Name: ________________________________________________________________________
Exam #2
Physics I
Spring 2003
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
_____ 14
_____ 5
_____ 7
_____ 10
_____ 11
_____ 15
_____ 12
M/R 8-10 (Washington)
M/R 10-12 (Schroeder)
M/R 10-12 (Zhang)
M/R 12-2 (Bedrosian)
M/R 12-2 (Adams)
M/R 2-4 (Hayes)
M/R 4-6 (Bedrosian)
T/F 10-12 (Wilke)
T/F 12-2 (Sperber)
T/F 12-2 (Adams)
T/F 2-4 (Wilke)
Questions
Part A
Value
24
B-1,2
22
B-3,4
22
C-1
16
C-2
16
Total
100
Score
If we catch you cheating on this exam,
you will be given 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 Sheet is the last page. 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 – 24 Points Total (6 at 4 Points Each)
Write your choice on the line to the left of the question number.
_______1.
A)
B)
C)
D)
E)
Conservation of linear momentum.
Conservation of angular momentum.
Conservation of mechanical energy (kinetic plus potential).
The Impulse-Momentum Theorem.
The Work-Energy Theorem.
_______2.
A)
B)
C)
D)
E)
Block A moves on a horizontal, frictionless surface with a velocity in the positive X
direction. It experiences an elastic collision with block B, initially at rest. After the
collision, block A is observed to be moving in the negative X direction, and block B
is observed to be moving in the positive X direction. We can conclude that:
The mass of block A is greater than the mass of block B.
The mass of block A is less than the mass of block B.
The mass of block A is equal to the mass of block B.
Momentum was not conserved during the collision.
Kinetic energy was not the same after the collision as before the collision.
_______3.
A)
B)
C)
D)
Two automobiles skidding on an icy road collided and became entangled (stuck
together). Luckily, no one was injured! Which principle of physics below could
you not correctly use when analyzing the collision for the insurance companies?
(Assume road friction and air resistance were negligible during the crash.)
Two blocks, A and B, start at rest on a frictionless surface. Block A has less mass
than block B. Both blocks experience the same constant force of magnitude F.
After each block has moved D meters (not necessarily together), which block has
the greater magnitude of linear momentum?
Block A.
Block B.
Both are the same.
There is not enough information given to determine which block.
2
Name: ________________________________________________________________________
_______4.
A)
B)
C)
D)
E)
F)
North.
South.
East.
West.
Up.
Down.
_______5.
A)
B)
C)
D)
A competitor in the Olympics springs off a diving board and attempts a triplesomersault dive. While she is in the air, neglecting air resistance, she cannot
change her
Angular velocity.
Angular momentum.
Rotational kinetic energy.
Rotational inertia.
_______6.
A)
B)
C)
D)
You are the pilot of a small, single-propeller airplane flying east. The propeller is
turning clockwise as you observe it directly in front of you. Preparing to land, you
adjust the throttle to reduce the flow of fuel to the engine, slowing the propeller
down. While the propeller is slowing down, what is the direction of the net torque
acting on the propeller?
Two point particles, A and B, move in circular paths about a common point with the
same angular velocity. Particle A has half the mass of particle B. The distance of
particle A from the center of the circle is twice the distance of particle B. Which
particle has the greater magnitude of angular momentum about the center point?
Particle A.
Particle B.
Both are the same.
There is not enough information given to determine which particle.
3
Name: ________________________________________________________________________
Part B – Shorter Problems – 44 Pts. Total (2 at 10 Pts. + 2 at 12 Pts.)
B-1 (10 Points)
A flywheel with rotational inertia of 50 kg m2 takes 10,000 revolutions to slow from 3,600
rev/min to a complete stop. Assuming the only torque on the flywheel while it is slowing is a
constant torque due to friction in the bearings, what is the magnitude of that torque?
Answer: _____________________ units ________
B-2 (12 Points)
A hockey puck (A) sliding on frictionless ice with an initial speed of 4.0 m/s hits a second puck
of the same mass (B) initially at rest and bounces off with a speed of 2.5 m/s at an angle of +20°
from its original direction. What is the speed of puck B? What is its angle with respect to the
original direction of puck A? (Take + angles as counter-clockwise and – angles as clockwise.)
A
befor e
2.5 m/s
20°
4 m/s
after
A
?
B
B
Speed: _____________________ units ________
Angle: _____________________ units ________
4
Name: ________________________________________________________________________
B-3 (12 Points)
A toy gun fires a plastic pellet with a mass of 0.5 g. The pellet is propelled by a spring with a
spring constant of 1.25 N/cm which is compressed 2.0 cm before firing. The plastic pellet
travels horizontally 10 cm down the barrel (from its compressed position) with a constant friction
force of 0.0475 N. What is the speed of the bullet as it emerges from the barrel?
k = 1.25 N/cm
d = 10 cm travel
x = 2 cm compression
Answer: _____________________ units ________
B-4 (10 Points)
A frictionless turntable with rotational inertia of 0.010 kg m2 is spinning at 3.0 rev/s. A book is
dropped straight down onto the turntable and the turntable slows down to 2.5 rev/s. What is the
rotational inertia of the book about the rotation axis of the turntable?
Answer: _____________________ units ________
5
Name: ________________________________________________________________________
Part C – Longer Problems – 32 Points Total (2 at 16 Pts.)
This section contains longer numerical problems.
C-1 (16 points)
A student volunteer begins a class demonstration with a rotational inertia of 1.400 kg m2 sitting
on a stool with his hands outstretched. The stool has a rotational inertia of 0.100 kg m2 and
negligible friction. The student and stool are spinning at 4 rad/sec. The professor says “catch”
and throws him a 0.100 kg ball at 16.35 m/s. The student catches it in his hand 0.800 m from the
axis of rotation. At the instant before the ball is caught, the student is facing north and the ball is
traveling south, as shown in the diagram below.
16.35 m/s
0.8 m
N
E
W
S
rotation
A. What is the rotational inertia of the student+stool+ball system after the catch?
Answer: ______________________________ units ________
B. What is the angular speed of the student+stool+ball system after the catch?
Answer: ______________________________ units ________
6
Name: ________________________________________________________________________
C-2 (16 points)
A block with mass 2 kg is sliding on frictionless ice with a velocity of 5.0 m/s east at time t = 0.
It is subjected to a changing (not constant) net force over 10 seconds resulting in an impulse of
6.0 N s in the north direction and 18.0 N s in the west direction. What is the total work done by
the force from t = 0 to t = 10 seconds?
Important note: Do not use “average acceleration” to solve this problem!
Answer: ______________________________ units ________
7
Name: ________________________________________________________________________
Formula Sheet for Exam 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