Name _______________________________________________________________________
Exam #1
Physics I
Fall 2004
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
_____ 5
_____ 6
_____ 7
_____ 8
_____ 10
M/R 8-10 (Bedrosian)
M/R 10-12 (Wetzel)
M/R 12-2 (Wetzel)
T/F 10-12 (Bedrosian)
T/F 12-2 (Cummings)
T/F 2-4 (Cummings)
M/R 2-4 (Schroeder)
M/R 12-2 (Bedrosian)
Questions
Part A
Value
24
B-1
20
B-2
12
C-1
20
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 – 24 Points Total (6 at 4 Points Each)
Write your choice(s) on the line to the left of the question number.
______ 1.
A.
B.
C.
______ 2.
A.
B.
C.
D.
______ 3.
What principle of physics states that all forces exist in equal and opposite pairs?
Newton’s Second Law.
Newton’s Third Law
The Impulse-Momentum Theorem.
In which of the following situations is an object accelerating (as measured by
someone at rest) in a direction that is not the same direction as the net force on it?
Put all that apply or “0” if none.
A driver in a moving car forcibly applies the brakes and groceries spill out of a
grocery bag in the back seat.
A driver in a moving car makes a sudden turn to the right and the passengers in the
back seat are pressed against each other
A boy is twirling a rock on a string when the string breaks.
A rider on a roller coaster is temporarily upside-down at the top of a loop.
Two drivers with the same mass have a drag race in two electric cars, A and 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. The mass of car A is greater than the mass
of car B. Which car has greater magnitude of momentum at t = 20 seconds?
F (N)
Fmax
A.
B.
C.
D.
Car A.
t (sec)
0
Car B
0
10
20
Both have the same magnitude of momentum at t = 20 seconds.
There is not enough information to determine which car has the greater magnitude
of momentum at t = 20 seconds.
2
Name _______________________________________________________________________
For questions 4 and 5, consider angles in the range [0°,180°].
______ 4.

Consider an object at a specific instant of time that is moving with velocity v1 and

acceleration a 1 . At this instant, it is slowing down. What can one correctly


conclude about the angle between v1 and a 1 ?
C.


The angle between v1 and a 1 is greater than 90°.


The angle between v1 and a 1 is equal to 90°


The angle between v1 and a 1 is less than 90°.
D.
There is not enough information to conclude any of A-C above.
A.
B.
______ 5.
Consider an object at another specific instant of time that is moving with velocity


v 2 and acceleration a 2 . At this instant (not the same as question 4 above), it is
moving at a constant speed and changing direction. What can one correctly


conclude about the angle between v 2 and a 2 ?
C.


The angle between v 2 and a 2 is greater than 90°.


The angle between v 2 and a 2 is equal to 90°


The angle between v 2 and a 2 is less than 90°.
D.
There is not enough information to conclude any of A-C above.
A.
B.
______ 6.
Which equation(s) is/are correct Newton’s Second Law equation(s) based on the
free-body diagram below? Select all that apply or put “0” if none are correct.
N
T
Y

F
m
a
X

W
A.
N  T sin   W cos  0
E.
T cos  F  m a
B.
N  T sin   W sin   0
F.
T cos  F  W sin   m a
C.
N  T sin   W sin   m a
G.
N  T cos  F  W cos  m a
D.
T  F cos  m a
H.
N  T sin   F  W sin   0
3
Name _______________________________________________________________________
B-1 – Graphing – 20 Points
This question involves one-dimensional motion. An object’s acceleration is shown below for the
time interval t = 0.0 s to t = 12.0 s. The initial position of the object is x = 0.0 m and the initial
velocity of the object is v = +4.0 m/s. Plot the position (x) and velocity (v) of the object in the
time interval t = 0.0 s to t = 12.0 s. Make sure to include the following features:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values of x and v at any minimum or maximum point(s), including the time value(s)
3. The values of x and v at t = 0.0, t = 6.0, and t = 12.0 s.
x (m)
0
t (sec)
2.0
4.0
6.0
8.0
10.0
12.0
v (m/s)
t (sec)
0
2.0
4.0
6.0
8.0
10.0
12.0
a (m/s2)
1.0
t (sec)
0
2.0
4.0
6.0
8.0
10.0
-1.0
4
12.0
Name _______________________________________________________________________
B-2 – Graphing – 12 Points
Y
30°
cliff
X
V0
A hiker knocked a large rock loose and the rock rolled off a cliff at an angle of 30° below
horizontal. The rock fell for 5.0 seconds before hitting the ground 130 meters below. In this
problem, use a coordinate system where +X is horizontal (to the right) and +Y is vertical (up).
The initial location of the rock is (0,130). Use g = 9.8 m/s2 and ignore air resistance.
Plot X and Y for the rock from the time it falls off the cliff (t = 0.0 s) to the time it hits the
ground (t = 5.0 s). Include the following features:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values of X and Y at t = 0.0 and t = 5.0 s
X(m)
t (sec)
0
Y (m)
1
2
3
4
5
t (sec)
0
0
1
2
3
4
5
5
Name _______________________________________________________________________
Problem C-1 (20 Points)
A boy riding in a car notices that when his mother drives around a curve, his yo-yo hangs on its
string at a 15° angle from vertical. The constant speed of the car is 15 m/s and the road is flat
(not banked). Assume that the yo-yo is not swinging back and forth on the string.
Find the radius of the curve. Assume the curve is circular and use g = 9.8 m/s2. For partial
credit, you must show a free-body diagram. (Please draw it here ↓ )
The motion of the
car is into the page.
15°
Direction toward the
center of the curve.
Radius of curve = _________________________________________________ m
6
Name _______________________________________________________________________
Problem C-2 (24 Points)
You are a traffic safety engineer analyzing a two-car crash at an intersection. You have data
from both cars’ on-board sensors and computers, but there is a question about the calibration of
some of the sensors. Your objective is to determine the maximum force magnitude (Fmax)
exerted on car #1 during the crash as an independent check of calibration. The known facts:
1. Car #1 with mass = 1500 kg was moving at 14.0 m/s due east just before the crash.
2. Car #2 with mass = 2000 kg was moving at 10.5 m/s due north just before the crash
3. After the crash, the cars became entangled and moved together at the same velocity.
4. The road was icy and so all forces external to the two cars can be ignored during the crash.
5. The graph of net force magnitude on car #1 versus time is shown below. (Fmax is unknown.)
N
F (N)
Fmax
#1
E
14 m/s
10.5 m/s
t (sec)
0
#2
0.00
0.10
0.20
Part I: Find the magnitude of the change of momentum of car #1 (show your work):
Magnitude of Change of Momentum =
(Part II is on the next page.)
7
15,000 kg m/s
Name _______________________________________________________________________
N
F (N)
Fmax
#1
E
14 m/s
10.5 m/s
t (sec)
0
#2
0.00
0.10
0.20
From Part I:
Magnitude of Change of Momentum =
15,000 kg m/s
(Part I was on the previous page)
Part II: Find Fmax for the force magnitude versus time curve for car #1 shown above. Assume
that the direction of the force was constant during the crash.
Fmax = _______________________________________ N
8
Name _______________________________________________________________________
Formula Sheet for Homework and Exams – 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   Fnet 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
9
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 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
10