Name _______________________________________________________________________
Exam #3
Physics I
Spring 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
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Bedrosian)
M/R 10-12 (Washington)
M/R 10-12 (Shannon)
M/R 12-2 (Bedrosian)
M/R 2-4 (Bedrosian)
M/R 4-6 (LaGraff)
T/F 10-12 (Yamaguchi)
T/F 10-12 (Wilke)
T/F 12-2 (Korniss)
T/F 2-4 (Wilke)
M/R 12-2 (Shannon)
T/F 12-2 (Yamaguchi)
Questions
Part A
Value
32
B-1
20
C-1
24
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 answer in the context of what we have learned in Physics I.
On graphing and numerical questions, show all work to receive credit.
Part A – Multiple Choice – 32 Points Total (8 at 4 Points Each)
_______1.
A)
B)
C)
D)
In comparison to the magnitude of the electric force of attraction between an
electron and a proton, the magnitude of the gravitational attraction between an
electron and a proton
is much smaller than the electric force of attraction.
is about the same as the electric force of attraction.
is much larger than the electric force of attraction.
could be larger or smaller depending on how far apart they are.
_______2.
The earth orbits the sun along an elliptical path with one focal point at the center of
the sun. When the earth is at its closest point to the sun along its path, the
gravitational potential energy of the sun-earth system
A) is at its minimum.
B) is at its maximum.
C) has the same constant value it keeps for the entire orbit.
_______3.
A)
B)
C)
D)
Particle A with charge +5 x 10–9 C exerts an electrostatic force on particle B with
charge –2 x 10–9 C one centimeter away. The magnitude of this force is FAB.
Particle B exerts an electrostatic force on particle A with magnitude FBA.
Which statement below is true?
FAB < FBA.
FAB > FBA.
FAB = FBA.
There is not enough information to decide A-C above.
_______4.
Electric equipotential lines in a certain region of space are shown in the figure
below, along with their respective values. What is the direction of the electric field
in this region of space?
A) .
E) .
B) .
F) .
C) .
G) .
D) .
H) .
V = 10
V=5
V=0
2
Name _______________________________________________________________________
_______5.
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
_______6.
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
_______7.
The figure below shows an electron moving in the +X direction in a region where
the electric field (E) points in the +Y direction.
What is the direction of the electric force on the electron?
electron
v
E
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 +Y direction.
What is the direction of the magnetic force on the electron?
electron
v
B
Y
(Z out of page)
X
The figure below shows the respective paths taken by two particles, A and B, in a
region containing a constant, uniform magnetic field directed into the plane of
motion (into the page). There is no electric field. Both particles have charge +e.
What can we correctly conclude about particles A and B?
A) The mass of A > the mass of B.
B) The speed of A > the speed of B.
C) The magnitude of momentum of A >
B
the magnitude of momentum of B.
A
D) The kinetic energy of A >
the kinetic energy of B.
E) There is not enough information to conclude any of A-D above.
_______8.
A)
B)
C)
D)
Select the correct statement(s) about the magnetic force on a moving charged
particle from the list below. Select all that are correct or put “0” if none are.
If the force is not zero, its direction is at a right angle to the particle’s velocity.
If the force is not zero, its direction is at a right angle to the magnetic field.
If the magnetic field and particle’s velocity are in the same direction, the force is zero.
The magnetic force cannot change the particle’s kinetic energy.
3
Name _______________________________________________________________________
B-1 – Graphing – 20 Points
An electron has an initial velocity of (1.0 x 10+6 i + 3.5 x 10+6 j) m/s at location (0,0) just above a
metal plate with an electric potential of 50 V. There is another metal plate 5.0 cm away in the
+Y direction with an electric potential of 0 V. Assume that the electric field is uniform and
static, meaning it is constant in space and time. Only the electric force acts on the electron.
(a)
Show that the electric field between the plates is (+1000 j N/C).
(b)
Plot the trajectory (path in X and Y space) of the electron from the initial position to the
point at which it hits either the upper or lower plate – you decide which one.
From your plot it should be clear what is the shape of the path, where it ends, and any minimum
or maximum points with their numerical values.
Hint: You do not need to solve a quadratic equation to solve this problem.
Upper Plate, V = 0
Y
X
5
4
3
2
1
0
0
2
4
6
8
10
12
14
Lower Plate, V = 50 Volts
4
16
18
20 cm
Name _______________________________________________________________________
Problem C-1 (24 Points)
Three particles are (separately) accelerated from rest beginning at potential V0 = 30,000 volts
and ending at potential 0 volts, where they enter a uniform magnetic field of 0.50 T directed into
the page as shown in the figure below. The particles initially are moving to the right on the page
and then follow the circular paths marked as A and B.
The three particles are a proton with charge +e and mass mp, a deuterium nucleus with charge +e
and mass 2 mp, and a helium nucleus with charge +2 e and mass 4 mp. Determine the radii of
paths A and B and determine which path each particle takes. Your calculations should show
clearly why there are only two distinct paths for the three particles.
A
B
magnetic field
into the page
Particles start here
A. Radius of Path A = ______________________________________________ units ________
B. Radius of Path B = ______________________________________________ units ________
C. Path that the proton takes (A or B):
_______
D. Path that the deuterium nucleus takes (A or B): _______
E. Path that the helium nucleus takes (A or B):
_______
5
Name _______________________________________________________________________
Problem C-2 (24 Points)
Four point charges, A, B, C, and D, are arranged at the corners of a square 0.6 m on a side as
shown in the figure below. Charges A, B, and C are +2.0 x 10–9 C and charge D (the one on the
lower left) is –2.0 x 10–9 C. 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.
A (-0.3,+0.3)
B (+0.3,+0.3)
Y
X
D (-0.3,-0.3)
C (+0.3,-0.3)
Electric Field X Component: ________________________________________ units ________
Electric Field Y Component: ________________________________________ units ________
Electric Potential:
________________________________________ units ________
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  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.
7
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
8