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Physics 2020
Spring 2009
Stephan LeBohec
DATA SHEET - FINAL
SEAT #
Constants & mathematics:
N A =6.02×1023
Boltzmann's constant k =1.38×10−23 J⋅K −1
k=
R=8.31 J⋅mol−1⋅K −1
1
=9.0×10 9 N⋅m2⋅C−2
4  0
−7
−1
0=4 ×10 T⋅m⋅A
e=1.602×10−19 C
Q Proton=e & Q Electron=−e
c=
1
=299,792,458 m⋅s−1≈3×10 8 m⋅s−1
 0  0
1
2
Kinetic energy E K = m⋅v
2
cos 2  f t 
≈−2  f sin 2  f t 
t
sin 2 f t
≈2  f cos 2  f t
t
Thermodynamics:
T  K =T  C 273
P⋅V =N⋅k⋅T =n⋅R⋅T
n=
N
m
=
& R=N A⋅k
NA M
e Actual =
3
Ideal mono­atomic gas:  U = n⋅R⋅ T
2
Isobaric: W =P V f −V i 
Isochoric: W =0
Isothermal W =n⋅R⋅T ln 
First law of thermodynamics:  U =Q−W
Vf

Vi
W Cycle
Q
=1− C
QH
QH
3
Adiabatic: W =− n⋅RT f −T i  &
2

P⋅V =Constant
5
with = for mono­atomic gases
3
e Carnot =1−
TC
TH
Waves:
=c⋅T =
c
1
as f =
f
T
In a gas c Sound =
Isotropic sound intensity: I =
c String =

5
P
with = for a mono­atomic ideal gas
3

P
2
4 ⋅r
Comparing intensities =10 log10
Doppler effect: f o= f s
Standing wave frequency (string or open pipe)
c
f n=n
with n=1,2,3,⋯
2L
Electric force, field and potential:
Force on a point charge in an electric field:
 =q E

F
Force between two point charges:
q q
 ∣=k 1 2 2
∣F
r
Electric potential from a point charge: V r =k
Capacitance: C=
q
r
q
V
R=
I1
in dB
I2
c±v o
c∓v s
Standing wave frequency in pipe open at one end
c
f n=n
with n=1,3,5,⋯
4L
Electric field generated by a point charge:
 ∣=k q
∣E
r2
Work by operator moving a charge in an electric potential: W =q⋅V f −V i 
Electric circuits:
Power in an electric circuit: P=V⋅I
Resistivity:

m
F
with =
L

L
A
Power from harmonic voltage and current:
I
V
P=I RMS⋅V RMS with I RMS = 0 and V RMS= 0
2
2
Equivalent resistance for resistors in parallel:
1
1 −1
R Parallel =  
R1 R2
Equivalent capacitance for capacitors in series:
1
1 −1
C Series =  
C1 C 2
Electric field in a parallel plate capacitor:
 ∣=  V = 
∣E
d
0
Energy stored in a capacitor:
1
1
1 q2
U = q⋅ V = C⋅ V 2=
2
2
2C
Ohm's law: V =R⋅I
Temperature dependence of resistivity:
=0 1T −T 0
Equivalent resistance for resistors in series:
R Series= R1R 2
Kirchhoff's junction rule: ∑ I IN =∑ I OUT
and loop rule: ∑  V UP =∑  V DOWN
Equivalent capacitance for capacitors in parallel
C Parallel =C 1C 2
Magnetic force and field:
 ∣=∣q∣⋅∣v∣⋅∣ 
Magnetic force on a charge: ∣F
B∣sin 
Magnetic field produced by an infinitely long wire:
 r ∣= 0 I
∣B
2 r
Electromagnetic induction:
Magnetic flux: = A⋅∣
B∣cos 
Self inductance: L=
Transformers:
Magnetic field inside a solenoid:
N
∣
B∣=0 I =0 n I
L
Faraday's law: V =−N
Induction in a moving wire
V =L⋅∣v∣⋅∣
B∣
Mutual inductance: M =
 ∣=I⋅L∣ 
Magnetic force on a current: ∣F
B∣sin 

t
Induction in a rotating set of coils
V =2  f N⋅A⋅∣
B∣sin 2  f t 
S
IP
Mutual induction: V =−M

I
Self induction: V =−L
VS NS IP
=
=
V P NP IS
I
t
I
t
Work, force & displacement relation
 ∣⋅ x⋅cos 
 W =∣F
Electromagnetic waves:
=c⋅T =c / f
Doppler effect: f o= f s
1±v o /c
≈ f s 1±v rel /c 
1∓v s /c
Reflection of light:
Law of reflection:  R = I
Mirrors equation:
Spherical mirror: f =
1 1
1
= 
f dI dO
Magnification: M =
Snell's refraction law n1 sin 1 =n2 sin 2
Triangle geometry:
a
Malus law: I T =I I cos 2 
µ
E
b
c 2=a 2b2
cos =b/c
sin =a /c
tan =a/b
hI
d
=− I
hO
dO
Brewster angle: tan  B=n 2 /n1
(ABD) and (ECD), similar triangles
AB DB AD
=
=
EC DC ED
c
R
2
A
D
C
B
Physics 2020
Spring 2009
Stephan LeBohec
1
FINAL
Name:_____________________________________
TA (circle one): Adam
Isaac
Michael
Student ID #:___________________________
Sarah
A)
[36 points, 3 points per question] For each statement, circle all the options you find appropriate.
You do not need to show your work.
1)
When the temperature of an ideal gas doubles, the root mean square velocity of the molecules is multiplied by
1/2
2)
1
1/  2
2
2
Two different gases are in thermal equilibrium. Their molar masses are in a ratio
square velocities of the two species of molecules are in a ratio v1RMS /v 2RMS =
1/2
1
1/  2
4
m1 /m2 = 2. The root mean
2
2
4
3)
When two different gases are mixed in a container they are always both at the same pressure.
TRUE
FALSE
4)
When the distance from a spherical wave source is multiplied by 10, the intensity is multiplied by
0.01
5)
0.1
 0.1
1
10
100
When the distance from a spherical wave source is multiplied by 10, the intensity level is changed by
0dB
1dB
2dB
 10 dB
10dB
20dB
100dB
6)
An acoustic wave is perceived by an observer at a higher frequency than the emitted frequency. With time, the
observer and the source are getting
FURTHER APART
CLOSER TOGETHER
7)
Two waves are interfering. A given point is reached by wave crests from one wave at the same time as by wave
troughs from the other wave. The interference at that point is then said to be:
DESTRUCTIVE
CONSTRUCTIVE
8)
A standing wave arises when two waves with different frequencies are propagating in opposite directions.
TRUE
FALSE
9)
The electric force acting on an electron points in the opposite direction of the electric field.
TRUE
FALSE
10)
In order to bring two electric charges of opposite signs closer together, an operator needs to provide a positive
amount of work.
TRUE
FALSE
11)
The electric field points in the direction of increasing electric potential.
TRUE
FALSE
12)
Two 12V batteries connected in series can be made equivalent to a 24V battery.
TRUE
FALSE
Physics 2020
Spring 2009
Stephan LeBohec
2
FINAL
Name:_____________________________________
TA (circle one): Michael
Sarah
Student ID #:___________________________
Adam
Isaac
B)
Four moles of a monatomic ideal gas go though a temperature change from T i =600K to T f =400K while
2972J of heat flow out of the system.
1)
[5 points] What is the change in internal energy?
3
3
 U = n R  T = ×4×8.31×400−600=−9972 J
2
2
2)
[6 points] How much work is done by the gas?
W =Q− U =−2972 J −−9972 J =7000 J
3)
[5 points] Assuming the process is isobaric at
W =P⋅ V so  V =
P=105 Pa , what is the change in volume?
W 7000 J
= 5 =0.07 m 3
P 10 Pa
P=3.96×10 26 W . The Earth is at a distance
C)
The total power radiated by the Sun, is
from the Sun.
1)
[4 points] What is the intensity of the solar radiation at this distance?
I=
2)
P
3.96×10 26 W
=
=1400 W.m−2
2
9
2
4  R 4 ×150×10 m
[6 points] A solar panel of area A=0.5m 2 is used during 1 hour to charge up a 12V battery with no
initial charge. What is the total amount of electric charge available in the battery? (We assume an ideal solar panel
with a 100% efficiency at converting all of the solar radiation to electric energy)
W = AI  t=Q V so Q=
3)
R=150×10 9 m
AI  t 0.5 m2×1400 W.m−2×3600 s
=
=2.1×10 5 C
V
12V
[6 points] After it has been charged, how long can the battery be used to power a
Q⋅ V 2.1×105 C×12 V
Q
P=V⋅I =V⋅
=
=9×10 4 s=25 hours
so  t=
−1
t
P
28 J.s
28W light bulb?
Physics 2020
Spring 2009
Stephan LeBohec
FINAL
Name:_____________________________________
TA (circle one): Michael
D)
Sarah
Adam
3
Student ID #:___________________________
Isaac
A loud speaker at A and a loudspeaker at B ( AB=3.2m ) are
in phase and producing harmonic waves of frequency f =214Hz .
The speed of sound is c=343 m⋅s −1 .
1) [5 points] How are the two waves interfering at location C?
( BC =2.4m )?
c 343 m.s−1
= =
=1.6 m
f
214 Hz
∣AC −BC∣= 3.222.42−2.4=1.6m= so the interference is constructive at point C.
2)
[13 points] What is the closest location D can be from A so that there is destructive interference at location D?
Start with D = A, there ∣BD− AD∣=3.2 m−0 m=2  and the interference is constructive. The closest point D where
there is destructive interference is such that ∣BD− AD∣=1.5=2.4 m so we write  AB2 AD 2− AD=2.4m or
AB2 AD 2=2.4 m AD 2 =2.4m2 AD 24.8 m× AD and finally
AD=
E)
AB2−2.4 m 2 3.2m2−2.4 m 2
=
=0.9333 m
4.8 m
4.8 m
A particle with
vi =4m⋅s −1
1)
m=0.04kg and electric charge q=3×10−6 C is released with an initial velocity
at a distance d i=3m from a charge Q=20×10−6 C which can not move.
[7 points] What is the closest possible distance charge q can get from the fixed charge Q ?
qQ
qQ 1
=k
 m v 2I and d F =k qQ . Numerically,
dF
dI 2
E
6
6
3×10 ×20×10 1
3×106×20×106
E=9×10 9
 ×0.04×42=0.5 J and d F =9×10 9×
=1.08 m
3
2
0.5
E=U F =U I  K I so
2)
E=k
[7 points] What is the speed of the particle once it is a very great distance from the fixed charge Q ?
E=K F =U I K I so
1
2
E= m⋅v F and
2
vF=
 
2E
2×0.5
=
=5 m.s−1
m
0.04
Physics 2020
Spring 2009
Stephan LeBohec
4
FINAL
Name:_____________________________________
TA (circle one): Michael
Sarah
Adam
Student ID #:___________________________
Isaac
F)
[36 points, 3 points per question] For each statement, circle all the options you find appropriate.
You do not need to show your work.
1)
Two 12V batteries connected in parallel can be made equivalent to a 24V battery.
TRUE
FALSE
2)
A resistor is connected to a generator. Increasing the resistance value by a factor four results in multiplying the
power delivered by the generator by:
1/ 4
1/2
1
2
4
3)
A freely moving charged particle in a region with a uniform magnetic field always has uniform circular motion.
TRUE
FALSE
4)
A straight wire transporting an electric current is under the effect of a magnetic force. The magnetic field must be
perpendicular to the wire.
TRUE
FALSE
5)
A circuit with a resistor is placed in a uniform magnetic field that varies harmonically with time. Doubling
the frequency of the magnetic field variation results in multiplying the power dissipated in the resistor by:
1
2
6)
1
2
1
2
2
4
A transformer steps the voltage down from 110V to 11V. The current in the secondary is like the current in the
primary multiplied by
0.01
0.1
1
10
100
7)
coil
A circular coil is exposed to an electromagnetic wave polarized horizontally. Electromagnetic induction in the
is maximal when the coil is
HORIZONTAL
VERTICAL,WITH NORMAL
VERTICAL , WITH NORMAL
TOWARD THE SOURCE
90o FROM THE SOURCE
8)
The exact value of the speed of light c=299,792,458m / s was set to define the meter.
TRUE
FALSE
9)
A polarizing filter is rotating at a rate of 10 rotations every second. A constant intensity of non polarized light is
sent through the rotating filter. The transmitted intensity varies with a frequency of:
0Hz
10)
10Hz
20Hz
A polarizing filter is rotating at a rate of 15 rotations every second. A constant intensity of vertically polarized
light is sent through the rotating filter. The transmitted intensity varies with a frequency of:
0Hz
15Hz
30Hz
11)
In water, nothing can go faster than light.
TRUE
FALSE
12)
One can start a fire by placing a piece of paper at the location of the image of the Sun formed by a
diverging lens.
TRUE
FALSE
Physics 2020
Spring 2009
Stephan LeBohec
5
FINAL
Name:_____________________________________
TA (circle one): Michael
Sarah
Student ID #:___________________________
Adam
Isaac
G
In the circuit in the figure, V =3V , R1 =30  , R 2=60  ,
R 3=40 and R 4=20  . With an ammeter, it is verified that the
current flowing through R 4 is I 4=0 Amps .
1)
[8 points] What is the value of
RX ?
Since there is not current through R 4 , the two points it is connected to are at the
V⋅R2
V⋅R 3
=
or
R1 R2 R X R 3
R 1 R 3 30 ×40
RX=
=
=20 
R2
60 
same electrical potential and
so
2)
[8 points] What is the power dissipated in
P 2=R 2 I 22=R 2 
H
R X=
R 3  R 1R 2
−R 3
R2
R2 ?
2
2
V
3V
 =60 ×
 =0.0666 W
R1R 2
30 60 
[16 points] A compass is placed inside a solenoid with 100 coils per
°
meter. The solenoid is positioned with its axis at 90 from the
direction of the terrestrial magnetic north pole. When the solenoid is
powered with a V =9V battery through a R=50  resistor in
°
series, the needle of the compass is observed to point =30 from
the direction of the terrestrial magnetic north pole. What is the
magnitude of the terrestrial magnetic field?
BSolenoid
BEarth
B Solenoid
B Solenoid 0 n I 0 n V
so B Earth=
=
=
.
B Earth
tan 
tan R tan
4 ×10−7×100×9
Numerically, B Earth=
=39.2×10−6 T
50 tan 30°
tan =
(A top view of the problem)
Physics 2020
Spring 2009
Stephan LeBohec
FINAL
Name:_____________________________________
TA (circle one): Michael
Sarah
Adam
6
Student ID #:___________________________
Isaac
[16 points] A circular coil A=1.0m 2 with N =4000 loops is r =10.0m from a f =60Hz power
line transporting a current I t= I 0 sin 2 f t with I 0=400A . What is the amplitude V 0 of the
induced electromotive force in the coil? (As an approximation, you can consider the magnetic field to be uniform
over the entire area of the coil as if the entire coil was 10.0 m from the power line)
I
0 I t 
NA  0 I t 
and the flux is =NAB=
so the absolute value of the induced
4r
4 r
  NA0  I
NA 0
NA 0 f I 0
=
=V 0 cos 2  f t  with V 0=
2  f I 0=
electromotive force is ∣V∣=
.
t
4 r  t
4 r
2r
4000×1×4 ×10−7×60×400
Numerically we obtain V 0=
=12.06 V
10
The magnetic field is
B t=
0.5mm in diameter.
J
The dot at the end of this sentence is
1)
[5 points] When you hold the page 30cm from your eyes, what is the angle under which you see the dot?
≈tan−1 0.5mm /300mm=0.0955° or 1.666×10−3 rad
2)
[6 points] You use a f =30mm converging lens to better examine the dot. You place the lens 20cm from
you eye and just 30mm from the paper. What is the angle under which you see the dot through the lens?
Lens ≈tan−1 0.5mm /30mm=0.955° or 16.66×10−3 rad
3)
[5 points] Does your answer to question 2) depend on the distance from your eye to the lens? In a short sentence,
explain why it does or does not.
The paper is in the focal plane of the lens so the virtual image of the dot is at an infinite distance. Changing the distance
from the eye to the lens does not change the distance from the eye to the virtual image. For the reason the answer to
question 2) does not depend on the distance from the eye to the lens.