Mark answers in spaces 53-75 on the answer sheet
No class Friday April 16
No class Friday April 16
PHYSICS 221
Spring 2004
EXAM 3: April 15 2004 8:00pm—9:30pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice.
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. Note also formula sheets pages 11-14.
"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⇒31. 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 (page 14) 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. There are 23
questions on this exam labeled 53-75.
Mark answers in spaces 53-75 on the answer sheet.
Best of luck, David Atwood and Anatoli Frishman
Physics 221 2004 S Exam 3
Page 1 of 17
Mark answers in spaces 53-75 on the answer sheet
[53] Disk #1 of uniform density of mass 1kg and radius 2m is spinning centered on a
massless turntable with angular velocity ω=12 rad/s. Disk #2 of uniform density of mass
2kg and radius 1m is dropped on it and due to friction between the disks, the system of
two disks eventually rotate at a common angular velocity about the axis of the turntable.
What is the final angular velocity of the system?
(A) 2 rad/s
(B) 4 rad/s
Disk 2 r2=1m; M2=2kg
(C) 6 rad/s
Disk 1 r1=2m; M1=1kg
(D) 8 rad/s
(E) 10 rad/s
Massless Turntable
[54] What is the x-component of the angular momentum about the origin of a particle
G
G
located at the point r = (2 ˆj ) m with mass 2kg and a velocity of v = (iˆ + 2 ˆj + 3kˆ) m / s
(A) +6 kg m²/s
(B) -6 kg m²/s
(C) +12 kg m²/s
(D) -12 kg m²/s
(E) 0 kg m²/s
[55]
Three balls are rolled down an incline ramp and roll without slipping. Ball X is a
solid ball of radius 5cm and mass 1kg. Ball Y is another solid ball of radius 10cm and
mass 0.5kg. Ball Z is a hollow ball of radius 5cm and mass 1kg. Neglecting drag, kinetic
and rolling friction, if these three balls are released simultaneously from the top of the
ramp, in which order do they arrive at the bottom?
(A) X, Y, Z
(B) Z, Y, X
(C) X tied with Y followed by Z
(D) X tied with Z followed by Y
(E) All three tied.
Physics 221 2004 S Exam 3
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[56] Consider an object with weight 100N suspended from the ceiling by three
massless strings as shown. What is the ratio between the tension in string 1 and the
tension in string 3
(A)
(B)
(C)
(D)
(E)
T1:T3=4:5
T1:T3=5:4
T1:T3=3:5
T1:T3=5:3
T1:T3=3:4
5m
Ceiling
3m
4m
T1
T2
T3
100N
[57] The horizontal beam in the figure weighs
150N and is of uniform density. Find the tension
in the 5m cable.
(A) 1200N
(B) 200N
(C) 300N
(D) 500N
(E) 625N
Hinge
Tension =?
[58] Two uniform spheres, each with mass M and radius R , touch each another. What
is the magnitude of their gravitational force of attraction?
(A) F=GM²/(R²)
(B) F=GM²/(2R²)
(C) F=GM²/(4R²)
(D) F=GM²/(8R²)
(E) F=GM²/(16R²)
Physics 221 2004 S Exam 3
Page 3 of 17
[59] The mass of the Sun is about 3×105 times the mass of the Earth. The magnitude of
the gravitational force exerted by the Sun on the Earth is ________ the magnitude of the
gravitational force the exerted by the Earth on the Sun.
(A) About 9×1010 times lager then
(B) About 3×105 times lager then
(C) The same as
(D) About 3×105 times smaller then
(E) About 9×1010 times smaller then
[60] Consider the three spherical masses S, T and U shown in
the diagram. S has a mass of 15kg and is located at (0m,0m,0m).
T has a mass of 50kg and is located at (0m,2m,0m). U has a mass
of 10kg and is located at (-1m,0m,0m). Assume that all the
masses are initially at rest in a region remote from any
gravitational forces aside from the forces they exert on each
other. In addition the gravitational force between these masses is
the only force they are subject to. What is the magnitude of the
initial acceleration of mass S?
40kg
2m
(A) 0.67 nm/s²
(B) 0.95 nm/s²
(C) 1.34 nm/s²
(D) 1.90 nm/s²
(E) 2.68 nm/s²
15kg
10kg
1m
Physics 221 2004 S Exam 3
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[61] Three satellites orbit the earth as shown . Satellite X orbits in a circular orbit with
radius R and period TX. Satellite Y orbits in a circular orbit with radius 2R and period TY.
Satellite Z orbits in an elliptical orbit where the distance to the center of the earth varies
between R and 2R and has period TZ. What is the ratio between the periods of the three
satellites?
Z
(A) TX:TY:TZ= 2 : 4 : 3
(B) TX:TY:TZ= 2 : 2 : 3
(C) TX:TY:TZ= 2 : 4 : 6
(D) TX:TY:TZ= 2 : 2 : 6
(E) TX:TY:TZ= 8 : 8 : 27
Y
2R
R
X
[62] Planet X has a radius of 1000km and the surface gravity is 1m/s². If a projectile is
fired straight upwards from the surface of X with initial velocity 1km/s what is the
maximum height above the surface of X which the projectile achieves? (neglect air
resistance)
(A) 414 km
(B) 500 km
(C) 1000 km
(D) 1500 km
(E) 2500 km
[63] Which of the following relationships between the acceleration, a, and the
displacement x of a particle describes a case of simple harmonic motion?
(A) 3x-a=0
(B) 3x+a=0
(C) 3xa=1
(D) 3x²+a=0
(E) 3x²-a=0
Physics 221 2004 S Exam 3
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[64] A stick of length L is suspended at one of its ends. What is the period of its small
oscillations?
L
(A) T = 2π
g
(B) T = 2π
2L
g
(C) T = 2π
L
2g
(D) T = 2π
L
3g
(E) T = 2π
2L
3g
Period=?
[65] A particle of mass m=2.0 kg is connected to a spring with spring constant
k=4.0N/m. If it oscillates with total mechanical energy E=16 J, what is the maximum
velocity of the mass during the oscillation? Take the zero of potential energy to be the
equilibrium point of the spring
(A)
(B)
(C)
(D)
(E)
0.5 m/s
1.0 m/s
2.0 m/s
4.0 m/s
8.0 m/s
[66] A block of mass M=4.00kg rests on a horizontal frictionless track. It is connected
to either end of the track by two identical ideal springs with spring constant k=50.0N/m.
If the mass is displaced by a small amount, what is angular frequency of oscillation, ω?
(A) ω=3.5s−1
(B) ω=5.0s−1
(C) ω=7.1s−1
k=50.0N/m M=4.00k k=50.0N/m
−1
(D) ω=10.0s
(E) ω=50.0 s−1
Frictionless Track
Physics 221 2004 S Exam 3
Page 6 of 17
[67] Four blocks of insulating material of mass m1=1kg, m2=2kg, m3=3kg, m4=4kg are
on a frictionless horizontal surface as shown on the figure below. They are evenly spaced
and the distance between the 1kg and the 4kg blocks is 10m. The 1kg block has a net
electric charge of Q1=−20µC while block 4 has a net electric charge of Q4=+50µC. The
other blocks are electrically neutral. The blocks are connected by ideal massless strings
and they are in an electric field of magnitude 3.00 × 106 N / C directed to the right as
shown below. What is the magnitude of the tension T in the string between m2 and m3.
E= 3.00 × 106 N / C
T=?
m1=1kg
Q1=−20µC
m2=2kg
Q2=0
(A) T=18N
(B) T=60N
(C) T=87N
(D) T=108N
(E) T=150N
m3=3kg
Q3=0
m4=4kg
Q4=+50µC
10m
[68] A uniform electric field E=100 N/C is directed in the plane of a circular plate of
radius R=1 m. What is the magnitude of electric flux
through the plate?
(A) Φ=1000 Nm²/C
(B) Φ=628 Nm²/C
(C) Φ=314 Nm²/C
(D) Φ=100 Nm²/C
(E) Φ= 0
1m
Physics 221 2004 S Exam 3
Page 7 of 17
E=100N/C
[69] A conducting sphere of radius 10 cm has an unknown charge. If the electric field
15 cm from the center of the sphere has the magnitude 3x103 N/C is directed radially
inward, what is the net charge on the sphere?
(A) +5.0x10-9 C
(B) -5.0x10-9 C
(C) +7.5x10-9 C
(D) -7.5x10-9 C
(E) -2. 5x10-9 C
[70] Three charges of size 1nC, 2nC and 1nC are placed on the x-axis spaced 1m apart
with the 2nC in the middle. Point P is half way between the left 1nC and 2nC while
point Q is half way between the 2nC and the right 1nC. What is the ratio of the xcomponent of the electric field at point P ( EPx )to the x-component of the electric field
at point Q ( EQx ).
(A) EPx : EQx = +1:1
(B) EPx : EQx = −1:1
(C) EPx : EQx = +1:2
(D) EPx : EQx = −2:1
+1nC
+2nC
+1nC
(E) EPx : EQx = +4:3
[71] Consider two parallel charged sheets of charge with charge density + 3nC / m 2
and − 2nC / m 2 respectively. The two sheets are perpendicular to the x-axis where the
positively charged sheet is to the left of the negatively
y
charged sheet as shown below. What is x-component of
the electric field at a point half way between the two
E=?
sheets?
nC
(A) E x = +1
2ε 0 m 2
nC
(B) E x = −1
+3nC/m²
−2nC/m²
2ε 0 m 2
nC
(C) E x = +5
2ε 0 m 2
nC
(D) E x = −5
2ε 0 m 2
nC
(E) E x = +3
2ε 0 m 2
Physics 221 2004 S Exam 3
Page 8 of 17
x
[72]
is
The magnitude of the electric field at a distance 3.0m from a 1.0 µC point charge
(A) 200 N/C
(B) 400 N/C
(C) 600 N/C
(D) 800 N/C
(E) 1000N/C
[73] Four point charges of charge Q are arranged in a square with side length L. What
is the magnitude of the net electrostatic force on one of the charges.
F=?
2
k Q
(A) E 2 1 + 12 2
L
Q
Q
L
kEQ2
(B) 2 2 − 2
L
L
L
2
L
k Q
(C) E 2 1 + 2
Q
Q
L
k Q2
(D) E 2 3 2
L
k Q2
(E) E 2 12 + 2
L
[
]
[ ]
[ ]
[ ]
[ ]
[74] A two identical cylindrical surfaces of length 1m and diameter 2m are in a
uniform electric field directed in the +x direction. Cylinder #1 has its axis parallel to the
x-axis while cylinder #2 has its axis
Cylinder #1
Cylinder #2
parallel to the y-axis. In which case is
there the greatest total flux though the
surface.
(A) Cylinder #1
(B) Cylinder #2
(C) Both the same
(D) Depends on the magnitude of E
y
x
Physics 221 2004 S Exam 3
Page 9 of 17
G
E
[75] A conducting spherical shell has an
inner radius R and an outer radius 2R. The
shell has a total charge of +Q. If a point
charge of +q placed at the center of the shell,
What is the total charge on the outer surface
of the shell?
(A) −q
(B) +Q
(C) Q+q
(D) –Q-q
(E) Q-q
Charge on outer
surface =?
2R
R
Total Charge Q
Charge q
Physics 221 2004 S Exam 3
Page 10 of 17
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)
d
dx
x n = nx n −1
d
dx
sin x = cos x
x n +1
n +1
d
dx cos x = − sin x
n
∫ x dx =
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
mv 2
R
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
Physics 221 2004 S Exam 3
Page 11 of 17
Formula Sheet for Exam 2
8. Kinetic Energy and Work
8.1) Linear Motion: K = 12 mv 2
8.2) Rotational Motion: K rot = 12 Iω 2
G G
8.3) Work by a constant force W = F ⋅ s = Fs cosθ
8.4) Work done by a variable force in 1 dim:
9. Potential Energy
9.1) Gravitational: Ugrav=mgy
9.2) Spring: Uspring=kx²/2
9.3) Force from potential in 1D: Fx ( x) = −
dU
dx
x2
W = ∫ Fx dx
x1
G G P2
8.5) Work in 3D: W = ∫ F ⋅ dl = ∫ F cos φ dl
P2
P1
8.6) Power: P=dW/dt
P1
G G
P = F ⋅v
10. Momentum and Impulse
G
G
G G
10.1) Momentum: p = mv F = ddtp
G t2 G
G
G
10.2) Impulse: J = ∫ Fnet dt = p 2 − p1
t1
G
G
10.3) Center of mass position: M tot rcm = ∑ mi ri
G
G
10.4) Center of mass velocity: M tot vcm = ∑ pi
G
G
G
10.5) Center of mass acceleration: M tot a cm = ∑ Fi = Fexternal
11. Collisions
11.1) 1-dimensional totally inelastic collision: v1 f = v 2 f = v cm
11.2) 1-dimensional elastic collision:
v1 f = 2vcm − v1i
v 2 f = 2vcm − v 2i
G
G
G
11.3) 3-dimensional totally inelastic collision: v1 f = v 2 f = v cm
Physics 221 2004 S Exam 3
12. Rotation
12.1) Angular velocity ω = ddtθ
12.2) Angular Acceleration α =
dω
dt
2
12.3) Circular motion: a rad = Rω ; a tan = rα .
12.4) Moment of Inertia: I = ∑ mi Ri2
12.5) Parallel Axis Thm.: I P = I cm + Md 2
G G G
12.6) Torque: τ = r × F
Page 12 of 17
Physics 221 2004 S Exam 3
Page 13 of 17
Formula Sheet for Exam 3
13. Physical Constants
13.1) Gravitational Constant G=6.673×10−11 Nm²/kg²
13.2) Coulomb’s Constant k E = 4πε1 0 = 8.9876 × 109 Nm 2 / C 2
13.3) Permeability of vacuum ε 0 = 8.8542 × 10−12 C 2 /( Nm 2 )
13.4) Magnitude of electron charge e=1.6022x10-19 C
13.5) Mass of electron me = 9.11 × 10−31 kg
14. Angular Momentum
G G G
14.1) For Particle L = r × p
G
G
14.2) For rigid body L = Iω
G
G dL
14.3) Relation to torque τ =
dt
18. Coulombs Law etc.
18.1) Coulomb’s Law: F = k E q1q2 / r 2
G
18.2) Electric Field from charge E = k E Qrˆ / r 2
G
G
18.3) Force exerted by an electric field: F = qE
15. Static Equilibrium
G
G
15.1) Condition for static equilibrium: τ net = 0; Fnet = 0
16. Gravity
16.1) Newton’s Law of Gravitational Attraction: F = G
m1m2
r2
19. Gauss’s Law
19.1) Gauss’s Law Φ E = qenclosed / ε 0
19.2) Inside a conductor: E=0; ρ=0
19.3) Electric Field near a charged sheet:
E = σ /(2ε 0 )
m1m2
r
M
16.3) Acceleration of gravity g = G 2
r
16.4) Escape velocity ve = 2 gR = GM / R
16.2) Gravitational Potential U = −G
17. Harmonic Oscillation
17.1) Period/frequency: f = 1 / T
ω = 2π f = 2π / T
17.2) Force law for harmonic motion: F = −kx
17.3) Angular frequency of oscillator: ω = k / m
17.4) Solution to oscillator x = A cos(ωt + φ )
17.5) Simple pendulum ω =
g/L
17.6) Physical Pendulum ω = mgd / I
Physics 221 2004 S Exam 3
Page 14 of 17
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
51
61
71
52
62
72
53
63
73
54
64
74
55
65
75
56
66
76
57
67
77
58
68
78
59
69
79
50
70
80
Physics 221 2004 S Exam 3
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Exam 3
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Exam 3
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