Name _______________________________________________________________________
Final Exam
Physics I
Spring 2007
If you took all three unit exams, this Final Exam is optional. It may bring your grade up, but it
may also bring your grade down. If this exam is optional for you, you may decide at any time
before you hand it in that you do not want it graded.
If you do NOT want this graded, check here and sign your name __
________________________________________________________
If you would like to get credit for having taken this exam, we need
your name (printed clearly) at the top of every page,
and section number below.
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
80
B-1
20
B-2
20
B-3
20
C-1
20
C-2
20
C-3
20
Total
200
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.
IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas
given with the exam and standard math (trigonometry, algebra, etc.). If you want to use a
formula not on the list, you must derive it using the formulas on the list and standard math.
Part A-1 – 80 Points Total (20 at 4 Points Each)
IMPORTANT: There is only ONE correct answer for each question in Part A.
Questions 1-3 refer to the following situation: Two cars, A and B, have a drag race in the X
direction. Both cars experience the same net force as a function of time as shown in the graph
below. Both start from rest at t = 0. The mass of car A is greater than the mass of car B.
F (N)
Fmax
t (sec)
0
0
______ 1.
A.
B.
C.
______ 2.
A.
B.
C.
______ 3.
A.
B.
C.
10
20
Which car has greater speed at t = 20 seconds?
Car A.
Car B.
Both have the same speed at t = 20 seconds.
Which car has greater magnitude of momentum at t = 20 seconds?
Car A.
Car B.
Both have the same magnitude of momentum at t = 20 seconds.
Which car has greater kinetic energy at t = 20 seconds?
Car A.
Car B.
Both have the same kinetic energy at t = 20 seconds.
2
Name _______________________________________________________________________
Questions 4-7 refer to the following situation: Two particles A and B, with masses mA and mB
respectively, have initial velocities that take them into a region in which they interact, as shown
by the dotted square. After the interaction, they emerge from the region with different final
velocities. Assume that the particles exert forces on each other only within the dotted square.
The system consists of particles A and B. Assume that mA > mB.
initial
mA
Y
X
mB
Y
mA
X
mB
interaction
final
Y
mA
X
mB
3
Name _______________________________________________________________________
______ 4.
A.
B.
C.
D.
______ 5.
A.
B.
C.
D.
______ 6.
A.
B.
C.
D.
______ 7.
A.
B.
C.
D.
*
What condition is necessary and sufficient* for the linear momentum of the system
to be conserved?
The net external force is zero.
Only conservative external forces act on the system.
The interaction forces between the two particles are conservative forces.
The objects remain separate during the interaction and do not stick together.
Assume that no external forces act on the system. Which statement below can be
correctly concluded about the magnitude of impulse on particle A, JA, compared to
the magnitude of impulse on particle B, JB, during the interaction?
JA > JB
JA < JB
JA = JB
There is insufficient information to determine the correct relationship.
Assume that the linear momentum of the system is conserved. What condition
below is necessary for the interaction to be considered an elastic collision?
The collision is one-dimensional.
Only conservative external forces act on the system.
The initial kinetic energy of the system equals the final kinetic energy of the system.
The center of mass of the system does not move.
Assume the center of mass of the system moves with a constant velocity. Which
statement below is a correct conclusion about the system?
The linear momentum of the system is conserved.
Only conservative external forces act on the system.
The interaction force between the particles is zero.
The interaction of the particles is an elastic collision.
"Necessary" means if the condition is not true, momentum is never conserved.
"Sufficient" means if the condition is true, momentum is always conserved.
4
Name _______________________________________________________________________
For questions 8 and 9, consider angles in the range [0°,180°].

Consider an object at a specific instant of time that is moving with velocity v1 and

acceleration a 1 . At this instant, it is slowing down. What can one correctly


conclude about the angle between v1 and a 1 ?


A. The angle between v1 and a 1 is greater than 90°.


B. The angle between v1 and a 1 is equal to 90°.


C. The angle between v1 and a 1 is less than 90°.
______ 8.
D. There is not enough information to conclude any of A-C above.
______ 9.
A.
B.
C.
D.
Consider an object at another specific instant of time that is moving with velocity


v 2 and acceleration a 2 . At this instant (not the same as question 8 above), it is
moving at a constant speed and changing direction. What can one correctly


conclude about the angle between v 2 and a 2 ?


The angle between v 2 and a 2 is greater than 90°.


The angle between v 2 and a 2 is equal to 90°.


The angle between v 2 and a 2 is less than 90°.
There is not enough information to conclude any of A-C above.
_______10. The net force acting on the object in Question 8 is doing
A. Positive work.
B. Negative work.
C. Zero work.
_______11. The net force acting on the object in Question 9 is doing
A. Positive work.
B. Negative work.
C. Zero work.
5
Name _______________________________________________________________________
_______12. The figure below shows an electron at an instant of time 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?
A.
B.
C.
D.
E.
F.
+X.
–X.
+Y.
–Y.
+Z.
–Z.
electron
v
E
Y
(Z out of page)
X
_______13. The figure below shows an electron at an instant of time 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?
A.
B.
C.
D.
E.
F.
+X.
–X.
+Y.
–Y.
+Z.
–Z.
electron
v
B
Y
(Z out of page)
X
_______14. 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 are no other forces acting on A and B.
We know that both particles have charge +e.
However, we do not know the mass of either particle.
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 linear momentum of A >
the magnitude of linear momentum of B.
D. The kinetic energy of A >
the kinetic energy of B.
6
B
A
Name _______________________________________________________________________
Questions 15-20 refer to the figure shown below and the directions given as A-I. At the instant
shown, the fan is rotating at –2 rad/s (clockwise as seen from the front). It is slowing down with
a constant angular acceleration of +4 rad/s2.
The questions refer to directions of six vector quantities at the instant shown in the figure.
Take the center of rotation as the origin of the coordinate system.
A) .
B) .
C) .
D) .
E) .
F) .
G) Out of the page.
H) Into the page.
I) Direction is undefined because the quantity is zero or insufficient information was given.

_______15. What is the direction of the angular velocity vector ( ) of the fan?

_______16. What is the direction of the angular momentum vector ( L ) of the fan?

_______17. What is the direction of the angular acceleration vector (  ) of the fan?

_______18. What is the direction of the net torque vector (  ) acting on the fan?

_______19. What is the direction of linear velocity ( v ) at point X on the tip of the fan blade?
Note: “Linear” velocity is motion measured in m/s.

_______20. What is the direction of linear acceleration ( a ) at point X on the tip of the fan


blade? Note: “Linear” acceleration is the acceleration we refer to in “ Fnet  m a ”.
7
Name _______________________________________________________________________
Part B – Graphing – 60 Points Total (3 at 20 Points Each)
IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas
attached to the exam and standard math (trigonometry, algebra, etc.). If you want to use a
formula not on the list, you must derive it using the formulas on the list and standard math.
Show all work on Parts B and C, particularly what formulas and/or principles you used.
B-1 – One-Dimensional Motion (20 Points)
An object moves in one dimension (x) according to the velocity graph shown below. It begins at
x = 0 at t = 0. Plot displacement (x) and acceleration (a) versus time for the object.
Make sure to show the following features.
1. Shapes of the curves.
2. Maximum/minimum points.
x (m)
t (sec)
0
2
4
6
v (m/s)
+2
t (sec)
0
2
4
6
-2
a (m/s2)
t (sec)
0
2
4
6
8
Name _______________________________________________________________________
B-2 – Mass on a Spring (20 Points)
A mass on a vertical spring begins its motion at rest at y = 0 cm. It reaches a maximum height
of y = 10 cm. The two forces acting on the mass are gravity and the spring force. The graph of
the total potential energy (PE) of the system versus position is given below.
Graph the kinetic energy of the mass and the total (net) force on the mass versus y.
Be sure to include:
1. Shape of the curve(s).
2. Minimum and maximum points.
3. Clearly labeled scales on the axes.
Show all work, including what equations and/or principles of physics you are using.
PE (J)
2
1
y (cm)
0
-1
5
10
-2
KE (J)
y (cm)
0
5
10
0
Net Force (N)
0
y (cm)
5
10
9
Name _______________________________________________________________________
B-3 – Helium Nucleus in Electric and Magnetic Fields (20 Points)
In the figure below, Regions A and B are squares with side lengths = 10.0 cm.
A helium nucleus (charge = +2e and mass = 6.64  10–27 kg) enters into Region A at the tip of
the arrow as shown, halfway along a side, with a velocity of 7.00  10+5 m/s in the +X direction.
There is a uniform electric field of 1.00  10+5 N/C in the +X direction and no magnetic field in
Region A. In Region B, the electric field is zero and the magnetic field is uniform with the value
0.500 T in the –Z direction (into the page).
Plot the path of the helium nucleus as it travels through region A, then into region B, through
region B, and finally exiting region B.
Show all work. Your plot should clearly show the shape of the path through each region
(straight line, parabola, circle, etc.) and exactly where the particle exits each region.
Y
X
10 cm
10 cm
10 cm
Region A
Region B
10
Name _______________________________________________________________________
Part C – Problems – Three Problems – 60 Points Total
IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas
attached to the exam and standard math (trigonometry, algebra, etc.). If you want to use a
formula not on the list, you must derive it using the formulas on the list and standard math.
Show all work on Parts B and C, particularly what formulas and/or principles you used.
C-1 – The Pirate Ship in a Harbor (20 Points)
A pirate ship in a harbor at sea level fired its cannon and hit the top of a hill 310 meters above
sea level. The cannon ball was in the air for 10.0 seconds. The elevation angle of the cannon
was 30° above horizontal. What was the horizontal distance from the pirate ship to the top of the
hill (distance d as shown in the figure below)? Use g = 9.8 m/s2 and ignore air resistance.
h = 310 m
 = 30°
d=?
Horizontal Distance to Top of Hill: _________________________ units _______
11
Name _______________________________________________________________________
C-2 – Calculating Torque (20 Points)
A particle at location (3.0,4.0) m is moving in the +X direction at 2.0 m/s at the instant shown.
Gravity is the only force acting on the particle (in the –Y direction). Use g = 9.8 m/s2.
The +Y direction is “up.” The +Z direction is out of the page and the particle is at Z = 0.
Find the X, Y, and Z components of the torque acting on the particle about the origin at the
instant shown.
0.5 kg
+2 m/s
Y
(3,4) m
X
Torque X Component: _________________________________________________ units _________
Torque Y Component: _________________________________________________ units _________
Torque Z Component: _________________________________________________ units _________
12
Name _______________________________________________________________________
C-3 – Electric Field and Electric Potential (20 Points)
Find the electric field and electric potential at the origin of the (X,Y) coordinate system due to
the three point charges as shown in the figure below. ("X marks the spot.") The point charges
are located at the corners of a square 0.10 m on a side. The origin is the lower left corner.
Note: 1.0 nC = 1.0 × 10–9 C.
Assume that the electric potential is defined to be zero at infinity.
-1.0 nC
+4.0 nC
0.10 m
0.10 m
0.10 m
Y
X
0.10 m
-1.0 nC
Electric Field X Component:
_________________________________ units ________
Electric Field Y Component:
_________________________________ units ________
Electric Potential:
_________________________________ units ________
13
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.
14
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
15