Name _______________________________________________________________________
Exam #1
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)
Write your choice(s) on the line to the left of the question number.
______ 1.
Your friend took some data for the motion of an object in Physics I class during the
activity, but he ran out of time and had to finish the activity at home. He had the
following sketches of the data, labeled G1, G2, and G3, but he forgot to note which
one was displacement, which one was velocity, and which one was acceleration.
Help him out by picking the correct quantities for the graphs.
G1
G2
G3
0
0
t
0
A.
B.
C.
D.
E.
F.
______ 2.
t
G1 = acceleration, G2 = velocity, G3 = displacement.
G1 = acceleration, G2 = displacement, G3 = velocity.
G1 = velocity, G2 = acceleration, G3 = displacement.
G1 = velocity, G2 = displacement, G3 = acceleration.
G1 = displacement, G2 = acceleration, G3 = velocity.
G1 = displacement, G2 = velocity, G3 = acceleration.
The graphs below show the X and Y centers of mass of a system versus time.
In what direction(s) is the momentum of the system conserved, if any?
Xcom
Ycom
0
A.
B.
C.
D.
t
t
0
t
Momentum is conserved in the X direction, but not in the Y direction.
Momentum is conserved in the Y direction, but not in the X direction.
Momentum is conserved in both the X and Y directions.
Momentum is not conserved in either direction.
2
Name _______________________________________________________________________
The next three questions (3, 4, and 5) refer to the graph below. Object A is acted on in one
dimension by the net force shown by the solid lines labeled A. Object B is acted on in one
dimension by the net force shown by the dashed lines labeled B. Both forces reach the same
maximum, but at different times. Both objects start at rest at t = 0.
Fnet
A
B
0
t
0
______ 3.
A.
B.
C.
D.
______ 4.
A.
B.
C.
D.
______ 5.
A.
B.
C.
D.
t1
t2
Which object has the greater magnitude of momentum at t = t1?
Object A.
Object B.
Both have the same magnitude of momentum at t = t1.
There is not enough information to determine which object has the greater
magnitude of momentum at t = t1.
Which object has the greater magnitude of momentum at t = t2?
Object A.
Object B.
Both have the same magnitude of momentum at t = t2.
There is not enough information to determine which object has the greater
magnitude of momentum at t = t2.
Which object has traveled the greater distance from t = 0 to t = t2?
Object A.
Object B.
Both have traveled the same distance.
There is not enough information to determine which object has traveled the greater
distance.
3
Name _______________________________________________________________________
The next three questions (6, 7, and 8) refer to the figure below and the following situation:
A bicycle racer is pedaling her bicycle at a constant speed, v, around a smooth, flat, circular track
of radius r. The total mass of the bicycle + rider = M. The force of wind resistance acts in the
direction opposite to the velocity of the bicycle and has a constant magnitude = F. Friction of the
tires on the track cannot be neglected – otherwise she would not be able to ride in a circle. The
acceleration constant of gravity is g.
The figure below shows the coordinate system we have selected at one instant of time. The point
of view is looking down at the rider. The X axis points in the direction from the bicycle toward
the center of the track. The Y axis points in the direction of the velocity of the bicycle. The Z
axis is vertical, pointing from the rider up toward the viewer (out of the page).
What are the X, Y, and Z components of the total force on the bicycle + rider at this instant?
Y
(top view)
Z
(out of page)
______ 6.
A.
B.
C.
D.
______ 7.
A.
B.
C.
D.
______ 8.
A.
B.
C.
D.
X
The X component of the total force is
0.
+M v2/r.
–M v2/r.
There is not enough information to find the X component of total force.
The Y component of the total force is
0.
+F.
–F.
There is not enough information to find the Y component of total force.
The Z component of the total force is
0.
+M g.
–M g.
There is not enough information to find the Z component of total force.
4
Name _______________________________________________________________________
B-1 – Graphing – 20 Points
A cart with a fan, total mass = 1.000 kg, and a second cart without a fan, mass = 0.500 kg, begin
at rest on a frictionless track. The fan generates a constant external net force on the first cart of
+0.600 N (to the right). The system consists of the two carts. Plot the horizontal component of
the center of mass (x-com) and the velocity of the center of mass (v-com) of the system from t =
0 to t = 2 s. Define x-com = 0 m at t = 0 s. Assume the track is long enough so that the carts do
not reach the end and ignore friction and air resistance forces (other than the force of the fan).
1.000 kg
0.500 kg
Your plots must have scales on the vertical axes and clear indications of values at t = 0 and t = 2.
x-com (m)
0
t (sec)
1.0
2.0
v-com (m/s)
0
t (sec)
1.0
2.0
5
Name _______________________________________________________________________
Problem C-1 (24 Points)
A cannon on a cliff overlooking a flat valley fires at an elevation angle  = 30° and a launch
speed of 196 m/s. The cannonball is 1470 m above the valley when it begins its trajectory.
Ignore air resistance and use g = 9.8 m/s2.
A. How long does it take for the cannonball to reach its maximum height?
B. How high above the valley is the cannonball at its maximum height?
C. How long does it take the cannonball to fall from its maximum height to the ground?
D. How far does the cannonball travel horizontally (shown as d below)?
 = 30°
1470 m
max h = ?
d=?
A. Time to reach max height = _________________________________________________ s
B. Maximum height above valley = _____________________________________________ m
C. Time to fall from maximum to ground = _______________________________________ s
D. Total horizontal distance (d) = _______________________________________________ m
6
Name _______________________________________________________________________
Problem C-2 (24 Points)
An asteroid in deep space, mass = 1.250 x 106 kg, is moving at 4000. m/s when it hits a second
asteroid of unknown mass, initially at rest. The second asteroid splits into two pieces (not
necessarily equal halves) moving as shown below. The first asteroid continues in the same
direction but at a lower speed. Ignore all forces external to the asteroids.
Find the total mass of the second asteroid:
2000. m/s
30°
4000. m/s
2268. m/s
1000. m/s
Before
After
Total mass of second asteroid = _______________________________ kg
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  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