Exam 3
PHY 2140
Row:
Seat:
Date, 2003
Please type your name here
Please type your student number here
Instructions:
The following procedure must be followed in order to correct any (unlikely) mistakes in
the grading.
1. Do all the questions. Show your work for partial credit. I must be able to
understand what you have done while I am reading the exam – not when you
explain it to me after the exam is graded and returned.
2. For each problem:
(a) write down any formula(s) used
(b) justify why you used that particular formula(s)
(c) copy the answer you have circled from the exam pages
to the General Purpose Answer Sheet and fill in the ovals.
(d) show your work! No work – no point.
3. The formula sheet is on the last page of the exam. You may detach it from the rest
of the exam.
I read and understood the statement above
Your signature
NAME
1. An inductor has a 54 Ohm reactance at 60 Hz. What will be the peak current if this inductor
is connected to a 50 Hz source that produces 100 V rms voltage?
a.
b.
c.
d.
e.
0.69 A
1.41 A
2.71 A
3.14 A
none of the above
2. An inductor and a resistor are connected in series. When connected to a 60 Hz, 80 V
source, the voltage drop across the resistor is found to be 35 V rms and the power
dissipated in the circuit is 11 W. What is the value of the resistance?
a.
b.
c.
d.
e.
f.
97 
111 
123 
134 
151 
167 
3. If a 2.0 H inductor is used in a tuning circuit in a radio, what is the capacitance needed to
tune in Phat Matt on 89X at a frequency of 88.7 MHz?
a.
b.
c.
d.
e.
0.54 pF
0.71 pF
0.91 pF
1.61 pF
That station sucks!
NAME
4. A new elementary particle is detected. Moving with a speed of 0.98c, the lifetime of the
particle is measured to be 1.3 x 10-7 s by a stationary observer. What is its proper lifetime?
a.
b.
c.
d.
e.
1.12 x 10-9 s
2.45 x 10-9 s
4.52 x 10-9 s
6.02 x 10-9 s
2.59 x 10-8 s
5. Marilyn Monroe and Albert Einstein go for a ride in a rocket ship at a speed of 0.7c. Albert
finds that Marilyn’s heart beats 90 times per minute (I think she likes him). What is her
heart rate according to a stationary observer on the Earth? Hint: what is the time interval
between heart beats?
a.
b.
c.
d.
e.
36 beats/min
64 beats/min
122 beats/min
160 beats/min
zero beats per minute
6. Stephen Hawking and Albert Einstein each blast off in rockets, labeled “e” and “h” in the
figure. In a cosmic game of “chicken,” they fly towards one another on a collision course.
Each rocket has a speed of 0.8c as measured by a stationary observer on the Earth. What is
the speed of Einstein’s rocket as measured by Hawking?
ee
a.
b.
c.
d.
e.
zero
0.26c
0.74c
0.98c
1.60c
hh
NAME
7. A radio wave has a frequency of 5.00 MHz. Find its wavelength.
a.
b.
c.
d.
e.
60 mm
15 mm
60 m
15 m
zero
8. If the total energy of a rocket ship is three times its rest energy, what is its speed?
a.
b.
c.
d.
e.
0.63c
0.72c
0.94c
0.99c
none of the above
9. The phasor diagrams below represent three oscillating emfs having different amplitudes
and frequencies at a certain instant of time t =0. As t increases, each phasor rotates
counterclockwise and completely determines a sinusoidal oscillation. At the instant of time
shown, the magnitude of E associated with each phasor given in ascending order by
diagrams?
a.
b.
c.
d.
e.
a, b, c
b, c, a
a, c, b
c, b, a
need more info
10. Radio The light bulb has a resistance R, and the emf drives the circuit with a frequency .
The light bulb glows most brightly at
a. Very low frequencies
b. Very high frequencies
c. Resonant frequency
11. A supertrain of proper length 100 m travels at a speed of 0.95c as it passes through a tunnel
having proper length 50 m. As seen by a trackside observer, is the train ever completely
within the tunnel?
a.
b.
c.
d.
e.
yes
no
halfway
not enough information
what are you talking about?
12. (bonus) Imagine that the entire Sun collapses to a sphere of radius Rg such that the work
required to remove a small mass m from the surface would be equal to its rest energy, mc2.
This radius is called the gravitational radius for the Sun. Find Rg. (It is believed that the
ultimate fate of very massive stars is to collapse beyond their gravitational radii into black
holes.)
a.
b.
c.
d.
e.
3347 km
127 km
1.47 km
1.14 m
impossible to find
I
Im
2
V
VR  IR ,, VC  IX C
VL  IX L
Vm
2
Z  R2  X L  X C 
2
f 
1
2 LC
L  LP 
KE  mc 2  mc 2
En  nhf
V  IZ
c  f
p  mv
XC 
tan  
 
v AB 
1
2 f C
X L  2fL
XL  XC
R
Pav  IV cos
1
1  v2 c2
v AC  vCB
v v
1  AC 2 CB
c
t  t P
E  mc 2
E 2  p 2c2  m2c 4
cc == 33..0000 xx 1100888 m
m//ss
hh == 66..6633 xx 1100---333444 JJ ss
KEmax  hf  
max T  0.2989  10 2 m  K
-19
11 eeV
V == 11..66 xx 1100--1199 JJ