Post on 04-Apr-2018
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BASIC CONCEPTS OF PHYSICS
Vietnamese-German University
Foundation Year course of Physics2012
Instructor: Ho Trung Dung Dr.
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8 weeks course (subject to changes)
1. Laws of motion, conservation laws
2. Hydrostatics, hydrodynamics
3. Electromagnetism I4. Electromagnetism II
5. Oscillations, sound and light I
6. Oscillations, sound and light II7. Students project presentations I8. Students project presentations II
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1.1 Units of measurement
- ancient times: inch, foot
- French Revolution 1790:
kilogram
meter: one-ten-millionth of the Earthsmeridian quadrant
- unit of time: 24-hours day was introduced
in Ancient Egypt, 60-minutes hour and60-seconds minute in Babilon
- the Earths rotation is slowing down
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Weight and mass
- weight is the force with which a body is attracted
by the Earth
- at a pole 0.5% more than at the equator
- ratio of the weights remains unchanged
- mass: invariant property
- kilogram: 1 cubic decimeter of water at 4oC
- the General Conference on Weights and Measures,
2011: redefine kilogram in terms of the Planck const.
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stretching or contracting spring
balance scales
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The International System of Units (SI) 1960:
7 base units
- the meter
- the kilogram
- the second
- the mole- the ampere
- the kelvin
- the candela CGS system
1832 GaussMaxwell, Thomson
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The meter
- 1960: 5d5 2p10 transition in Kr86
:one meter = 1 650 763.73 wavelengths
- 1983: the length of the path travelled by light
during 1/299,792,458 second
- uncertainty of 2.11011
The second
- 1967: 9 192 631 770 periods in a transition incaesium-33
- error: 1 second in 300 000 years
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The mole: the quantity of entities (elementary particles
like atoms or molecules) equal to the number of
atoms in 12 grams of carbon-12
- Avogadro number: 6.02214129(27)1023- 100012(83) moles of12C has a mass of one kilogram
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in England, the US
- mile (1609m)- foot (30.48cm) = 12 inches
- inch (2.54cm)
- yard (0.9144m)
- pound (454g)- 1 pound = 16 ounces
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Action and Reaction
- every action of a force is accompanied by a reaction
- equal in magnitude and opposite in direction
The horse is pulling the wagon,
the wagon is also pulling the horse;
why do they move?
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How velocities are added
- 200g of grapes+400g of grapes=600g of grapes
- vector: length and direction
- parallelogram rule
- triangle rule
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Force is a vector
T h
P l
sinT P
30o angle of inclination: T=P/245 and 60o: save 0.7 and 0.9 of the weight
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1.2 Laws of Motion
Inertial frame of reference: bodies at rest do not
budge without the action of a force
The law of inertia:
- Ancient Greeks: if there is nothing causing a body
to keep moving, it must halt (psychology)
- What would happen if there were no resistance?
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Galileo Galilei
(1564-1642)
physicsist,
astronomer
In 1558 Nguyn Hong wentto present-day Quang Binh
to Binh Dinh
In 1592, Trnh Tngconquered Hanoi and
executed Mc Mu Hp
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- the first to apply experiments
- the concept of inertia
- relativity of motion- investigated laws of free falls, motion of bodies on
an inclined plane, thrown at an angle
- used pendulum for the measurement of time
- looked at the sky through a telescope
- the Milky Way: enormous number of stars
- Jupiters statelites
- sunspots and the rotation of the Sun- structure of the Moons surface- supported Copernicus heliocentric system
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Galilean principle of relativity phenomena in twoinertial frames of references are equivalent
- space is relative- (v1-v2) is absolute
a celestial observer:
- The Earth turns (1/240)o per second: inertial withrespect to a great many phenomena
- non inertial to prolonged phenomena
- solar observer: period of 180 million years,
(610-14)o per second
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Lon Foucault (1819-1868)
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Acceleration and Force
- acceleration: change in velocity
- acceleration is absolute
- a force is required
- How a force is related to the acceleration? aF
- Galileo: all bodies fall with same acceleration
- Sir Isaac Newton a= F/m
-in the SI system: 1N=1kg-m/s2
- in CGS 1dyn=1g-cm/s2
2 1
v va
t
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Sir Isaac Newton
(1643-1727)
16271672 Trnh Nguyn war
1651 Alexandre de Rhodes
romanized alphabet Quc ng
1690s Gia nh established
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Isaac Newton:
- basic concepts and laws of mechanics
- the law of gravitation
- theory of the motion of celestial bodies
- the Moons motion and tides
- optics
- differential and integral calculus
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Rectilinear motion with constant acceleration
0v v
at
0
1( )
2s v v t
2
0
1
2s v t at
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0v v
t
a
2 2
0
1( )
2
s v v
a
If the initial speed is zero
2
, 22
vs v as
a
10m: 3-storey house, a free fall would reach
2 9.8 10m/s 14m/s 50km/hv
Air resistance will not reduce this speed much
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lunar miracles:
- acceleration of gravity is 1/6 terrestial, 1.6m/s2
- a jump from a height hrequires
2 / s, 6 2.45t h g
2 1.6 10m/s 20km/hv
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Circular motion
22 / , 2 / , / a v T T R v a v R
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- the velocity is tangent to the path
- the acceleration is directed along the radius
- the force the stone acts on the string: centrifugal
2/F mv R
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- The Earth is holding on to the Moon:
gravitational force
- speed of a satellite at 300km from surface,
distance to the center of the Earth 6600km
68.9 6.6 10 m/s 7.7km/sv gR
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Life at gzero
- in an interplanetary spaceship: objects loose their
weight
- turn on the engine, at 9.8m/s2 things are back
to normal- equivalence principle: indistinguishability of anacceleration from gravitation
- small differences: gravitation on the Earth depends
on direction and height
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Life in the cabin of a spaceship:
- how to pour water from a bottle into a glass
- how to cook if water cannot be heated on a stove
- how can one write
- neither a match, nor a candle, nor a gas burner
will burn
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2tan / v Rg does not depend on m
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highways are built with sharp turns inclined
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wheel of laughs
acceleration a=v2/Rnrevolutions/second v=2Rn a=42n2R
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Centrifugal phenomena: widely employed in tech.
Centrifuge: - a metall ball comes to a halt at the side,
- a cork moves toward the axis
- its bottom is the lateral surface
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A sufficiently perfected contrifuge:
- 60 000 rpm or 1000 rps
2 2 2/ ( 2 ) / 4a v R n R R nR
- at R=10cm
6 6 240 10 0.1 4 10 m/sa
400 000 times greater than terrestial acceleration
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Applications:
- chemical industry: separating crystals from the
solution out of which they grew; dehydrating salts;
separating varnishes- food industry: processing milk
- metallurgy: pipes cast
- centrifugal gorvernor
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Coriolis forces:Gaspard Gustav de Coriolis (1792-1843), 1835
What does rectilinear motion look like in a rotating lab.?
- the lab. rotates counterclockwise
- the body is deflected to the right
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Why we did not come across the Coriolis force?
Motion from the point of view of a rotating observer
4CF nv m
perpendicular to the axis of rotation and thedirection of the motion
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Many phenomena on the Earth: Coriolis forces
A falling body at the equator, looked from the North:deflected to the East
h=80m, t=4s, average v=20m/s, n=1/(243600)rps
24 /1080 m/sa nv deflection 2.3cm
A horizontally moving body at the North pole:deflected to the right
a bullet, 500m/s, deflection 3.5cm during 1s
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-gunners: Big Bertha used by the Germans to shell
Paris during WWI: 110km, deflection 1600m
- aviators- railroaders: rails wear out differently
- river banks are washed away differently
- the origin of cyclones: air streams flowing into a
low-pressure area
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1.3 Conservation Laws
Recoil
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1 2
1 2
1 2
1 2
1 2
2 1
, ,
(action=reaction)
F Fa a
m m
F F
a m
a m
1 11 1 2 2
2 2
1 1 2 2
, , then ,
and so m 0
v mv a t v a t
v mm
v v
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The Law of Conservation of Momentum
momentum: mv
Newtons law F=ma
2 1
2 1
2 1
( ) /
( ) /
a v v t
F mv mv t
Ft mv mv
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Let us return to recoil
A gun mounted on a platform of velocity V
1 1 2 20m m u u
to an observer at rest
1 1 2 2
1 2 1 1 2 2
, ,
( )m m m m
v u V v u V
V v v
the law of conservation of momentum
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Jet propulsion
- persons, trains, cars move
by pushing off the Earth
- boats, ships push against
the water
recoil jet propulsion
airplanes, missiles,artificial satellites, rockets
ancient toy(2nd century B.C.)
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How to launch a rocket into space?
- rocket of mass M- mass DM of gas ejected with speed u
, i.e.M
u M M V V uM
DD D D
integration ln inM
V u
M
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M= 0.5 MinV= 0.7 u
to raise Vto 3u(6-8 km/s foru=2 km/s), burn up(19/20)Min
to attain 7u, Min must decrease by 1000 times
multi-stage rockets, the take-off weight of a
3-stage rocket is 6 times less than that of a
1-stage rocket
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Motion under the action of gravity
2 boards, one much shorter than the other
1 cart, same height
In which case the cart acquires the greater speed?
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or
2 2
h sas gh
ma mg
v as gh
independent of the angle
of inclination
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The speed at two heights h1 and h2
2 2
1 1 2 2
2 2
2 1 1 2
2 2
1 21 2
2 ( ), 2 ( )
2 ( )
2 2
v g h h v g h h
v v g h h
v vgh gh
(frictionless motion along any path)
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An example:
When the body breaks away from the dome?
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2
2
/
2
/ 3
mv r r h
mg h
v gh
h r
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The Law of Conservation of Mechanical Energy
One might think
2 2
body1 body 2
...2 2
v vgh gh
is conserved
We shall show
2 2
1 2
body1 body 2
...2 2
v vm gh m gh
is conserved
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Mand mconnected by a cord passing over a pulley
2 2
2 22 2
2 2
1 11 1
1 1 2 2
2 2
2 1 1 2 1 2
2 2
2 1
2 2
2 2
,
( ) ( ) ( )2
( ) ( )2
v Vm gh M gH
v Vm gh M gH
v V v V
m Mv v mg h h Mg H H
m Mv v g M m s
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2 2
1 2 2
( ) ( )
v v as
m M a M m g
Newtons law
2 2
2
const2 2
K=2
mv MV mgh MgH
mv
U mgh
kinetic energy
potential energy
law of conservation of mechanical energy
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Work work A performed by the force
2 22 1
2 2
2 1
2 2
2
t
mv mvA
v v asA mas F s
work = distance
component of the force alongthe direction of the displacement
1J=1N 1m
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Power and Efficiency of Machines
power = work per unit time
1W=1J/s
kgf kilogram force, force exerted by 1kg of massin a 9.8m/s2 gravitational field
1hp = 75 kgf m/s=0.735 kW
a kilowatt-hour = 1 kilowatt 1 hour
(exclusively for electricity)
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invented in 1634
French Academy, 1775, not to accept any more
projects for perpetual motion
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Collisions
ideally elastic: insignificant energy loss
(3-4% with ivory billiard balls)
1 1 1 1 2 2
2 2 2
1 1 1 1 2 2
2 2 2
m v m u m u
m v m u m u
head-on collisions
12 1 1
2
11 1 1 1
2
1 21 1
1 2
( )
1 1( ) ( )2 2
mu v u
m
mv u v um
m mu v
m m
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oblique collision between bodies of equal mass
1 1 2
2 2 21 1 2v u u
v u u
velocity triangle = right triangle
bodies fly apart at right angles
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1.4 Gravitation
What holds the Earth up? the three whales.
Newtons discovery:
- motion of the Sun and the Moon
- the ocean tides
- the free fall of apples to the Earthare manifestations of same law of nature
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Law of universal gravitation
The first question Newton asked himself:How does the Moons acceleration differ from thatof an apple?
acceleration of the Moon v2/R 0.27 cm/s2
3600 times less than g, 980 cm/s2
acceleration decreases, but how rapidly?
R 60 terrestrial radii factor of 602
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2
MmF G
r
law of universal gravitationvalid for any pair of bodies
8 3 1 26.67 10 cm g sG
measuring G
100 tons of lead
two 1000 kg loads, 1m 0.007gf
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24h satellite: how large is the friction?
2 2 2
2 2 2
2 2 2 23
2 2 2
2 / ,
acceleration / 4 /
on the other hand / / 4
, i.e.4
v r T
v r r T
GM r gR r gR r gR T
rr T
R=6106m, T=24h r 40 000 km, no air friction
Measuring g in the Service of Prospecting
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Measuring gin the Service of Prospecting
find deposits of minerals without digging
methods for determining g: spring balance, quartztorsion balance, pendulum
relative change up to one millionth
2 /T l g
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gdecreases from a pole to the equator
2 reasonsthe Earth isnt a spherecentrifugal force
at same latitude same height, gshould be identical
2( )
GMg
R h
R radius of the Earth, h- height above sea level
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deviations:
g-force due to a large body =sum of the forces emanating from individual particles
heavy ore where gis maximum
light salt deposits where gis lowered
looking for oil
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H h b d h f h
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How can we ensure that a body thrown from theEarth will not return?
escape velocity from the Earth v2
2
2
22
2 1 1
2
, i.e. 2 11km/s
2 , 7.7 km/s
mv MmG
RGM
g v gRR
v v v gR
v1 orbital velocity of a satellite
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If we want the rocket to move with speed v
2 2 2 2 2 20 2 0 2, i.e.
2 2 2m m mv v v v v v
v3 for overcoming the gravitation of the Sun
2 2 2
3 3
2 30km/s (speed of the Earth)=42km/s
we need to add only 42-30=12km/s
v 11 12 16km/sv
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How Planets move?
Johannes Kepler (1571-1630): laws of planetary motionNewton (1643-1727)
2
22 3
2 2
2 2
1 1
2 2
2 2
2,
4 4, . .
F v rv
m r T
r GMi e T r
T r GM
T r
T r
empirically by Kepler
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The trajectories of the planets:
ellipses, very close to circles
Sun
perihelion
aphelion
Mercury: - nearest to the Sun- differs most from a circle
- aphelion = 1.5 perihelion
comets: greatly elongated ellipses, hyperbolas
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area swept out by a radius in a unit of time = const
conservation of angular momentum mvd
quite a few double stars in the sky:
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quite a few double stars in the sky:
masses of the same order
of magnitude
1 1
2 2
m rm r
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Interplanetary travel: trip to the Moon
the Earths escape velocity is a must different trajectories require different amounts of
fuel initial velocity +0.5 km/s: 5 days 24 h
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V = 0.8 km/s
the rocket will collide with the Moon at 2.5km/s braking fuel
return to the Earth fuel
gentle reentry into the Earths atmosphere
return pay-load 5 tons: lift-off 4500 tons
If th M
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If there were no Moon
acceleration of the Earth with respect to
the Moon Gm/r2,
m mass of the Moon
acceleration of a body with respect to the Moon Gm/r12
Gm/r12 is different at various points
acceleration of a body with respect to the center
of the Earth: subtract the two above
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body
body
Earth
Earth
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At A (nearest to the Moon)
2 2 2 2 3
(2 ) 2
( ) ( )
m m mR r R GmRG G G
r R r r r R r
At B
2 2 32
( )m m GmRG G
r R r r
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At the median line
3GmR
r
one half of that at the
extreme points
directed downward
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weight diminishes at the nearest and farthest pointsfrom the Moon, but grows on the median line
numerical value 23
20.0001cm/s
GmR
r
this insignificant effect is the cause of powerfultidal waves
1015 J of kinetic energy daily = that borne by allthe Earths rivers
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Hydrostatic pressure:
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Hydrostatic pressure:
Pascals law fails to take into account weight
2 1
2 1
F F ghS
p p gh
pressure exerted by water: hydrostatic pressure exerted by air: atmospheric pressure at a depth: sum of the two
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Pascals paradox:
the forces acting on the identical bottoms of the twovessels are the same
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at a depth of 10m: water pressure = 2 atm
1km: 100 atm
ocean depth: 10km at places
submarine depth: a few hundred meters
kilo class submarines: 240-250m operational
300m maximum
At h i
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Atmospheric pressure
barometers
76 cm column of mercurycrossection: 1 cm2
1.033 kgf
a pressure of 760mm Hg: standard atmosphere (atm)1 atm = 1.013 bar , 1 bar = 106 dyn/cm2
1 Pa = 1N/m2=10-5 bar
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a syphon
How atmospheric pressure was discovered
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Suction pumps were known to ancient civilizations
explanation: nature fears a vacuum
Duke of Tuscany in Florence tried to pump > 10m
Evangelista Torricelli (1608-1647): the column ofwater of area 1cm2 weighted 1kgf
1654: Burgomaster of Magdeburg, Otto von Guericke,
2 copper hemispheres, diameter 37 cm, 1000kgf,
16 horses
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Atmospheric pressure and weather
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osp e c p essu e a d ea e
At one time: pressure alone determines the weather
they marked clear, dry, rain, storm, even earthquake
on the barometers
a Coriolis force is directed to the right in the NorthernHemisphere, to the left in the Southern Hemisphere
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Archimedes principle
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Archimedes principle
the force is vertically upwardsequal to the weight of the displaced fluid
origin: hydrostatic pressure
hydrometers: alcoholometers, lactomaters
density of the water in the Bay
of Kara-Bogaz-Gol in theCaspian Sea: 1.18
Extremely low pressure:
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t e e y o p essu e
in the best vacuum instruments: 10-8 mm Hg,still several hundred million molecules / cm3
interstellar space 1 particle / several cm3
Pressures of millions of atmospheres: a nail of dimension 0.1mm 0.0001 cm2 areaforce 10kgf 100 000 atm
hydraulic presses: several thousand atm
artificial diamonds: 100 000 atm, 2000K center of the Earth: 3 mils. atm
Id l fl id i ti
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Ideal fluids in motion:
1. steady or laminar flow (the velocity at any fixed
point does not change with time)
2. incompressibility
3. nonviscous flow
4. irrotational flow
Equation of continuity
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q y
1 1 2 2
const
A v t A v t
AvD D
the flow is faster in the narrower parts of a tube
Bernoullis equation
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2 2
2 1 2 1
2 1
2
( )
1( ) ( )
2( )
1
const.2
F x pA x p V
V v v Vg y y
p p V
p v gy
D D D
D D
D
if y=const then 21
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ify=const. then 2 const.2
p v
If the speed increases, the pressure must decrease,and conversely.