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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≤
11
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=
12
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
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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)