Transcript Some Concepts of Physics

Some Concepts of
Physics
Simple concepts, Big
Physics
Mass
• Usually defined as the quantity of
matter in a body
• Does this definition need
improvement?
• Why?
Mass Varies with Velocity
• A body moving
at very high
speeds has
mass
depending on
its speed, if
you believe in
relativity.
m
m0
1
v
2
c
2
Variation of
mass with
velocity
See in the
figure
alongside how
the mass of a
body changes
with velocity.
Here m 0
is the mass of
the body at
rest.
Definition of Mass
• Is it, then, correct to say that
mass is the quantity of matter
contained in a body?
• Is there a better way of
defining mass?
An Alternative definition of Mass
• Would it not be better to define
mass as a measure of inertia?
• Greater the resistance of a
body to a change in its state of
motion, greater the inertia and
hence the mass.
Unit of Mass
• At present the kg is the only
unit which is arbitrarily defined
in terms of the mass of a
certain body kept at specified
conditions somewhere in
Paris. Copies are kept in
many countries.
Prototype Kilogram
International
Prototype
Kilogram
(IPK),
A platinumIridium
Cylinder.
Present
Definition
Since 1901.
A Better Defintion of a Unit
• It is more natural to construct units from
natural physical constants which have
some physical significance. Notice that
the other two fundamental units, those of
length and time, are now no longer
arbitrary.
• One metre is defined as the distance
travelled by light in vacuum in a time
interval of 1/299792458 second.
About the metre
• Remember that the Metre was
once based on a measurement of
a meridian between Dunkirk and
Barcelona. It was defined as one
ten-millionth of the length of the
Earth's meridian through Paris
from the equator to the north pole.
Released into the public domain
http://commons.wikimedia.org/
Definition of
Metre
North Pole
Meridian through Paris
The figure is based
on a figure from
www.npl.co.uk
Equator
A bar with a rectangular
cross section, made of
90% platinum and 10%
iridium,
with
polished
parallel ends, and kept at
0 degree C, was made to
represent the meter.
Standard of Length
• In 1960 the General Conference
on Weights and Measures
redefined the International
Standard of Length as
1,650,763.73 vacuum
wavelengths of light resulting from
certain unperturbed atomic
transition of krypton - 86.
Refinement in the Definition of
the Unit of Length
• In 1983 the meter was redefined
again to further reduce
uncertainty. The metre was
defined in terms of the speed of
light and time. It is now the length
of the path travelled by light in
vacuum during a time interval of
1/299,792,458 of a second.
Definition of Second
• In 1956 the second was defined
in terms of the period of revolution
of the Earth around the Sun for a
particular epoch, because by then
it had been recognized that the
Earth's rotation on its own axis
was not sufficiently uniform as a
standard of time
Sun
Earth
Earth
Equator
Vernal Equinox
The time taken by the Sun to go round
from vernal equinox and back to it is
called a tropical year.
The tropical year is not a
constant interval of time.
GNU Free Documentation License
. commons.wikimedia.org
Unit of Time
• The second thus defined was
–the fraction
1/31,556,925.9747 of the
tropical year for epoch1900
January 0 at 12 hours
ephemeris time.
Ephemeris Time (ET) is the
closest approximation to a uniform
time. It uses the best available
theory of the earth's rotation which
removes the known changes in
rotation rate. The use of
Ephemeris Time continued until
1984.
Refinement in the Unit of Time
• With the development of the
atomic clock, it was decided to
use atomic clocks as the basis
of the definition of the second,
rather than the revolution of
the Earth around the Sun.
Second Defined
• As a result, in 1967 the General
Conference on Weights and
Measures defined the second of time
in the International System of Units as
–the duration of 9,192,631,770
periods of the radiation
corresponding to the transition
between the two hyperfine
levels of the ground state of the
caesium-133 atom.
Latest Defintion of Second
• One second is the time
required for a Cesium – 133
atom (at rest at 0 K) to undergo
9192631770 vibrations between
two hyperfine levels of its
ground state.
Goal Of Changes
• In all of these changes in
definitions, the goal was not
only to improve the precision
of the definition, but also to
change its magnitude as little
as possible.
Unit of Mass
• The mass is still defined in terms
of a man-made body. This
worries scientist.
• There are reports that the mass of
the prototype kilogram is
decreasing. The cause is not
known.
A Possibility
• A quantity
consisting of a
combination of
physical
constants has
dimensions of
mass.
However, its
value 2.1765 ×
10-8 kg is very
inconvenient for
every - day use.
c
G
IUPAP Commission
• Efforts be continued to refine
experiments that link the unit of mass
to fundamental constants with a view
to improving the connection between
macroscopic and microscopic masses
and the realization of macroscopic
mass measurements in terms of a
fundamental definition of the
kilogram.
Mass – Energy Equivalence
• Just one more
trivial thing: In
particle physics,
the mass is
routinely stated
in terms of
energy using the
relation between
mass and
energy.
E  mc
2
Mass in Terms of Energy
• It is more convenient to say that
the mass of an electron is 0.5
Mev, rather than saying me = 9 ×
10-31 kg. This is also a good
exercise for the students to
calculate the mass of an electron
and a proton (940 Mev) in terms
of energy.
"The most likely Higgs mass has
now been increased from 96 to
117 GeV/c²" ? GeV/c² is a
common particle-physics unit of
mass; the mass of the proton
measures about 1 GeV/c²?
“Which means it's probably June 2004
beyond the sensitivity of current
experiments, but very likely to
be found in future experiments
at the Large Hadron Collider
being built at CERN."
Centre of Mass
• Exercise: Where would be the
CM of the sun-earth system?
• Mass of the sun: 2 × 1030 kg
• Mass of the earth: 6 × 1024 kg
• Would it be close to the centre of
the earth, or that of the sun, or
somewhere in between?
Common Centre of Mass
• We must also remember that the
earth and the sun must revolve
round their common centre of
mass. We are used to
considering only the earth
revolving round the sun.
Two stars move about their
common CM
CM
For animation, visit http://upload.wikimedia.org/wikipedia/commons/7/73/Orbit1.gif
Centre of Mass of the Sun –
Earth System
• If the centre of mass of the
sun-earth system lies close to
the centre of the sun (only 449
km away from the centre of the
sun of radius 696000 km),
what is the implication?
CM of the Sun-Earth System
Notice slight displacement from
the centre of the sun.
Earth
Sun
Based on zebu.uregon.edu
Doppler Shift
• Illustration of Doppler Shift
Source: http://www.astrosociety.org/education/publications/tnl/67/music.html
Doppler Shift
• Notice that the
spectral lines shift
towards red when
the object is
moving away from
us, and towards
blue when it moves
towards us.
Source of Fig.
spheroid.wordpress.com/2007/02/18/astro-seminarfinding-exoplanets/
Wobble of
a star
The star
wobbles
because of the
presence of a
planet. What
we see is the
shift in the
spectral lines
from the star.
For animation, visit www.astronomynotes.com/lifezone/star-wobble.gif
Motion of the Sun seen from
Outside
• If alien astronomers began tracking
the motion of the Sun in the year
2000, viewing it from its North Ecliptic
Pole, this is what they would see over
the next 50 years, adjusted for the
normal motions of the star and
system.
Wobble of the sun
For animation
of the
wobbling
motion, visit:
http://plus.maths.
org/issue10/new
s/planet/wobble.
gif
Credit: The New York Times
Velocity Curve of a Wobbling
Star
• 51 Peg is a variable star
Source: www.seti.org
Estimate of the Mass
• Once the time
period of the
wobbling motion is
determined, then
Kepler’s third law is
used to get the
combined mass of
the star and the
planet.
GP
2
4
2
( M star  M
planet
)a
3
Extrasolar Planets
• More than 150 extrasolar planets
have been discovered. Most of
them have masses similar to that
of Jupiter. Technology not yet
sufficiently advanced to detect
planets of the size of the earth.
Prerequisite for Life to Exist
• In order to be able to say whether
life exists outside our solar
system, it is necessary not only to
find planets of the size of the
earth, but also to detect
molecules which form the basis of
life.
Complex Molecules Discovered
• Astronomers have found the first
signature of complex organic
molecules in the dust cloud
around a distant star, suggesting
that these building blocks of life
may be a common feature of
planetary systems.
Tholins
• In our solar system, the large
carbon molecules, called
tholins, have been found in
comets and on Saturn's moon,
Titan, giving its atmosphere a
red tinge.
Titan, A Moon of Saturn
A picture of Titan from The Hubble
Space Telescope, the orange is
caused by a thick atmosphere.
Precursors to Biomolecules
• Tholins are thought to be
precursors to the biomolecules
that make up living organisms on
Earth (though they are no longer
found on our planet because the
oxygen in our atmosphere would
quickly destroy them).
Detection of Tholins
• A new study, reported recently,
features observations of the
spectrum of the dust disk
surrounding the star HR4796A
that indicate the presence of
tholins there.
Habitable Zone
• For life to exist on a palnet, it must
also be in the habitable zone. This is
the region in the solar system which
is neither too hot nor too cold, but just
right. Astronomers believe that in
other solar systems, too, such
habitable zones exist and life is more
probable in those planets which fall in
this zone.
Habitable Zone in the Solar System
0.95 – 1.37 AU
1 AU is the
distance of
Earth from
The Sun.
Fig from www.dur.ac.uk
Habitable Zones
• But the habitable zone may be larger than
originally conceived. The strong
gravitational pull caused by large planets
may produce enough energy to sufficiently
heat the cores of orbiting moons. Life has
proven itself tough here on Earth. Perhaps
it could thrive in more extreme
environments.