Some of my favourites

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Some of my favourites

• ... not all physics

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Moments

• The Law of the Lever
• and
• the Principle of Moments

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The law of the lever

• The law of the lever is typically represented as
  followsF1 D1 F2 D2

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Principle of moments

• The law of the lever is a special case of the
  principle of moments, which states that...
• ... when a body is in equilibrium under the
  action of any number of forces then the sum of
  the clockwise moments about any point is equal to
  the sum of the anticlockwise moments about the
  same point.
• There is no mention of a fulcrum.

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Lets look a little closer
x
y
A
2 N
1 N (total)
3 N
3 N

• What are the values of x and y ?
• Calculate the moments about A.
• -32 0 12 34 - y5 26 0
• 5y 12 12 2 - 6 20

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Choose another point

• Since y 4 N, x must be 5 N.
• Take the moments about another point and see if
  they add to zero.
• Does this work for a point that is not located on
  the rod? Try it out.

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Integral moments

• If you use integral numbers of newtons on the
  rod/stick you will not necessarily get integral
  readings on the dynamometers in fact you are
  more likely to get non-integral values.
• The moments will still work out but the
  calculation gets messy and the learning point can
  be lost.
• The next slide has a list of integral values.
• Excel spreadsheet

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List of integral moments
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Notes from Lego

• Vibrations, sound, notes, octaves and other
  harmonics

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Measuring the frequency of a note

• This employs a simple Lego assembly in which a
  motor drives a set of toothed wheels.

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Gear arrangement
40 teeth
24
f1
16
8
motor
24 teeth
f1 (teeth per second)
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The notes produced (harmonics)

• The four notes have frequencies in the ratios8
  16 24 40 or
• 1 2 3 5
• The frequencies correspond to the notesd1, d, s,
  m1

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Can we measure the frequency?

• Yes.
• By adding another wheel we can measure the rate
  of rotation of the main drive shaft.
• From this the frequencies of the notes can easily
  be computed.

worm gear
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Finding the speed of the motor

• The speed of the motor is found by driving a
  large wheel (with 40 teeth) from a worm gear on
  the main axle. Its rate of rotation is
  sufficiently slow to be easily timed.
• This wheel advances by one tooth for each
  revolution of the main axle, so the motor rotates
  at 40 times the rate of the extra wheel.
• The frequency with which the teeth of the first
  drive gear (24 teeth) strike the paper is 24
  times the frequency of rotation of the motor,
  i.e. 960 times the rate of rotation of the timed
  wheel.

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• The first wheel (with 24 teeth) rotates at the
  motor speed.
• The number of teeth per second is 24 times the
  speed of rotation.
• The frequency from the wheel with 8 teeth is the
  same.

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Calculation of frequency

• 40 teeth turning at (for example)
• 10 revs. in 77 s equals
• 1 rev. in 7.7 s
• or 0.13 rev. /s
• So the main drive shaft rotates at 40 0.13 or
  5.2 rev. /s
• The drive shaft has a gear wheel with 24 teeth so
  the tooth frequency is
• 24 5.2 or 125 teeth/s
• It drives a second shaft via a gear wheel with 8
  teeth whose tooth frequency must be the same (125
  teeth/s). This is the fundamental.

 
 
 
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So...

• The same Lego assemble illustrates the following
• sound is caused by vibrations
• regular vibrations produce a note
• an octave on the scale corresponds to a doubling
  in frequency (d to d1 )
• along with other simple multiples (3 and 5) they
  produce harmony (d, m, s, d1 )
• the 3rd harmonic corresponds to s and the 5th to
  m.

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Notes from an organ pipe

• All harmonics and odd harmonics

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Harmonics in an air column

• The harmonics that can form in a pipe depend on
  whether it is open or closed.

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d1
m
s
d
m
s
d
d
100 200 300 400 500 50
150 250
F1
F5
F3
f1
f4
f3
f2
f5
f1
f4
f3
f2
f6
f5
f8
f7
f16
f10
f12
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Weighing air

• Density of air, pressure-volume relationship,
  atmospheric pressure

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Weighing air

• On a simple scale a 3 L bottle is balanced by a
  counter weight.
• Air is pumped into the bottle until the pressure
  is doubled.
• The bottle is then heavier.
• A small extra weight (3.6 g) is used to restore
  equilibrium.

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Sealed syringe as pressure gauge

• The 3 L bottle has a bicycle valve in the cap.
• Inside there is a sealed syringe (e.g. 25 cm3)
• The bottle is pumped until the air in the syringe
  is reduced to half its original volume.
• Then the bottle contains twice as much air as it
  did at the start, but at twice the pressure.

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Atmospheric pressure

• Atmospheric pressure is due to the weight of air
  on a unit area of the Earths surface.
• If the atmosphere were uniformly dense it would
  be about 8 km deep (8000 m)
• The mass of a cubic metre of air is 1.2 kg. The
  weight of a cubic metre of air is 1.2 9.8 N
  12 N
• The weight of air over each m2 of the Earths
  surface is about 8000 12 N
• The pressure of the atmosphere is about 8000 12
  N/m2 100,000 N/m2

1 m2
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1 N/m2 1 pascal

• The unit of pressure is the pascal (Pa).
• 1 Pa 1 N/m2
• Atmospheric pressure is about 100,000 Pa
• This might be written as 100 kPa or 1000 hPa
• Meteorologists prefer hectopascals (hPa) because
  1000 hPa 1000 millibar.

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A simple spectroscope
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A simple spectroscope

• From the early 1800s the spectra of elements
  fascinated and puzzled many people. The origin of
  spectra was a mystery until ca. 1914 when Neils
  Bohr proposed a mechanism.
• Atomic spectra are not continuous (unlike the
  continuous spectrum of incandescent solids such
  as the filament of a bulb).
• The functional item in this spectrometer is a
  small piece (1 cm2) cut from a CD from which the
  metal film has been removed.

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The outside and the inside

• The coating cannot be easily removed from all
  CD-Rs.

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Fraunhofer lines

• By directing the spectroscope to a bright cloud
  or sky Fraunhofer lines may be seen.
• It is difficult to photograph them this is the
  best I could get so far. They look much better
  than this.

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Alternative models

• A reflecting version is easier to make and is
  probably more effective.

Piece of a CD with metal film removed
ca. 45
slit
Piece of a CD, intact
ca. 30
look in here
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Diamagnetism of water

• Water is repelled by a magnet

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Concave water surface
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Water is diamagnetic

• The picture shows a distorted reflection of a
  table lamp with a mesh in front of it.
• Water in the Petri dish just covers a neodymium
  magnet.
• The magnet repels the water a concave depression
  is formed in the water surface.

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The Barkhausen effect

• Evidence of magnetic domains

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The Barkhausen effect

• A steel needle of nail (e.g. a carpet tack) is
  set near the playback head of an audio tape
  player in PLAY mode with the volume high.
• As a magnet is slowly brought near the pin a
  scratchy sound is heard, not unlike sand being
  poured onto paper
• The pin is magnetised in discrete steps as the
  atoms in individual domains flip together.

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The record/playback head
carpet tack
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Heinrich Barkhausen

• This phenomenon was first noted by Heinrich
  Barkhausen in 1919. He hypothesised the existence
  of magnetic domains.
• Water, silver, gold and lead are diamagnetic
  aluminium, platinum and liquid oxygen are
  paramagnetic.

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Have a look at YouTube

• http//www.youtube.com/watch?vIsd9IEnR4bw
• This shows liquid oxygen being poured between the
  poles of a strong magnet the liquid is held
  between the poles until it evaporates.

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Electromagnetism

• The force on a coil in a magnetic field

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Small coil on a card

• Wind a coil of about 30 turns of fine enamelled
  copper wire and stick it to a piece of light card
  using adhesive tape.
• Remove the enamel from the ends of the coil and
  attach an audio lead.
• Connect a battery and reversing switch.
• Hold the card near a magnet and switch on the
  current. The card is attracted to or repelled by
  the magnet depending on the direction of the
  current.

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Attach an audio source

• Connect the coil to an audio source.
• It makes no sound...
• ... unless it is held near a magnet.

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Interference of water waves

• Are interference lines straight?

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Straight lines?

• The lines along which interference occurs appear
  to be straight. But are they?
• If you throw two stones into water you will see
  overlapping circular waves but the interference
  bands are always curved outward (i.e. away from
  the normal to the line joining the sources).
• Why does this happen?
• A calculation shows that the lines are not quite
  straight but are curved outward but they become
  straighter with distance.

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Spreadsheet check
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Real waves

• In reality the interference bands are more curved
  and do not seem to straighten out at a distance.

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Interference of waves on water
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A solution

• It appears that the waves produced by dropping
  objects into water do not have a constant
  wavelength.
• The earlier waves have longer wavelengths.
• This can be modelled by drawing concentric
  circles whose radii increase in ever larger steps.

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Newtons first law of motion

• A demonstration

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B52 over Vietnam

• Length 48.5 m
• Speed 230 m/s(ca. 515 mph)

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Newtons laws of motion

• In the 1st second each bomb falls 5 m.
• In that time the plane flies 230 m (almost five
  times the length of the plane). Each bomb moves
  with the plane at first and after some seconds
  the effect of air resistance is noticeable.
• It falls 20 m in 2 s, by which time the plane has
  flown almost half a kilometre.
• (alt. pic.)

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Independence of components

• The vertical and horizontal components of the
  motion are independent.
• Neglecting some oscillation, the direction the
  bombs point is the direction of their velocity
  vectors the sum of the horizontal and vertical
  velocity components.

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Another plane

• Measuring distance and speed

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Dublin Bay from Seapoint
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How far away is the plane?

• At full zoom the camera field width is 3.4
  degrees.
• Tan(3.4) 0.06. This is the ratio of the width
  of the field of view at the position of a given
  object and the distance to the object.
• The field is 16 times the length of the plane
  an Airbus 300 (length 54 m) with Monarch
  Airlines livery.
• So the distance is 16 54 0.06 m, or about
  14.4 km.

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Google Earth

• The distance can be checked using Google Earth.
• The distance from Seapoint via the Ringsend
  chimneys to the line of the runway at Dublin
  Airport is 14.5 km

Shadows of the tall chimneys at Ringsend power
station
Point from which the photograph was taken
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The speed of the plane

• The pictures are taken at three frames per
  second.
• The plane travels about its own length (54 m) in
  0.66 s
• Its speed is therefore 54 0.66 m/s 82
  m/s 294 km/h 183 mph

Monarch Airlines, Airbus 300
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Iron in the fire
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A block of iron in the flame

• When a large block of iron is held in the flame
  for 30 seconds the most noticeable change is that
  it gets...
• wet.
• The water is one of the products of the
  combustion of hydrocarbons.
• C4H10 6½O2 gt 4CO2 5H2O(butane)

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Steel wool in the flame

• When steel wool is held in the flame it...
• burns, forming iron II oxide (FeO).

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Metal crystal

• Feel the collapse of the regular atomic pattern

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Preparation

• Another possible effect of heat on steel is that
  the atoms rearrange into a more regular pattern.
• Heat pieces of steel wire to red heat and allow
  them to cool slowly. (The easiest way to do this
  is just to draw them slowly through a flame.)
• Suitable wire can be obtained from florists,
  preferably without paint. Straightened paper
  clips are also suitable.

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Apply a bending force

• Hold the piece of wire between the finger and
  thumb so that about 1 cm protrudes.
• Press lightly on the free end gradually
  increasing the force until the wire bends.
• What do you find?

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Crystal collapse

• You should notice that the wire gives suddenly.
  This happens when the regular pattern at the
  bending point collapses.
• This can be repeated at different points along
  the length of the wire.
• If you wind the wire around your finger you will
  notice that it forms a series of bends with
  straight pieces in between.

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Work hardening

• Hold the ends of the wire with pliers and pull it
  firmly over and back around a steel bar. This
  will destroy the neat regular crystal pattern.
• If you wind it around you finger again you will
  find that if forms neat curves.
• You will also find that the wire becomes more
  springy.
• The process is called work hardening. It can also
  be accomplished by hammering.

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Bouncing water drops

• Drops of water can bounce on a water surface

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Procedure

• A narrow jet of water is directed at the water
  surface as shown.
• In suitable conditions a narrow jet will form
  discrete drops.
• As they hit the surface they usually merge with
  the water in the container. However, if a little
  detergent is added they may roll along the
  surface, bouncing off one another and off
  barriers.
• Occasionally they will bounce over barriers.

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Blackbody radiation

• Does your hand radiate more than you mobile phone?

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Radiated power /m2 ?T 4

• Radiated power per square metre sT 4where s is
  the StefanBoltzmann constant,1.3810-23 JK-1
• The energy (E) of electromagnetic quanta
  (photons) is given by E h ?, where h is Planks
  constant and ?is the frequency.
• Mobile phone power is 0.4 W and the frequency is
  1.8 GHz. The photon energy is 1.1810-24 J or 7.4
  10-6 eV

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Blackbody radiation
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Radiation from the hand at 300 K

• Assume the hand is 10 cm10 cm or 0.01 m2 and
  that it is at 27 C or 300 K.
• Blackbody radiated power at that temperature is
  460 W m-2 and peaks at a frequency of 31,000 GHz.
• The photon energy is 2.0410-20 J or 0.127 eV
• So there is about 23 times as much radiation from
  your hand as there is from one side of a mobile
  phone and the photon energy from your hand is
  about 17,000 times greater.

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Spreadsheets

• You may be able to download a spreadsheet call
  BlackbodyRad.xls along with this file.
• The spreadsheet contains a simple (and safe)
  macro. You must enable macros or it will not
  work.
• Another spreadsheet (Balanced Moments)
  generates random integral moments. Press F9 to
  generate new ones. Those that are flagged with
  green are balanced. Paste the ones you want to
  keep into the blank lines at the top but be sure
  to use Edit / Paste Special / Values.

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Thats it
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List

• Moments
• Lego notes
• Harmonics in organ pipe
• Weigh air
• CD spectroscope
• Diamagnetism
• Barkhausen effect
• Paper speaker
• Water waves
• B52
• Aeroplane distance and speed
• Heat iron block
• Metal crystal
• Work hardening
• Bouncing water drops
• Blackbody radiation

• Transmission line
• Glass and card variation
• Measure the pressure above the water
• Link to capillarity
• Zinc crystal
• Electroplate
• Even tempered scale
• Electronic boards
• Newtons apple
• Metal expansion