Name _______________________________________________________________________
Final Exam
Physics I
Fall 2006
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
_____ 3
_____ 5
_____ 6
_____ 7
_____ 8
_____ 9
_____ 10
M/R 8-10 (Bedrosian)
M/R 10-12 (Bedrosian)
M/R 12-2 (Zhang)
M/R 2-4 (Schroeder)
T/F 10-12 (Wetzel)
T/F 12-2 (Wetzel)
T/F 2-4 (Eah)
M/R 4-6 (Bedrosian)
T/F 12-2 (Eah)
Questions
A-1
Value
48
A-2
24
B-1
20
B-2
20
B-3
24
C-1
16
C-2
8
C-3
12
C-4
28
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 answers 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 – 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 _______________________________________________________________________
_______5.
A)
B)
C)
D)
E)
In the pulley system shown to the right (“Atwood’s Machine”), the weight of the
smaller mass is 2 N and the weight of the larger mass is 6 N. Assume
the rope and pulley are frictionless and massless. The masses are
released from rest and begin accelerating. What is the magnitude of
the tension in the rope when the masses are accelerating?
2 N.
3 N.
4 N.
6 N.
8 N.
2N
6N
_______6.
Which equation(s) is/are correct Newton’s Second Law equation(s) based on the
free-body diagram below? Select all that apply or put “0” if none are correct.
N
T
Y

F
m
a
X

W
A.
N  T sin   W cos  0
E.
T cos  F  m a
B.
N  T sin   W sin   0
F.
T cos  F  W sin   m a
C.
N  T sin   W sin   m a
G.
N  T cos  F  W cos  m a
D.
T  F cos  m a
H.
N  T sin   F  W sin   0
_______7.
The diagram below shows two pennies, A and B, glued to a rotating turntable. The
axis of rotation is at the center of the turntable, pointing out of the page.
Which penny has greater magnitude of centripetal acceleration?
A) Penny A.
B) Penny B.
C) Both have the same magnitude
of centripetal acceleration.
D) There is not enough information
to decide which one.
A
3
B
Name _______________________________________________________________________
Questions 8-12 refer to the figure below. At the instant of time shown, an electron is moving in
the +X direction with speed v in a region of space with a static and uniform electric field, E, in
the –X direction; and a static and uniform magnetic field, B, in the –Z direction (into the page).
The effect of the moving electron on E and B is negligible.
The figure identifies three points (A, B, and C) with associated electric potentials at those points
(VA, VB, and VC respectively). Point B has the same Y coordinate as Point A. Point C has the
same X coordinate as Point A. The electron does not necessarily pass through any of the points.
In questions 8 and 9, choose the direction from the list to the right of the figure.
Y
VA
VB
point A
A) +X.
point B
E
B) –X.
C) +Y.
v
B
D) –Y.
electron
E) +Z.
VC
point C
F) –Z.
X
______ 8.
What is the direction of the electric force on the electron?
______ 9.
What is the direction of the magnetic force on the electron?
______ 10. The work being done by the magnetic field on the electron is
A)
B)
C)
D)
positive.
negative.
zero.
impossible to determine from the information given.
______ 11. The correct mathematical relationship between VA and VB is
A)
B)
C)
D)
VA > VB.
VA < VB.
VA = VB.
impossible to determine from the information given.
______ 12. The correct mathematical relationship between VA and VC is
A)
B)
C)
D)
VA > VC.
VA < VC.
VA = VC.
impossible to determine from the information given.
4
Name _______________________________________________________________________
Part A-2 – Equation Matching – 24 Points Total (24 at 1 Point 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
Momentum of a system is conserved (or not) depending on external forces.
______ 6
In a system where momentum is conserved, the center of mass moves at a constant
velocity.
______ 7
Conservation of momentum in a two-dimensional collision.
______ 8
The definition of work done by an arbitrary force.
______ 9
Work done by a constant force.
______ 10
The Work-Kinetic Energy Theorem
______ 11
The definition of potential energy.
______ 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 _______________________________________________________________________
B-1 – Cart in Motion on a Track with Constant Force – 20 Points
Push
onand
cart
(not
on force
probe)
release--keep
hand
out
of way
of motion
detector
initial velocity is negative
+X
In the illustration above, the student gives the cart a push to the left and releases it at t = 0.00 s
when the cart is 1.00 m from the motion detector. A constant force is applied by the string
tension after the push. The cart reaches its closest point 0.50 m from the motion detector at t =
1.00 s. Neglect friction. Plot x (displacement measured from the detector), v (velocity), and a
(acceleration) versus time from after the student releases the cart at t = 0.00 until t = 2.00 s.
Show the following information, including the equations and/or principles you used:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values at any minimum or maximum points, and the values of t where these occur.
3. The values at t = 0.00, t = 1.00, and t = 2.00 s. (Note: x = 1 at t = 0!)
x (m)
0
t (sec)
1.0
2.0
v (m/s)
t (sec)
0
1.0
2.0
a (m/s2)
t (sec)
0
1.0
2.0
6
Name _______________________________________________________________________
B-2 – Torque and Angular Momentum – 20 Points
An object with mass = 0.50 kg begins at rest at location (10.0, 490, 0.0) m. It then falls in freefall at 9.8 m/s2 in the –Y direction. Ignore air resistance.
Plot the torque () on the mass and angular momentum (l) of the mass with respect to the origin
of the coordinate system. Indicate clearly the directions of torque and angular momentum.
Show the equations and/or principles of physics you used to draw the graphs.
Your plots must include:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. Clearly labeled axes with units and directions.
3. The values of torque and angular momentum at t = 0 and t = 10 sec.
Show all work.
(10, 490, 0)
Y
(0,0,0)

t (sec)
0
5
10
l
t (sec)
0
5
10
7
X
Z out of page
Name _______________________________________________________________________
B-3 – Electron Moving in an Electric Field – 24 Points (On Two Pages)
An electron moves in one dimension, from x = 0.0 cm to x = 100.0 cm. The initial KE of the
electron at x = 0.0 cm is 1.6 × 10–17 J. The only force on the electron is the electric force.
Graph the X component of the force on the electron, the kinetic energy of the electron, the
potential energy of the electron, and the electric potential from x = 0.0 cm to x = 100.0 cm.
Assume the potential energy and electric potential are zero at x = 0.0 cm.
Make sure your plots clearly show:
A. Any minimum or maximum points.
B. Whether each graph is curved or straight (could be in sections).
Show what equations and/or principles of physics you are using.
Ex (N/C)
x (cm)
0
40
80
100
-500
Fx (N)
0
x (cm)
40
80
8
100
Name _______________________________________________________________________
KE (J)
x (cm)
0
40
80
100
PE (J)
x (cm)
0
40
80
100
V (volts)
0
x (cm)
40
80
9
100
Name _______________________________________________________________________
Part C – Problems – Four Problems – 64 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.
C-1: Lead-Foot Driver – 16 Points
A driver trying out his new car starts from rest, speeds up at 2.0 m/s2, reaches the maximum
speed, and then presses the brake hard and slows down at –4.0 m/s2 until he comes to a stop.
The car goes 1350 meters in a straight line. How much time has elapsed for this motion?
Travel Time: ____________________________________________________ units _________
10
Name _______________________________________________________________________
C-2: Tarzan and Jane – Part I – 8 Points
Tarzan swings across a ravine to Jane on the other side. The vine is 18 m long and Tarzan
begins 2.5 m above his lowest position at the bottom of his swing.
What is Tarzan's speed at his lowest point (where  = 0 and the vine is vertical)?
Assume the vine is massless, neglect air resistance, and use g = 9.8 N/kg.
The illustration shows Tarzan as he starts.
We are interested in his motion when the vine
is vertical as shown by the dashed line.

L = 18 m
Speed at Bottom: ____________________________________________________ units _________
11
Name _______________________________________________________________________
C-3: Tarzan and Jane – Part II – 12 Points
Tarzan is swinging across a ravine to Jane on the other side, as in C-2 on the previous page.
The vine is 18 m long and Tarzan is moving at 7.0 m/s when he reaches his lowest position at the
bottom of his swing. Tarzan's mass is 90 kg.
What is the tension in the vine at the lowest point (where  = 0 and the vine is vertical)?
Assume the vine is massless, neglect air resistance, and use g = 9.8 N/kg.
The illustration shows Tarzan as he starts.
We are interested in the tension when the vine
is vertical as shown by the dashed line.

L = 18 m
Tension on Vertical Vine: _________________________________________________ units _________
12
Name _______________________________________________________________________
C-4: Electric Field and Electric Potential – 28 Points
Find the electric field and electric potential at the origin of the (X,Y) coordinate system due to
the four point charges as shown in the figure below. The point charges are all 3.0 m from the
origin and the angles between the lines in the figure are all 30°. Note: 1.0 nC = 1.0 × 10–9 C.
Assume that the electric potential is defined to be zero at infinity.
Y
+1 nC
3m
30°
+1 nC
3m
30°
30°
X
(0.0)
30°
30°
3m
3m
-1 nC
+1 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

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
V
53z. E z  
z

 
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
15