Final: Tuesday, April 29, 7pm, 202 BrooksMakeup Monday April 28, 1pm, 437 White Hall

• 67% focused on this last section of the course

• Chapters 10.1-3, 11.1-2, 11.4-5, 13 (all), 14.1-5, 5.4

• There will also be problems from Chapters 1-7

(motion, forces, energy, momentum, rotation)

• Totaling 25 multiple choice questions

You should be able to convert between

K/C/F temperature scales

• Fahrenheit to Celsius

– TF = TC x (9/5) + 32

– TC = (TF - 32) x (5/9)

• Kelvin to Celsius

– TK = TC + 273.15

– TC = TK - 273.15

Not a simple factor conversion

∆∆∆∆TC = ∆∆∆∆TF *5/9

∆∆∆∆TC = ∆∆∆∆TK For more problems on Ch. 10 & 11, see lectures

and following problem solving day

You should be able to calculate the

amount of thermal expansion

• Length expansion

(thermometer)

∆L=αLo∆T

• Area expansion (ring)

∆A=γAo∆T

• Volume expansion

(basketball) ∆V=βV∆T

• Note: ∆T is in °C (or K)

• Note: γ =2α, β= 3α Thermometers rely on a thermal

expansion of a liquid (e.g. mercury)

Main Ideas in Chapter 11

You should be able to:

• Understand the ways to transfer heat (mostly conceptually except conduction)

• Calculate heat necessarily to raise the temperature or change the phase of a material

Extra Practice: 11.1, 11.3, 11.5, 11.7, 11.9, 11.15, 11.17, 11.25, 11.27, 11.33

Phase changes (e.g. solid to liquid)

When heating ice into water and then into steam the temperature does not go up uniformly

–Different slopes since cwater > cice

–Flat bits at phase changes

Time

Tem

pe

ratu

reice

water

steam

Melting Point

Boiling Point

Q = m c ∆∆∆∆Tc called the specific heat of a material

cwater = 4190 J/(kg K) - difficult to heatcice = 2090 J/(kg K)

Applying constant heat per second

mLv

mLf

Lf<Lv

https://www.youtube.com/watch?v=lTKl0Gpn5oQ

Transferring heat energy

• 3 mechanisms

– Conduction

• Heat transfer through material (rods, windows, etc.)

– Convection

• Heat transfer by movement of hot material (hot air, hot

liquid while cooking)

– Radiation

• Heat transfer by light

(sun, fire, tanning bed)

Rate of heat flow

(Conduction)

Energy flows from higher temp. to lower temp. (0th law)

Rate of energy transfer (P=power) depends on

– Temperature difference (TH-TC)

– Area of contact (A) and length (L) over which heat flows

– Thermal conductivity of the material (k)

• k (copper) = 385 W/(m K) good conductor

• k (air) =0.02 W/(m K) good insulator

• Higher k means more heat flow

- P in Watts, Q in Joules, t in seconds

L

TTkA

t

Q CH −=

∆=P

L

L

Main Ideas in Chapter 13

You should be able to:

• Understand Simple Harmonic Motion (SHM)

• Determine the Position, Velocity and Acceleration over time

• Find the Period and Frequency of SHM

• Relate Circular Motion to SHM

Extra Practice: C13.1, C13.3, C13.11, 13.1, 13.3, 13.5, 13.9, 13.11, 13.17, 13.19, 13.21, 13.23, 13.25, 13.27, 13.31

Period and Frequency Independent of Amplitude

• Period of a spring

– The period (T) of a mass on a spring is dependent upon the

mass m and the spring constant k

• Frequency

– The frequency, ƒ, is the number of complete cycles or

vibrations per second; units are s-1 or Hertz (Hz)

k

m2T π=

T

1ƒ =

• The angular velocity is related to the frequency

• The angular velocity/speed (or angular frequency)gives the number of radians per second

m

kƒ2 =π=ω

Graphical

Representation

of Motion

When x is a maximum or

minimum, velocity is zero

When x is zero, the speed is

a maximum (slope of x)

Acceleration vs. time is the

slope the of velocity graph.

When x is max in the

positive direction, a is max

in the negative direction

Velocity as a Function of Position

• Conservation of Energy allows a calculation of the

velocity of the object at any position in its motion

– Speed is a maximum at x = 0

– Speed is zero at x = ±A

– The ± indicates the object can be traveling in either

direction

( )2 2kv A x

m= ± −

2

212

212

21 kAkxmv =+

22

max

2

212

max21

Am

kv

kAmv

=⇒

=

More Ideas in Chapter 13

You should be able to:

• Understand the pendulum

• Determine different kinds of waves

• Find the wavelength, frequency and speed of a wave

• Damped Oscillations

The Simple Pendulum

xL

mgF −=

Since restoring force is proportional

to negative of displacement,

pendulum bob undergoes SHM.

Effective “spring constant” is

keff = mg/L

effk

mT π2=

g

LT π2=

spring pendulum

Pendulum

If a pendulum clock keeps perfect time at the

base of a mountain, will it also keep perfect

time when it is moved to the top of the

mountain? If not, will it run faster or slower?

No, g is slightly smaller at higher

altitude.

g

LT π2=

T will be bigger so it will take longer

to complete an oscillation.

Types of Waves

traveling wave

Transverse

Longitudinal

fv λ=

Are you on the right wavelength?

6 m/s 2 m

If the wave below has a velocity of 6 m/s, answer the following:

What is the wavelength?

What is the wave’s period?

What is the wave’s frequency?

2 m

T= λ/v = 2 m/(6 m/s) = 0.333 s

f =1/T = 1/0.333s = 3 Hz

fT

v λλ

==

Main Ideas in Chapter 14

You should be able to:

• Explain how a vibrating object

affects the nearby air molecules

to produce sound waves

• Calculate the speed, intensity

and decibels of sound

A man shouts and

hears his echo off a

mountain 5 seconds

later. How far away

is the mountain?

Speed of sound ~343m/s at room temperature

Compare to thunder

Determining distance

with echoes

One of the loudest sounds on Earth was made by the

volcanic eruption of Krakatoa in Indonesia in August

of 1883. At a distance of 161 km, the sound had a

decibel level of

180 dB. How far

away from the

source would

you be to not

experience pain

(<120 dB).

θθθθ = 35°

m= 12 kg

D = 3m

A 12 kg block slides 3 m from rest down a

frictionless ramp with an incline angle of 35°

before being temporarily stopped by a spring

with spring constant k=30,000 N/m. By how

much is the spring compressed when the block

stops?

How should we

approach this

problem?

A spring with spring constant 300 N/m is

attached to an object whose mass is 2.0 kg.

If the spring is initially stretched A=0.25 m,

what is the velocity of the object at x = 0, -A

and A/2?

2

212

212

21 kAkxmv =+

( )2 2kv A x

m= ± −