Transcript ISNS3371_020107_bw - The University of Texas at Dallas

ISNS 3371 - Phenomena of Nature
The first test will be next Thursday, Feb 8 at the regular class time.
We will have two review sessions, one at 1:00 PM Monday and one at 1:00 PM
Tuesday - both in FN 2.212 on the SW corner of Founder’s North. Bring questions.The
test will cover any topic we have discussed in class. These include:
Exploration of Nature, Science
Fundamental quantities
Measurement units
Vectors, Scalars
Motion - distance, velocity, acceleration, projectiles
Forces - types, net
Mass, momentum, impulse
Newton’s Laws of Motion
Law of Conservation of Momentum
Torque, angular momentum, conservation
Matter
Energy, Work
Law of Conservation of Energy
Forms of Energy
Transformation of energy
Power
Gravity - Law of, force, acceleration, weight, weightlessness, orbits
Tides
ISNS 3371 - Phenomena of Nature
The Ballistic Pendulum
The ballistic pendulum is used to determine the speed of a projectile.
Invented in the 18th century by Benjamin Robins to determine the
speed of a bullet.
A bullet of mass m is fired at a block of wood (mass M) hanging from a string.
The bullet embeds itself in the block, and causes the combined block plus
bullet system to swing up a height h. Conservation of momentum and
conservation of energy are used to determine the bullet’s speed.
ISNS 3371 - Phenomena of Nature
Conservation of momentum
mb v b  ma v a
mav a
v

(1)
b
mb
b = before collision- mb and vb are for the ball/bullet
a = after collision- ma and va are for the ball/bullet and pendulum

Conservation of energy
Kinetic Energy of ball and pendulum just after collision = Potential
Energy of ball and pendulum at end of swing:
1
2
ma v a  ma gh
2
h = height of pendulum at end of swing
va  2gh
2
Substitute into (1):

ma
v b  2gh
mb
ISNS 3371 - Phenomena of Nature
Alternate Way Using Projectile Motion and g
Fire ball from top of table. Measure initial height of ball (h) and horizontal
distance traveled (x).
h
x
Vertical motion
1 2
2h
h  gt  t 
2
g
Horizontal motion
x
x  vt  v 
t
Substitute from (1)
g
vx
2h
(1)
ISNS 3371 - Phenomena of Nature
•
Gravity
Law of Gravitation:
Objects in the universe attract each other with a force that varies directly
as the product of their masses and inversely as the square of their
distances from each other.
Gm1m2
F
d2
G is called the Universal Gravitation Constant

Consider a light source (for instance the
sun). Light travels in all directions from
source. At 2 AU, is covers a patch 4 times as
large as at 1 AU since the patch is twice as
high and twice as wide. A 3 AU, it covers a
patch 9 times as large as at 1 AU
ISNS 3371 - Phenomena of Nature
Newton’s Law of Universal Gravitation.
ISNS 3371 - Phenomena of Nature
Newton’s 2nd Law and the Acceleration Due to Gravity
The force on a body of mass m1 is:
F  m1a
(Newton’s Second Law)
If this force is due to gravity, then:
Gm1m2
m1a 
d2
m1 cancels out, and:
Gm2
a 2
d
ISNS 3371 - Phenomena of Nature
The acceleration due to the force of gravity is:
Gm2
g 2
d
Mass of the Earth (m2) = 5.97 X 1024 kg
Radius of Earth (d) = 6.378 X 106 m
G= 6.67 x 10-11 Nm2/ kg2
g= (6.67 x 10-11 Nm2/ kg2) X (5.97 X 1024 kg)/(6.378 X 106 m)2
g= 9.79 m/s2
g does not depend on the mass of the body m1 - so the feather falls
at the same speed as the steel ball - Galileo learned this by
experimentation (the Leaning Tower of Pisa experiment) - Newton
showed why.
The mass of the Earth was calculated using this formula in the 18th
century.
ISNS 3371 - Phenomena of Nature
Weightlessness and Free-Fall
Remember: Weight is the result of the force of gravity on a body of
mass m1:
W  m1g
Therefore all objects on earth having the same mass have the same
weight.
Free-fall - condition of weightlessness - whenever nothing is
preventing you from falling - e.g., an elevator floor drops away at
same rate you fall
Apparent Weight Animation
ISNS 3371 - Phenomena of Nature
Orbit and Velocity
Weightlessness - a state of being in free fall towards the Earth.
The Earth is round - its surface drops about 5 m for every 8 km of
distance. If you were standing at sea level, you would only see the
top of a 5-meter mast on a ship 8000 m away - remember the story
of Columbus and the orange.
Given h=1/2gt2, if t=1 s then h = 5 m. So if a projectile is fired
horizontally at 8 km/s, it will fall fast enough to keep “falling around”
the Earth - becomes a satellite. So a spacecraft is in free fall around
the Earth - free fall is not an absence of gravity. If a satellite is given
a velocity greater than 8 km/s, it will overshoot a circular orbit and
trace an elliptical path.
Cannonball Animation
ISNS 3371 - Phenomena of Nature
Geosynchronous/Geostationary Orbits
Since gravity decreases with altitude (inversely proportional to square of
distance from the center of the Earth), the orbital velocity varies with altitude.
A geosynchronous orbit has a period the same
as the rotational speed of the Earth - e.g., it
orbits in the same amount of time that the
Earth rotates - 1 sidereal day. A geostationary
orbit is a geosynchronous orbit at the equator
- it always stays above the same place on the
Earth - communications satellites, satellite TV,
etc…
A geostationary orbit is 42,000 km above the center of the Earth and the altitude is
about 35,600 km
ISNS 3371 - Phenomena of Nature
Calculating Geosynchronous Orbit Altitude
For an orbiting body, the inward and outward forces must equal each other
(Newtons 3rd Law) - the centripetal force from orbital motion has to equal the
centrifugal force from gravity:
Fcentripetal  Fcentrifugal
m sat ag  m sat ac
a g  ac
ac   2 r
MG
ag  2
r
MG
2
 r 2
r
MG
3
r  2

r3
MG
2
 is angular velocity - at geosynchronous
orbit,  of satellite is equal to the angular
velocity of the Earth
 = 2/86164 (length of sidereal day)
M = 5.97 X 1024 kg
G= 6.67 x 10-11 Nm2/ kg2
Plug in the numbers and you get
r = 42,164 km
ISNS 3371 - Phenomena of Nature
Escape Velocity
If a projectile is fired straight up with a large enough velocity, it will escape
the Earth’s gravity. It will travel slower and slower due to the Earth’s gravity,
but never to zero. Escape velocity - velocity at which gravity can not stop
outward motion. Note that the gravitational attraction of Earth never ceases,
it just gets infinitesimally small.
Escape velocity is calculated by using conservation of energy - a body
achieves escape velocity when the all of its initial gravitational energy is
converted to kinetic energy.
ISNS 3371 - Phenomena of Nature
Gravitational potential energy at PE(at Earth' s surface)  mgh  mgR
E
the Earth’s surface
Acceleration due to gravity
Potential energy
Kinetic energy
KE=PE
Escape velocity
GM E
g
RE
GM E m
PE 
RE
1
KE  mv 2
2
1 2 GM E m
mv 
2
RE
2GM E
v
RE
Starting from the surface of the Earth:
RE = 6.378 X 106 m, ME = 5.97 X 1024 kg, G= 6.67 x 10-11 Nm2/ kg2
v= 11,174 m/s

ISNS 3371 - Phenomena of Nature
Center of Mass
Newton also showed that
two objects attracted to
each other by gravity
actually orbit about their
center of mass - the point
at which the objects
would balance if the were
connected.
Center of Mass - Binary Star
This idea is used to find planets orbiting other stars - massive
planets cause star to move against background stars
ISNS 3371 - Phenomena of Nature
Tides
The gravitational attraction of the Moon varies as the square of the
distance (Newton’s Law of Gravitation) - gravity stronger on side facing the
Moon than on opposite side. The Moon pulls the ocean water towards it on
facing side - creates tide - and pulls the Earth away from the ocean water
on the other side - reason for tides twice a day. Time of tides varies by 50
min per day - Moon at its highest point every 24 hrs 50 min because Moon
orbits Earth while Earth rotates.
ISNS 3371 - Phenomena of Nature
The Sun also causes tides - why are
they weaker than the Moons’ (by
about 1/2)? The Sun’s gravitational
attraction on the Earth is about 180
times that of the moon. But the Sun’s
greater distance means the difference
on opposite sides of the Earth is much
smaller - only about 0.02% as
opposed to 7% for the moon.
Neap tides - when Moon’s and Sun’s
gravitational forces oppose each other
Spring tides - when
Moon’s and Sun’s
gravitational forces
add up
ISNS 3371 - Phenomena of Nature
Tides
ISNS 3371 - Phenomena of Nature
Tidal Bulge
Because the Earth rotates, friction drags the tidal bulges off of the EarthMoon line. This tidal friction causes the Earth’s rotation to slow and the
Moon to move farther out.
ISNS 3371 - Phenomena of Nature
The Moon pulls on tidal bulge - slows Earth’s rotation
The excess mass in Earth’s tidal bulge exerts a gravitational attraction on the
Moon that pulls the Moon ahead in its orbit - Moon moves farther away Conservation of Angular Momentum!
ISNS 3371 - Phenomena of Nature
Tidal Heating in Jovian Moons
The four inner moons of Jupiter - Io, Europa, and Ganymede - all show
evidence of geological activity - indicators of molten interiors. The heat
source is tidal heating.
Moons have elliptical orbit and synchonous rotation - one side always faces
Jupiter
- as Ganymede completes one orbit, Europa completes exactly two orbits,
and Io completes exactly four orbits - moons periodically line up - causes
orbital ellipticity.
- tidal bulges are constantly being flexed in different directions - generates
friction inside
ISNS 3371 - Phenomena of Nature
Io
Jupiter’s tidal forces flex Io like a
ball of silly putty.
- friction generates heat
- interior of Io is molten
Volcanoes erupt frequently.
- sulfur in the lava accounts for
yellow color
- surface ice vaporizes and
jets away
Evidence of tectonics and impact
cratering is covered.
ISNS 3371 - Phenomena of Nature
Volcanic Plumes
ISNS 3371 - Phenomena of Nature
Lava fountain - active lava hot
enough to cause "bleeding" in
Galileo's camera - overloading of
camera by the brightness of the
target
Newly erupted hot lava flow. Dark,
"L"-shaped lava flow marks the
location of the November 1999
eruption.
ISNS 3371 - Phenomena of Nature
Gas and Dust Plume
A broad plume of gas and dust about 80 km high above a lava flow
ISNS 3371 - Phenomena of Nature
Europa
Metallic core, rocky mantle, and a crust
made of H2O ice
Its fractured surface tells a tale of
tectonics.
- few impact craters seen
- double-ridged cracks
- jumbled icebergs
These provide photographic evidence
of a subsurface ocean.
Europa has a magnetic field.
- implies liquid salt water beneath
the icy crust
Where liquid water exists, there could
be life!
ISNS 3371 - Phenomena of Nature
ISNS 3371 - Phenomena of Nature
Evidence of a Subsurface ocean
Jumbled crust with icebergs and surface cracks with double-ridged
pattern - caused by tidal flexing of thick layer of ice on top of liquid
ocean of water.
ISNS 3371 - Phenomena of Nature
Europa Ice Rafts
Thin, disrupted, ice crust in the Conamara region of Europa
- white and blue colors outline areas blanketed by a fine dust of ice
particles ejected at the time of formation of the large (26 kilometer in
diameter) crater Pwyll 1000 kilometers to the south.
- a few small craters - less than 500 meters in diameter were probably
formed at the same time as the blanketing occurred by large, intact,
blocks of ice thrown up in the impact explosion that formed Pwyll.
ISNS 3371 - Phenomena of Nature
Ganymede
Largest moon in the Solar System
Its surface has 2 types of terrain:
- heavily cratered, implies old
- long grooves, few craters, implies
young like Europa
It also has a magnetic field.
Could it have subsurface ocean?
- case not as strong as Europa’s
- tidal heating would be weaker
- would need additional heating
from radioactive decay