PHY 2130
EXAM 3 A
April 3, 2013
Name (print): ___________________________________
(Last)
(First)
WSU ID Number (9 digit): _____________________________
Please circle your quiz section:
Monday
Tuesday
Wednesday
Thursday
11:45 AM
10:40 AM
11:45 AM
10:40 AM
(K. Dhindsa)
(J. Huang)
(K. Dhindsa)
(J. Huang)
Instructions:
1) Print your name and ID number at the top. Indicate on the scantron sheet which exam
you have (A or B) by marking either “A” or “B” in a blank area near the top center of the
scantron sheet.
2) Keep the cover of exam CLOSED until the exam has started!
3) Using a pencil, fill out the answer sheet boxes and bubbles with your name and
identification number (include leading 0’s in ID number) before starting the exam (you do
not need to include date of birth, grade, sex, etc.).
4) You will have 50 minutes to do the exam.
5) The scantron sheet will not be returned. You will get back the exam itself from your
quiz instructor. An exam key will be posted on Blackboard/lecture website.
6) You may use a non-graphing calculator. No other electronic devices may be used.
Cellphones, PDAs, etc., cannot be used as a calculator.
7) When you are finished with the exam, please bring your student ID, the answer sheet
and the exam to the instructor.
8) You are NOT to use notes or books during the exam, or to communicate with another
student, or to look at another student’s exam. Any violation can result in a grade of “zero”
for this exam or a failing grade for this course.
All questions carry the same weight.
1. A mechanic turns a wrench using a force of 24 N at a distance of 17 cm from the rotation
axis. The force is perpendicular to the wrench handle. What magnitude torque does she
apply to the wrench?
A.
B.
C.
D.
E.
408 N·m
118 N·m
4.08 N· m (Problem 11 chapter 8)
1.18 N·m
0.63 N·m
2. Four point masses of 1.4 kg each are arranged in a square on
massless rods. The length of a side of the square is d = 0.56 m. What is
the rotational inertia for rotation about an axis passing through masses
B and C?
A.
B.
C.
D.
E.
0.878 kg · m2 (Problem 5 chapter 8)
0.439 kg · m2
-0.878 kg · m2
0 kg · m2
-0.439 kg · m2
3. A skater is initially spinning at a rate of 17.7 rad/s with a rotational inertia of 2.93 kg · m2
when her arms are extended. What is her angular velocity after she pulls her arms in and
reduces her rotational inertia to 1.65 kg · m2?
A.
B.
C.
D.
E.
3.1 rad/s
17.7 rad/s
21.3 rad/s
31.4 rad/s (Problem 7 from Review Questions for Exam 3 (chapters 8-12)))
0 rad/s
4. A container is filled with gas at a pressure of 4.3 105 Pa. The container is a cube, 0.10 m
on a side, with one side facing south. What is the magnitude of the force on the south side
of the container due to the gas inside?
A.
B.
C.
D.
E.
4.3 N
43 kN
43 N
430 N
4.3 kN (Problem 7, chapter 9)
5. A hydraulic lift is lifting a car that weighs 14 kN. The
area of the piston supporting the car is A2, the area of the
other piston is A1, and the ratio A2/A1 is 108.5. How far
must the small piston be pushed down to raise the car a
distance of 2.0 cm? [Hint: Consider the work to be done.]
A.
B.
C.
D.
2.17 cm
14 m
14 cm
2.17 m (Problem 9 from Review Questions for
Exam 3 (chapters 8-12))
E. Impossible to determine
6. Imagine holding two identical bricks under water. Brick A is just beneath the surface of
the water, while brick B is at a greater depth. Which of the following statements is correct?
A. The force needed to hold brick B in place is larger than the force required to hold
brick A in place.
B. The force needed to hold brick B in place is the same as the force required to hold
brick A in place.
C. The force needed to hold brick B in place is smaller than the force required to hold
brick A in place.
D. There is not enough information to assess the relationship between the force needed
to hold brick B and the force required to hold brick A in place.
E. None of the above.
7. A clock has a pendulum that performs one full swing every 5.0 sec. What is the length
of the pendulum?
A.
B.
C.
D.
E.
1.5 m
6.2 m (Problem lecture 26)
5.0 m
12 m
Impossible to determine
8. A mass on the spring in simple harmonic oscillator has amplitude A and period T. If the
mass is quadrupled (increased by a factor of four), what will happen to the period?
A.
B.
C.
D.
E.
The period will increase by a factor of two
The period will increase by a factor of four
The period will decrease by a factor of four
The period will decrease by a factor of two
The period will not change
9. A 1.0 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial
velocity is 0.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum
kinetic energy of the simple harmonic motion?
A.
B.
C.
D.
E.
0.014 J
0.0090 J
0.0075 J
0.0018 J
0.0012 J
10. A fisherman notices a buoy bobbing up and down in the water in ripples produced by
waves from a passing speedboat. These waves travel at 3.3 m/s and have a wavelength of
7.8 m. At what frequency does the buoy bob up and down?
A.
B.
C.
D.
E.
100 Hz
12.2 Hz
4.23 Hz
3.3 Hz
0.423 Hz (Problem 21 from Review Questions for Exam 3 (chapters 8-12)))
11. By shaking one end of a stretched string, a single pulse is generated. The traveling
pulse carries
A.
B.
C.
D.
E.
mass
energy
momentum
energy and momentum
mass, energy and momentum
12. An ambulance traveling at 44 m/s approaches a car heading in the opposite direction at
a speed of 28 m/s. The ambulance driver has a siren sounding at 550 Hz. At what
frequency does the driver of the car hear the siren? You can take the speed of sound in the
air as equal to 343 m/s.
A.
B.
C.
D.
E.
580 Hz
527 Hz
682 Hz
448 Hz
100 Hz
13. A guitar’s E-string has a length 65 cm and a mass 0.29 g. It vibrates with a
fundamental frequency of 329.63 Hz. Determine the tension with which the string is
stretched. [Hint: Consider the speed of the wave.]
A.
B.
C.
D.
E.
32 N
65 N
82 N (Lecture 27).
122 N
Impossible to determine
14. The intensity of the sound wave from an airplane is 1.0×102 W/m2 at 5.0 m. What is
the intensity at 100 m?
A.
B.
C.
D.
E.
0.25 W/m2
0.53 W/m2
5.0 W/m2
0.25 mW/m2
Impossible to determine
15. Consider an organ pipe, which is closed at one end and open at the other. If you
increase the length of the pipe, the fundamental frequency of the standing sound wave will
A.
B.
C.
D.
E.
increase
decrease
not change
disappear
impossible to determine
Possibly useful equations:
Physical Constants
•
g = 9.80 sm2 (always down!)
•
•
•
•
G = 6.67 × 10-11 m3/kg⋅s2
Patm = 101.3 kPa
ρwater = 1000 kg/m3
0ºC = 273.15 K
Chapter 1
o Surface area of a sphere: 𝑆 = 4𝜋𝑟 ! (r is a radius)
o Surface area of a cube: 𝑆 = 6𝑎! (a is a side)
!
o Volume of a sphere: 𝑉 = ! 𝜋𝑟 !
o Volume of a cube: 𝑉 = 𝑎!
o Quadratic equation: 𝑎𝑥 ! + 𝑏𝑥 + 𝑐 = 0; solution: 𝑥!,! =
!!± ! ! !!!"
!!
Chapter 2
  
o Displacement (change in position): Δr = rf − ri .




Δr
Δv
o Average velocity: vav =
; average acceleration: aav =
Δt
Δt
o Constant acceleration equations: Δvx = v fx − vix = ax t
Δx = x f − xi = 12 (v fx + vix ) Δt
2
Δx = vix Δt + 12 ax ( Δt )
v 2fx − vix2 = 2ax Δx
Chapter 3
• Two-dimensional motion
opposite
sin =
hypotenuse
cos =
adjacent
hypotenuse
tan =
opposite
adjacent
Right triangle: a2 + b2 = c2
Chapter 4
• Force and Newton’s Laws of Motion

F
∑

o Newton’s 2nd Law: a =
or
m


F
∑ = ma
o The magnitude of the gravitational force: F =
o Weight : W = mg .
o Static friction: f s ≤ µs N
o Kinetic friction: f k = µk N
Chapter 5
• Circular Motion
o
o
o
o
Gm1m2
r2


Δθ
Angular displacement: Δθ = θ f − θ i ; average angular velocity ω av =
Δt
1
s = rθ , 1 complete circle = 1 revolution = 2π radians; f = , ω = 2πf
T
To relate linear to angular quantities: v = rω
v2
Acceleration in uniform circular motion: ar =
= ω 2r
r
Δω = ω f − ω i = αΔt
1
Δθ = (ω f + ω i )Δt
2
1
Δθ = ω i Δt + αΔt 2
2
2
2
o ω f −ω i = 2αΔθ
o


v2
∑ Fr = mar = m r
Chapter 6
• Work and Energy
o Work: W = F Δr cos θ (If F and r are along the x-axis then W = Fx Δx ).
o Translational kinetic energy: K trans = 12 mv 2 .
o The Work-Kinetic Energy Theorem: Wtotal = ΔK
o The gravitational potential energy close to earth: U grav = mgy
o Gravitational potential energy everywhere: Ugrav = -Gm1m2/r
o The potential energy associated with a spring : U spring = 12 kx 2 .
o The force required to pull on a spring: Fspring = −kx
o Conservation of energy : Einitial = E final .
o Power: P =
Chapter 7
•
ΔE
= Fv cosθ
Δt
Momentum, Impulse and Conservation of Momentum


o Linear momentum: p = mv (add as vectors)


o Conservation of momentum: ∑ pinitial = ∑ p final


o Impulse: Δp = ∑ F Δt
Chapter 8
• Rotations, torques, and angular momentum
o The rotational kinetic energy: K rot = 12 I ω 2
o Rotational inertia: I = ∑ mr 2
o Torque: τ = ±rF⊥ = ±r⊥ F = rF sin θ
o Torque and angular acceleration α: τ = Iα, α ≡
lim Δω
Δt → 0 Δt
o Angular momentum: L = I ω
o Conservation of angular momentum: if ∑τ = 0, Li = L f
o Rotational work: W = τ·Δθ
Chapter 9
P = F/A
ρ = m/V, S.G. = ρ/ρwater, P = Patm + ρgd, FB = ρflgVsub
ΔV
= A1v1 = A2 v2 , P1 + ρgy1 + 12 ρv12 = P2 + ρgy 2 + 12 ρv 22
Δt
ΔV π ΔP / L 4
Viscous flow (Poiseuille):
=
r
Δt
8 η
Viscous drag: FD = 6πηrv
Surface Tension in a bubble: ΔP = 2γ/r
Chapter 10
•
•
F
ΔL
F
Δx
ΔV
=Y
=S
ΔP = − B
A
L
A
L
V
Simple Harmonic Motion (SHM)
o The maximum displacement, velocity and acceleration in SHM:
xm = A
vm = ω A am = ω 2 A
o The equations of motion for SHM:
Assume x = A at t = 0: x = Acosωt, vx = -ωAsinωt, ax = -ω2Acosωt
mech
o The mechanical energy for SHM: ESHM
= 12 kA2 = 12 mv 2 + 12 kx 2
o The angular frequency (velocity) for a mass-spring system: ωspring =
o The angular frequency for a pendulum:
ω pendulum =
k
m
g
L
Chapter 11
•
Waves
Power
P
=
Area
4πr 2
F
o The speed of transverse wave on a string: vstring =
µ =mL
µ
2π 2π f
o f, ω, λ are related!
=
2π f = ω ; k =
λ
v
o Wave intensity (for an isotropic source): I =
o The speed of a wave : v = λ f =
ω
k
o The distance between two adjacent nodes is ½ λ (also the distance between
two adjacent antinodes
2L
v
o Standing waves on a string: λn =
; fn = n
(n=1,2,3,...)
n
2L
Chapter 12
• Sound
o
o
v=
B
ρ
v=
Y
ρ
v = 331 + 0.606TC m/s
o Pressure amplitude Vs displacement amplitude: p0 = ωvρs0
p2
o I= 0
2 ρv
⎛ I ⎞
o Sound intensity level: β = (10 dB) log ⎜ ⎟ ; I 0 = 1.00 ×10−12 W m2
⎝ I 0 ⎠
o Standing sound wave in a pipe open at both ends: see formulas for standing
waves on strings in Chapter 11 section
o Standing sound wave in a pipe closed at one end:
4L
v
λn = ; f n = n
(n=1,3,5,...)
n
4L
⎛ v − vo ⎞
⎟⎟ f s
o Doppler shift: f o = ⎜⎜
⎝ v − v s ⎠
Conversion factors: 1 m = 39.37 inches;
1 mi = 1.609 km;
1 km = 1000 m = 100,000 cm;
1 kg = 2.20 lb