Download Lecture 6 Newton

Lecture 6
Non Inertial Frames
Energy-Waves-Radiation
ASTR 340
Fall 2006
Dennis Papadopoulos
FRAMES OF REFERENCE
We have already come across idea of frames of reference
that move with constant velocity. In such frames,
Newton’s law’s (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
doesn’t hold – this is a non-inertial frame of reference.
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.
Non – Inertial Frames
• Monkey and hunter
g
• Accelerometer
f
a
T
Two real forces mg downwards and T. When car
ma accelerates they must add to ma by Newton’s 2nd law
mg
An observer in the car feels a force that pushes
everything backwards. To explain his result
He adds a “fictitious force” equal to Fin=-ma
This is known as inertial force.
T
Sum of forces equal to zero
ma
mg
Centrifugal vs. Centripetal
vt
vt
a
vr
The only real force is the
o
Centripetal force pulling
towards the center so the
ball must be accelerating
An observer sitting on the ball feels a fictitious force Centrifugal that
pushes him outwards balanced by the string held at O.
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.
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?
NEWTON’S WORRIES
• Newton knew that his theory has problems
– Gravity is “action at a distance” – he didn’t like
that!
– A static universe would be gravitationally
unstable.
Reading this week Chapter 4
• WHAT IS WORK ?
 
W  F d
Given in Joules
• WHAT IS ENERGY ? -> CAPACITY TO DO WORK in Joules
KE vs PE
Forms of Energy -> 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
1. Conservation of Energy
2. 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)
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
Sun’s hydrogen nuclei were created from energy of the event that
created the universe
ALL ENERGY CAME FROM THE BIG BANG
• Energy : The measure of a system’s 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
Earth’s 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. [E=1/2 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.
Electromagnetic Spectrum
EM Spectrum