Final Exam, Thursday May 4th 8 pm,
Room TBA
25 Multiple choice questions
~17 from material since Test 3Chapter 11 (except section 11.3 and 11.6):
• Heat, specific heat, latent heat
Chapter 13 (all of it)
• Hooke’s law, spring potential energy, SHM,
pendulum, waves
Chapter 14 (through section 14.5)
• Sound waves, speed of sound, intensity of sound,
spherical waves
• Heating an object-specific heat
– Different slopes since cwater > cice
Time
Tem
per
ature
ice
water
steam
Melting Point
Boiling Point
Q = m c ∆T
Changing phase-latent heat
Q = ±m L
Applying constant heat per second
mLv
mLf
Lf<Lv
Transferring heat energy
• 3 mechanisms
– Conduction
• Heat transfer through material
– Convection
• Heat transfer by movement of hot material
– Radiation
• Heat transfer by light
Hooke’s Law (Restoring Force)
FS = -kx (Hooke’s Law)
k is the spring constant (N/m)
Spring Potential Energy
(x)
Fs= slope=k
ersonpring
pring
erson
2
21 kxPES
Energy in an oscillator
• Total energy of system (no frictional forces
doing work):2
212
21 kxmvPEKEE
• E is the same everywhere - as KE increases
PE decreases and vice-versa
• E in terms of amplitude: when x = A, v = 0
2
21 kAE
• The period is the time for one oscillation
• The frequency gives the number of cycles per second
• The angular velocity/speed (or angular frequency)gives the number of radians per second
m
kƒ2
m
k
2
1
T
1ƒ
k
m2T
tAx cos
tAv sin
tAa cos2
m
kAa max
Note: v is slope of x vs. t
a is slope of v vs. t
m
kf 2
Pendulum = Simple Harmonic Motion
xL
mgFpendulum
Effective “spring constant” is keff = mg/L
g
LTpendulum 2
bob
Period of simple pendulum is independent of mass or amplitude;
instead depends on the length of cord
Transverse
Longitudinal
Mechanical Wave Definitions
Amplitude: maximum height of crest or depth of trough (not both!)
Wavelength (l): distance over which wave repeats itself
Frequency (f): Number of crests that pass a given point per unit time
Wave velocity: a crest travels one wavelength in one period T:
Tv
l fl
Waves on Strings
fv l
F = tension in the string
µ = linear density = mass/Length
F
Constructive
Interference in a String
Destructive Interference
in a String
Speed of sound waves depends on the material
through which they travel
lfv
Vibration of an object drives a longitudinal wave in
the air (or other material) molecules to create sound
The Intensity of Sound
24area
power
r
PI
0
10logI
I
• The speed of sound in a solid
– Y is the Young’s Modulus of
the material
– ρ is the density of the material
Yv
• The speed of sound in a liquid
– B is the Bulk Modulus of the liquid
– ρ is the density of the liquid
Bv
331 /273
Tv m s
K
• The speed of sound increases with temperature, in air:
– T is in Kelvin
• Start ID in 2nd column
• Write: Name, 11:30, Post-test
