Name _______________________________________________________________________
Exam #2
Physics I
Spring 2005
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 (Washington)
M/R 10-12 (Shannon)
M/R 12-2 (Bedrosian)
M/R 2-4 (Bedrosian)
M/R 4-6 (LaGraff)
T/F 10-12 (Yamaguchi)
T/F 10-12 (Wilke)
T/F 12-2 (Korniss)
T/F 2-4 (Wilke)
M/R 12-2 (Shannon)
T/F 12-2 (Yamaguchi)
Questions
Part A
Value
32
B-1
20
C-1
24
C-2
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.
Part A – Multiple Choice – 32 Points Total (8 at 4 Points Each)
For questions 1-4, please refer to the figure below. Two trains, A and B, start at rest at t = 0 in a
rail yard and move in one direction following parallel straight tracks for 20 seconds. Both trains
experience the same net force as shown in the graph below. Train B has more mass than train A.
F (N)
Fmax
t (sec)
0
0
_______1.
A)
B)
C)
D)
Which train has the greater magnitude of (linear) momentum at t = 20 seconds?
Which train has the greater kinetic energy at t = 20 seconds?
Train A.
Train B.
Both have the same kinetic energy.
There is not enough information to decide which one.
_______4.
A)
B)
C)
D)
Which train has the greater displacement from t = 0 to t = 20 seconds?
Train A.
Train B.
Both have the same magnitude of linear momentum.
There is not enough information to decide which one.
_______3.
A)
B)
C)
D)
20
Train A.
Train B.
Both have the same displacement.
There is not enough information to decide which one.
_______2.
A)
B)
C)
D)
10
Which train has the greater magnitude of angular momentum at t = 20 seconds?
Train A.
Train B.
Both have the same magnitude of angular momentum.
There is not enough information to decide which one.
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Name _______________________________________________________________________
_______5.
A)
B)
C)
D)
E)
What are correct SI units for angular momentum?
rad/s.
rad/s2.
kg m/s.
kg m/s2.
kg m2/s.
_______6.
The figure below shows a point particle moving in the +X direction in the XY
plane. What is the direction of its angular momentum about the origin (“+”)?
(0.0,0.5)
A)
B)
C)
D)
E)
F)
+X.
–X.
+Y.
–Y.
+Z.
–Z.
______ 7.
A.
B.
C.
D.
Y
(Z out of page)
X
origin
(0.0,0.0)
A satellite in space spinning on its axis uses its internal motors to unfold its solar
panels as shown in the figure below, so that in the final position its solar panels are
farther from the axis of rotation than in the initial position. During the unfolding of
the solar panels, which quantity below is conserved (stays constant)?
initial
Rotational inertia.
Angular velocity.
Angular momentum.
Rotational kinetic energy.
_______8.
A)
B)
C)
D)
v
final

An object moves from point A to point B while acted on by force F .

Which condition below determines whether F is a Conservative Force?

F is an internal force in the system containing the object.
The kinetic energy of the object is the same at point A and point B.
The momentum of the object is the same at point A and point B.

The work done by F does not depend on the path taken from point A to point B.
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Name _______________________________________________________________________
B-1 – Graphing – 20 Points
A metal ring initially at rest is dropped onto a rotating metal disk. This is similar to the activity
we did in Class 15. The first figure below shows the rotation speed of the ring as a function of
time. From 0.0 to 0.1 s, the ring is dropping straight down and not rotating. From 0.1 to 0.2 s,
the ring has contacted the disk and is speeding up its rotation. After 0.2 s, both the ring and disk
are rotating together at 10. rad/s. Ignore the friction of the bearings of the disk and ignore all
forces external to the system consisting of the ring and disk.
The rotational inertia of the ring is 5.2 x 10-4 kg m2.
The rotational inertia of the disk is 2.6 x 10-4 kg m2.
Plot rotation speed of the disk from 0.0 to 0.3 s. Make sure to put a scale on the vertical axis and
clearly show the values at t = 0.0 and t = 0.3 s, as well as the shape of the graph.
ring  (rad/s)
10
5
0
t (sec)
0.1
0.2
0.3
disk  (rad/s)
0
t (sec)
0.1
0.2
0.3
4
Name _______________________________________________________________________
Problem C-1 (24 Points) (Put your work and answers on the next page.)
A block with a mass of 10. kg is released from rest at a position 0.48 m above the equilibrium
position of a spring at time t = 0. It falls straight down and contacts the spring at time A. The
block continues moving downward as the spring slows it, until it temporarily comes to rest at
time B after compressing the spring 0.020 m from equilibrium.
The system is the block and the spring.
The spring is massless and obeys Hooke’s Law. Ignore air resistance. Use g = 9.8 N/kg.
Take the position of the block at time B as the zero of gravitational potential energy.
time t = 0
time A
time B
Vi = 0
h = 0.48 m
V=?
Vf = 0
x = 0.02 m
The questions to answer about this problem are on the next page.
Please put your work and answers on the next page.
5
Name _______________________________________________________________________
Problem C-1 (24 Points) (Put your work and answers below.)
A. Total mechanical energy at time 0 = _________________________________ units ________
B. Total mechanical energy at time A = ________________________________ units ________
C. Speed of the block at time A = _____________________________________ units ________
D. Total mechanical energy at time B = ________________________________ units ________
E. Spring constant = ________________________________________________ units ________
6
Name _______________________________________________________________________
Problem C-2 (24 Points)
Consider the system of two point masses moving in the XY plane as shown below. The mass of
particle 1 is m1 = 0.001 kg and its velocity is 20 m/s in the +X direction. The mass of particle 2
is m2 = 0.002 kg and its velocity is 10 m/s in the –X direction. The origin of the coordinate
system is at the center of mass of the two-particle system and the coordinates are in meters.
Find all three components (X,Y,Z) of the angular momentum of the system about the origin.
(-0.6,+0.8)
v1
m1
Y
(Z out of page)
origin
(0.0,0.0)
X
m2
v2
(+0.3,-0.4)
Angular Momentum X Component: ____________________________ units ________
Angular Momentum Y Component: ____________________________ units ________
Angular Momentum Z Component: ____________________________ units ________
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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.
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