

FB = ρLVsubg

Torque

I = Σmir2i

Σ~τ = I~α

τ = rF sin θ

Momentum

Σ ~Fav =∆~p

∆t~p = m~v

Σ ~τav =∆~L

∆t~L = I~ω

Work and Energy

W = Fd cos θ

W = τθ

Power =E

∆t∆E = W +Q

Ei = Ef

KEtrans =1

2mv2

KErot =1

2Iω2

PEgrav = mgh

PEspring =1

2kx2

Circular Motion

x = θr

v = ωr

a = αr

Σ~F = m~ac = mv2

r= mω2r

ω = 2πf

T =1

f=

2π

ω=

2πr

v

T 2 =

(4π2

GMsun

)r3

Density and Pressure

ρ =m

VP =

F

AP2 = P1 + ρgh

P1 +1

2ρv21 + ρgh1 = const

ρA1v1 = ρA2v2

Elasticity

F

A= Y

∆L

L0

F

A= S

∆x

L0

∆P = −B∆V

V0

Sound

β = (10dB) log10

I

I0

fobs = fsource1 ± vobs/vsound

1 ∓ vsource/vsound

Temperature

TF =9

5TC + 32

TK = TC + 273.15

∆L = L0α∆T

∆V = V0β∆T

Rotational Motion

ωav =∆θ

∆t

αav =∆ω

∆t

θ = θ0 + ω0t+1

2αt2

ω = ω0 + αt

ω2 = ω20 + 2α(θ − θ0)

Simple Harmonic Motion

x = A cos(ωt)

v = Aω sin(ωt)

a = −Aω2 cos(ωt)

ω = 2πf T =1

f=

2π

ω

ω =

√k

mT = 2π

√m

k

ω =

√g

LT = 2π

√L

g

Waves

v = λf

v =

√FT

µµ =

M

L

λn =2L

nfn =

nv

2L

λn =4L

nfn =

nv

4Ly = A cos(ωt− kx)

ω = 2πf k = 2π/λ

Intensity =Power

Area

Heat

Q = mc∆T

Q = mL

Q

t= κA

∆T

LQ

t= σeAT 4


Constants

g = 9.8 m/s2

G = 6.67 × 10−11 Nm2/kg2

ME = 5.98 × 1024 kg

RE = 6.34 × 106 m

Patm = 1.013 × 105 Pa

I0 = 1 × 10−12 W/m2

vsound = 343 m/s

σ = 5.67 × 10−8 W/(m2 K4)

NA = 6.02 × 1023 mol−1

kB = 1.38 × 10−23 J/K

R = 8.31 J/(mol K)

Ideal Gas

PV = nRT PV = NkBT

N = nNA R = kBNA

P1V1T1

=P2V2T2

∆U = Q−W

W = P∆V

∆U =3

2nR∆T =

3

2NkB∆T

Heat Engines

QH −QC = W

e =benefit

cost=

W

QH

e = 1 − QC

QH

erefrig =QC

QH −QC

e = 1 − TCTH

erefrig =TC

TH − TC

∆S =Q

T

Some Common DensitiesDensity Density

Substance (kg/m3) Substance (kg/m3)Helium 0.18 Aluminum 2,700Air 1.29 Steel 7,800Oil 800 Lead 11,300Ice 917 Gold 19,300Water 1,000 Platinum 21,500

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Physics 220 - Final Exam Summer 2013