Name ________________________________________________________________________
Exam #1
Physics I
Spring 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.
Section #
_____ 1
_____ 2
_____ 3
_____ 4
_____ 5
_____ 6
_____ 7
_____ 9
_____ 10
_____ 11
_____ 12
_____ 14
_____ 15
M/R 8-10 (Schowalter)
M/R 10-12 (Schowalter)
M/R 10-12 (Stoler)
M/R 12-2 (Bedrosian)
M/R 2-4 (Bedrosian)
M/R 2-4 (Schroeder)
M/R 4-6 (Bedrosian)
T/F 10-12 (Adams)
T/F 10-12 (Washington)
T/F 12-2 (Wilke)
T/F 2-4 (Wilke)
M/R 12-2 (Stoler)
T/F 12-2 (Adams)
Questions
Part A
Value
16
B-1
18
B-2
12
C-1
16
C-2
18
C-3
20
Total
100
Score
Cheating on this exam will result in an F in the course.
Sharing information about this exam with people who have not yet
taken it is cheating on the exam for both parties involved.
The Formula Sheets are the last two pages. Detach carefully for easier reference if you wish.
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 numerical questions, show all work to receive credit.
Part A – Warm-Ups – 16 Points Total (4 at 4 Points Each)
Write your choice on the line to the left of the question number.
______ 1.
Which equation on the Formula Sheet represents the Impulse-Momentum Theorem?
(Write the equation number on the line to the left.)
______ 2.
Which of the following force pairs are Newton’s 3rd Law pairs, if any?
A.
B.
C.
D.
E.
F.
______ 3.
A.
B.
C.
D.
______ 4.
A.
B.
C.
D.
E.
The weight of an airplane in straight and level flight and the lift of its wings.
The friction of the wheels of a horse-drawn wagon moving at a constant velocity
and the force of the horses pulling the wagon.
The weight of a cart and the normal force of the track on the cart.
The force on an insect from hitting the windshield of a moving car and the force on
the windshield from the insect.
All of the above (A-D).
None of the above (A-D).
Two identical cars, A and B, are racing each other around a circular track. Car A is
on the outside lane (greater radius), car B is on the inside lane (lower radius). Both
cars complete one lap (one circle) in the same time. Which car requires greater
magnitude of net force to move around the track in uniform circular motion?
Car A.
Car B.
Both require the same force.
There is not enough information to determine which car requires greater force.
A cannon fires a cannon ball that explodes into three pieces in mid-air. In the time
after firing the cannon ball but before the first piece hits the ground, neglecting air
resistance, which statement is true about the momentum of the system consisting of
the cannon ball before the explosion and all three pieces after the explosion?
Momentum is conserved in the horizontal and vertical directions.
Momentum is conserved in the horizontal direction only.
Momentum is conserved in the vertical direction only.
Momentum is not conserved in either the horizontal or vertical directions.
There is not enough information to determine if momentum is conserved or not.
2
Name ________________________________________________________________________
B-1 – Graphing – 18 Points
Push on cart (not on force
probe) and release--keep
hand out of way of motion
detector
In the illustration above, the student releases the cart at t = 0.00 s when the cart is 1.00 m from
the motion detector. A constant force is applied by the string tension after the push. The cart
reaches its closest point 0.50 m from the motion detector at t = 1.00 s. Neglect friction. Plot x
(displacement from the detector), v (velocity), and a (acceleration) versus time from after the
student releases the cart at t = 0.00 until t = 2.00 s. Show the following information:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values at any minimum or maximum points.
3. The values at t = 0.00, t = 1.00, and t = 2.00 s.
x (m)
0
t (sec)
1.0
2.0
v (m/s)
t (sec)
0
1.0
2.0
1.0
2.0
a (m/s2)
t (sec)
0
3
Name ________________________________________________________________________
B-2 – Graphing – 12 Points
Consider another cart on a track. The cart can move in the + or – X direction on the track. The
track has a magnetic bumper on each end to prevent the cart from running off the track. The cart
and track are similar to the carts and tracks we use in class with one important difference:
The track is on frictionless ice and free to slide in the + or – X direction.
The mass of the cart is 0.500 kg and the mass of the track (including the bumpers) is 2.000 kg.
The center of the cart starts at X = 0.000 m and the cart’s initial velocity is +1.000 m/s.
The center of the track starts at X = 0.000 m and the track’s initial velocity is 0.000 m/s.
The system is the cart and the track. Plot the center of mass location and velocity of the center of
mass from t = 0.000 s (the initial time) to t = 10.000 s. Include the following:
1. General shapes of the curves, noting any points where the curvature or slope changes.
2. The values at any minimum or maximum points.
3. The values at t = 0.000 and t = 10.000 s.
Xc-m (m)
t (sec)
0
Vc-m (m/s)
2
4
6
8
10
t (sec)
0
2
4
6
8
10
4
Name ________________________________________________________________________
Part C – Problems – 54 Points Total
C-1 (16 points)
A pirate ship in a harbor at sea level fired its cannon and hit the top of a hill 310 meters above
sea level. The cannon ball was in the air for 10.0 seconds. The elevation angle of the cannon
was 30° above horizontal. What was the horizontal distance from the pirate ship to the top of the
hill? Use g = 9.8 m/s2 and ignore air resistance.
h = 310 m
 = 30°
d=?
Horizontal Distance to Top of Hill: _________________________ units _______
5
Name ________________________________________________________________________
C-2 (18 points)
Masses m1 and m2 are free to slide up and down their respective tracks, connected by a string
passing over a pulley, as shown in the figure below. Neglect the masses of the string and pulley
and neglect all sources of friction. In this problem, we will use the following variables:
Masses:
m1, m2
String Tension:
T
Inclination angle of track 1:

Inclination angle of track 2:

Acceleration of mass m2:
a (positive to the right and down track 2)
Acceleration constant of gravity:
g
m1
m2


(a) Write Newton’s 2nd Law equation for m1 in terms of m1, , a, g, and T:
______________________________________________________
(b) Write Newton’s 2nd Law equation for m2 in terms of m2, , a, g, and T:
______________________________________________________
(c) Find the acceleration (a) in terms of m1, , m2, , and g:
a = __________________________________________________
6
Name ________________________________________________________________________
C-3 (20 points)
The asteroid 433 Eros is on a direct collision course with Earth at 1000.00 m/s! Intrepid oil rig
workers, quickly retrained as astronauts, detonate thermonuclear bombs deep inside the asteroid
and split it into two pieces. Each piece must deviate from the original path by more than
1.00000° in order to miss Earth. The astronauts determine that after the explosion, Piece 1 ( ⅓ of
the total mass) has a speed of 1000.61 m/s at an angle of 2.00000° from the original course, and
so it will miss. Determine if Piece 2 ( ⅔ of the total mass) will also miss.
You can ignore gravity and all other forces external to the asteroid or its pieces.
433 Eros
1000.00 m/s
Piece 2
angle = ?
Earth
Vy
Vx
Earth
2.00000°
Piece 1
1000.61 m/s
Does Piece 2 miss Earth? _______________________
7
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
8
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
9