Name _______________________________________________________________________
Exam #3
Physics I
Spring 2006
If you would like to get credit for having taken this exam, we need
your name (printed clearly) at the top and section number below.
Your name should be at the top of every page.
Section #
_____ 1
_____ 2
_____ 3
_____ 4
_____ 5
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Bedrosian)
M/R 10-12 (Hayes)
M/R 10-12 (Eah)
M/R 12-2 (Bedrosian)
M/R 2-4 (Hayes)
M/R 4-6 (Hayes)
T/F 10-12 (Wilke)
T/F 10-12 (Washington)
T/F 12-2 (Yamaguchi)
T/F 2-4 (Wetzel)
M/R 12-2 (Eah)
T/F 12-2 (Wilke)
Questions
Part A
Value
48
Part B
28
Part C
24
Total
100
Score
You may not unstaple this exam.
Only work written on the same page as the question will be graded.
Cheating on this exam will result in an F in the course.
1
Name _______________________________________________________________________
On this exam, please neglect any relativistic and/or quantum mechanical effects. If you don’t
know what those are, don’t worry, we are neglecting them! On all multiple-choice questions,
choose the best answer in the context of what we have learned in Physics I.
On graphing and numerical questions, show all work to receive credit.
For each question, please assume we have given you enough information to answer it.
Part A – Multiple Choice – 48 Points Total (12 at 4 Points Each)
Write your choice on the line to the left of the question number.
Questions 1-3 refer to the figure below. Two electrons (A and B) are moving in circles in the
XY plane in a magnetic field. The +Z direction is out of the page. The magnetic force is the
only force in the problem and the electrons are far enough apart so they do not interact.
______ 1.
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
______ 2.
A)
B)
C)
D)
Y
X
B
A
Which electron has the greatest kinetic energy?
Electron A.
Electron B.
Both have the same kinetic energy.
There is not enough information to decide which one has the greatest kinetic energy.
______ 3.
A)
B)
C)
D)
What is the direction of the magnetic field?
Which electron takes the longest time to make one complete circle?
Electron A.
Electron B.
Both take the same amount of time.
There is not enough information to decide which one takes the longest time.
2
Name _______________________________________________________________________
Questions 4-8 refer to the figure below. Five electrons (A-E) are shown at a certain instant of
time in a region where the electric field is static and uniform (constant in time and space). All
electrons have the same initial speed v0 = 1.0 x 10+6 m/s. Equipotential lines are shown as dotted
lines for 0, 5, and 10 volts respectively – assume they extend indefinitely in the horizontal
direction. The electric force is the only force in the problem and all electrons are far enough
apart so they do not interact with each other.
0 volts
V0
V0
Y
D
X
E
V0
A
B
5 volts
C
V0
V0
10 volts
_______4.
A)
B)
C)
D)
What is the direction of the electric field?
+X.
–X.
+Y.
–Y.
______ 5.
Which electron(s) will reach the 0 volt potential line at some future time?
Put all that apply or “none” for none.
______ 6.
Of the electron(s) that reach the 0 volt potential line (if any), which one has the
greatest speed upon reaching that line?
Put the one electron with greatest speed, “none” for none, “same” for all the same.
______ 7.
Which electron(s) will reach the 10 volt potential line at some future time?
Put all that apply or “none” for none.
______ 8.
Of the electron(s) that reach the 10 volt potential line (if any), which one has the
greatest speed upon reaching that line?
Put the one electron with greatest speed, “none” for none, “same” for all the same.
3
Name _______________________________________________________________________
______ 9.
A)
B)
C)
D)
E)
F)
An electron is moving in the +Y direction in a region with a static magnetic field in
the –Z direction (into the page). What is the direction of the magnetic force?
Y
+X.
–X.
+Y.
–Y.
+Z.
–Z.
B
electron
X
______ 10. An electron is moving in the +Y direction in a region with a static electric field in
the –Z direction (into the page). What is the direction of the electric force?
A)
B)
C)
D)
E)
F)
Y
+X.
–X.
+Y.
–Y.
+Z.
–Z.
E
electron
X
Questions 11-12 refer to the figure below. Two point charges are located on a line (the X axis)
as shown. To answer the questions, pick the region or regions where the named quantity is zero
at a finite point on the line. Select all that apply. For example, if you think the quantity is zero
in regions A and C, you would put “A, C.” If you think the quantity is not zero at any finite
point on the line, put “none.” Assume that electric potential is zero at infinity.
Region A
x=0
Region B
+3e
x=1
Region C
-2e
______ 11. On which region(s) of the line, if any, is there a point where the electric field is
zero? Put all that apply or “none” if you think there are none.
______ 12. On which region(s) of the line, if any, is there a point where the electric potential is
zero? Put all that apply or “none” if you think there are none.
4
Name _______________________________________________________________________
Part B – Graphing – 28 Points (Two Pages)
An electron moves in one dimension, from x = 0.0 cm to x = 100.0 cm. The initial KE of the
electron at x = 0.0 cm is 1.6 x 10–17 J. The only force on the electron is the electric force.
Graph the X component of the force on the electron, the kinetic energy of the electron, the
potential energy of the electron, and the electric potential x = 0.0 cm to x = 100.0 cm.
Assume the potential energy and electric potential are zero at x = 0.0 cm.
Make sure your plots clearly show:
A. Any minimum or maximum points.
B. Whether each graph is curved or straight (could be in sections).
Ex (N/C)
x (cm)
0
40
80
100
-500
Fx (N)
0
x (cm)
40
80
5
100
Name _______________________________________________________________________
KE (J)
x (cm)
0
40
80
100
PE (J)
x (cm)
0
40
80
100
V (volts)
0
x (cm)
40
80
6
100
Name _______________________________________________________________________
Part C (24 Points)
A mass spectrometer detects an ion and it is your job to figure out what ion it is and show your
management your calculations to back up your findings. The mass spectrometer accelerates the
ion from rest from an initial electric potential +125.6 volts to a final electric potential of 0.0
volts. The magnetic field in the spectrometer is 0.0500 T and the radius is 0.125 m.
All ions have a charge of +e.
Important note: If you want to use a formula for q/m that is not on the formula sheet, you have to
derive it from formulas that are on the sheet.
Isotope
C12
C13
N14
N15
O16
F19
Mass (x 10–26 kg)
1.9926
2.1592
2.3252
2.4908
2.6560
3.1547
Which ion is it? ___________________________________________________
7
Name _______________________________________________________________________
Formula Sheet for Homework and Exams – Page 1 of 2


U    Fcons  dx
1.
v  v 0  a t  t 0 
23.
2.
x  x 0  v 0 ( t  t 0 )  12 a ( t  t 0 ) 2
24.
U g  m g (y  y 0 )
3.
x  x 0  ( v0  v)( t  t 0 )
25.
U s  12 k ( x  x 0 ) 2
4.
x  x 0  v( t  t 0 )  12 a ( t  t 0 ) 2
26.
27.
28.
 K   U  Wnoncons
s  r
v tangential   r
29.
a tangential   r
1
2
6.
v  v  2a x  x 0 
 

F
  Fnet  m a
7.
T
5.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2
2
0
2r
v
a centripetal 
2
v
 2 r
r
a radial  a centripetal


p  mv

 
dp
 F  Fnet  d t



J   Fnet dt   p


P   pi


dP
  Fext
dt
30.
  0  t  t 0 
31.
   0  0 ( t  t 0 )  12 ( t  t 0 ) 2
32.
   0  12 (0  )( t  t 0 )
33.
   0  ( t  t 0 )  12 ( t  t 0 ) 2
 2  02  2   0 
   
35a. a  b  a b sin( )
 
a  b  a y b z  a z b y î 
35b.
a z b x  a x b z  ĵ  a x b y  a y b x k̂
34.

36.
37.
M   mi
1
1
x cm   m i x i y cm   m i y i
M
M


P  M v cm
   
a  b  a b cos()  a x b x  a y b y  a z b z
 
W  Fd
 
W   F  dx
21.
K  12 m v 2  12 m (v x  v y )
22.
K f  K i  Wnet
2
38.
39.
40.
41.
42.
43.
2
I   m i ri


2
K rot  12 I  2
 
W     d
  
  r F

 dL

  I  d t
  
l  r p


L  l i


L  I
44x. m1 v1, x ,before  m 2 v 2, x ,before  m1 v1, x ,after  m 2 v 2, x ,after
44y. m1 v1, y ,before  m 2 v 2, y ,before  m1 v1, y ,after  m 2 v 2, y,after
44z. m1 v1,z ,before  m 2 v 2,z ,before  m1 v1,z ,after  m 2 v 2,z ,after
45a. v1,f 
m1  m 2
2 m2
v1,i 
v 2 ,i
m1  m 2
m1  m 2
45b.
8
v 2,f 
2 m1
m  m1
v1,i  2
v 2 ,i
m1  m 2
m1  m 2

Name _______________________________________________________________________
Formula Sheet for Homework and Exams – Page 2 of 2

m m
46a. | F |  G 1 2 2
r

m m
46b. F  G 1 2 2 r̂
r

1 | q1 || q 2 |
47a. | F | 
4  0
r2

1 q1 q 2
47b. F 
(r̂ )
4  0 r 2

1 | qi |
48a. | E i | 
4   0 ri 2

1 qi
(r̂i )
48b. E  
4   0 ri 2


49. F  q E
50.
51.
52.
1 qi
4   0 ri
U  qV
 
V    E  dx
V
V
x
V
53y. E y  
y

 
54. F  q v  B
mv
55. r 
qB
53x. E x  
Useful Constants
(You can use the approximate values on tests.)
Universal Gravitation Constant
G  6.67310 11 N m 2 kg 2  6.67 10 11
Electrostatic Force Constant
1
 8.987551788 10 9 N m 2 C  2  9.0 10 9
4  0
Magnetic Constant
 0  4  10 7 H m 1  1.26 10 6
Speed of Light in Vacuum
c  2.99792458 10 8 m s 1  3.010 8
Charge of a Proton
e  1.602176462 10 19 C  1.6 10 19
Electron-Volt Conversion Constant
1eV  1.602176462 10 19 J  1.6 10 19
Mass of a Proton
m p  1.6726215810 27 kg  1.67 10 27
Mass of an Electron
m e  9.10938188 10 31 kg  9.110 31
9