Phy 2053 Announcements
Final Exam
–
April 24 Saturday, 8 – 10 pm
•
Please get there at least 10 minutes early
–
Covers all material taught in this course.
–
Room assignments
•
Last name
Room
A–G
Chemistry Lab Bldg C130
H – LE
Little Hall 101
LF – RI
Pugh 170
RJ – Z
Weil 270
–
You will be allowed one handwritten formula sheet (both sides)
–
Sample exam from last year posted on website.
Phy 2053 Announcements
Make-up Exam
–
To take the make-up, you must have obtained permission from one
of the instructors (Profs. Acosta, Chan or Hirschfeld)
–
April 21 Wednesday, 6:15 – 8:10 pm
–
Location: NPB 1101
–
Covers all material taught in this course.
–
You will be allowed one handwritten formula sheet (both sides)
Prof. Hirschfeld is out of town due to cancelled flights.
Prof. Chan holds regular office hours (Tue 5th period, Thu 4th period)
Chapter 9 - Solids and Fluids
•
States of matter
•
Strength of materials and elastic moduli
–
Young’s modulus:
Y = stress/strain
•
F
∆L
=Y
A
Lo
Pressure and Density
–
Pressure: P = F/A
m
ρ ≡
V
–
Density:
–
Pressure and depth equation for a fluid:
•
Pressure depends only on depth
Chapter 9 - Solids and Fluids (cont’d)
•
Buoyant Force: B = ρ fluidVfluid g = wfluid
– buoyant force equals the weight of the displaced fluid
– For floating objects, the forces balance
ρobj
ρ fluid
Vfluid
=
Vobj
Bernoulli’s Equation
1 2
P + ρv + ρgy = constant
2
due to energy conservation
Pressure and Depth equation
•
• Po is normal
atmospheric pressure
1.013 x 105 Pa
The pressure does not
depend upon the shape
of the container
A bucket is full of water. It has a tiny hole
at the bottom. Find the velocity of water
leaking through the hole.
h
Equation of Continuity
• A1v1 = A2v2
• The product of the
cross-sectional area of
a pipe and the fluid
speed is a constant
– Speed is high where the
pipe is narrow and speed
is low where the pipe has
a large diameter
• Av is called the flow
rate (volume per time).
Chapter 13 – Vibrations and Waves
•
•
Begins with Hooke’s Law: F =
- kx
Leads naturally to simple
harmonic motion
–
oscillations between the
positions x = ±A
•
•
A is the amplitude
T is the period - time for the object
to complete one cycle of motion
–
•
Maximum potential
energy
Maximum kinetic
energy
Different from tension!
ƒ is the frequency - number of
complete cycles per unit time
ƒ=1/T
ƒ measured in cycles/second (s-1) or hertz
(Hz)
Anywhere:
v =±
k
A2 − x 2
m
(
)
Chapter 13 – Vibrations and Waves (cont’d)
•
•
•
•
•
x = A cos ωt
v = -A ω sin ωt
a = -Aω2 cos ωt
2πf = ω
k
ω=
m
1
f =
2π
F = -kx = ma
k
T = 2π
m
m
k
NB: kinematic equations don’t work for SHM
• SHM: Simple pendulum
L
T = 2π
g
Chapter 13 – Vibrations and Waves (cont’d)
λ
• Waves
– Transverse
– Longitudinal
λ = wavelength
– Wave velocity
λ
c = λ/T = λƒ
y
x
Waves
Chapter 14 – Sound
• Production of sound waves
• Characteristics of sound waves
– Audible, infrasonic waves, ultrasonic
• Speed of Sound
– Liquid:
v =
B
ρ
Solid rod: v = Y
ρ
– General: v = elastic property
inertial property
m⎞
T
⎛
– Speed of sound in air: v = ⎜ 331 ⎟
s ⎠ 273 K
⎝
Doppler Effect-General Case
⎛ v + vo ⎞
ƒo = ƒ s ⎜
⎟
v
⎝
⎠
⎛ v ⎞
ƒo = ƒ s ⎜
⎟
⎝ v − vs ⎠
• Use positive values of vo and vs if the motion is
toward each other--Frequency appears higher
• Use negative values of vo and vs if the motion is
away from each other--Frequency appears lower
• Both the source and the observer could be
moving
⎛ v + vo ⎞
ƒo = ƒ s ⎜
⎟
⎝ v − vs ⎠
Combine the two equations
Chapter 8
•
•
Στ = Iα
Torque and angular acceleration:
Moment of inertia I:
I = Σmi ri2 = MR2
– Table 8-1 lists moments of inertia for different objects
•
Rotational dynamics – Newton’s 2nd Law for rotation
– Bucket problem
•
Rotational kinetic energy:
1 2
KE = Iω
2
– Mechanical conservation laws still apply!
L=Iω
•
Angular momentum:
•
Conservation of angular momentum (isolated system): The angular
momentum of a system is conserved when the net external torque acting
on the systems is zero.
Στ = 0, Li = Lf or Iiω i = If ω f
8.65 A cylinder with moment of inertia I1 rotates with angular
velocity ωo about a frictionless vertical axle. A second cylinder,
with moment of inertia I2, initially not rotating. Because the
surfaces are rough, the two cylinders eventually reach the same
angular speed ω. (a) Calculate ω. (b) Show that kinetic energy is
lost in this situation, and calculate the ratio of the final to the initial
kinetic energy.