Name _______________________________________________________________________
Exam #3
Physics I
Spring 2007
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
_____ 4
_____ 5
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Bedrosian)
M/R 10-12 (Wilke)
M/R 12-2 (Yamaguchi)
M/R 2-4 (Yamaguchi)
M/R 4-6 (Wilke)
T/F 10-12 (Wetzel)
T/F 10-12 (Washington)
T/F 12-2 (Eah)
T/F 2-4 (Eah)
M/R 12-2 (Zhang)
M/R 2-4 (Bedrosian)
Questions
Part A
Value
24
Part B
28
Part C-1
24
Part C-2
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 answers 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 A – Multiple Choice – 24 Points Total (6 at 4 Points Each)
Please read the following description carefully. It applies to Questions A1-A6.
An electron begins the problem at Point A, time t = 0, moving with an initial
velocity (represented by the arrow) in the XY plane (Z = 0) as shown in the figure
below. The Z location, Z component of velocity, and Z component of acceleration
are all zero for the entire motion of the electron.
Y
+Z out of page
X
A
At t = t1, the electron has reached its maximum location in the Y direction at Point
C. The velocity of the electron at Point C is in the +X direction with zero Y
component. The path from Point A to Point C is shown by the dashed curve.
Y
+Z out of page
X
C
A
At t = t2, the electron has returned to its initial Y location at Point B. The path
from Point C to Point B is shown by the dashed curve.
Y
+Z out of page
X
C
A
B
2
Name _______________________________________________________________________
As you answer Questions A1-A6, please keep in mind that the figures on pages 2-4
were not drawn precisely to scale. You will find the correct answers using
principles of physics, not by trying to measure the drawings.
Write your choice on the line to the left of the question number.
______ 1.
A)
B)
C)
D)
E)
F)
An electron moves in the XY plane (Z = 0) from Point A to Point B on a curved
path as shown in the figure below. The only force on the electron is due to a
uniform electric field in one of the directions below.
The +Z direction is out of the page.
Y
What is the direction of the electric field?
X
+X
–X
+Y
–Y
+Z
–Z
C
A
B
______ 2.
What should be the shape of the curved path in Question 1 based on the information
given?
A)
B)
C)
D)
The curve should be a section of a parabola.
The curve should be a section of a circle.
The curve should be a section of a helix*.
There is insufficient information in Question 1 to determine what the shape of the
curve should be.
______ 3.
In Question 1, at what point on the electron's path is the electron's kinetic energy at
a minimum value, if anywhere?
A)
B)
C)
D)
E)
Point A
Point B
Point C
The electron's kinetic energy is the same at all points on the curve.
There is insufficient information to determine where the kinetic energy of the
electron is a minimum value, if anywhere.
*
A helix is a three-dimensional curve that looks like a corkscrew spiral. Since the electron's path is confined to the
two-dimensional XY plane (Z = 0), the shape of the curve could not possibly be a helix.
3
Name _______________________________________________________________________
Write your choice on the line to the left of the question number.
______ 4.
A)
B)
C)
D)
E)
F)
An electron moves in the XY plane (Z = 0) from Point A to Point B on a curved
path as shown in the figure below. The only force on the electron is due to a
uniform magnetic field in one of the directions below.
The +Z direction is out of the page.
Y
What is the direction of the magnetic field?
+X
–X
+Y
–Y
+Z
–Z
X
C
A
B
______ 5.
What should be the shape of the curved path in Question 4 based on the information
given?
A)
B)
C)
D)
The curve should be a section of a parabola.
The curve should be a section of a circle.
The curve should be a section of a helix.
There is insufficient information in Question 4 to determine what the shape of the
curve should be.
______ 6.
In Question 4, at what point on the electron's path is the electron's kinetic energy at
a minimum value, if anywhere?
A)
B)
C)
D)
E)
Point A
Point B
Point C
The electron's kinetic energy is the same at all points on the curve.
There is insufficient information to determine where the kinetic energy of the
electron is a minimum value, if anywhere.
4
Name _______________________________________________________________________
B – Graphing – 28 Points
A negative ion with charge = –1.6 × 10–19 C begins at x = 0 moving in the +X direction with
kinetic energy = 3.2 × 10–18 J. It moves through a region where the net force is due to an electric
field with an X component only. The electric field (Ex) is shown in the graph below.
Graph the force on the ion (Fx), the electric potential (V), the electric potential energy (U), and
the kinetic energy (K) of the ion as it moves from x = 0 cm to x = 100 cm.
The electric potential and electric potential energy start at zero at x = 0 cm.
Make sure your plots clearly show:
A. Any minimum or maximum points.
B. Whether the graph segments are curved or straight.
C. Values of all quantities at x = 0, 20, 40, 60, 80, and 100 cm.
D. The correct SI units.
Show all work, including what equations and/or principles of physics you are using.
Ex (V/m)
200
100
0
x (cm)
-100
20
40
60
80
100
-200
Fx (
)
0
x (cm)
20
40
60
80
Continued on the next page.
5
100
Name _______________________________________________________________________
B – Graphing – 28 Points (Continued)
V(
)
0
x (cm)
20
U(
40
60
80
100
)
0
x (cm)
20
K(
40
60
80
100
)
0
x (cm)
20
40
60
80
100
6
Name _______________________________________________________________________
Problem C-1 (24 Points) – e/m Experiment
In the e/m experiment that we did in class, electrons are accelerated by an electron gun from rest
to a final speed v through a potential difference V. Subsequently, the electrons move in a
uniform magnetic field B generated by Helmholtz coils. The velocity of the electrons is
perpendicular to the direction of the magnetic field. As a result of the magnetic force, electrons
move in circle of radius r.
Your friend is writing up his activity report for the e/m experiment, but he made a mistake in
class and forgot to write down the V that he set. You will help him answer two questions.
He wrote down the following information in his lab notebook:
B = 7.80 × 10–4 Tesla/Ampere × I from the Helmholtz coils
I = 1.20 Ampere
You can use the known values of the electron's charge and mass to answer these questions:
C-1-A: How long does it take for an electron to make one complete circle inside the e/m tube at
the value of the magnetic field set by your friend? (12 points)
C-1-B: What V (potential difference) should have been set to achieve the largest possible
circle, with radius = 0.0557 m? (Don't use this V to answer C-1-A.) (12 points)
7
Name _______________________________________________________________________
Problem C-2 (24 Points) – Electric Field and Potential
Four point charges are arranged at the corners of a square 0.6 m on a side as shown in the figure
below. Charge +q = +1.0 x 10–9 C is on the upper left corner. The other charges are integer
multiples of q as shown.. Assume the electric potential is zero at infinity.
Find the electric field (X and Y components) and electric potential at the center of the square.
Note: The center of the square is also the origin of the coordinate system.
(-0.3,+0.3)
+q
(+0.3,+0.3)
-2q
Y
X
-q
(-0.3,-0.3)
+2q
(+0.3,-0.3)
Electric Field X Component: ________________________________________ units ________
Electric Field Y Component: ________________________________________ units ________
Electric Potential:
________________________________________ units ________
8
Formula Sheet for Homework and Exams – Page 1 of 2


U    Fcons  dx
1.
v f  v 0  a t f  t 0 
23.
2.
x f  x 0  v 0 ( t f  t 0 )  12 a ( t f  t 0 ) 2
24.
U g  m g (y  y 0 )
3.
x f  x 0  ( v 0  v f )( t f  t 0 )
25.
U s  12 k ( x  x 0 ) 2
4.
x f  x 0  v f ( t  t 0 )  12 a ( t f  t 0 ) 2
26.
27.
28.
 K   U  Wnoncons
s  r
v tangential   r
29.
a tangential   r
5.
6.
1
2
v f  v 02  2ax f  x 0 
 

 F  Fnet  m a
2
7.
2r
T
v
8.
a centripetal 
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
v2
 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
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.
9
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  
N 1 N
56.
1 qi q j
ri j
ji 1 4   0
U config   
i 1
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
10