ISNS 3371 Phenomena of Nature The first test

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ISNS 3371 - Phenomena of Nature The first test will be next Thursday, Feb

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, weightlessness, orbits Tides

ISNS 3371 - Phenomena of Nature The Ballistic Pendulum The ballistic pendulum is used

ISNS 3371 - Phenomena of Nature The Ballistic Pendulum The ballistic pendulum is used to determine the speed of a projectile. Invented in the 18 th 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 (1) b = before collision-

ISNS 3371 - Phenomena of Nature Conservation of momentum (1) 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: h = height of pendulum at end of swing Substitute into (1):

ISNS 3371 - Phenomena of Nature Alternate Way Using Projectile Motion and g Fire

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) Horizontal motion Substitute from (1)

ISNS 3371 - Phenomena of Nature • Gravity Law of Gravitation: Objects in the

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. 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 Law of Universal Gravitation.

ISNS 3371 - Phenomena of Nature Newton’s 2 nd Law and the Acceleration Due

ISNS 3371 - Phenomena of Nature Newton’s 2 nd Law and the Acceleration Due to Gravity The force on a body of mass m 1 is: (Newton’s Second Law) If this force is due to gravity, then: m 1 cancels out, and:

ISNS 3371 - Phenomena of Nature The acceleration due to the force of gravity

ISNS 3371 - Phenomena of Nature The acceleration due to the force of gravity is: Mass of the Earth (m 2) = 5. 97 X 1024 kg Radius of Earth (d) = 6. 378 X 106 m G= 6. 67 x 10 -11 Nm 2/ kg 2 g= (6. 67 x 10 -11 Nm 2/ kg 2) X (5. 97 X 1024 kg)/(6. 378 X 106 m)2 g= 9. 79 m/s 2 g does not depend on the mass of the body m 1 - 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 18 th century.

ISNS 3371 - Phenomena of Nature Weightlessness and Free-Fall Remember: Weight is the result

ISNS 3371 - Phenomena of Nature Weightlessness and Free-Fall Remember: Weight is the result of the force of gravity on a body of mass m 1: 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

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=1/2 gt 2, if t=1 s then h = 5 m. So if a projectile is fired horizontally at 8 km/s, it will 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

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,

ISNS 3371 - Phenomena of Nature Calculating Geosynchronous Orbit Altitude For an orbiting body, the inward and outward forces must equal each other (Newtons 3 rd Law) - the centripetal force from orbital motion has to equal the centrifugal force from gravity: 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 Nm 2/ kg 2 Plug in the numbers and you get r = 42, 164 km

ISNS 3371 - Phenomena of Nature Escape Velocity If a projectile is fired straight

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 the Earth’s surface Acceleration

ISNS 3371 - Phenomena of Nature Gravitational potential energy at the Earth’s surface Acceleration due to gravity Potential energy � Kinetic energy KE=PE Escape velocity 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 Nm 2/ kg 2 v= 11, 174 m/s

ISNS 3371 - Phenomena of Nature Center of Mass Newton also showed that two

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

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

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 Tides

ISNS 3371 - Phenomena of Nature Tidal Bulge Because the Earth rotates, friction drags

ISNS 3371 - Phenomena of Nature Tidal Bulge Because the Earth rotates, friction drags the tidal bulges off of the Earth. Moon 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

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

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

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 Volcanic Plumes

ISNS 3371 - Phenomena of Nature Lava fountain - active lava hot enough to

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

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

ISNS 3371 - Phenomena of Nature Europa Metallic core, rocky mantle, and a crust made of H 2 O 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

ISNS 3371 - Phenomena of Nature Evidence of a Subsurface ocean Jumbled crust with

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

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

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