Name ________________________________________________________________________
Final Exam
Physics I
Spring 2003
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
_____ 14
_____ 5
_____ 7
_____ 10
_____ 11
_____ 15
_____ 12
M/R 8-10 (Washington)
M/R 10-12 (Schroeder)
M/R 10-12 (Zhang)
M/R 12-2 (Bedrosian)
M/R 12-2 (Adams)
M/R 2-4 (Hayes)
M/R 4-6 (Bedrosian)
T/F 10-12 (Wilke)
T/F 12-2 (Sperber)
T/F 12-2 (Adams)
T/F 2-4 (Wilke)
Questions
Part A
Value
28
B-1,2,3
18
B-4,5
16
B-6,7
16
B-8,9
18
B-10,11
16
B-12
14
C-1
16
C-2
16
C-3,4
8
C-5
16
C-6
18
Total
200
Score
If we catch you cheating on this exam,
you will be given 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.
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 numerical questions, show all work to receive credit.
Part A – Warm-Ups – 28 Points Total (7 at 4 Points Each)
Write your choice on the line to the left of the question number.
_______1.
Which of the following statements is not one of Newton’s Laws of Motion?
A) All objects fall with equal acceleration regardless of mass.
B) Objects at rest tend to stay at rest and objects moving with a constant velocity maintain that
velocity unless acted on by a force.
 

C)  F  Fnet  m a
D) For every action there is an equal and opposite reaction.
_______2.
A)
B)
C)
D)
E)
Your weight and the force of gravity pulling on the earth due to your mass.
Your weight and the normal force from the seat holding you up.
The weight of an airplane and the lift from its wings holding it up.
All of the above.
None of the above.
_______3.
A)
B)
C)
D)
A competitor in the Olympics springs off a diving board and attempts a triplesomersault dive. While she is in the air, neglecting air resistance, she cannot
change her
Angular velocity.
Angular momentum.
Rotational kinetic energy.
Rotational inertia.
_______4.
A)
B)
C)
D)
E)
F)
Which of the following are Newton’s Third Law Pairs?
A car is heading north at 100 km/hr when the driver steps on the brakes. While the
car is slowing down, what is the direction of the net torque on the wheels?
Up (Toward the Sky).
Down (Toward the Ground).
North.
South.
East.
West.
N
W
E
S
2
Name ________________________________________________________________________
_______5.
A)
B)
C)
D)
For this question, take right as the positive direction. A 0.25 kg rubber ball
traveling horizontally to the left at 12 m/s hits a wall and bounces back at 8 m/s to
the right. The total impulse exerted by the wall on the ball is
+5.0 N s.
–5.0 N s.
+3.0 N s.
–3.0 N s.
E)
F)
G)
H)
+2.0 N s.
–2.0 N s.
+1.0 N s.
–1.0 N s.
_______6.
A)
B)
C)
D)
E)
F)
An electron is moving East in a uniform magnetic field directed North. What is the
direction of the Lorentz force on the electron?
N
B
Up (Out of the Page).
Down (Into the Page).
W
E
North.
South.
v
East.
S
electron
West.
_______7.
A)
B)
C)
D)
E)
An electron is moving in a region of space with a static electric field and a static
magnetic field. The electron begins with a kinetic energy of 6.0 x 10–17 J at point P
where the electric potential is +100 V. It moves to point Q where the electric
potential is –100 V. All forces but the electric force and the magnetic force can be
neglected. What is the electron’s kinetic energy at Q (to two significant digits)?
2.8 x 10–17 J
4.4 x 10–17 J
6.0 x 10–17 J
7.6 x 10–17 J
9.2 x 10–17 J
3
Name ________________________________________________________________________
Part B – Short Questions and Problems – 84 Points Total
B-1 (8 Points)
Starting at rest, a car accelerated in the +X direction for 2.0 seconds with an acceleration of +a.
It continued for an additional 8.0 seconds with an acceleration of +a/2 in the +X direction,
reaching a final speed of 30 m/s. How far did the car travel in the total time of 10.0 seconds?
Answer: _____________________ units ________
B-2 (6 Points)
Jack threw a ball straight up into the air and caught it some time later. It reached a maximum
height of 19.6 meters above the height of his hand. Assuming he caught it at the same height he
released it, how long was it in the air? Use g = 9.8 m/s2 and neglect air resistance.
Answer: _____________________ units ________
B-3 (4 Points)
_______
A)
B)
C)
D)
Jack threw a ball straight up into the air and caught it. He then threw it a second
time to his sister, Jill, who was standing some distance away. The ball reached the
same maximum height both times. Jack and Jill both caught the ball at the same
height above the ground. Compared to the first throw, how long was the ball in the
air on the second throw? Neglect air resistance.
It was in the air for less time on the second throw.
It was in the air for the same time on the second throw.
It was in the air for more time on the second throw.
There is not enough information to answer this question.
4
Name ________________________________________________________________________
B-4 (8 Points)
A block of mass 2.0 kg moving on a horizontal surface starts with a velocity of 5.0 m/s in the +X
direction and 0.0 m/s in the +Y direction. It experiences a net impulse of 18.0 N s in the –X
direction and 6.0 N s in the +Y direction. What is the velocity of the block after the impulse?
X Component: _____________________ units ________
Y Component: _____________________ units ________
B-5 (8 Points)
A block of unknown mass on a horizontal surface experiences a constant force of 8 N in the +X
direction and 6 N in the –Y direction. It moves from X = 2 m, Y = –2 m to X = 5 m, Y = 2 m.
How much work does the force do on the block during the move?
Answer: _____________________ units ________
5
Name ________________________________________________________________________
B-6 (10 Points)
A hockey puck (Puck A) sliding on frictionless ice initially at 12 m/s collided with two other
pucks of the same mass initially at rest (Pucks B and C). What is the speed of the center of mass
of the system consisting of Pucks A, B, and C after the collision?
Answer: _____________________ units ________
B-7 (6 Points)
A wheel initially spinning at 10 rev/s took 100 revolutions to come to a stop. What was the
magnitude of its angular acceleration assuming it was constant?
Answer: _____________________ units ________
6
Name ________________________________________________________________________
B-8 (6 Points)
A rod with a mass of 0.60 kg and a length of 0.50 meters has two 0.50 kg masses attached, one at
each end. It is rotating about its center. What is the rotational inertia of the system consisting of
the rod and the two attached masses? The rotational inertia of the rod is 121 M L2 .
center of rotation
0.50 meters
Answer: _____________________ units ________
B-9 (12 Points)
An ice skater began a spin with her arms out. Her rotational inertia was 1.25 kg m2 and her
angular speed was 12.0 rad/s. She changed her rotational inertia to 0.75 kg m2 by pulling her
arms in. How much work did the skater do while pulling her arms in? Neglect the friction of her
ice skates on the ice and neglect air resistance.
Answer: _____________________ units ________
7
Name ________________________________________________________________________
B-10 (8 Points)
An electron is traveling in a vacuum tube at 5.6 x 10+6 m/s in a horizontal direction toward the
south. There is a constant magnetic field in the tube with a magnitude of 2.5 x 10–4 T. The
direction of the magnetic field is 30º from vertical toward the north, as shown. What is the
magnitude of the magnetic force on the electron?
B
Up
30°
v
S
N
-e
Down
Answer: _____________________ units ________
B-11 (8 Points)
An ion with the same charge as a proton but unknown mass is moving in a circular path in a
magnetic field. The magnetic field is 1.0 T at a right angle to the path of the ion and the radius
of the path of the ion is 0.5 meters. What is the magnitude of the linear momentum of the ion?
Answer: _____________________ units ________
8
Name ________________________________________________________________________
B-12 (14 Points) Concept and Equation Matching
In this question, you will match important concepts in Physics I will their corresponding
equations on the Formula Sheet. In each case, you will pick the equation number that best
exemplifies the concept.
In some cases, there are two equations with the same number, like 48a and 48b. In that case, we
want only the number and we will assume you mean either or both of the equations as
appropriate for the correct answer.
Example: (You would put “1” as the correct equation from the sheet for this concept.)
1
Relationship of Time Interval and Change of Velocity for Constant Acceleration
____ The Impulse-Momentum Theorem
____ The Work-Kinetic Energy Theorem
____ Change in Mechanical Energy from Non-Conservative Forces
____ Potential Energy of an Ideal Spring
____ Newton’s 2nd Law of Motion
____ Newton’s Law of Universal Gravitation
____ Coulomb’s Law
____ The Magnetic or Lorentz Force on a Moving Charged Particle
____ Finding the Scalar or Dot Product of Two Vectors
____ Finding the Vector or Cross Product (Magnitude) of Two Vectors
____ Collision in Two Dimensions with Conservation of Momentum
____ Elastic Collision in One Dimension
____ Definition of Torque
____ Definition of Angular Momentum for a Particle
9
Name ________________________________________________________________________
Part C – Extended Problems – 88 Points Total
C-1 (16 points)
A toy gun fires a plastic pellet with a mass of 0.5 g. The pellet is propelled by a spring with a
spring constant of 1.25 N/cm which is compressed 2.0 cm before firing. The plastic pellet
travels horizontally 10 cm down the barrel (from its compressed position) with a constant friction
force of 0.0475 N opposing the motion of the pellet.
k = 1.25 N/cm
d = 10 cm travel
x = 2 cm compression
The toy gun is held 1.0 m above the floor. How far does the pellet go horizontally from the point
it leaves the barrel until it hits the floor? Use g = 9.8 m/s2 and neglect air resistance.
Answer: _____________________ units ________
10
Name ________________________________________________________________________
C-2 (16 points)
A small ball of mass 300 g is given a charge of +2.0 x 10–3 C. It is suspended by a nearly
massless string in an electric field of 735 V/m in the horizontal direction. The only forces on the
ball are the electric force, gravity, and string tension. The ball is at rest in equilibrium. What is
the angle of the string with respect to vertical (shown as )? Treat the ball as a point mass and
charge. Use g = 9.8 m/s2.
Answer: _____________________ units ________
11
Name ________________________________________________________________________
C-3 (4 points)
For questions C-3, C-4, and C-5, we will refer to the two-particle system shown below. It
consists of an electron and a positron. A positron has the same mass as an electron but a positive
charge (+e). The center of mass of the electron-positron system is located at (0,0) and the center
of mass is not moving. At the instant shown in the figure below, the location of the electron is
(4.0 x 10–12 , 3.0 x 10–12) m and its velocity is 6.0 x 10+6 m/s in the +X direction.
electron
Y
6.0 x 10+6 m/s
Location: (4.0 x 10–12 , 3.0 x 10–12) m
X
Center of Mass
(not moving)
location = ?
velocity = ?
positron
Important Note: In C-3 and C-4, if you think you can write down the answer without
doing a calculation with equations, state why in a complete sentence.
First question: What is the location of the positron at the instant shown above?
X Coordinate: _________________________ m
Y Coordinate: _________________________ m
C-4 (4 points)
What is the velocity of the positron at the instant shown above?
X Component: _________________________ m/s
Y Component: _________________________ m/s
12
Name ________________________________________________________________________
C-5 (16 points)
What is the angular momentum of the electron about the center of mass? Give all 3 components.
(Note: The +Z axis is out of the page in the diagram on page 11.)
Angular Momentum:
X Component: ___________________ units ________
Y Component: ___________________ units ________
Z Component: ___________________ units ________
13
Name ________________________________________________________________________
C-6 (18 points)
The figure below shows two charged spheres, A and B. Sphere A is directly above sphere B.
The initial distance between their centers is d = 4.0 cm. Sphere A has a weight: W = 0.90 N.
Both have the same charge: q = 2.0 x 10–6 C.
Initially, both spheres are held in place. Then sphere A is released while sphere B remains held
in place. Neglecting air resistance, treating the spheres as point charges, considering only the
electric and gravitational forces on sphere A, and assuming only vertical motion, what is the
maximum height of sphere A above the height of sphere B after being released?
Do not try to use “F = m a” to solve the problem.
ax  bx c  0  x 
2
force of
gravity
A
 b  b2  4 a c
2a
d = 4.0 cm
B
Maximum Height: ___________________ units ________
14
Name ________________________________________________________________________
Formula Sheet for Exam 3 and Final – 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
15
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 Exam 3 and Final – 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
16