Foundation Year Physic

7/30/2019 Foundation Year Physic

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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.

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