Name _______________________________________________________________________
Final Exam
Physics I
Fall 2005
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
_____ 4
_____ 5
_____ 6
_____ 7
_____ 8
M/R 8-10 (Bedrosian)
M/R 10-12 (Wetzel)
M/R 12-2 (Wetzel)
M/R 12-2 (Bedrosian)
M/R 2-4 (Schroeder)
T/F 10-12 (Washington)
T/F 12-2 (Yamaguchi)
T/F 2-4 (Yamaguchi)
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 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 – Multiple Choice – 80 Points Total (20 at 4 Points Each)

Questions 1-4 refer to the objects A-E shown below at a certain instant of time. F is the net

force acting on the object at that instant and v is the velocity of the object. The angles between


F and v are, going from left to right in the figure: 180°, 135°, 90°, 45°, and 0° respectively.


Select the object(s) for which the relationship between F and v is consistent with the
description of motion of the object in the questions. Select all that apply or “0” if none.
F
F
F
v
A
F
v
B
v
C
F
v
D
E
_______1.
The object is moving in a straight line.
_______2.
The object is moving at a constant speed.
_______3.
The object is slowing down.
_______4.
The net force is doing positive work on the object as it moves.
v
Question 5 does not refer to the figure above.
_______5.
A)
B)
C)
D)
E)
In the pulley system shown to the right (“Atwood’s Machine”), the
weight of the smaller mass is 3 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?
9 N.
6 N.
4 N.
3 N.
2 N.
3N
6N
2
Name _______________________________________________________________________
Questions 6-9 refer to the graphs shown below. Two objects, A and B, moving in one dimension
are subjected to different non-constant net forces, Fa and Fb respectively. The graphs below
show the velocity of each object, va and vb respectively, from t = 0 to t = 6 seconds.
To answer questions 6-9, pick one correct answer for each question from these choices:
A) Object A.
B) Object B.
C) The quantities are equal for both objects.
D) Not enough information was given to decide.
va (m/s)
vb (m/s)
+4
+4
+2
+2
t (sec)
0
2
4
6
-2
t (sec)
0
2
4
6
-2
_______6.
Which object had the greatest total displacement from t = 0 to t = 6 seconds?
_______7.
Which object had the greatest magnitude of acceleration at any time from t = 0 to t
= 6 seconds?
_______8.
Which object had the greatest magnitude of force acting on it at any time from t =
0 to t = 6 seconds?
_______9.
Which object had the greatest total amount of work done on it by its force over the
time interval t = 0 to t = 6 seconds?
Question 10 does not refer to the graphs above.
_______10. Which equation number from the formula sheet best represents the ImpulseMomentum Theorem? Write the number on the line to the left.
3
Name _______________________________________________________________________
______ 11. An electron is moving in the +Y direction in a region with a static magnetic field in
the –Z direction (into the page). What is the direction of the magnetic force?
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
Y
B
electron
X
______ 12. An electron is moving in the +Y direction in a region with a static electric field in
the –Z direction (into the page). What is the direction of the electric force?
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
Y
E
electron
X
Questions 13-15 refer to the figure below. Two electrons (A and B) are moving in circles in the
XY plane in a magnetic field. The magnetic force is the only force in the problem and the
electrons are far enough apart so they do not interact with each other.
______ 13. What is the direction of the magnetic field?
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
Y
X
B
A
______ 14. Which electron has the greatest kinetic energy?
A)
B)
C)
D)
Electron A.
Electron B.
Both have the same kinetic energy.
There is not enough information to decide which one has the greatest kinetic energy.
______ 15. Which electron takes the longest time to make one complete circle?
A)
B)
C)
D)
Electron A.
Electron B.
Both take the same amount of time.
There is not enough information to decide which one takes the longest time.
4
Name _______________________________________________________________________
Questions 16-20 refer to the figure below. Five electrons (A-E) are shown at a certain instant of
time in a region where the electric field is static and uniform (constant in time and space). All
electrons have the same initial speed v0 = 1.0 x 10+6 m/s. Equipotential lines are shown as dotted
lines for 0, 5, and 10 volts respectively – assume they extend indefinitely in the horizontal
direction. The electric force is the only force in the problem and all electrons are far enough
apart so they do not interact with each other.
0 volts
V0
V0
Y
D
X
E
V0
A
B
5 volts
C
V0
V0
10 volts
_______16. What is the direction of the electric field?
A)
B)
C)
D)
+X.
–X.
+Y.
–Y.
______ 17. Which electron(s) will reach the 0 volt potential line at some future time?
Put all that apply or “0” for none.
______ 18. Of the electron(s) that reach the 0 volt potential line (if any), which one has the
greatest speed upon reaching that line?
Put the one electron with greatest speed or “0” for none or “same” for all the same.
______ 19. Which electrons will reach the 10 volt potential line at some future time?
Put all that apply or “0” for none.
______ 20. Of the electron(s) that reach the 10 volt potential line (if any), which one has the
greatest speed upon reaching that line?
Put the one electron with greatest speed or “0” for none or “same” for all the same.
5
Name _______________________________________________________________________
B-1 – Cart in Motion on a Track with Constant Force – 20 Points
Push on cart (not on force
probe) and release--keep
hand out of way of motion
detector
In the illustration above, the student releases the cart 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:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values at any minimum or maximum points.
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 – Mass on a Spring – 20 Points
A mass on a spring begins at y = 0.0 cm at rest but with a net force in the +Y direction (up).
After being released, it reaches a maximum height of y = 10.0 cm. The mass of the object is 2.0
kg and the equilibrium position of the spring (y0) is at the object’s maximum height.
The only forces in the problem are gravity and the spring force (assumed to be ideal).
Spring force (Hooke’s Law): Fs = –k (y–y0) = +k (y0–y). Use g = 9.8 N/kg.
Plot the total force on the mass (Fy), the potential energy (PE), and kinetic energy (KE) of the
system as functions of y.
Your plots must include:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values of Fy, PE and KE at y = 0, 5, and 10 cm.
Show all work.
Fy
0
y (cm)
5
10
y =10 cm
PE
y = 0 cm
y (cm)
0
5
10
KE
y (cm)
0
5
10
7
Name _______________________________________________________________________
B-3 – 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 free-fall
at 9.8 m/s2 in the –Y direction. Ignore air resistance.
Plot the torque on the mass and its angular momentum with respect to the origin of the
coordinate system. Indicate clearly the directions of torque and angular momentum.
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.
Y
X
Z out of page

t (sec)
0
5
10
l
t (sec)
0
5
10
8
Name _______________________________________________________________________
Part C – Problems – 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.
C-1: Dragster – 20 Points
A drag racing car starts from rest, speeds up at 5.0 m/s2, reaches top speed, and then slows down
at –2.5 m/s2 until it comes to a stop. The car goes 750 meters in a straight line. How long does it
take to travel that distance?
Travel Time: ____________________________________________________ units _________
9
Name _______________________________________________________________________
C-2: When Hydrogen and Helium Collide – 20 Points
A hydrogen atom moving at +5.0 x 10+6 î m/s collided with a helium atom initially at rest.
After the collision, the velocity of the helium atom was +1.0 x 10+6 î –1.0 x 10+6 ˆj m/s. For
this problem, we will assume that the mass of a helium atom is exactly four times the mass of a
hydrogen atom (to make the calculations easier) and we will neglect all external forces during
the collision.
Was the collision elastic? Explain your answer in a few sentences supported by calculations.
initial
+5000 km/s
H
Y
He
?
final
X
He
+1000 km/s
H
-1000 km/s
10
Name _______________________________________________________________________
C-3: Potential Energy of a Charge Configuration – 20 Points
The configuration shown below consists of three point charges at the vertices of an equilateral
triangle with side lengths of 0.6 m. There are two –2.0 x 10–9 C charges and one +1.0 x 10–9 C
charge. What is the potential energy of this configuration, assuming the potential energy of
charges infinitely far apart is zero?
+1.0 x 10–9 C
0.6 m
0.6 m
0.6 m
–2.0 x 10–9 C
–2.0 x 10–9 C
Potential Energy of the Configuration: ______________________________ units ________
11
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.
12
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

 
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
13