MOTION AND GRAVITY

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MOTION AND GRAVITY

• The key LAWS of the key branch of physics known
  as MECHANICS were formulated by Isaac Newton
• Three LAWS of MOTION
• The LAW of GRAVITY
• The LAWS of CONSERVATION OF ENERGY and MOMENTUM
  give a more general way to understand motion
• While a physics course would spend the whole
  first semester on these laws well just get a
  taste of them!

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Speed, Velocity and Acceleration

• Speed distance traveled per time (car at 110
  km/hr or 70 mph)
• Velocity is a speed a direction (70 mph NE)
• Acceleration is a change in velocity per time
  speed and/or direction (10 km/s2)

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MATHEMATICS AND UNDERSTANDING

• Isaac NEWTON (1642-1727) of Woolsthorpe, England
  is the most important scientist in history.
• His work completely changed the way educated
  people looked at the world. Effectively, Newton
  was the founder of PHYSICS as well as THEORETICAL
  ASTRONOMY
• HE CO-INVENTED THE CALCULUS (w/ Leibnitz)
• HE DID PIONEERING WORK IN
• OPTICS PRISM, REFLECTING TELESCOPE
• MECHANICS AND GRAVITY his Philosophiae
  Naturalis Principia Mathematica, (pub. 1684)
  reflected work he'd mostly done in 1665-1666.
• Newton was knighted, and became first president
  of the Royal Society, later Director of the Mint.

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Isaac Newton
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NEWTON'S LAWS OF MOTION

• 1. An object at rest remains at rest and an
  object moving at a certain velocity retains that
  velocity unless a FORCE acts on it.
• Aristotle's view forces were needed merely to
  keep something moving at a constant speed
• Newton realized friction or air resistance were
  forces that slowed things down
• Galileo had already understood this.

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Forces Change Velocity
Gravity is a FORCE that causes downward
vertical acceleration
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Which of the following is true?

• A. You can have acceleration not equal zero, but
  velocity equal to zero
• B. You can have acceleration equal to zero, but
  velocity not equal to zero
• C. You can accelerate without changing your speed
• D. A and B.
• E. A, B and C.

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Which of the following is true?

• A. You can have acceleration not equal zero, but
  velocity equal to zero
• B You can have acceleration equal to zero, but
  velocity not equal to zero
• C. You can accelerate without changing your
  speed
• D. A and B.
• E. A, B, and C.

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Newtons SECOND LAW

• The core of Newtonian mechanics, it allows
  trajectories of cannon balls, rockets, planets,
  comets, stars and galaxies to be computed.
• F m a
• is the most important relation in physics one
  can equivalently write
• a F/m
• This clearly says less massive objects obtain
  larger accelerations from the same force.
• Think of stepping on the gas and going from 0 mph
  to 60 mph in 10 seconds your acceleration is 6
  mph/s (forwards)
• 2nd Law Applet

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Momentum and Force

• Momentum mass X velocity (p mv)
• It takes a force to change a bodys momentum
• Slightly more general version of Newtons 2nd
  Law F ?p/?t
• Think of a 1000 kg car colliding with a 6000 kg
  truck head on -- if they have the same speeds the
  truck has 6 times the momentum and will push the
  car down the road

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More on the 2nd Law

• Breaking takes you from 60 mph back to 0 in 4 sec
• or a negative acceleration of 15 mph/s.
• These are VECTOR equations -- with magnitude and
  direction
• Velocity distance covered / time
• V ?d/?t
• Acceleration change in velocity/time change
• a ?V/?t
• - both the Speed and Direction are needed
• I.e. 50 mph to the East is the same speed, but
  different velocity, from 50 mph to the North
• Going around a curve at a constant speed DOES
  involve an acceleration (you feel pushed to one
  side of the car, right?)

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Newtons Third Law

• 3. EVERY ACTION (FORCE) HAS AN EQUAL AND
  OPPOSITE REACTION.
• Forces don't act in isolation
• the Earth pulls the Moon and the Moon pulls back
  on the Earth
• we push down and back on the ground with our
  muscles, it pushes us up and forward
• a rower or gondolier pushes water (or canal
  bottom) in one direction and the scull or gondola
  goes the other way
• a rocket expels gases rearward and it flies
  forward.

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Newtons Laws of Motion, Illustrated
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Changing an objects momentum requires

• A. Gravity
• B. Applying a force
• C. Applying a torque
• D. Friction
• E. None of the above

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Changing an objects momentum requires

• A. Gravity
• B. Applying a force
• C. Applying a torque
• D. Friction
• E. None of the above

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Newtons second law, F ma, (force mass x
acceleration), means that with no force,

• A. Objects remain at rest
• B. An objects speed doesnt change
• C. An objects velocity doesnt change
• D. B and C.

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Newtons second law, F ma, (force mass x
acceleration), means that with no force,

• A. Objects remain at rest
• B. An objects speed doesnt change
• C. An objects velocity doesnt change
• D. B and C

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Conservation Laws in Astronomy

• Momentum
• Angular Momentum
• Energy

Conservation of (linear) Momentum is implied by
Newtons Laws of Motion. One ball hits another,
exerts a force, which accelerates Second ball
(2nd law) 3rd Law says opposite force
decelerates the first ball
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Angular Momentum Conservation

• AM m x v x r (mass x velocity x distance)
• Orbital AM conservation says no push needed to
  keep Earth orbiting and also faster motion at
  perihelion than aphelion v x r constant
• Rotational AM conservation says Earth keeps
  spinning on its axis and also faster spin when
  contracted ballerina, gas cloud making planets

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Conservation of Energy

• Energy comes in many forms but three classes can
  contain them all
• Kinetic (energy of motion)
• Radiative (energy of light or electromagnetic
  radiation)
• Potential (stored energy -- gravitational,
  chemical, atomic, mass-energy)

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Energy is Converted but not Lost
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Thermal or Heat Energy

• Random kinetic energy of atoms and molecules
• Heat or thermal energy is the sum total of all of
  them
• Temperature is related to the average energy

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Gravitational Potential and Kinetic Energy

• No KE, maximum gravitational potential energy at
  top of throw
• Maximum KE, minimum gravitational PE when thrown
  and when caught
• KE (1/2)mv2
• Energy of Thrown Ball

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Temperature is a measure of

• A. How much heat an object contains
• B. How fast atoms are moving
• C. How hot you feel when you touch something
• D. Energy

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Temperature is a measure of

• A How much heat an object contains
• B How fast atoms are moving
• C How hot you feel when you touch something
• D Energy

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A cake is baking at 400 degrees. If you briefly
touch the cake you will not be burned. Touch the
metal pan for the same length of time and you
will be burned. Why?

• A. The metal is hotter than the cake
• B. The metal is denser than the cakethere are
  more atoms per unit volume
• C. The metal is a better conductor
• D. B. and C.
• E. All of the above

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A cake is baking at 400 degrees. If you briefly
touch the cake you will not be burned. Touch the
metal pan for the same length of time and you
will be burned. Why?

• A. The metal is hotter than the cake
• B. The metal is denser than the cakethere are
  more atoms per unit volume
• C. The metal is a better conductor
• D. B and C.
• E. All of the above

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NEWTON'S LAW OF GRAVITY

• The ATTRACTIVE FORCE OF GRAVITY IS DIRECTLY
  PROPORTIONAL TO THE PRODUCT OF THE MASSES
• AND INVERSELY PROPORTIONAL TO THE SQUARE OF THE
  DISTANCE, r, BETWEEN THEM.
• where Newtons gravitational constant
• G 6.673 x 10-11 m3 kg-1 s-2

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Inverse square law of gravity
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Gravitational Acceleration 1

• Combine 2nd Law of Motion w/ Law of Gravity
• ACCELERATION DUE TO GRAVITY, g, OF AN OBJECT IS
  PROPORTIONAL TO ITS MASS AND INVERSELY
  PROPORTIONAL TO THE SQUARE OF THE DISTANCE FROM
  ITS CENTER.

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Gravitational Acceleration 2

• Example if mE ME and r RE

g 9.80 m s-2 (or 32 ft/s2) YOU SHOULD
VERIFY THIS CALCULATION! Gravitational
Acceleration
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Newtons law of gravity is F G m1 m2 / d2Can
this be used to find the force between the Sun
and a planet? If so, what is d?

• A. No
• B. Yes, d is the diameter of the Sun
• C. Yes, d is the diameter of the planet
• D. Yes, d is the distance from the Sun to the
  planet

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Newtons law of gravity is F G m1 m2 / d2Can
this be used to find the force between the Sun
and a planet? If so, what is d?

• A. No
• B. Yes, d is the diameter of the Sun
• C. Yes, d is the diameter of the planet
• D. Yes, d is the distance from the Sun to the
  planet

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When I drive my car at 30 miles per hour, it has
more kinetic energy than it does at 10 miles per
hour.

• Yes, it has three times as much kinetic energy.
• Yes, it has nine times as much kinetic energy.
• No, it has the same kinetic energy.
• No, it has three times less kinetic energy.
• No, it has nine times less kinetic energy.

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When I drive my car at 30 miles per hour, it has
more kinetic energy than it does at 10 miles per
hour.

• Yes, it has three times as much kinetic energy.
• Yes, it has nine times as much kinetic energy.
• No, it has the same kinetic energy.
• No, it has three times less kinetic energy.
• No, it has nine times less kinetic energy.

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Gravitational Acceleration
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Weight v. Mass

• Weight (Newtons, dynes) is the force due to
  gravity acting on a mass (amount of matter,
  kilograms, grams) so
• W m g (special case of F
  m a). Since gravity gets weaker a greater
  distances, you actually weigh less at the top
  of a building than you do at its base, even
  though your mass hasn't changed.
• Since Atlanta is about 300 m above sea level, you
  weigh a little less here than in Savannah
• -- at sea level, and closer to the center of the
  earth.
• You weigh more in an elevator as it just
  accelerates to go up and less in one that
  accelerates to go down
• you are weightless in one that is falling w/o
  support!

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Weight and Weightlessness

• Take a scale in an elevator with you. No cable ?
  free fall
• Fast leap from a tower ? constant free-fall
  (weightlessness)

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Gravitational Acceleration
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Figuring Out the Law of Gravity 1

• Newton compared the acceleration the Moon feels
  compared to that felt at the surface of the
  Earth.
• Knew the Earth-Moon distance was about 60 x RE
• Found the inertial ("centripetal") acceleration,
  a, due to rotation at speed v and at distance r
  (experiment rock swung on string)

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Figuring Out the Law of Gravity 2
Start from vM circumference of orbit divided by
period

• This gives, aM 2.7 x 10-3 m s-2
• Newton realized aM g/(3625) g/(rEM /RE )2
• concluded the INVERSE SQUARE RELATION OF GRAVITY
  ON DISTANCE was LIKELY to be true EVERYWHERE.

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Gravity Keeps the Moon from Flying off on a
Tangent Constantly Falling
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Circular Velocity and Escape Velocity

• Newton also showed that the general shape of a
  BOUND ORBIT was an ELLIPSE (with a circle as a
  special situation)
• and that the general shape of an ESCAPE ORBIT was
  a HYPERBOLA (with a parabola as a special case).
  
• The simplest case a CIRCULAR orbit, just
  skimming the earth

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Orbital Types
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Orbit Shape Depends on Speed

• v vc circular orbit
• vc lt v lt vesc elliptical orbit w/ center of E
  at near focus
• Both BOUND (NEGATIVE ENERGY ORBITS)
• v vesc parabolic escape orbit reaches
  infinity with no energy left (ZERO ENERGY ORBIT)
• v gt vesc
• hyperbolic escape orbit reaches infinity still
  moving away (POSITIVE ENERGY ORBIT)
• For earth, vesc 11.2 km/s, or about 25,000 mph!

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Newton DERIVED Keplers Laws

• FUNDAMENTAL LAWS explain EMPIRICAL ONES
• Consider a general circular orbit of a low mass
  object around a much more massive one

• This is Kepler's Third Law!
• Newton also derived Keplers first and second
  laws, but these are actually harder (you do this
  in a sophomore, not freshman, physics course).

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Orbital acceleration
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Two Bodies Orbit Each Other
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Weighing Astronomical Bodies

• For example, to get the mass of the Sun Earth
  (basically just Sun)

m 2.0 x 1030 kg