Name_____________________________________________
Final Exam
Physics I
Fall 2002
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
_____10
_____ 8
_____ 5
_____ 6
_____ 7
M/TH 8-10 (Bedrosian)
M/TH 10-12 (Hayes)
M/Th 12-2 (Hayes)
M/Th 12-2 (Sperber)
M/Th 2-4 (Schroeder)
Tu/F 10-12 (Bedrosian)
Tu/F 12-2 (Sperber)
Tu/F 2-4 (Sperber)
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
considered 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
Questions
Part A
Value
32
B-1,2
12
B-3,4
12
B-5,6
12
B-7,8
12
B-9,10
12
C-1
16
C-2
12
C-3,4
8
C-5,6
12
C-7
16
C-8
16
C-9,10
16
C-11
12
Total
200
Score
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 – 32 Points Total (8 at 4 Points Each)
Write your choice on the line to the left of the question number.
_______1.
Which one graph below represents a motion for which it would be incorrect to use
equations 1-5 from the formula sheet to solve a one-dimensional motion problem –
even if you broke the motion into two time intervals? Note: The respective graphs
are straight line segments and v = velocity, a = acceleration.
v
A)
v
t
B)
t
a
C)
_______2.
a
t
D)
t
Two cannon crews, A and B, are practicing shooting their cannons in a large, flat
field. Crew A points their cannon at an angle of 30° up from horizontal. Crew B
points their cannon 60° up from horizontal. They both fire at the same time and
they notice that their respective cannon balls hit the ground at the same time.
Neglecting air resistance, and assuming both cannon balls start from the same
height when fired, which cannon ball reaches the greatest maximum height?
(Do not assume that the cannons and cannon balls are identical.)
A) The cannon ball from crew A goes higher.
B) The cannon ball from crew B goes higher.
C) Both cannon balls reach the same maximum height.
2
Name_____________________________________________
_______3.
A)
B)
C)
D)
–6.0 N s.
+6.0 N s.
–1.5 N s.
+1.5 N s.
_______4.
A)
B)
C)
D)
E)
F)
Greg LeMond is riding his bicycle due east in the Tour de France bicycle race.
What is the direction of the angular momentum of his bicycle wheels?
North.
South.
East.
West.
Up.
Down.
_______5.
A)
B)
C)
D)
E)
F)
For this question, take right as the positive direction. A 0.375 kg rubber ball
traveling horizontally to the right at 10 m/s hits a wall and bounces back at 6 m/s to
the left. The total impulse exerted by the wall on the ball is
You and a friend are playing toss and catch with two balls of Silly Putty. (“Silly
Putty” is a soft, pliable, slightly sticky substance originally developed as a synthetic
rubber. Although it has practical uses, it is most famous as a children’s toy.) On
one toss, your balls happen to collide in mid-air, stick together, and fall to the
ground. Which of the following quantities, if any, was conserved during that toss
for the system consisting of the two balls of Silly Putty – counting after the throw
until hitting the ground? (Neglect air resistance.)
Horizontal momentum.
Vertical momentum.
Potential energy.
Kinetic energy.
Potential + Kinetic energy.
None of the above.
_______6.
An electron is moving in a magnetic field, with no forces on the electron except the
Lorentz force due to the magnetic field. The magnetic field is not uniform; in other
words, its direction and magnitude change depending on location. Which of the
following statements, if any, is always true in this situation?
A) The force on the electron, if not zero, is perpendicular to its velocity at every instant of time.
B) The force on the electron, if not zero, is perpendicular to the magnetic field at the electron’s
location at every instant of time.
C) The kinetic energy of the electron is constant.
D) All of the above (A-C).
E) None of the above.
3
Name_____________________________________________
_______7.
A)
B)
C)
D)
E)
F)
Each of the following particles begins with kinetic energy = 1,000 eV. Which
particle has the greatest final kinetic energy? The only force is due to a static
electric field. Note: An alpha particle consists of two neutrons plus two protons.
Neutrons have no electric charge.
Proton “A” starts at an electric potential of –100 V and ends at +100 V.
Proton “B” starts at an electric potential of +100 V and ends at –100 V.
Alpha particle “C” starts at an electric potential of –50 V and ends at +100 V.
Alpha particle “D” starts at an electric potential of +100 V and ends at –50 V.
Neutron “E” starts at an electric potential of –500 V and ends at 0 V.
Neutron “F” starts at an electric potential of +500 V and ends at 0 V.
_______8.
A charged sphere of mass M with positive charge +Q is at rest in a uniform electric
field in the horizontal direction (to the right) with magnitude E. There is a uniform
magnetic field in the positive vertical (up) direction with magnitude B. The sphere
is attached to a string with tension T. There is zero net force on the sphere. Let g
be the acceleration constant of gravity. Which free-body diagram best corresponds
to this situation?
N
A) T
QB
QE
B) T
Mg
Mg
T
T
QE
C)
QE
D)
Mg
Mg
E) T
QE
QE
Mg
4
Name_____________________________________________
Part B – Short Problems – 60 Points Total (10 at 6 Points Each)
Show all work.
B-1 (6 Points)
A construction worker on a new high-rise building drops a wrench and it falls 78.4 m to the
ground. How fast is it moving when it hits, assuming no air resistance? Use g = 9.8 m/s2.
Answer: _____________________ units ________
B-2 (6 Points)
Mike is pulling a box along the floor with a rope. The angle of the rope with respect to
horizontal () is 20°. The tension on the rope is 200 N. There is a friction force on the box of 50
N in the opposite direction. The mass of the box is 100 kg. What is the acceleration of the box?


F
X
Mike
Answer: _____________________ units ________
5
Name_____________________________________________
B-3 (6 Points)
You take your little sister to the park and go for a ride on the park’s carousel (“Merry-GoRound”). You warn her to hang on tightly to the carousel horse so that she does not slide off.
(You stand next to her on the platform just to make sure.) The horse is 4 m from the axis of
rotation of the carousel and the carousel takes 8 seconds to make one revolution at full speed.
Your sister’s mass is 25 kg. What is the centripetal force needed to keep her on the horse?
Answer: _____________________ units ________
B-4 (6 Points)
The carousel in B-3 takes exactly one revolution to reach its full speed from a complete stop.
What is the magnitude of its angular acceleration while speeding up, assuming that its angular
acceleration is constant?
Answer: _____________________ units ________
6
Name_____________________________________________
B-5 (6 Points)
The wind exerts a constant force on a small sailboat of 150 N in the north direction and 250 N in
the east direction. The boat moves on a straight course 90 m north and 30 m west. How much
work does the wind do on the boat?
Answer: _____________________ units ________
B-6 (6 Points)
The graph below shows the net horizontal force on a sports car accelerating from rest. (Note that
all line segments on the graph are straight and the maximum force is 15,000 N.) The mass of the
car is 1,500 kg. What is its speed at the end of six seconds?
F (kN)
15
12
9
6
3
0
t (sec)
0
1
2
3
4
5
6
Answer: _____________________ units ________
7
Name_____________________________________________
B-7 (6 Points)
A hockey puck sliding on frictionless ice collides with another hockey puck of the same mass
initially at rest. The speed of the first hockey puck before the collision is 20 m/s. What is the
speed of the center of mass of the two hockey pucks after the collision?
Answer: _____________________ units ________
B-8 (6 Points)
Calculate the acceleration due to gravity at the surface of the Moon. Assume the Moon is a
perfect sphere and neglect effects due to rotation. Use M = 7.36 10 22 kg and R = 1.74 10 6 m.
Answer: _____________________ units ________
8
Name_____________________________________________
B-9 (6 Points)
The electric potential difference between two parallel plates that are 5.0 cm apart (d) is 60 V.
(The plates are equipotential surfaces as shown in the figure below.) What is the magnitude of
the electric field between the plates? (Assume the electric field is uniform.)
V=0
d
E
V = 60
Answer: _____________________ units ________
B-10 (6 Points)
A point charge Q creates an electric potential that has the value 100 V at a distance of 4 cm from
the charge. (Assume the electric potential is zero at infinity.) What is the magnitude of the
electric field created by this charge at 4 cm distance?
Answer: _____________________ units ________
9
Name_____________________________________________
Part C – Extended Problems
This section contains numerical problems and some follow-up multiple-choice questions.
The points vary depending on a combination of difficulty and importance of the concepts.
Show all work.
C-1 (16 points)
Crew A from Problem A-2 aims their cannon at an angle of 30° up from horizontal and fires it as
shown below in a large, level field. The initial speed of the cannon ball is 196 m/s. Neglect air
resistance and assume that the cannon ball starts at ground level for simplicity. Use g = 9.8 m/s2.
What is the maximum height reached by the cannon ball? How far has the cannon ball gone in
the horizontal direction when it reaches its maximum height?
30°
Maximum height: _________________________ units ________
Horizontal distance at maximum height: _________________________ units ________
10
Name_____________________________________________
C-2 (12 Points)
Ike and Mike are having a game of tug-of-war, where each pulls on the end of a rope to see
which one is pulled forward into a mud pit between them. To pull on the rope effectively, they
must each exert a horizontal force on the ground through the soles of their shoes. Ike is exerting
a horizontal force on the ground of 500 N (magnitude) while trying to pull Mike in the –X
direction . Mike is exerting a horizontal force on the ground of 514 N (magnitude) while he tries
to pull Ike in the +X direction. They each have mass = 70 kg. Assume that the mass of the rope
is negligible and that its tension, T, is not near its breaking point. Find Ike’s acceleration, Mike’s
acceleration, and the tension of the rope.
X
Ike
Mike
Ike’s Acceleration:
_____________________ units ________
Mike’s Acceleration: _____________________ units ________
Tension of the Rope: _____________________ units ________
11
Name_____________________________________________
C-3 (4 points)
You are a civil engineer designing a road. The road has a curve with a radius of 200 m. Your
objective is to calculate the proper banking angle () of the road so that the sideways friction
force (F) of the tires will be minimized (hopefully to zero) as cars go around the curve at an
average speed of 100 km/hr. (Note: The car is moving into the page.)
to center of curve

Step 1: Identify all forces. Put a check mark or X next to each separate physical force acting on
the car:
______F: The sideways friction force of the road on the car.
______N: The normal force of the road on the car.
______W: The weight of the car.
______C: Centripetal force.
C-4 (4 points)
Step 2: Pick a correct free-body diagram for the car going around the curve.
______
(Pick a letter A-D from the choices below.)
Y
Y
N
N
X
A) F
a
C
X
a
B) F
W
W
Y
Y
N
N
X
X

C)

C

a
a
D)

F
F
W
W
12
Name_____________________________________________
C-5 (4 points)
Step 3: Given free-body diagram D above, what is the correct resolution of forces N and F into
components in the X and Y coordinate system?
______
(Pick a letter A or B from the choices below.)
Y
Y
N cos()
N sin()
X
A)N sin()
F cos()
a
X
B)N cos()
F sin()
F sin() W
a
F cos() W
C-6 (8 points)
Step 4: Using free-body diagram A in C-5, write Newton’s 2nd Law (Equation 6) in X and Y
components using the symbols and coordinate system shown. You do not need to evaluate the
symbols further. Use M for the mass of the car if you need that in any of the equations.
13
Name_____________________________________________
C-7 (16 points)
An electron (call it "E") approaches a proton (call it "P") at a speed of +1.5 x 107 m/s at the
instant of time shown, the “initial” time. Its initial velocity is in the +X direction as we define it
and the location of E is –4.0 x 10-12 m in the X direction and +3.0 x 10-12 m in the Y direction.
The center of the coordinate system is at P. For simplicity, assume that P is so much more
massive than E that it does not move and assume that the only force is the electric force.
Note that the +Z direction is out of the page.
What is the angular momentum of E about P at the instant shown?
v = +1.5 x 107 m/s (+X direction)
Y
E
M = 9.1 x 10-31 kg
X = –4.0 x 10-12 m
Y = +3.0 x 10-12 m
Z=0
X
P
Magnitude: ___________________ units ________
X Component: ________________
Y Component: ________________
Z Component: ________________
14
Name_____________________________________________
C-8 (16 points)
Calculate the electric field due to the proton (P) at the position of the electron (E) in C-7.
Magnitude: ___________________ units ________
X Component: ________________
Y Component: ________________
Z Component: ________________
15
Name_____________________________________________
C-9 (6 points)
Calculate the electric force on the electron (E) in C-7. (Use the result of C-8 for this.)
Magnitude: ___________________ units ________
X Component: ________________
Y Component: ________________
Z Component: ________________
C-10 (10 points)
Calculate the potential energy of the charge configuration in C-7 assuming the potential energy
would be zero with the electron at infinite distance from the proton.
Potential Energy: ___________________ units ________
16
Name_____________________________________________
C-11 (12 points)
Calculate the speed of the electron (E) in C-7 after it passes the proton and reaches its “final”
position very far away (essentially infinite distance).
Final Speed: ___________________ units ________
17
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   F 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
18
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
46.
47.
48.
49.
50.
51.

m m
F  G 1 2 2 r̂
r

1 q1 q 2
F
r̂
4  0 r 2

1 qi
E  
r̂i
4   0 ri 2


F  qE
1 qi
V
4   0 ri
U  qV
52.
 
V    E  dx
dV
dx
dV
53y. E y  
dy

 
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
19