EXAM I
Phys 172H Fall 2009
Modern Mechanics - Honors
Instructor: Prof. E. W. Carlson
TEST FORM “A”
There are two parts to Exam I: The machine-graded part of this test,
and the last page that you turn in to be graded by hand.
Machine Answer Sheet
(This part of the exam is worth 75 points.)
Using a pencil, fill in Last Name, First Name, and Middle Initial, plus your 10-digit Purdue
University ID number, which starts with 00. Enter “Carlson” for instructor, Course (PHYS
172H), Date (9/17/09), and Test (1). Enter “Test Form” from the box above. Leave
“Section” blank. You must include your Signature.
Fill in only one answer per question. If your answer is slightly different,
choose the closest answer. You must use a PENCIL and fill in the circle completely.
Hand-Graded Part: (This part of the exam is worth 25 points.)
Enter Name, Signature, PUID.
Your work must be legible and clear! Correct reasoning is required for full credit -a correct answer with incorrect or no reasoning will be counted as wrong.
Cross out anything you do not want us to read in the hand-graded part.
FINISHED? Turn in all parts of this exam to the front of the classroom,
including question sheets and scratch paper.
Show ID to the instructor or teaching assistant when turning in your exam.
Each multiple choice question is worth 5 points.
Problem 1. Vectors. Which statement is true about these vectors?
1)
2)
CORRECT 3)
4)
Problem 2. Carnival Game. To win the the following carnival game, you must
throw a ball such that it goes through the cylinder on the left without touching
the sides at all. That is, the ball must land in the cylinder with no horizontal
component to its velocity.
B A
C
Carnival Game
At what angle should you throw the ball in order to win the game and take
home the giant teddy bear? (Neglect air resistance.)
CORRECT
1)
2)
3)
4)
Steeper than 45O
45O
Less steep than 45O
This game is a scam, since it is not possible to win.
Problems 3 and 4 are about the Earth and Moon. (Not to scale)
mEearth =6.0 x 1024 kg
REarth = 6.4 km
RE-M = 380,000 km
mass
radius
mMoon = 7.3 x 1022kg
RMoon = 1.7 km
Earth-moon distance
Problem 3. What is the magnitude of the force of gravity that the Moon exerts
on the Earth?
CORRECT 1) 2.0 x 1020 N
2) 5.6 x 10-20 N
3) 8.4 x 1025 N
4) -1.2 x 1020 N
Problem 4. How many electrons would you have to move from the Earth
to the Moon for the magnitude of the electric force between the Earth and Moon
to equal that of the gravitational force between them? Choose the closest answer.
(There are about 1051 electrons in all of the atoms on Planet Earth.)
1) 10
electrons
21
2) 10 electrons
CORRECT 3) 1032 electrons
4) 1048 electrons
Problem 5. A stationary particle in otherwise empty space decays into two fragments.
One of the fragments is obsesrved to have a momentum of <5.6, -4.3, 2.0> kg m/s
just after the decay. The other particle is invisible to the detector and so its
momentum cannot be directly measured. What is the momentum of the invisible
particle?
1.
CORRECT 2.
3.
4.
5.
<5.6, -4.3, 2.0> kg m/s
<-5.6, 4.3, -2.0> kg m/s
<5.6, 4.3, -2.0> kg m/s
<-5.6, -4.3, 2.0> kg m/s
Not enough information is given
Problems 6-8 are about four bees, with the following velocities:
Bee A:
Bee B:
Bee C:
Bee D:
<0,1,1> m/s
<1,0,1> m/s
<0,3,3> m/s
<-1,1,1> m/s
Problem 6. Which of the bees fly with the same velocity?
1) only A & C
2) only B & D
3) only A & D
4) A, B, & C
CORRECT 5) None of the bees fly with the same velocity
Problem 7. Which of the bees fly in the same direction?
1) only A & B
CORRECT 2) only A & C
3) B, C, & D
4) None of the bees fly in the same direction
Problem 8. Which of the bees fly with the same speed?
1) only C & D
2) only A & D
CORRECT 3) only A & B
4) None of the bees fly with the same speed
Problems 9-11 are about the following scenario. The windshield of a
speeding car hits a hovering insect.
Problem 9. Compare the magnitude of the force that the car exerts on the bug
to the force that the bug exerts on the car. (Note: the interatomic forces
between bug and windshield are electric forces.)
1) The force that the car exerts on the bug is bigger.
CORRECT 2) The two forces are equal.
3) The force that the bug exerts on the car is bigger.
Problem 10. Compare the magnitude of the change of momentum of the bug
to that of the car:
CORRECT 1) The magnitudes of the change of momentum are equal.
2) The magnitude of change of momentum of the bug is bigger.
3) The magnitude of change of momentum of the car is bigger.
Problem 11. Compare the magnitude of the change of velocity of the bug to
that of the car:
1) The magnitudes of the change of velocity are equal.
2) The magnitude of change of velocity of the car is bigger.
CORRECT 3) The magnitude of change of velocity of the bug is bigger.
Problems 12-14 are about the following scenario. In outer space, far
from other objects, block 1 of mass 45 kg is at position < 9, 8, 0 > m,
and block 2 of mass 1100 kg is at position < 17, 8, 0 > m.
Problem 12. What is the (vector) gravitational force acting on block 2
due to block 1? It helps to make a sketch of the situation.
1) <0, -5.18 x 10-8, 0 > N
2) < 8.02 x 10-7, 0, 0 > N
CORRECT 3) < -5.18 x 10-8, 0, 0 > N
4) <0, 0, 8.02 x 10-7 > N
Problem 13. At 4.2 seconds after noon both blocks were at rest at the
positions given above. At 4.3 seconds after noon, what is the (vector)
momentum of block 2?
CORRECT 1) < -5.18 x 10-9, 0, 0 > kg·m/s
2) <0, 2.1 x 10-2, 0 > kg·m/s
3) < 8.02 x 10-7, 0, 0 > kg·m/s
4) < -5.18 x 10-9, 8.02 x 10-7, 0 > kg·m/s
Problem 14. At 4.3 seconds after noon, what is the (vector)
momentum of block 1?
1) < 2.1 x 10-2, 0, 0 > kg·m/s
2) < 3.9 x 10-5, 0, 0 > kg·m/s
3) <0, 7.09 x 108, 0 > kg·m/s
CORRECT 4) < 5.18 x 10-9, 0, 0 > kg·m/s
Problem 15.
A star of mass 7 x 1030 kg is located at <5 x 1012, 2 x 1012 , 0> m.
A planet of mass 3 x 1024 kg is located at <3 x 1012 , 4 x 1012, 0> m
and is moving with a velocity of <0.3 x 104 , 1.5 x 104, 0> m/s.
What is the initial force due to gravity of the star on the planet?
1) 9.2 x 1015 <0.7, -0.7 ,0> N
2) 9.2 x 1015 <-0.7, 0.7, 0> N
CORRECT 3) 1.8 x 1020 <0.7, -0.7, 0> N
4) 1.8 x 1020 <-0.7, 0.7, 0> N
PHYS 172H -- Fall 2009
Name (Print): __________________________
Signature: ____________________________
PUID: _______________________________
Problem 16. (Hand Graded, 15 total points)
You jump off of a platform, and catch a ball in mid-air.
Your center of mass is at initial position <0,0,0>m. Just after you
leave the platform, your initial velocity is <12,5,0>m/s. Your friend throws you a
ball of mass 2kg, and you catch it in mid-air, when the y-component of your
position again reaches ry = 0m. The velocity of the ball right before you
catch it is <0,0,22>m/s.
Name ______________
A)
(5 points) What is your momentum just after you leave the
platform? State your assumptions clearly. For the purposes of this
problem, it is okay to lie about your own weight, but you should
state a reasonable number.
Name ______________
B) (10 poins) What is your momentum just after you catch the ball?
Name ______________
C)
(10 poins) Approximately how long was your friend’s hand in contact
with the ball in order to accelerate it to roughly 22m/s? State your assumptions
and approximations clearly.
Constants and Equations
! ! !
"r rf ! ri
!
vavg =
#
"t t f ! ti
!
!
p = ! mv
!
!
!ptotal = Fext ,net !t
!=
1
! 2
"v #
1$ % &
'c(
!
!
!
!psystem + !psurroundings = 0
!
mm
Fgrav on 2by1 = !G ! 2 21 rˆ2!1
r2!1
!
v=
!
p/m
! 2
! p "
1+ #
$
% mc &
vavg , x =
vix + v fx
2
!
!
Fgrav on m by M E = ! gm
!
1 q2 q1
Felec on 2by1 =
rˆ2#1
4!" 0 r!2#1 2
!
Fspring = kS s
G = 6.7 $10
#11
N·m
N?
m22
kg 2
1
N?
m22
N·m
= 9 $109
4!" 0
C2
c = 3 $108 m/s
g = 9.8 N/kg
M Earth = 6 $1024 kg
REarth = 6.4 $106 m
melectron = 9 $10#31 kg
mproton = 1.7 $10#27 kg
mneutron % mproton
1 kg = 2.2 pounds
1 inch = 2.54 cm
1 foot = 30.5 cm
1 mile = 1609 m