Name ________________________________________________________________________
Final Exam
Physics I
Spring 2004
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 and section number below.
Section #
_____ 1
_____ 2
_____ 3
_____ 4
_____ 5
_____ 6
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Schowalter)
M/R 10-12 (Schowalter)
M/R 10-12 (Stoler)
M/R 12-2 (Bedrosian)
M/R 2-4 (Bedrosian)
M/R 2-4 (Schroeder)
M/R 4-6 (Bedrosian)
T/F 10-12 (Adams)
T/F 10-12 (Washington)
T/F 12-2 (Wilke)
T/F 2-4 (Wilke)
M/R 12-2 (Stoler)
T/F 12-2 (Adams)
Questions
Part A-1
Value
48
Part A-2
48
B-1
20
B-2
16
B-3
16
C-1
24
C-2
16
C-3
12
Total
200
Score
Cheating on this exam will result in an F in the course.
Sharing information about this exam with people who have not yet
taken it is cheating on the exam for both parties involved.
*** Taking this exam out of the room with you is cheating. ***
The Formula Sheets are the last two pages. Detach carefully for easier reference if you wish.
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-1 – Warm-Ups – 48 Points Total (12 at 4 Points Each)
For questions 1-4, please refer to the figure below. Two objects, A and B, start at rest and are
acted upon by the same net force, F, directed toward the right. The mass of object A is less than
the mass of object B. The finish line is distance d from the start line.
start
finish
object A
F
object B
d
_______1.
A)
B)
C)
D)
Object A.
Object B.
Both reach the finish line at the same time.
There is not enough information to decide which one.
_______2.
A)
B)
C)
D)
Which object reaches the finish line with greater magnitude of momentum?
Object A.
Object B.
Both have the same magnitude of momentum when reaching the finish line.
There is not enough information to decide which one.
_______4.
A)
B)
C)
D)
Which object reaches the finish line with greater speed?
Object A.
Object B.
Both have the same speed when reaching the finish line.
There is not enough information to decide which one.
_______3.
A)
B)
C)
D)
Which object reaches the finish line first?
Which object reaches the finish line with greater kinetic energy?
Object A.
Object B.
Both have the same kinetic energy when reaching the finish line.
There is not enough information to decide which one.
2
Name ________________________________________________________________________
For questions 5-7, please refer to the figure below. An asteroid in space initially at rest explodes
into two pieces, A and B, which then move in opposite directions. Piece A has less mass than
piece B. Ignore all external forces.
Piece A
_______5.
A)
B)
C)
D)
Which piece has greater magnitude of momentum after the explosion?
Piece A.
Piece B.
Both have the same magnitude of momentum after the explosion.
There is not enough information to decide which one.
_______7.
A)
B)
C)
D)
Which piece has greater speed after the explosion?
Piece A.
Piece B.
Both have the same speed after the explosion.
There is not enough information to decide which one.
_______6.
A)
B)
C)
D)
Piece B
Which piece has greater kinetic energy after the explosion?
Piece A.
Piece B.
Both have the same kinetic energy after the explosion.
There is not enough information to decide which one.
Question 8 has nothing to do with the asteroid explosion shown above.
_______8.
A)
B)
C)
D)
An object might move from Point A to Point B along Path 1 or Path 2 depending on
its initial velocity at Point A. The object is acted upon by a conservative force,
which we will call F, as the object moves from Point A to Point B. Which
statement below is a correct conclusion based on the principles of physics?
The kinetic energy of the object increases from Point A to Point B.
Potential energy at Point A is equal to potential energy at Point B.
F does the same amount of work on Path 1 and Path 2.
F acts at a right angle to both Path 1 and Path 2.
Path 2
A
B
Path 1
3
Name ________________________________________________________________________
_______9.
A)
B)
C)
D)
E)
F)
What is the direction of the angular momentum of the particle shown in the figure
below? (r indicates the displacement from the origin. v is the particle’s velocity.)
To the right on the page.
To the left on the page.
Up on the page.
Down on the page.
Into the page.
Out of the page.
r
v
_______10. An electron moves with a velocity that is directed to the right on the page in a
region where there is an electric field. The electric force on the electron is directed
up on the page as shown below. What is the direction of the electric field?
A)
B)
C)
D)
E)
F)
To the right on the page.
To the left on the page.
Up on the page.
Down on the page.
Into the page.
Out of the page.
F
v
_______11. An electron moves with a velocity that is directed to the right on the page in a
region where there is a magnetic field. The magnetic force on the electron is
directed up on the page as shown below. What is the direction of the magnetic field
out of the choices below?
A)
B)
C)
D)
E)
F)
To the right on the page.
To the left on the page.
Up on the page.
Down on the page.
Into the page.
Out of the page.
F
v
_______12. An electron traveling in interplanetary space spirals around a magnetic field line
coming from the geomagnetic south pole of the earth. As the electron moves closer
to the top of the atmosphere, the work done by the magnetic force on the electron is
A) positive.
B) negative.
C) zero.
4
Name ________________________________________________________________________
Part A-2 – Equation Matching – 48 Points Total (24 at 2 Points Each)
For each description of a situation or principle of physics given below, match the equation
number from the equation sheet that best describes or exemplifies the situation or principle.
For equations that have two parts (like 46a and 46b), just give the number.
No equation number is the correct answer for more than one question.
______ 1
When acceleration is constant, the graph of velocity versus time is a straight line.
______ 2
Newton’s Second Law for linear motion (first form).
______ 3
Newton’s Second Law for linear motion (second form).
______ 4
The Impulse-Momentum Theorem
______ 5
The definition of the linear momentum of a system.
______ 6
Momentum of a system is conserved (or not) depending on external forces.
______ 7
In a system where momentum is conserved, the center of mass moves at a constant
velocity.
______ 8
Conservation of momentum in a two-dimensional collision.
______ 9
The definition of work done by an arbitrary force.
______ 10
Work done by a constant force.
______ 11
The Work-Kinetic Energy Theorem
______ 12
Mechanical energy is conserved (or not) depending on work done by nonconservative forces, if any.
______ 13
A one-dimensional elastic collision.
______ 14
The definition of torque.
______ 15
The definition of angular momentum of a particle.
______ 16
The definition of rotational inertia for a collection of particles.
______ 17
The angular momentum of a rotating body.
______ 18
Newton’s Second Law for rotation.
______ 19
Newton’s Universal Law of Gravitation
______ 20
Coulomb’s Law
______ 21
The electric field created by a set of point charges.
______ 22
The electric potential created by a set of point charges.
______ 23
The magnetic force on a moving charged particle.
______ 24
A charged particle is moving in a circle at a constant speed in a magnetic field at a
right angle to the plane of the particle’s path.
5
Name ________________________________________________________________________
Part B – Graphing – 52 Points Total = 20 + 16 + 16
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.
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.
3. Values of x at t = 1.0, 3.0, 5.0 and 6.0 s.
4. Values of a at t = 0.5, 2.0, 4.0, and 5.5 s.
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
6
Name ________________________________________________________________________
B-2 Mass Connected to a Spring on a Frictionless Horizontal Table (16 Points)
x = 0 cm
v = 2 m/s
x = 10 cm
An object with mass 0.500 kg is connected to an ideal massless spring on a frictionless
horizontal table as shown above. It begins at the equilibrium position of the spring (x = 0) with a
velocity of 2.00 m/s in the +X direction. At its maximum displacement, it is at x = 0.100 m.
Plot P.E. (potential energy) and K.E. (kinetic energy) for the system. Include the following:
1. Shapes of the curves.
2. Minimum/maximum points.
3. Values at x = 0, 10 cm.
PE (J)
0
x (cm)
0
2
4
6
8
10
KE (J)
0
x (cm)
0
2
4
6
8
10
7
Name ________________________________________________________________________
B-3 Rotational Motion (16 Points)
A satellite in space rotates about its axis at an initial rotation speed of  = 4.0 rad/s at t = 0. As it
deploys its solar panels, it changes its rotational inertia as shown in the graph below. Ignore all
external forces for the purpose of this problem.
Graph the satellite’s rotation speed and magnitude of angular momentum as functions of time.
Include the following features:
1. Shapes of the curves.
2. Values at t = 0, 3, and 6 seconds.
I (kg m^2)
40
30
20
10
t (sec)
0
2
4
6
 (rad/s)
t (sec)
0
L (kg m^2/s)
2
4
6
t (sec)
0
0
2
4
6
8
Name ________________________________________________________________________
Part C – Problems – 52 Points Total = 24 + 16 + 12
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.
C-1 Plastic Ball Launcher for Physics I Demos (24 Points)
Two companies, Company A and Company B, sell plastic ball launchers for physics demos.
Both launchers cost the same and both are the same size. Both launch a plastic ball of 10 grams.
The two companies send us specifications of the net force on the ball during launch in graphical
form. The respective graphs are shown below and on the next page. Both launchers reach a
maximum force of 1.2 N and the graphs are composed of straight line segments.
We want to pick the launcher that gives the highest final speed to the ball, starting from rest.
Use principles of physics to show which one we should select. If you think both are the same
explain why. You can use this page and the next page for your calculations.
Important: If you attempt to use equations 1-5 to solve this problem, you will get 0 credit!
F (N)
1.2
1.0
0.8
0.6
0.4
0.2
0
t (s)
0
0.02
0.04
0.06
0.08
0.10
Company A Graph of Force versus Time
9
Name ________________________________________________________________________
F (N)
1.2
1.0
0.8
0.6
0.4
0.2
x (cm)
0
0
12
24
36
Company B Graph of Force versus Distance
Which Company to Pick: ___________________________________________
10
Name ________________________________________________________________________
C-2 Electric Field of Two Point Charges (16 Points)
Two point charges are located at the base corners of an equilateral triangle as shown below.
Find the X and Y components of the electric field created by the two charges at the top of the
triangle, marked with an “X” and labeled “Point A”.
Y
Point A
0.6 m
0.3 m
-9
–1.0 x 10 C
0.6 m
0.3 m
X
-9
+1.0 x 10 C
E field X Component: ____________________________ units ________
E field Y Component: ____________________________ units ________
11
Name ________________________________________________________________________
C-3 Kinetic Energy of an Electron in an Electric Field (12 Points)
Two point charges are located at the base corners of an equilateral triangle as shown below.
An electron moves from Point A, where its kinetic energy is 6.0 x 10–19 J, to Point B. The only
force on the electron is due to the electric field created by the charges at the base of the triangle.
The charges at the base of the triangle are fixed in place and do not move.
Find the kinetic energy of the electron at Point B.
Y
Point A
0.6 m
0.3 m
-9
–1.0 x 10 C
0.6 m
0.3 m
0.6 m
Point B
X
-9
+1.0 x 10 C
Kinetic Energy of the Electron at Point B: __________________________ units ______
12
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
13
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
14