Name: _______________________________________________________________________
Exam #2
Physics I
Fall 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
_____ 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
A-1
Value
12
A-2
18
B
24
C-1
22
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 (Parts B and C), show all work to receive credit.
Part A1 – Multiple Choice – 12 Points Total (3 at 4 Points Each)
Write your choice(s) on the line to the left of the question number.
_______1.
On the line to the left, write the equation number from the equation sheet that best
expresses the Work – Kinetic Energy Theorem.
_______2.
An object is moving with a constant speed but changing direction. Which statement
below is always true?
A.
B.
C.
D.
The object is moving along a closed path.
The net force on the object is zero.
There is no net work being done on the object.
All forces acting on the object are conservative forces.
Question 3 refers to the figure below. At a certain instant in time, five stones of equal mass, AE, are moving with the same speed, v0, but in different directions as shown. They are all at a
height h above level ground. Ignore air resistance and assume a constant force of gravity down.
V0
V0
Y = Up
D
X
E
V0
A
B
C
V0
V0
_______3.
Which stone will reach the ground with greatest speed?
A. Stone A.
B. Stone B.
C. Stone C.
D. Stone D.
E. Stone E.
F. All will hit with the same speed.
2
Name: _______________________________________________________________________
Part A2 – Multiple Choice – 18 Points Total (6 at 3 Points Each)
Questions 6-11 refer to the figure shown below and the directions given as A-I. At the instant
shown, the fan is rotating at –2 rad/s (clockwise as seen from the front). It is slowing down with
a constant angular acceleration of +4 rad/s2. The questions refer to the directions of six vector
quantities at the instant shown in the figure. “P” indicates a point on the tip of one fan blade.
Take the center of rotation as the origin of the coordinate system.
P
A) .
B) .
C) .
D) .
E) .
F) .
G) Out of the page.
H) Into the page.
I) Direction is undefined because the quantity is zero or insufficient information was given.
_______6.

What is the direction of the angular velocity vector ( ) of the fan?
_______7.

What is the direction of the angular momentum vector ( L ) of the fan?
_______8.

What is the direction of the angular acceleration vector (  ) of the fan?
_______9.

What is the direction of the net torque vector (  ) acting on the fan?

_______10. What is the direction of linear velocity ( v ) at point P on the tip of the fan blade?
Note: “Linear” velocity is motion measured in m/s.

_______11. What is the direction of linear acceleration ( a ) at point P on the tip of the fan


blade? Note: “Linear” acceleration is the acceleration we refer to in “ Fnet  m a ”.
3
Name: _______________________________________________________________________
B – Graphing – 24 Points
A mass on a spring begins at y = 0 cm moving up at velocity +V0. It reaches a maximum height
of y = 10.0 cm. A graph of the net force on the object during its travel is shown below. The
only forces in the problem are gravity and the spring force (assumed to be ideal).
Plot the potential energy (PE) and kinetic energy (KE) of the system as functions of y.
Define PE = 0 at y = 0. Your plots must include:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values of PE and KE at y = 0, 5, and 10 cm.
Show all work.
V=0
V0
y =10 cm
Fy (N)
y = 0 cm
0
y (cm)
5
-10
-20
-30
PE
y (cm)
0
5
10
KE
y (cm)
0
5
10
4
10
Name: _______________________________________________________________________
Problem C-1 (22 Points)
A mass m = 0.10 kg is attached to an ideal string wound around a spool of radius r = 5.0 cm and
rotational inertia I = 2.5 x 10–4 kg m2. The force of gravity acts on the hanging mass. The axis
of the spool is fixed in place. What is the acceleration, a (down direction), of the hanging mass?
Ignore bearing friction, ignore air resistance, and use g = 9.8 m/s2.
r
I
m
a
Acceleration = ______________________________________________ m/s2
5
Name: _______________________________________________________________________
Problem C-2 (24 Points)
A shooting gallery target consists of a horizontal rod of length 0.50 m and mass 0.24 kg, with
two 0.050 kg wooden blocks on the ends. The rod is free to rotate around its center in a
horizontal plane. A bullet of mass 0.0065 kg hits one of the wooden blocks at 60° with speed
960 m/s as shown below and becomes embedded inside.
What is the final rotation speed of the target?
You are looking at the system from above, looking down on it.
The target is initially at rest. Neglect friction. Gravity is not a factor in this problem.
You will need this formula: Irod = 1/12 M L2 for a rod of length L rotating around its center.
Treat the wooden blocks and bullet as point masses.
(top view)
L = 0.50 m
0.050 kg
0.24 kg (rod)
0.050 kg
60°
r = 0.25 m
960 m/s
0.0065 kg (bullet)
Rotation speed: _______________________________________________ units _________
6
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

F


net
dt



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
38.
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
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.
7
v 2,f 
2 m1
m  m1
v1,i  2
v 2 ,i
m1  m 2
m1  m 2

Formula Sheet for Homework and Exams – Page 2 of 2
46a.
46b.
47a.
47b.
48a.
48b.
49.

m m
| F | G 1 2 2
r

m m
F  G 1 2 2 r̂
r

1 | q1 || q 2 |
| F |
4  0
r2

1 q1 q 2
F
(r̂ )
4  0 r 2

1 | qi |
| Ei |
4   0 ri 2

1 qi
E
(r̂i )
4   0 ri 2


F  qE
50.
51.
52.
1 qi
4   0 ri
U  qV
 
V    E  dx
V
V
x
V
53y. E y  
y
V
53z. E z  
z

 
54. F  q v  B
mv
55. r 
qB
53x. E x  
Useful Constants
(You can use the approximate values on exams.)
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
8