EF 152 Final Exam, Spring, 2012
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The equation sheets may be removed when the test begins
Guidelines:
• Assume 3 significant figures for all given numbers unless otherwise stated
• Show all of your work – no work, no credit
• Write your final answer in the box provided - include units for all answers
• If you finish with less than 5 minutes remaining, remain seated until the end of the
exam and all exams are collected.
EF 152 Final Exam, Spring, 2012
Harmonic Motion
ω – angular frequency
A – amplitude
k – stiffness
m – mass
δ – phase angle
x0 – initial displacement
v0 – initial velocity
T – period
f – frequency
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Parallel Axis Theorem
Pendulums
Simple:
Physical:
Speed of Sound in Air
Stress and Strain
Uniform Circular Motion
an – centripetal acceleration
v – speed
ρ – radius of curvature
ω – rotational speed
T – period
f – frequency
– angle
(any curve)
Universal Law of Gravitation
T in °C
Natural Frequencies:
λ – wavelength
L – Length
n – harmonic
T – tension
µ – mass per unit length
f – frequency
v– wave velocity in medium
Kepler’s Third Law
Satellites
String
Density of Water
3
62.4 lb/ft
3
1000 kg/m
Conservation of Mass
(Continuity)
Atmospheric Pressure
1 atm = 101.3 kPa
1 atm = 14.7 psi
Bernouilli’s Equation
Lift
Pressure in a fluid
Doppler Shift
f0 – frequency
f′ – shifted frequency
v – velocity of medium
vS – velocity of source
vL – velocity of listener
Beat Frequency: | f2 – f1 |
G = 6.67x10-11 N-m2/kg2
Factor of Safety (FS)
Fluids
p – pressure
h – height
ρ – mass density
v – velocity
K – empirical constant
A – area
d – depth
p0 – pressure on top of fluid
Sound Level
I0 – reference intensity,
-12
2
1x10 W/m
I – intensity
Positive is from listener to source.
Wave Energy, Power, Intensity
E – energy
I – intensity
P – power
- average power
Air Columns
closed pipe:
n= 1, 3, 5…
rearth = 6.378x106 m
open pipe:
Conversions
3
1 ft = 7.48 gal
3
1 m = 1000 L
mearth = 5.976x1024 kg
Stokes’ Law
Sphere through fluid for
laminar flow
Wave Equation
v – wave velocity
A – amplitude
k – wave number
ω – angular frequency
λ – wavelength
f – frequency
Poiseuille’s Equation
n= 1, 2, 3…
Wave Speed
Cables, Ropes, etc.
T – tension
µ – mass per unit length
E – modulus of elasticity
ρ – mass density
Transverse:
Light Waves
Law of Reflection
Index of Refraction
Law of Refraction
Light Wavelength
Total Internal Reflection
η – viscosity
L – characteristic length
v – velocity
ρ – mass density
R – sphere radius
v is positive if sign of ω is negative
Longitudinal:
EF 152 Final Exam, Spring, 2012
Thermal Expansion
Linear
Work of Thermal Systems
Linear, Stresses
Isobaric (constant pressure)
Volumetric
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Heat
Q– heat
c – specific heat
κ – thermal conductivity
R – thermal resistance
EF 152 Final Exam, Spring, 2012
Constants
-31
me=9.109x10 kg
-27
mp=1.673x10 kg
-27
mn=1.675x10 kg
Capacitance
Magnetism
Capacitance – parallel plates
9
Heat Capacity
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k = 9x10
in a vacuum
-12
Ideal Gas Law
Isochoric (constant volume)
Thermal Conductivity
ε0 = 8.854 ·10
R = 8.314 J/(mol-K)
23
Avogadro’s Number: 6.02x10
Isothermal (constant temp)
Thermal Resistance
e = -1.6022 ·10 C (electron charge)
-19
eV = 1.6022·10 J (electron volt)
Capacitance – energy
storage
-19
Standard Pressure and Temp
273K 1.00 atm (101.3kPa)
Coulomb’s Law (electrostatic force)
Magnetic field of a
moving charged particle
Capacitors in series
Thermal Resistance, Series
st
1 Law of Thermodynamics
U – internal energy
W – work done by thermal
system
Q – heat flow into thermal
system
Molecular Thermal Physics
m – mass of a molecule
M – molecular mass
n – number of moles
N – number of molecules
k – Boltzmann constant =
-23
1.38065 × 10 J/ K
Adiabatic (∆Q = 0)
Efficiency
General
Otto Cycle
r – compression ratio
Capacitors in parallel
Thermal Resistance, Parallel
Refrigerators
General
K – coefficient of performance
H – heat current
P – power input
Electric Field – point charge
- unit vector from charge to a location
Magnetic field along the axis
of a looped wire
Potential energy - point charges
Current
Carnot Cycle
a – radius of the loop
x – distance from the center of the loop
to point of interest on the axis.
I – current in the wires
N – number of loops
Potential
Potential of a set of point charges
Entropy
Ideal Gas
Magnetic Field of
a straight wire
Resistors in series
Resistors in parallel
Carnot
Conversions
1 cal = 4.186 J
1 BTU = 1055 J
1 hp = 0.707 BTU/sec
3
1 L = 1000 cm
3
1 m = 1000 L
Magnetic force on
moving charged particle
Water Properties
c = 1 cal/(g-°C) = 4.186J/(g-°C)
Lf = 79.6 cal/g
Lv = 540 cal/g
3
ρ = 1 g/cm = 1 kg/L
3
3
= 1000 kg/m = 62.4 lb/ft
Lf = Latent heat of fusion
Lv = Latent heat of vaporization
Voltage, Resistance,
Current, Power
V=I·R
P=I·V
Kirchhoff’s Rules
for a closed loop
Potential difference between two
parallel plates
for a junction
EF 152 Final Exam, Spring, 2012
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Remove the 2 equation sheets, leaving the exam questions stapled together.
CLEARLY PRINT the information below.
EF 152 Final Exam, Spring, 2012
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5. (6 pts) Josh is on the International Space Station making 0.652 revolutions per hour in its orbit around the
earth. Assuming a circular orbit, how high is this satellite above the surface of the earth?
Name: __________________________________________________ EF 152 Section: ____________
NetID: ____________________________ (your computer login, NOT your student #, e.g. lazydog1)
1. (1 pt) How must the intensity of a sound be changed to cut the loudness in half?
a. 1/100
b. 1/10
c. 1/2
d. 1/√2
2. (1 pt) What is the change in internal energy for an adiabatic process?
a. +Q
b. –Q
c. +W
d. –W
e. 0
3. (2 pt) A uniform beam 10.0m long, weighing 400N rests symmetrically on two supports, A and B, 4.0m apart.
Todd weighs 800N and walks along the beam from A to B. How far beyond B can he walk before the beam
begins to tip?
a. 1m
b. 2m
c. 3m
d. 4m
6. (6 pts) A proposed elevator in Estabrook is suspended by a steel cable with cross-sectional area 3x10-4m2 and
an ultimate strength of 9.25 x 108 Pa. If the elevator weighs 10kN, how many 70kg students can the elevator
hold for a minimum factor of safety of 18?
4. (6 pts) A bracket hangs from a wall and is loaded as shown. Calculate the magnitude of the force supported by
the pin at A. Neglect the weight of the bracket. A separate, complete FBD is required for full credit.
7. (6 pts) A styrofoam buoy is held completely submerged in water by a rope. The volume of the buoy is
0.045 m3. What is the tension in the rope? = 180kg/m A separate, complete FBD is required for full credit.
EF 152 Final Exam, Spring, 2012
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8. (6 pts) Megan is using sewing machine and notices that the point of the needle moves in simple harmonic
motion with a frequency of 8.5 Hz. At t=0 its position and velocity are +1.2cm and -0.7cm/s, respectively. Find
the acceleration of the needle at t=0.5 seconds.
9. (6 pts) Patrick ties a rope to a post and finds several frequencies at which he can oscillate the other end of the
rope so that a light clothespin 1.25 ft from the post doesn’t move. If the speed of the wave is 4.3 ft/s, what is
the fundamental frequency of this oscillation?
10. (6 pts) A bat flies toward a wall, emitting a steady sound of frequency 2000 Hz. The bat hears its own sound
plus the sound reflected by the wall. If the bat is flying 22 m/s, what beat frequency does it hear? The speed
of sound in air is 343 m/s.
EF 152 Final Exam, Spring, 2012
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11. (6 pts) Shane strikes a brass rod at one end. Patrick hears the sound at the other end 0.22 seconds later. How
long is the brass rod? = 8600kg/m = 9x10 Pa
12. (6 pts) Geoff is designing an electronic circuit element made of 25x10-6 kg of silicon. The current going through
it adds energy at a rate of 8.3x10-3 J/s. His design does not allow any heat transfer out of the element. By how
much will its temperature increase in one minute? Specific heat of silicon is 705 J/kg-K.
13. (6 pts) Frances pours 0.375kg of coffee at 100°C into a well-insulated mug. How much ice at 0°C must be
added to achieve optimum drinking temperature of 92°C? Assume no heat is transferred to the mug.
EF 152 Final Exam, Spring, 2012
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EF 152 Final Exam, Spring, 2012
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17. (6 pts) A circuit operates as shown. How much electrical energy does it consume during 2 hours?
14. (6 pts) Water at 80°C is brought to a boil and 20% of its original mass is converted to steam. If the total change
in entropy of the system is 9600 J/K, what was the original mass of water?
18. (6 pts) For the system shown, the total charge is 47 μC. What is the potential drop from A to B?
15. (6 pts) A Carnot refrigerator removes 950 J of heat. If the interior is 10°C and the outside is 35°C, how much
heat is transferred to the outside?
!
19. (6 pts) An electron moves at 1.6x107 m/s as shown. Find the magnitude and direction of the magnetic field
this electron produces at point A, 2.0x10-6 m away.
16. (6 pts) What must the charge (sign and magnitude) of a 1.65g particle be for it to remain stationary when
placed in a downward directed electric field of 720 N/C?