Lecture 6 Non Inertial Frames Energy-Waves-Radiation

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Lecture 6 Non Inertial Frames
Energy-Waves-Radiation

• ASTR 340
• Fall 2006
• Dennis Papadopoulos

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FRAMES OF REFERENCE

• We have already come across idea of frames of
  reference that move with constant velocity. In
  such frames, Newtons laws (esp. N1) hold.
  These are called inertial frames of reference.
• Suppose you are in an accelerating car looking at
  a freely moving object (I.e., one with no forces
  acting on it). You will see its velocity
  changing because you are accelerating! In
  accelerating frames of reference, N1 doesnt hold
  this is a non-inertial frame of reference.

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Real and fictitious forces

• In non-inertial frames you might be fooled into
  thinking that there were forces acting on free
  bodies.
• Such forces are call fictitious forces.
  Examples
• G-forces in an accelerating vehicle.
• Centrifugal forces in fairground rides.
• The Coriolis force on the Earth.
• Fictitious forces are always proportional to the
  inertial mass of the body just like gravity.

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Non Inertial Frames
Two real forces mg downwards and T. When
car accelerates they must add to ma by Newtons
2nd law
An observer in the car feels a force that
pushes everything backwards. To explain his result
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He adds a fictitious force equal to
Fin-ma This is known as inertial force.
T
Sum of forces equal to zero
ma
mg
vt
Centrifugal vs. Centripetal
vt
a
vr
The only real force is the Centripetal force
pulling towards the center so the ball must be
accelerating
o
An observer sitting on the ball feels a
fictitious force Centrifugal that pushes him
outwards balanced by the string held at O.
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Look at the rotor in amusement park. People on
the outside See only a Centripetal force from the
wall pushing riders inwards into circular motion.
People inside the rotor feel the fictitious
Centrifugal force pushing them outward with the
force from the wall balancing it.
Centrifugal force Fc mvt2/R
An observer in a non-inertial system with
acceleration a should add to the real forces a
fictitous inertial force Fin -ma in order to
describe the dynamics of the system correctly,
i.e. to provide a description equivalent to an
observer observing from an inertial
frame. Weight-less-ness. Weight in an elevator
or the shuttle.
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Weak or Newtonian equivalence
principle

• Gravitational and inertial masses and forces are
  equivalent.
• Gravity is indistinguishable from any other form
  of acceleration

Maybe gravity is a fictitious force
and we live in an accelerating frame of
reference?
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NEWTONS WORRIES

• Newton knew that his theory has problems
• Gravity is action at a distance he didnt
  like that!
• A static universe would be gravitationally
  unstable.

Reading this week Chapter 4
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Given in Joules

• WHAT IS WORK ?

• WHAT IS ENERGY ? -gt CAPACITY TO DO WORK in Joules

KE vs PE Forms of Energy -gt Heat, Chemical,
nuclear Conservation of Energy and Conservation
of matter (Classical) What is Temperature ?
Energy of random motion in a unit volume

• Thermodynamics KE??HEAT
• Conservation of Energy
• Easy to transform KE to heat (rub your hands) but
• difficult to transform heat to KE
• Heat in KE heat out (Car, refrigerator) No
  perpetual motion
• Entropy ? Measure of Disorder
• 3. Difficult to cool at very low temperatures
• Absolute zero (0 K) cannot be attained (-273.15
  C)

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ENERGY TRANSFORMATIONS
Lift a classmate where is the energy coming from ?
Muscular Energy, ie. released chemical energy
caused by food oxidizing the body
What is chemical energy?
Form of PE stored due to the locations of
electrons in electric field of molecules. It
comes from the food, eg. plant you eat.
Plant converts radiant energy from Sun into
chemical energy by photosynthesis
Sunlight came from fusion of hydrogen in the Sun
Suns hydrogen nuclei were created from energy of
the event that created the universe
ALL ENERGY CAME FROM THE BIG BANG
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• Energy The measure of a systems capacity to
  do work

• Units of Energy Joule Nt x m, eV 1.6 x
  10-19 J, Cal 4.2 x 103 J

• Examples It takes 100 Joules to lift 10 kg by
  1 meter against the
• Earths gravity (g 10 m/sec2) It takes .4 MJ
  to accelerate a 1000 kg
• car to 30 m/sec (105 km/hr) It takes about
  1010J to accelerate a
• missile to 5 km/sec. E1/2 M(kg) v2 (m/sec) J

• Chemical Energy Storage Chemical energy is
  stored in the
• chemical bonds of molecules. As an order of
  magnititude a few eV
• per bond. A 1 kg steak store approximately
  1000 Cal or approximately 4 MJ. This is the
  amount (4-10 MJ/kg)stored in one kg of chemical
  explosives (TNT). Also a typical battery has few
  MJ of stored energy.

• Energy Transformations Energy has many forms,
  e.g. potential,
• kinetic, chemical, acoustic, radiation, light
  etc. Each can be transformed
• to the other, but overall energy is conserved.

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Electromagnetic Spectrum
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EM Spectrum