Physics 221 2005S Exam 1
PHYSICS 221
Spring 2005
EXAM 1: Feb 17 2005 8:00pm—10:00pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice.
Choose the best answer to each question.
Before turning over this page, put away all materials except for pens, pencils, erasers,
rulers, your calculator and “aid sheet”. An “aid sheet” is one two sided 8½×11 page of
notes prepared by the student. There is also a list of possibly useful equations at the end
of the exam.
"In general, any calculator, including calculators that perform graphing numerical
analysis functions, is permitted. Electronic devices that can store large amounts of text,
data or equations are NOT permitted." If you are unsure whether or not your calculator
is allowed for the exam ask your TA.
Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+
Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C.
Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket
computer, PDA or e-book reader.
In marking the multiple choice bubble sheet use a number 2 pencil. Do NOT use ink. If
you did not bring a pencil, ask for one. Fill in your last name, middle initial, and first
name. Your ID is the middle 9 digits on your ISU card. Special codes K to L are your
recitation section, for the Honors section please encode your section number as follows:
H1⇒02; H2⇒13 and H3⇒25.
If you need to change any entry, you must completely erase your previous entry. Also,
circle your answers on this exam. Before handing in your exam, be sure that your
answers on your bubble sheet are what you intend them to be.
It is strongly suggested that you circle your choices on the question sheet. You
may also copy down your answers on the record sheet at the end and take this page
with you for comparison with the answer key to be posted later.
When you are finished with the exam, place all exam materials, including the bubble
sheet, and the exam itself, in your folder and return the folder to your recitation
instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home.
Anyone answering a cell phone must hand in their work; their exam is over.
Total number of questions is 27.
Best of luck, David Atwood and Paula Herrera-Siklody
Page 1 of 12
Physics 221 2005S Exam 1
The following applies to questions [1] and
[2]: A 2-kg block slides up an incline. The
initial speed of the block, at the bottom of the
incline, is 2 m/s. The acceleration of the
block is 7.2 m/s2 down the ramp.
∆x=?
[1] How far along the incline will the block
go before it momentarily stops?
(A) 9cm (B) 13cm
(E) 33cm
(C) 20cm (D) 28cm
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[2] If a hand pushes on the sliding block perpendicularly to the incline surface,
(A) The magnitude of weight increases.
(B) The magnitude of the normal force by the incline on the block increases.
(C) The magnitude of the friction force by the incline on the block increases.
(D) Both A and B.
(E) Both B and C.
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[3] A train car moves along a straight track. The graph shows the position as a function
of time for this train. The graphs shows that the train:
Position
Time
(A) Speeds up all the time
(B) Slows down all the time
(C) Speeds up initially but then slows down.
(D) Moves at a constant speed
(E) Slows down initially but then speeds up.
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Physics 221 2005S Exam 1
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[4] If John walks 1km north at 5.0km/hr and then runs another 1km north at 15.0km/hr.
What is the magnitude of his average velocity during the 2km trip?
(A)20.0 km/hr (B)10.0 km/hr
(C)7.5 km/hr
(D)6.0 km/hr
(E) 5.0 km/hr
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[5] Suppose that a particle moving along the x-axis has velocity as a function of time
described by
v(t ) = a + bt 4
where a=3m/s and b=4m/s5. What is the acceleration of the particle at t=1s?
(A) a=4 m/s² (B) a=7 m/s² (C) a=12 m/s² (D) a=16 m/s² (E) a=20 m/s²
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The following applies to questions [6] and [7]: You want to throw a 400-g snowball to
one of your friends who stands unaware of your evil intentions 10m away from you. The
snowball leaves your hand 1 m from the ground at an angle of 50° with the horizontal and
hits him right on the top of his head. Your friend is 1.7-m tall. Neglect air resistance.
[6] Find the work done by gravity while the ball is in the air.
(A) – 6.7J
(B) −2.7J
(C) 0J
(D) +2.7J
(E) +6.7J
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[7] What is the direction of the acceleration of the snow ball at the top of its trajectory?
(A) Up.
(B) Down.
(C) In the direction of motion.
(D) Opposite to the direction of motion.
(E) The acceleration is instantaneously zero.
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[8] A rock is thrown straight upwards at a velocity of 9.8m/s from a bridge that is 39.2m
above a lake. What is the magnitude of the velocity of the rock when it strikes the lake?
Neglect air resistance.
(A) 9.8m/s (B) 19.6m/s
(C) 29.4m/s
(D) 39.2m/s
(E) 49.0 m/s
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Physics 221 2005S Exam 1
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[9] Cars B moves along a straight road. Shown below are the snapshots from a
stationary camera of the positions at t = 1, 2, 3 and 4 s. Assume that the motion is smooth
(no unexpected behaviors between consecutive snapshots)
B
1
2
3
4
What is the sign of the net work done on B ?
(A) Positive
(B) Negative
(C) Zero
(D) It cannot be said without knowing the detail of the forces acting on B.
(E) It depends on the choice of axes.
[10] City A is 480km directly west of city B. A plane has an air speed of 260 km/hr. If
there is wind blowing north at 100 km/hr, what is the time it takes to fly from city A to
city B? Assume that the air traffic controllers have routed the plane to fly directly over
the interstate which runs in a straight line from A to B.
(A)1.72hr
(B) 1.84hr
(C)2.00hr
(D)2.50hr
(E)3.00hr
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[11] The figure below shows the elliptical path along which a particle moves at a
constant speed clockwise. At which of the indicated points is the acceleration of the
particle the greatest in magnitude?
(A) point P
(B) point Q
(C) point R
(D) both P and R
(E) The acceleration is the same at all points
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Physics 221 2005S Exam 1
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a=3m/s²
[12] A watermelon of mass 10kg is hanging from the ceiling
of an elevator by a massless string. If the elevator is
accelerating upwards at a rate of 3m/s², what is the
magnitude of the net force on the watermelon?
10kg
(A) 128N
(B) 98N
(C) 78N
(D)30N
(E)0N
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[13] A 4-kg book is kept fixed against a vertical wall by a hand
that applies a 200-N force perpendicular to the surface of the
book. The coefficient of static friction between the book and the
wall is µS = 0.3. What is the magnitude of the friction force?
(A) 12N
(B) 20N
(C) 39N
(D) 59N
m=4kg
(E)200N
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[14] A 4.0-kg flower pot slips from a window sill and hits the street at 20 m/s.
What is the kinetic energy of the flower pot right before hitting the ground?
(A) 0J
(B) 80J
(C) 400J
(D) 600J
(E) 800J
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[15] In the figure below, in which case will the dot product of the two vectors be the
largest (including sign). All of the vectors are of the same length.
Case I
(A) Case I
(B)Case II
Case II
Case III
(C)Case III
(D)Case IV
Case IV
(E)All the same
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Page 5 of 12
Physics 221 2005S Exam 1
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The following applies to questions [16] and [17]: Pete applies a horizontal force F=20N
on the system depicted below, made of two boxes A and B placed on a frictionless
horizontal floor. The masses of the boxes are mA = 20 kg and mB = 40 kg.
B
A
[16] What is the magnitude of the acceleration of box B?
(A) 0, you cannot move an object whose weight is 400 N with a 20-N force.
(C) 0.5 m/s2
(D) 1 m/s2
(E)1.2 m/s2
(B) 0.3 m/s2
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[17] The magnitude of the force on A by B is _______________ the magnitude of the
force on B by A.
(A) Four times
(B)Twice
(C)The same as
(D) Half
(E)One fourth
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[18] Two people pull their suitcases along the same horizontal airport hallway. They
both exert the same force on the suitcases, but in case 1, the force is perfectly horizontal,
whereas in case 2, the force makes an angle of 25° with the floor.
What is the ratio (work in case 1):(work in case 2)?
(A) 1:1
(B) 1:sin25°
(C) sin25°:1
(D) 1:cos25°
(E)cos25°:1
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Page 6 of 12
Physics 221 2005S Exam 1
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[19] Consider the system shown below made of three identical blocks of mass m, two
ideal, massless strings and an ideal, massless pulley. The friction between the blocks and
the table is negligible.
T1
m
T2
m
m
Let T1 and T2 be the tension on each string, as shown in the figure. Which of the
following is true?
(B)T1 < T2 = mg
(C)T1 < T2 < mg
(A) T1 = T2 = mg
(D)T1 = T2 < mg
(E)T1 = T2 > mg
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[20] The graph below shows a position dependent net force acting on a 1kg block
moving along the x-axis. Initially the block is at x=0m, moving in the +x direction and
has a kinetic energy of 12J. When the block gets to x=8m, what is its kinetic energy?
(A) 12J
(B)18J
(C)24J
(D)36J
(E)48J
Net Force
3N
2N
1N
1m
2m
3m
4m
5m
6m
7m
8m
x
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Page 7 of 12
Physics 221 2005S Exam 1
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10m
30kg
[21] How much work does Bob do on a 30kg box by pushing it across a level floor
through a distance of 10m at a constant velocity. The coefficient of kinetic friction
between the floor and the box is µk=0.2?
(A)588J
(B)294J
(C)147J
(D)60N
(E)0J
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[22] Robin Hood fires an arrow at velocity v0=30m/s at an angle of θ=30o above the
horizontal from the top of a cliff of height h. The sheriff of Nottingham standing at
distance d from the base of the cliff notices that the arrow impacts him with a speed of
36m/s. What is the height h of the cliff? Neglect air resistance.
(A) h=10m
Robin
Hood
(B) h=20m
v0=30m/s
(C) h=30m
(D) h=40m
(E) h=50m
θ=30o
h
v=36m/s
d
Page 8 of 12
Sheriff of
Nottingham
Physics 221 2005S Exam 1
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The following applies to questions [23] and [24]: An 1kg particle is constrained to
move along the x-axis. At t=0 its velocity is v0 = 2m / s in the +x direction and its initial
position is x = 0m . The acceleration as a function of time is given by the graph below
Acceleration
(m/s²)
2
1
2
4
6
8
Time (s)
[23] Which of the following graphs is the velocity as a function of time for the particle?
(A) Graph I
6
Velocity 4
(m/s)
2
6
Velocity 4
(m/s)
2
6
Velocity 4
(m/s)
2
(B) Graph II
(C) Graph III
(D) None of the graphs.
Graph I
2
4
6
8
2
4
6
8
2
4
6
8
Graph II
Graph III
Time (s)
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Physics 221 2005S Exam 1
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[24] Continuing from the question [23], what is the particle’s position at t=8s.
(A)x=16m
(B)x=24m
(C)x=28m
(D)x=31m
(E)x=32m
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[25] A cannon is fired from a steep slope which makes a
constant 60o angle to the horizontal. It is fired in a direction
perpendicular to the slope and lands further down the slope.
If the cannon ball is fired with an initial velocity of 196m/s
how long after it is fired does it land? Neglect air resistance.
(A) 5s
(B) 10s
(C) 20s
(D) 40s
(E) 80s
60o
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[26] A small stone of mass m = 20 g is placed at the rim (R=27.0cm) of a level pottery
wheel of radius R = 27.0 cm. The wheel is initially at rest and begins moving with a
constant angular acceleration of 0.300 rad/s2. When the system reaches 7.00 rad/s, the
stone flies off. What is the coefficient of static friction between the wheel and the stone?
(A) 0.34
(B) 0.57
(C) 0.81
(D) 1.35
(E) 1.61
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[27] Four blocks of masses m1=1kg, m2=2kg, m3=3kg, m4=4kg are on a frictionless
horizontal surface as shown on the figure below. The blocks are connected by ideal
massless strings. A force FL=10N is applied to the left block and is directed to the left.
Another force FR=50N is applied to the right block, and is directed to the right. What is
the magnitude of the tension T in the string between m2 and m3.
FL=10N
T=?
m4=4kg
m3=3kg
m2=2kg
m1=1kg
FR=50N
(A) T=14N
(B)T=20N
(C)T=38N
(D)T=40N
(E)T=44N
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Best of Luck
David Atwood and Paula HerreraSiklody
Page 10 of 12
Physics 221 2005S Exam 1
Formula Sheet for Exam 1
1. Physical Constants
(numerical value used to derive answers in exam):
1.1) Acceleration of gravity on Earth’s Surface: g=9.8m/s²
1.2) Radius of Earth: Rearth=6.38×106m
1.3) Mass of Proton: mp=1.67×10-27kg
3. Vectors
G G
G G
3.1) Dot Product: A ⋅ B = Ax B x + Ay B y + Az B z =| A || B | cosθ
G
G
where θ is the angle between A and B .
G
3.2) Components: A = Ax iˆ + Ay ˆj + Az kˆ
G
G G
3.3) Magnitude: | V |= V = V x2 + V y2 + V z2 = V ⋅ V
5. One Dimensional Motion
5.1) Average Velocity: v = ∆x / ∆t
5.2) Instantaneous Velocity: v = dx / dt
2. Calculus
2.1)
n −1
d
dx
x = nx
d
dx
sin x = cos x
n
x n +1
∫ x dx = n + 1
d
dx cos x = − sin x
n
4. Algebra
4.1) The solutions to ax 2 + bx + c = 0
are x =
1
2a
(− b ±
b 2 − 4ac
)
6. Forces
G
G
6.1) Newton’s Second: F = ma
G
G
6.2) Newton’s Third: FAB = − FBA
6.2) Kinetic Friction: f k = µ k N
6.4) Static Friction: f s ≤ µ s N
6.5) Centripetal Force: F =
v x = v0 x + a x t
x = x0 + v0 x t + 12 a x t 2
5.3) For Constant Acceleration only: v 2 − v 2 = 2a ( x − x )
0x
0
x
x
x − x0 1
= 2 (v x + v 0 x )
t
7. Three Dimensional Motion
G
7.1) Position Vector: r = xiˆ + yˆj + zkˆ
G
G
G
G
2 G
7.2) Velocity and Acceleration: v = dtd r
a = dtd v = dtd 2 r
G G G
v = v0 + at
G G G
G
r = r0 + v 0 t + 12 at 2
7.3) Constant Acceleration only: v 2 − v 2 = 2aG ⋅ (rG − rG )
0
G G0
r − r0 1 G G
= 2 (v + v 0 )
t
ω = 2πf
v = Rω
7.4) Circular Motion: f = 1 / T
7.4a) Angular Velocity: ω = dθ / dt
7.5) Centripetal Acceleration: a rad = Rω 2 = v 2 / R = ( 4π 2 R ) / T 2
G
G
G
7.6) Changing Reference Frames: v PA = v PB + v BA
8. Kinetic Energy and Work
8.1) Linear Motion: K = 12 mv 2
8.2) Rotational Motion: K rot = 12 Iω 2
8.3) Work by a constant force
G G
W = F ⋅ s = Fs cosθ
8.4) Work done by a variable force in 1
dim:
x2
W = ∫ Fx dx
x1
8.5) Work in 3D:
P2
G G P2
W = ∫ F ⋅ dl = ∫ F cos φ dl
P1
P1
8.6) Power: P=dW/dt
Page 11 of 12
mv 2
R
G G
P = F ⋅v
Physics 221 2005S Exam 1
Record Sheet
You may fill in this sheet with your choices, detach it and take it with you after the exam
for comparison with the posted answers
1
11
21
2
12
22
3
13
23
4
14
24
5
15
25
6
16
26
7
17
27
8
18
28
9
19
29
10
20
30
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