Mark answers in spaces 31-43 on the answer sheet
PHYSICS 221
Summer 2005
EXAM 3: July 25 2005 9:50pm—10:50pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Some questions are one point, others are two points, as marked. Answer all questions.
All questions are multiple choice. Questions 31-36 are 1 point, 37-43 are 2 points.
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..
"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 12) 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 13 questions on this exam labeled 31-43.
Mark answers in spaces 31-43 on the answer sheet.
BEST OF LUCK !
1
31) (1 point) A pendulum in a science museum is designed to have a period of 5 s. The
length of the pendulum is
a) 6.2 m
b) 7.8 m
c) 12.4 m
d) 15.6 m
e) none of the above
32) (1 point) A thin shell of charge has a radius R and contains a total charge Q. What is
the electric field inside the shell at a point a distance r from the center of the shell (r<R) ?
a) E= kQ/r2
b) E= kQ/R2
c) E=0
d) E= kQ/r
e) can not be determined
33) (1 point) The units of electric flux (ΦE) are
a) Nm2
b) N/C
c) Cm2
d) Cm2/N
e) Nm2/C
34) (1 point) Consider a charge –Q enclosed within a spherical Gaussian surface of
radius R. Another charge 3Q is outside the sphere, as shown in the figure. What is the
flux through the sphere?
a) Q/ε0
b) - Q/ε0
c) 2 Q/ε0
d) -2Q/ε0
o -Q
e) none of the above
o 3Q
2
35) (1 point) A spring is oscillating with amplitude a, around a central position x=0. The
graph of position vs time is drawn below. Where is the speed maximum in simple
harmonic motion ?
a) A
b) B
c) C
d) D
e) E
36) (1 point) A positive charge +Q is shown in the figure. At which of the points A, B C,
D, E is the magnitude of the field a maximum ?
A)
B)
C)
D)
E)
A
C
E
B
+Q
D
3
37) (2 points) A harmonic oscillator is made by using a 0.6 kg block attached to an ideal
spring of force constant 150 N/m. The period of oscillation is
a) 15.8 s
b) 2.52 s
c) 0.8 s
d) 0.4 s
e) 0.06 s
38) (2 points) A machine part is undergoing simple harmonic motion with a frequency of
10 Hz and an amplitude of 1.5 cm. How long does it take the part to go from the central
position x=0 to the position x=-1.5 cm ?
a) 1s
b) 0.16 s
c) 0.1 s
d) 0.05 s
e) 0.025 s
39) (2 points) A new planet has a radius of twice the Earth’s radius but only twice the
Earth’s mass. If the acceleration due to gravity on Earth is g, then the acceleration due to
gravity at the new planet’s surface is
a) g/4
b) g/2
c) g
d) 2g
e) 4g
40) (2 points) Two satellites are in circular orbit around the Earth. The first has a radius
of r and the second at a radius of 3r, measured from the Earth’s center. The ratio of the
periods of the satellites is
a) 1:1
b) 1:3
c) 1:5.2
d)1:9
e) 1:27
4
41) (2 points) Three charges qa=+4 µC, qb=+6 µC and qc=-2µC are arranged along a
straight line. Charge b is between a and c with the distances shown in the figure. A) What
^
is magnitude and direction of the net force on charge qb. ( i is the unit vector along the
x axis)
qa
qb
0.1 m
qc
0.1 m
x
^
A) 32 i N
^
B) -32 i N
^
C) +11 i N
^
D) –11 i N
E) 0 N
42) (2 points) An electron is projected with a speed of 2x106 m/s into the uniform field
between the parallel plates shown in the figure. The electron deflects upwards by 1 cm,
after traveling a distance of 2 cm along the plates. The electric field between the plates is
a) 1.1x105 N/C downward
b) 570 N/C downward
c) 1140 N/C upward
d) 1140 N/C downward
e) none of the above
5
43) (2 points) The electric field at a perpendicular distance of 18mm from the middle of a
long thin uniformly charged rod is measured to be 3.5x104 N/C and directed away from
the rod. What is the linear charge density of the rod ?
a) 3.5x10-5 C/m
b) 6.2x10-7 C/m
c) 3.5x10-8 C/m
d) 7x 10-8 C/m
e) none of the above
6
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
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 =
3. Vectors
r r
r r
3.1) Dot Product: A ⋅ B = Ax B x + Ay B y + Az B z =| A || B | cosθ
r
r
where θ is the angle between A and B .
r
3.2) Components: A = Ax iˆ + Ay ˆj + Az kˆ
r
r r
3.3) Magnitude: | V |= V = V x2 + V y2 + V z2 = V ⋅ V
1
2a
(− b ±
b 2 − 4ac
)
6. Forces
r
r
6.1) Newton’s Second: F = ma
r
r
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
5. One Dimensional Motion
6.5) Centripetal Force: F =
5.1) Average Velocity: v = ∆x / ∆t
5.2) Instantaneous Velocity: v = dx / dt
mv 2
R
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
r
7.1) Position Vector: r = xiˆ + yˆj + zkˆ
r
r
r
r
2 r
7.2) Velocity and Acceleration: v = dtd r
a = dtd v = dtd 2 r
r r r
v = v0 + at
r r r
r
r = r0 + v 0 t + 12 at 2
7.3) Constant Acceleration only: v 2 − v 2 = 2ar ⋅ (rr − rr )
0
r r0
r − r0 1 r r
= 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
7
Formula Sheet for Exam 2
8. Kinetic Energy and Work
8.1) Linear Motion: K = 12 mv 2
9. Potential Energy
8.2) Rotational Motion: K rot = 12 Iω 2
r r
8.3) Work by a constant force W = F ⋅ s = Fs cosθ
8.4) Work done by a variable force in 1 dim:
x2
W = ∫ Fx dx
9.1) Gravitational: Ugrav=mgy
9.2) Spring: Uspring=kx²/2
dU
dx
9.4) Conservative force from potential in 3d: a
9.3) Force from potential in 1D: Fx ( x) = −
x1
r r P2
8.5) Work in 3D: W = ∫ F ⋅ dl = ∫ F cos φ dl
P2
P1
8.6) Power: P=dW/dt
P1
r r
P = F ⋅v
10. Momentum and Impulse
r
r
r r
10.1) Momentum: p = mv F = ddtp
r t2 r
r
r
10.2) Impulse: J = ∫ Fnet dt = p 2 − p1
t1
r
r
10.3) Center of mass position: M tot rcm = ∑ mi ri
r
r
10.4) Center of mass velocity: M tot vcm = ∑ pi
r
r
r
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
r
r
r
11.3) 3-dimensional totally inelastic collision: v1 f = v 2 f = v cm
13. Angular Momentum
r r r
13.1) For Particle L = r × p
r
r
13.2) For rigid body L = Iω
r
r dL
13.3) Relation to torque τ =
dt
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
r r r
12.6) Torque: τ = r × F
14. Static Equilibrium
r
r
14.1) Condition for static equilibrium: τ net = 0; Fnet = 0
8
9
Formula Sheet for Exam 3
15. Physical Constants
15.1) Gravitational Constant G=6.673×10−11 Nm²/kg²
15.2) Coulomb’s Constant k E = 4πε1 0 = 8.9876 × 109 Nm 2 / C 2
15.3) Permeability of vacuum ε 0 = 8.8542 × 10−12 C 2 /( Nm 2 )
15.4) Magnitude of electron charge e=1.6022x10-19 C
15.5) Mass of electron me = 9.11 × 10−31 kg
16. Gravity
16.1) Newton’s Law of Gravitational Attraction: F = G
m1m2
r2
m1m2
r
M
16.3) Acceleration of gravity g = G 2
r
16.2) Gravitational Potential U = −G
16.4) Escape velocity v e =
2 gR = 2GM / R
16.5) Gravitational acceleration at the Earth’s surface g=9.8 m/s2
16.6) Orbital motion centripetal force = mv2/R =GMm/R2
orbital speed v = v =
GM / R
17. Kepler’s Laws
17.1) Each planet moves in an elliptical
orbit with the sun at one focus of the
ellipse.
17.2) A line from the sun to a given
planet sweeps out equal areas in equal
times. Equivalently, the angular
momentum of a planet about the sun
remains constant.
17.3) The periods of the planets are
proportional to the 3/2 power of the
semi-manor axis lengths of the orbit. If a
is the length of the semi-major axis,
2πa 3 / 2
T=
.
Gmsun
18. Harmonic Oscillation
18.1) Period/frequency: f = 1 / T
ω = 2π f = 2π / T
18.2) Force law for harmonic motion: F = −kx
18.3) Angular frequency of oscillator: ω = k / m
18.4) Solution to oscillator x = A cos(ωt + φ )
18.5) Simple pendulum ω =
g/L
T = 2π L / g
18.6) Physical Pendulum ω = mgd / I
10
19. Coulombs Law etc.
19.1) Coulomb’s Law: F = k E q1q2 / r 2
r
19.2) Electric Field from charge E = k E Qrˆ / r 2
r
r
19.3) Force exerted by an electric field: F = qE
20. Gauss’s Law
20.0) General definition of electric flux :
r r
Φ E = ∫ E cos φ dA = ∫ E⊥ dA = ∫ E ⋅ dA
20.1) Gauss’s Law Φ E = qenclosed / ε 0
20.2) Inside a conductor: E=0; ρ=0
20.3) Electric Field near a charged sheet:
E = σ /(2ε 0 )
21. Various Fields and Potentials
Case
Electric Field
Magnitude
Point Charge Q
E=
Line charge, charge
per unit length λ
Charged sheet, charge
per unit area σ
Q
4πε 0 r
2
Potential
V =
Q
4πε 0 r
λ
2πε 0 r
σ
E=
2ε 0
E=
11
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
31
41
32
42
33
43
34
35
36
37
38
39
40
12
Scratch Paper (intentionally left blank)
13
Scratch Paper (intentionally left blank)
14