Name ________________________________________________________________________
Exam #2
Physics I
Spring 2006
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.
Your name should be at the top of every page.
Section #
_____ 1
_____ 2
_____ 3
_____ 4
_____ 5
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Bedrosian)
M/R 10-12 (Hayes)
M/R 10-12 (Eah)
M/R 12-2 (Bedrosian)
M/R 2-4 (Hayes)
M/R 4-6 (Hayes)
T/F 10-12 (Wilke)
T/F 10-12 (Washington)
T/F 12-2 (Yamaguchi)
T/F 2-4 (Wetzel)
M/R 12-2 (Eah)
T/F 12-2 (Wilke)
Questions
Part A
Value
32
B-1
20
B-2
24
C-1
24
Total
100
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 answer in the context of what we have learned in Physics I.
On graphing and numerical questions, show all work to receive credit.
For each question, please assume we have given you enough information to answer it.
Part A – Multiple Choice – 32 Points Total (8 at 4 Points Each)
Write your choice on the line to the left of the question number.
Questions 1-4 below refer to the following situation: Professor Bedrosian is standing on a
turntable holding a dumbbell at arm’s length in each hand and rotating as shown in Figure A. He
then pulls the dumbbells closer to his body while continuing to rotate as shown in Figure B. The
system consists of Professor Bedrosian, the turntable, and the dumbbells. The turntable is free to
rotate and friction in its bearings can be neglected. All quantities are to be taken with respect to
the axis of rotation.
For each of the quantities listed in questions 1-4, put
A if the quantity is greater in configuration A,
B if the quantity is greater in configuration B, or
C if they are equal.
For vector quantities, we are interested in the magnitude.
______ 1.
Angular Velocity.
______ 2.
Angular Momentum.
______ 3.
Rotational Inertia.
______ 4.
Rotational Kinetic Energy.
A
2
B
Name ________________________________________________________________________
______ 5.
Two drivers have a drag race in two electric cars, A and B. The mass of car A +
driver A is greater than the mass of car B + driver B. Both cars experience the same
net force as a function of time as shown in the graph below and both start from rest
at t = 0. Which car has greater kinetic energy at t = 20 seconds?
F (N)
Fmax
A)
B)
C)
D)
_______6.
A)
B)
C)
D)
_______7.
A)
B)
C)
D)
E)
t (sec)
0
Car A.
0
10
20
Car B.
Both have the same kinetic energy at t = 20 seconds.
There is not enough information to determine which car.
Two point particles, A and B, move in circular paths about a common point with
the same angular velocity. Particle A has half the mass of particle B. The distance
of particle A from the center of the circle is twice the distance of particle B. Which
particle has the greater magnitude of angular momentum about the center point?
Particle A.
Particle B.
Both have the same magnitude of angular momentum.
There is not enough information to determine which particle.
A naughty child threw a candy wrapper from the top of the Eiffel Tower. As the
wrapper fell to the sidewalk below, the work done on the wrapper by gravity was
Positive.
Negative.
Zero.
Depends on the direction we pick as positive.
Depends on whether we can neglect air resistance.
You may want to come back to question A-8 after doing problem C-1, but you should also think
about it before you start C-1.
_______8.
A)
B)
C)
D)
In problem C-1, the work done on ball 1 by string tension from position A to
position B was
Positive.
Negative.
Zero.
Depends on the direction we pick as positive.
3
Name ________________________________________________________________________
B-1 – Graphing – 20 Points
An object of unknown mass moves in one dimension subjected to a conservative net force. The
potential energy (PE) of the force is a parabola with an initial value of 4.0 J at x = 0 cm and a
minimum of 3.0 J at x = 5 cm. The object begins with kinetic energy (KE) = 1.0 J at x = 0 cm.
Graph the kinetic energy of the object and net force from x = 0 to x = 10 cm.
Make sure your plots clearly show:
A. Any minimum or maximum points.
B. Whether each graph is curved or straight.
PE (J)
4
3
2
1
x (cm)
0
KE (J)
5
10
x (cm)
0
0
5
10
Net Force (N)
0
x (cm)
5
10
4
Name ________________________________________________________________________
B-2 – Graphing – 24 Points
An object of mass m = 0.5 kg begins at time t = 0 s moving at 3.0 m/s in the +X direction at
location (0.0, 4.9, 0.0) m. The +Y direction is up and +Z is out of the page. The force of gravity
acts on the object in the –Y direction.
Plot the X, Y, and Z components of the torque acting on the object and the angular momentum of
the object from t = 0 s to t = 1 s. The reference point is the origin of the coordinate system.
Use g = 9.8 m/s2 and neglect air resistance.
Make sure your plots clearly show:
A. The values at t = 0 and t = 1 with correct units.
B. Whether each graph is curved or straight.
0.5 kg
+3.0 m/s
(0.0, 4.9, 0.0) m
Y
X
You can use this page for scratch work. We will not grade this page.
See the next page for the graphs that you will be drawing.
5
Name ________________________________________________________________________
B-2 – Graphing – 24 Points (Continued)
Torque Components
x (
Angular Momentum Components
lx (
)
0
t (s)
0
y (
ly (
0
t (s)
)
t (s)
0
lz (
0
1.0
0
1.0
)
t (s)
0
t (s)
0
)
z (
0
1.0
0
)
1.0
)
0
1.0
t (s)
0
6
1.0
Name ________________________________________________________________________
Problem C-1 (24 Points)*
Two balls with masses m1 and m2 hang from ideal, massless strings of length r = 1.00 m.
Initially, ball 1 is at rest a distance r above its lowest point and ball 2 is at rest at its lowest point
(h = 0) as shown in Figure A. Ball 1 is released and is moving to the right at the instant before it
hits ball 2 as shown in Figure B. In the instant after the elastic collision, ball 1 is moving to the
left and ball 2 is moving to the right as shown in Figure C. m2 = 3.00 m1.
What is the maximum height of each ball above h = 0 after the collision?
You can assume the collision is one-dimensional and elastic. Neglect air resistance.
A
B
C
r
m1
r
h=0
r
m2
r
m1
r
m2
m1
r
m2
h=0
Maximum height of Ball #1 = ___________________________________ units ____
Maximum height of Ball #2 = ___________________________________ units ____
*
Don’t forget to check A-8.
7
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  ( 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
1
2
6.
v  v  2a x  x 0 
 

F
  Fnet  m a
7.
T
5.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2
2
0
2r
v
a centripetal 
2
v
 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.
8
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
9