Name _______________________________________________________________________
Exam #3
Physics I
Fall 2004
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
_____ 5
_____ 6
_____ 7
_____ 8
_____ 10
M/R 8-10 (Bedrosian)
M/R 10-12 (Wetzel)
M/R 12-2 (Wetzel)
T/F 10-12 (Bedrosian)
T/F 12-2 (Cummings)
T/F 2-4 (Cummings)
M/R 2-4 (Schroeder)
M/R 12-2 (Bedrosian)
Questions
Part A
Value
24
B-1
16
B-2
16
C-1
20
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 – 24 Points Total (6 at 4 Points Each)
Write your choice(s) on the line to the left of the question number.
______ 1.
A.
B.
C.
D.
According to Newton’s Theory of Gravity…
(Select all that are true according to Newton’s Theory or put “0” for none.)
The earth exerts a greater gravitational force (magnitude) on the moon than the
moon exerts on the earth.
During a total lunar eclipse, the earth blocks the sun’s gravitational force from
reaching the moon.
Objects inside a spacecraft orbiting the earth have no gravity acting on them.
Gravitational force can only be created by stars, planets, and/or moons.
The figure below shows electric field lines in a region of space. Points A and B are empty space.
Point Q is a point charge of Q coulombs. No other charges exist in the region shown.
Questions 2 and 3 below refer to this figure.
B
A
Q
______ 2.
A.
B.
C.
D.
______ 3.
A.
B.
C.
D.
VA is the electric potential at point A and VB is the electric potential at point B.
Which statement below is true about VA and VB?
VA > VB.
VA = VB.
VA < VB.
There is not enough information to decide among choices A-C above.
Which statement below is true about charge Q?
Q > 0.
Q = 0.
Q < 0.
There is not enough information to decide among choices A-C above.
2
Name _______________________________________________________________________
The figure below shows two point charges and the line connecting them. Regions A-C refer to
points on this line not including the point charges and not including infinity.
Questions 4 and 5 below refer to this figure.
Region A
Region B
+3 nC
______ 4.
A.
B.
C.
______ 5.
A.
B.
C.
______ 6.
Region C
-5 nC
Which region(s) contain a point or points where the total electric field due to the
two charges equals zero? Select all that apply or put “0” for none.
Region A.
Region B.
Region C.
Define the electric potential to be zero at infinity. Which region(s) contain a point
or points where the total electric potential due to the two charges equals zero?
Select all that apply or put “0” for none.
Region A.
Region B.
Region C.
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?
B
A
A.
B.
C.
D.
E.
The mass of A > the mass of B.
The speed of A > the speed of B.
The momentum (magnitude) of A > the momentum (magnitude) of B.
The kinetic energy of A > the kinetic energy of B.
There is not enough information to conclude any of A-D above.
3
Name _______________________________________________________________________
B-1 – Graphing – 16 Points
An electron has an initial kinetic energy, K = 1.6 x 10–17 J at location x = 0. It travels in the +X
direction in a region where the electric potential is given in the graph below. The electric force
is the only force on the electron in this region. Plot the potential energy (U) and kinetic energy
(K) of the electron. If you think the electron stops (momentarily) at some point before 100 cm,
show that on the graphs and stop plotting at that point. If not, continue the graphs to x = 100 cm.
Potential (V)
200
100
0
-100
x (cm)
20
40
60
80
100
-200
U (J)
0
x (cm)
20
40
60
80
100
K (J)
0
x (cm)
20
40
60
80
100
4
Name _______________________________________________________________________
B-2 – Graphing – 16 Points
Part I (4 Points) –
A proton is accelerated from rest beginning at electric potential = 30,000 V and finishing at 0 V.
Show that the final speed of the proton is 2.4 x 10+6 m/s (to two significant digits).
Part II (12 Points) –
After reaching its final speed, the proton in Part I enters a region with a uniform magnetic field
B = 0.5 T in the +Z direction (out of the page) and electric field E = 0. The magnetic field
outside the region is zero. The size of the region in the (X,Y) plane is 10 cm by 10 cm. The
proton enters at the point shown with velocity in the +X direction (to the right). Plot the path of
the proton from the point of entry into the region to the point of exit from the region. Indicate
the speed of the proton at the point where it exits the region of uniform magnetic field.
10 cm
B = 0.5 T +Z direction (out of page)
Y
proton enters
here
X
5
10 cm
Name _______________________________________________________________________
Problem C-1 (20 Points)
The two point charges shown below are located on the X axis, 1.00 meters from each other. No
other charges exist in this problem. Find one point on the X axis, not at infinity, where the total
electric field is zero. Find one point on the X axis, not at infinity, where the total electric
potential is zero. Define the electric potential to be zero at infinity.
If you think either the electric field or electric potential is zero at more than one point, pick one.
If you think the electric field or electric potential cannot be zero except at infinity, explain why.
x=0
x=1m
+25 C
-16 C
X
Electric field = 0 at
x = _______________________________________ meters.
Electric potential = 0 at
x = _______________________________________ meters.
6
Name _______________________________________________________________________
Problem C-2 (24 Points)
A –1.0 x 10–9 C point charge and a +1.0 x 10–9 C point charge are located as shown in the figure
below. They are the only electric charges in the problem. Find the following quantities at point
A marked with the “X” at the vertex of the triangle: Electric field X component, electric field Y
component, and electric potential. Assume the electric potential = 0 at infinity.
Y
X
point A
0.50 m
-1 nC
0.50 m
0.50 m
+1 nC
Electric Field X Component = _______________________________________ units ________
Electric Field Y Component = _______________________________________ units ________
Electric Potential
= _______________________________________ units ________
7
Name _______________________________________________________________________
Formula Sheet for Homework and Exams – Page 1 of 2
1.
v  v 0  a t  t 0 
21.
2.
x  x 0  v 0 ( t  t 0 )  12 a ( t  t 0 ) 2
K  12 m v 2  12 m (v x  v y )
22.
3.
x  x 0  12 ( v0  v)( t  t 0 )
23.
K f  K i  Wnet


U    Fcons  dx
4.
x  x 0  v( t  t 0 )  12 a ( t  t 0 ) 2
24.
U g  m g (y  y 0 )
25.
U s  12 k ( x  x 0 ) 2
26.
27.
28.
 K   U  Wnoncons
s  r
v tangential   r
a tangential   r
2
2
6.
v 2  v 02  2a x  x 0 
 

 F  Fnet  m a
7.
T
8.
a centripetal 
29.
30.
  0  t  t 0 
Fcentripetal


p  mv

 
dp
 F  Fnet  d t



J   Fnet dt   p


P   pi


dP
  Fext
dt
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
M   mi
38.
5.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2r
v
v2
 2 r
r
v2
m
 m 2 r
r
35.
 2  02  2   0 
   
a  b  a b sin( )
36.
I   m i ri
34.
37.
39.
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
 
W  Fd
 
W   F  dx
40.
41.
42.
43.
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
m1  m 2
2 m2
v1,i 
v 2 ,i
m1  m 2
m1  m 2
2 m1
m  m1

v1,i  2
v 2 ,i
m1  m 2
m1  m 2
45a. v1,f 
45b. v 2,f
8
2
K rot  12 I  2
 
W     d
  
  r F

 dL

  I  d t
  
l  r p


L  l i


L  I
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