Name: _______________________________________________________________________
Exam #3
Physics I
Fall 2005
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
_____ 6
_____ 7
_____ 8
M/R 8-10 (Bedrosian)
M/R 10-12 (Wetzel)
M/R 12-2 (Wetzel)
M/R 12-2 (Bedrosian)
M/R 2-4 (Schroeder)
T/F 10-12 (Washington)
T/F 12-2 (Yamaguchi)
T/F 2-4 (Yamaguchi)
Questions
A-1
Value
16
A-2
12
B
24
C-1
28
C-2
20
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 (Parts B and C), show all work to receive credit.
Part A1 – Multiple Choice – 16 Points Total (4 at 4 Points Each)
Write your choice(s) on the line to the left of the question number.
_______1.
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
_______2.
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
______ 3.
A)
B)
C)
D)
The figure below shows an electron moving in the +X direction in a region where
the electric field (E) points in the –Z direction (into the page).
What is the direction of the electric force on the electron?
electron
v
E into page
Y
(+Z out of page)
X
The figure below shows an electron moving in the +X direction in a region where
the magnetic field (B) points in the –Z direction (into the page).
What is the direction of the magnetic force on the electron?
electron
v
B into page
Y
(+Z out of page)
X
Two electrons, A and B, are moving in respective circles in the X,Y plane in a
region where the magnetic field is in the +Z direction, as shown below. The
magnetic force is the only force. Which electron takes longer to make one complete
circle?
Electron A.
Electron B.
Both take the same time.
Not enough information was given to determine which one.
2
B
A
Name: _______________________________________________________________________
_______4.
The figure below shows electric equipotential lines in a certain region of 2D
space. The electric potentials in the figure below are in units of volts.
What is the direction of the electric field in this region?
A)
B)
C)
D)
E)
–X
+X
–Y
+Y
Cannot be determined.
Y
X
V=0
X = 0 cm
V = 50
X = 2 cm
V = 100
X = 4 cm
Part A2 – Basic Quantities – 12 Points Total (6 at 2 Points Each)
Questions 5-10 refer to the named quantities listed below. For each quantity, indicate in the
spaces provided whether it is a scalar (write “scalar” or “S”) or vector (write “vector” or “V”)
and indicate correct SI units for the quantity. For example:
Velocity
___Vector____
___m/s____
Quantity
_Vector/Scalar_
_SI Units___
5. Electric Force
______________
____________
6. Electric Charge
______________
____________
7. Electric Field
______________
____________
8. Electric Potential
______________
____________
9. Electric Potential Energy ______________
____________
10. Magnetic Field*
____________
______________
The quantity we have learned as the “magnetic field” is actually the “magnetic flux density” as it is known in
electromagnetic theory. Please answer this question based on the magnetic quantity used in the equations on the
formula sheet, the activities we did in class, and the textbook. We included this footnote just to be precise.
*
3
Name: _______________________________________________________________________
B – Graphing (24 Points)
An electron is traveling through a region of space where a static (constant in time) electric force
is the only force acting on the electron. The graph of the electron’s kinetic energy (KE) is shown
below as it travels from d = 0 cm to d = 100 cm. Note that the electron has the same KE at d = 0
as it does at d = 100 cm. Calculate and plot graphs of the electron’s potential energy (PE) and
the electric potential as functions of position along the electron’s path. Assume both PE and
electric potential start at zero at d = 0. Be sure to include:
1. Shape of the curve(s).
2. Minimum and maximum points.
3. Clearly labeled axes.
Electron
KE (J)
6.4 x 10-17
3.2 x 10-17
0
d (cm)
20
40
60
80
100
Electron
PE (J)
0
d (cm)
20
40
60
80
100
Potential (V)
0
d (cm)
20
40
60
80
4
100
Name: _______________________________________________________________________
Problem C-1: Electric Field and Electric Potential (28 Points)
Six point charges, four positive = +1.0 C and two negative = –1.0 C, are located at the vertices
of a regular hexagon with sides of 1.0 cm as shown in the figure below. 1.0 C = 1.0 × 10–6 C.
Note that the triangles shown as dashed lines are all equilateral triangles with a common vertex
at the center of the hexagon.
Find the total electric field and electric potential at the center of the hexagon due to the six
charges at the vertices. Assume the electric potential at infinity is zero.
+1 C
1 cm
+1 C
+1 C
Y
X
-1 C
-1 C
+1 C
Electric Field X Component: _______________________________________________ units _________
Electric Field Y Component: _______________________________________________ units _________
Electric Potential:
_______________________________________________ units _________
5
Name: _______________________________________________________________________
Problem C-2: e/m Experiment (20 Points)*
C-2-A (12 points): In the e/m experiment we did in class, the electrons were accelerated in the
electron gun from rest at an initial electric potential of –250 V to a final electric potential of 0 V.
What was the final speed of the electrons leaving the electron gun?
Electron speed: ________________________________________________ units _________
C-2-B (8 points): After leaving the electron gun, the electrons moved in a circle with radius =
5.0 cm. What was the magnitude of the magnetic field produced by the coils?
Magnetic Field (Magnitude): ______________________________________________ units _________
*
Note: You may not use the equation
e
2V
 2 2 for this problem unless you derive it.
m r B
6
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  12 ( 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
6.
v 2  v 02  2a x  x 0 
 

 F  Fnet  m a
7.
T
8.
a centripetal 
5.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2r
v
v2
 2 r
r
a radial  a centripetal


p  mv

 
dp
F

F


net
dt



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
38.
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
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.
7
v 2,f 
2 m1
m  m1
v1,i  2
v 2 ,i
m1  m 2
m1  m 2

Formula Sheet for Homework and Exams – Page 2 of 2
46a.
46b.
47a.
47b.
48a.
48b.
49.

m m
| F | G 1 2 2
r

m m
F  G 1 2 2 r̂
r

1 | q1 || q 2 |
| F |
4  0
r2

1 q1 q 2
F
(r̂ )
4  0 r 2

1 | qi |
| Ei |
4   0 ri 2

1 qi
E
(r̂i )
4   0 ri 2


F  qE
50.
51.
52.
1 qi
4   0 ri
U  qV
 
V    E  dx
V
V
x
V
53y. E y  
y
V
53z. E z  
z

 
54. F  q v  B
mv
55. r 
qB
53x. E x  
Useful Constants
(You can use the approximate values on exams.)
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
8