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PHY2130 Form A Fall 2012

Final Exam

NAME:___________________________________________________________ SIGNATURE:______________________________________________________ Instructions 1. Put your books, notebooks, and cellphones on the floor under your seat. You can keep your exam, calculator, and extra pens or pencils on your desk. Also place your OneCard on the desk. 2. All cellphones and other devices, except for calculator, should be powered OFF and OFF the desktop. 3. Print and sign where indicated above. 4. A scoring sheet is provided with your exam. 5. Write and bubble your name on the scoring sheet at the start of the exam. 6. Bubble your answers to the multiple-choice problems on the scoring sheet. 7. You may not leave the room in the 10 minutes before the end of the exam. Once the exam ends, you must stop writing immediately and stand up at your seat. Put the scoring sheet inside the exam booklet and turn both in. Once all the exams have been collected, you will be allowed to leave the room. 8. Answer all 35 multiple-choice problems on this exam. Choose the best answer for each. Questions 3 – 35 count for credit.

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1. On the top right of this page, what is the Form you have? Form A A. Form A B. Form B C. Form C

2. Which class are you in?

A. Bowen, MWF 9:35 – 10:30 B. Conn, MWF 12:50 – 1:45 C. Paz, TuTh 6 – 7:20 D. Thakur, Oakland Center

3. If the radius of a balloon shrinks to 79% of its original value, its new volume is what percentage of original volume?

A. 49% B. 79% C. 92% D. 63% E. 89%

4. The graph below shows the position y in m of a squirrel running up a flagpole but sliding back down. What is the velocity of the squirrel at 5.5 s?

A. -6.0 m/s B. -0.5 m/s C. -5.0 m/s D. 5.0 m/s E. 6.0 m/s

5. A car traveling at 10.0 m/s accelerates at 3.0 m/s2 for 4.00 s. How far does it travel during this 4.00 s?

A. 40 m B. 24 m C. 16 m D. 45 m E. 64 m

y  (m)  

t  (s)  

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6. A ball rolls East 4.4 m, bounces off a rock and rolls North before coming to rest 2.5 m from the rock. If the trip takes 2.3 s, what is the magnitude of the average velocity of the ball?

A. 5.1 m/s B. 2.2 m/s C. 3.0 m/s D. 1.9 m/s E. 11 m/s

7. A tennis ball is thrown at 15.0 m/s at an angle of 35° up from the horizontal. What are the velocity components of the ball 1.5 s later? The x axis is horizontal in the direction of travel and the y axis is up.

A. vx= -12.3 m/s, vy = 6.1 m/s B. vx = -2.4 m/s, vy = -6.1 m/s C. vx = 27.0 m/s, vy = 8.6 m/s D. vx = 12.3 m/s, vy = -6.1 m/s E. vx = 12.3 m/s, vy = 8.6 m/s

8. A 40 kg box is sliding down a ramp angled at 15° down from the horizontal. The box is accelerating at 1.5 m/s2 down the ramp. Ignoring air resistance, what is the force of friction between the box and the ramp?

A. 101.5 N B. 41.5 N C. 60.0 N D. 161.5 N E. 392 N

9. Two blocks are connected by a lightweight, flexible string over a massless frictionless pulley. If one block has a mass m2 = 15 kg and the other a mass m1 = 10 kg, find the acceleration of m1, the 10 kg mass.

A. 2.0 m/s2 upwards B. 9.8 m/s2 upwards C. 4.9 m/s2 downwards D. 6.5 m/s2 downwards E. 3.3 m/s2 upwards

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10. When a baseball is hit at an angle up from the horizontal (but not straight up), what can you say about its velocity and acceleration at the highest point of its motion?

A. The velocity is zero and the acceleration is straight down B. The velocity is horizontal and the acceleration is straight down C. The velocity and acceleration are both zero D. The velocity and acceleration are both straight down E. The velocity is straight up and the acceleration is straight down

   11. The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. The cylinder has a radius of 3.3 m. If the cylinder is to have a frequency of 0.50 Hz, what should be the minimum coefficient of friction, such that the people don’t fall out?

A. µ = 0.2 B. µ = 0.1 C. µ = 0.4 D. µ = 0.3 E. µ = 0.5

 

 

12. A space station is moving in a circular orbit around the Earth. It makes one revolution in 90 minutes. How high above the Earth’s surface is the space station? The mass of the Earth is 5.97×1024 kg and the radius of the Earth is 6.37 × 106 m.

A. 1000 km B. 6370 km C. 16300 km D. 10 km E. 280 km

 

 

13. A large crate is pulled along a horizontal path at a constant speed by a cable that is inclined at an angle of 20° with respect to the horizontal. The tension in the cable is 2.4×103 N. The power the cable supplies is 1.0 × 103 W. How far will the crate move in 10 seconds?

A. 2.2 m B. 4.2 m C. 12 m D. 4.4 m E. 0.44 m

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14. A potato sack of mass 20 kg, slides down a frictionless ramp of length 3.0 m inclined at an angle θ with respect to the horizontal. If the potato sack starts from rest, and at the edge of the ramp its speed is 5.0 m/s, what is the angle θ?

A. 23° B. 65° C. 25° D. 30° E. None of the above

 

 

15. A constant force is applied for the same duration of time on two objects. The mass of one object is twice as large as the other object. Which of the following is true?

A. Both objects will have the same momentum change, but the object with the larger mass will have the larger velocity change.

B. Both objects will have the same momentum change, but the object with the smaller mass will have the larger velocity change.

C. Both objects will have the same velocity change, but the object with the smaller mass will have the larger momentum change.

D. Both objects will have the same velocity change, but the object with the larger mass will have the larger momentum change.

E. None of the above. 16. Block A, with a mass of 200 g, is traveling north on a frictionless surface with a speed of 5.0 m/s. Block B, with a mass of 300 g, travels east on the same surface until it collides with A. After the collision, the blocks move off together with a velocity of 2.69 m/s at an angle of 48.0° to the north of east. What was B’s speed just before the collision?

A. 1.0 m/s B. 3.0 m/s C. 5.0 m/s D. 2.0 m/s E. 4.0 m/s

 

17. Four equal 2.0-kg masses are arranged at the corners of the square. They are connected by rigid, massless rods of 0.50-m length. What torque must be applied to cause an angular acceleration of 0.90 rad/s2 about one side of the square?

A. 0.90 N × m B. 1.8 N × m C. 0.45 N × m D. 0.60 N × m E. 1.2 N × m

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18. A uniform disk with a mass of 1.0 kg and radius of 20 cm is rotating on frictionless bearings with a rotational speed of 10 rad/s when a clod of clay is dropped on a point 10 cm from the center of the disk, where it sticks. If the new angular velocity of the disk is 8.7 rad/s, what is the mass of the clay? Idisk = ½ MR2.

A. 0.60 kg B. 0.075 kg C. 0.15 kg D. 1.2 kg E. 0.30 kg

19. What is the buoyant force on 1.00 kg of pine wood held completely submerged under mercury? Density of the pine wood is 350 kg/m3 and that of mercury is 13.6 × 103 kg/m3.

A. 10.7 N upward B. 0.25 N upward C. 381.0 N upward D. 6.21 N downward E. 2.22 downward

20. At the surface of the Earth the pressure is 105 kPa. What is the approximate change in pressure in going 40 m above the surface? The density of the air is 1.20 kg/m3.

A. -470 atm B. -410 Pa C. -470 Pa D. -410 N E. -500 Pa

21. A mass hanging vertically from a spring and a simple pendulum both have a period of oscillation of 1 s on Earth. An astronaut takes the two devices to another planet where the gravitational field is weaker than that of Earth. For each of the two systems, which one of the following is true?

A. The period of the mass-spring system will remain the same but the oscillations of the pendulum will slow down

B. The period of the mass-spring system will remain the same but the oscillations of the pendulum will become faster

C. There will not be any change in the period of either D. The oscillations of both will slow down E. The oscillations of both will become faster

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22. The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is 2.240 mm. If the maximum acceleration of the prong is 8560 m/s2, then what is the frequency of the tuning fork? Assume SHM.

A. 2765 Hz B. 880 Hz C. 356 Hz D. 440.0 Hz E. 565 Hz

23. The intensity of sunlight that reaches Earth's atmosphere is 1400 W/m2. What is the intensity of sunlight that reaches a spaceship which is 2.5 times as far away from the Sun as the Earth?

A. 560 W/m2 B. 1400 W/m2 C. 700 W/m2 D. 224 W/m2 E. 8750 W/m2

24. A string of length 2.0 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz. What is the speed of the transverse string waves?

A. 340 m/s B. Cannot be determined because the tension is unknown C. 1800 m/s D. 900 m/s E. 333 m/s

25. A sound wave with an intensity level of 90.0 dB is incident on an eardrum of area 0.60 × 10−4 m2. How much energy is absorbed by the eardrum in 5.0 min?

A. 20 J B. 18 µJ C. 1.1 µJ D. 5.2 µJ E. 0.5 µJ

26. A certain pipe has resonant frequencies of 264 Hz, 440 Hz, and 616 Hz, with no other resonant frequencies between these values. What is the fundamental frequency of this pipe?

A. 88 Hz B. 64 Hz C. 78 Hz D. 102 Hz E. 56 Hz

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27. A bubble of ideal gas with a volume of 1.00 cm3 forms at the bottom of a lake that is 20.0 m deep. The temperature at the bottom of the lake is 10.0 °C. The bubble rises to the surface where the water temperature is 25.0 °C. Assume the bubble is small enough that its temperature always matches that of its surroundings. What is the volume of the bubble just as it reaches the surface of the water? Ignore surface tension.

A. 1.24 cm3 B. 4.24 cm3 C. 2.78 cm3 D. 2.00 cm3 E. 3.09 cm3

28. The reaction rate for the prepupal development of male Drosophila is temperature-dependent. The activation energy for this development is then 2.81 × 10-19 J. A Drosophila is originally at 10.00 °C and it's temperature is increasing. If the rate of development has increased 3.5%, how much has its temperature increased?

A. 0.11 oC B. 0.14 oC C. 0.56 oC D. 0.73 oC E. 0.44 oC

29. Why does a helium weather balloon expand as it rises into the air? Assume that the temperature remains constant.

A. The pressure outside the balloon increases B. The number of helium atoms in the balloon increases C. The pressure outside the balloon decreases D. The number of helium atoms in the balloon decreases E. Each helium atom undergoes a transition to a larger form

30. How much heat is required to raise the body temperature of a 51.0 kg woman from 37.00 °C to 38.40 °C? The specific heat for human tissue is 3.50 kJ/K.

A. 125 kJ B. 454 kJ C. 207 kJ D. 250 kJ E. 350 kJ

31. In a physics lab, a student accidentally drops a 25.0-g brass washer into an open Dewar of liquid nitrogen at its boiling point of 77.2 K. How much liquid nitrogen boils away as the washer cools from 293 K to 77.2 K? The latent heat of vaporization for nitrogen is 199.1 kJ/kg. The specific heat of brass is 0.384 kJ/(kg K)

A. 6.45 g B. 10.4 g C. 8.25 g D. 4.08 g E. 8.27 g

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32. Two copper bars are placed in series (end-to-end) between two temperature baths. The temperature of one of the heat baths is 104 oC. If the conductive heat flow is 0.16 W, what is the temperature of the other, cooler, heat bath? The thermal conductivity of copper is 401 W/(m·K). The length of each bar is 0.10 m and the cross-sectional area of each is 1.0 x 10-6m2.

A. 10 oC B. 24 oC C. 52 oC D. 0 oC E. 60 oC

 

33. An ideal gas engine has an efficiency of 0.725 and uses gas from a hot reservoir at a temperature of 622 K. What is the temperature of the cold reservoir to which it exhausts heat?

A. 171 K B. 101 K C. 311 K D. 298 K E. 373 K

34. What is the change in entropy of 4.00 g of water evaporating at 100 °C? The latent heat of vaporization of water is 2256 kJ/kg.

A. -24.2 J/K B. +3.07 J/K C. -3.07 J/K D. -4.00 J/K E. +24.2 J/K

35. A thermal system follows the cycle shown in the figure.(Let V1 = 0.200 m3 and P1 = 1atm) (a) How much net work, W, is done on the system in one cycle?; (b) What is the heat flow, Q, into the system per cycle?

A. W = -182 kJ; Q = 182 kJ B. W = 182 kJ; Q = -182 kJ C. W = -1200 kJ; Q = 1200 kJ D. W = 1200 kJ; Q = -1200 kJ E. W = 182 kJ; Q = 182 kJ

       END  OF  EXAM

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PHY  2130  Formulas

Physical  Constants  

• 29.80 ms

g =  (always  down!)  • G  =  6.67  ×  10-­‐11  m3/kg⋅s2  • Patm  =  101.3  kPa  • ρwater  =  1000  kg/m3  • Boltzmann  constant  in  Ideal  Gas  Law:  kB  =  1.38x10-­‐23  J/K  • Universal  gas  constant  in  Ideal  Gas  Law:  R  =  8.31   /J K

mol    

• 0ºC  =  273.15  K  • Avagadro’s  Number:  NA  =  6.022  x  1023  mol-­‐1  • 1  u  =  1.66  ×  10-­‐27  kg  • 1  cal  =  4.186  J  

Chapter  1  

• Introduction  Chapter  2  

• Vectors  and  motion  along  a  line  o Displacement  (change  in  position):   f ir r rΔ = −

r r r .  

o Average  velocity: avrvt

Δ=Δ

rr    

o Average  acceleration: avvat

Δ=Δ

rr  

o Constant  acceleration  equations:     x fx ix xv v v a tΔ = − =                                                              

( )12f i fx ixx x x v v tΔ = − = + Δ ( )21

2ix xx v t a tΔ = Δ + Δ   2 2 2fx is xv v a x− = Δ  

Chapter  3  

• Two-­‐dimensional  motion  

sin oppositehypotenuse

= cos adjacenthypotenuse

= tan oppositeadjacent

=

Chapter 4 • Force  and  Newton’s  Laws  of  Motion  

o Newton’s  2nd  Law:  F

am

=∑r

r  or     F ma=∑r r  

o The  magnitude  of  the  gravitational  force: 1 22

GmmFr

=  

o  Weight  :W mg= .      o Static  friction:     s sf Nµ≤  

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o Kinetic  friction:   k kf Nµ=      Chapter  5  

• Circular  Motion  

o Angular  displacement:   f iθ θ θΔ = −  ;  average  angular  velocity   av tθ

ωΔ

=Δ

rr  

o   s rθ= ,  1  complete  circle  =  1  revolution  =  2π  radians        

o To  relate  linear  to  angular  quantities:    v  =  rω    

o Acceleration  in  uniform  circular  motion:    2

2rva rr

ω= =  

o 2

r rvF ma mr

= =∑r r  

o 1fT

= ,  ω  =  2πf  

Chapter  6  

• Work  and  Energy  o Work:   cosW F r θ= Δ  (If  F  and  r  are  along  the  x-­‐axis  then     xW F x= Δ ).  o Translational  kinetic  energy:   21

2transK mv= .  o The  Work-­‐Kinetic  Energy  Theorem  : totalW K= Δ  o The  gravitational  potential  energy  close  to  earth: gravU mgy=  o Gravitational  potential  energy  everywhere:  Ugrav  =  -­‐Gm1m2/r    o The  potential  energy  associated  with  a  spring  : 21

2springU kx= .      o The  force  required  to  pull  on  a  spring:   springF kx= −  o Conservation  of  energy  : initial finalE E= .  

o Power:   θcosFvtEP =Δ

Δ=  

Chapter  7  

• Momentum,  Impulse  and  Conservation  of  Momentum  o  Linear  momentum: p mv=

r r  (Vector).  o Conservation  of  momentum  ∑ ∑= finalinitial pp    

o p F tΔ = Δ∑rr .  

Chapter  8  

• Rotations,  torques,  and  angular  momentum    o The  rotational  kinetic  energy:   21

2rotK Iω=  

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o Rotational  inertia: 2I mr=∑  o Torque:   θτ sinrFFrrF =±=±= ⊥⊥    

o Torque  and  angular  acceleration  α:  τ  =  Iα,  α  ≡  tt Δ

Δ→Δ

ω0

lim  

o Angular  momentum:   L Iω=  o Conservation  of  angular  momentum:   if 0, i fL Lτ = =∑  o Rotational  work:  W  =  τ·Δθ  

 

Chapter  9  

P  =  F/A  

ρ  =  m/V,  S.G.  =  ρ/ρwater,  P  =  Patm  +  ρgd,  FB  =  ρflgVsub  

  2211 vAvAtV

==Δ

Δ ,   222

122

212

111 vgyPvgyP ρρρρ ++=++  

  Viscous  flow  (Poiseuille):   4/8

rLPtV

ηπ Δ

=Δ

Δ  

  Viscous  drag:  FD  =  6πηrv  

  Surface  Tension  in  a  bubble:  ΔP  =  2γ/r  

Chapter  10  

• LLY

AF Δ=  

LxS

AF Δ=  

VVBP Δ

−=Δ  

• Simple  Harmonic  Motion  (SHM)  o The  maximum  displacement,  velocity  and  acceleration  in  SHM:                  xm  =  A   mv Aω=           2

ma Aω=  

o The  equations  of  motion  for  SHM:    Assume  x  =  A  at  t  =  0:  x  =  Acosωt,  vx  =  -­‐ωAsinωt,  ax  =  -­‐ω2Acosωt          

o The  mechanical  energy  for  SHM:   2 2 21 1 12 2 2

mechSHME kA mv kx= = +      

o The  angular  velocity  for  a  mass-­‐spring  system:   springkm

ω =  

o The  angular  velocity  for  a  simple  pendulum:           pendulumgL

ω =  

 

 

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Chapter  11  

• Waves    

o Wave  intensity  (for  an  isotropic  source):  24 r

PAreaPowerI

π==  

o The  speed  of  transverse  wave  on  a  string:   stringF mv Lµµ

= =  

o f,  ω,  λ  are  related!               2 fπ ω= ;     2 2 fkv

π πλ

= =  

o The  speed  of  a  wave  :  v fkω

λ= =  

o The  distance  between  two  adjacent  nodes  is  ½  λ  (also  the  distance  between  two  adjacent  antinodes  

o Standing  waves  on  a  string:   2 ; (n=1,2,3,...)2n n

L vf nn L

λ = =  

Chapter  12    

• Sound    o  

o ρBv =    

ρYv =   v  =  331  +  0.606TC  m/s  

o Pressure  amplitude  Vs  displacement  amplitude:  p0  =  ωvρs0  

o vp

Iρ2

20=  

o Sound  intensity  level:   ( ) 212

00

10 dB log ; 1.00 10 Wm

I II

β −⎛ ⎞= = ×⎜ ⎟

⎝ ⎠  

o Standing  sound  wave  in  a  pipe  open  at  both  ends:  see  formulas  for  standing  waves  on  strings  in  Chapter  11  section  

o Standing  sound  wave  in  a  pipe  closed  at  one  end:  

              4 ; (n=1,3,5,...)4n n

L vf nn L

λ = =  

o Doppler  shift:   ss

oo f

vvvv

f ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−=  

 

 

Chapter  13  

• Temperature  and  the  ideal  gas  o Temperature  scales  and  conversions  :    

    273.15CT T= − ;   (1.8 / ) 32F CT F C T F= +o o o  

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o Thermal  expansion:       One  dimensional  (linear)-­‐-­‐-­‐-­‐-­‐ ( )0L L TαΔ = Δ  

    Two  dimensional  (area)-­‐-­‐-­‐-­‐-­‐-­‐ ( )0 2A A TαΔ = Δ  

    Three  dimensional  (volume)-­‐-­‐ ( )0V V TβΔ = Δ ,  β  =  3α  

o Ideal  Gas  Law:  PV  =  NkBT;  PV  =  nRT    

o Kinetic  theory  of  gases:   23 trNP KV

= ;   23 12 2tr rmsK kT mv= =  

 

° 2vvrms = ,   mkTvrms /3=  

° reaction  rate  ∝   kTEae /−  

° Mean  free  path  )/(2

12 VNdπ

=Λ  

° xrms  =   Dt2    

Chapter  14  

• Heat  

o Heat  capacity  (C)    and  specific  heat  (c):   QCT

=Δ

,   Qcm T

=Δ

 

o Specific  heat  of  ideal  gases:   VQCn T

=Δ

 (molar  specific  heat  at  constant  

volume)    

              For  a  monatomic  ideal  gas:    molKJRCV/5.12

23

==  

              For  a  diatomic  ideal  gas:            molKJRCV/8.20

25

==  

 

o Phase  transitions  and  latent  heat:   Q mL=  

o Thermal  conduction:  P TAd

κΔ

= ,  where  P is  the  rate  of  heat  flow    

o Stefan’s  Law  P  =  eσAT4  

o Wien  Displacement  Law:  λmaxT  =  2.898  ×  10-­‐3  m∙K    

  15  

 

Chapter  15  

• Thermodynamics  o The  first  law  of  thermodynamics:   U Q WΔ = +                o Thermodynamic  processes:                In  general,  the  magnitude  of  the  work  done  is  the  total  area  under  the  PV  curve.    

1. Constant  pressure:  W P V= − Δ      2. Constant  volume:   0;W U Q= Δ =  3. Constant  temperature  process  for  an  ideal  gas: 0UΔ =  4. In  an  adiabatic  process:   0;Q U W= Δ = .      

o The  change  in  internal  energy  for  an  ideal  gas: VU nC TΔ = Δ  o P VC C R= +  

o Efficiency  H

net

QW

e =  

o Energy  conservation  for  heat  engine:  QH  –  QC  =  Wnet  

o Carnot  efficiency  for  heat  engine:  H

Cr T

Te −=1  

o Entropy  change  of  a  system:   QST

Δ =  (=  ΔSH  +  ΔSC  for  two  objects  in  

thermal  contact)