Download Jan. 27 - Feb. 5

Jan. 27th - Feb. 5th
SIR ISAAC NEWTON
1642-1727
Gravity and Motion
Newton’s Laws
1. Inertia
An object in motion remains in motion in a
straight line at a constant speed and an
object at rest remains at rest unless acted
upon by and outside force.
Some force is making planets stay in near circular orbits or they would move in a
straight line.
2. acceleration
The acceleration (change in velocity) of an
object is directly proportional to the
unbalanced force exerted upon it and
inversely proportional to its mass.
F = ma
F is force (N)
m is mass (Kg)
a is acceleration (m/sec2)
Because planets change speed during their orbits, their must be changes in force
to accelerate and decelerate the planets.
3. reaction
When an object exerts a force upon a second
object, the second object exerts a force on
the first that is equal in magnitude and
opposite in direction.
Universal Gravitation
Every mass exerts a force of attraction on every
other mass. The strength of the force is directly
proportional to the product of the masses divided
by the square of their separation
F = Gm1m2/r2
F is force of gravity (N)
m’s are masses (Kg)
r is the distance between the masses (m)
and G is the universal gravitational constant
G = 6.67E-11 m3/kgs2
Measuring an objects mass using orbital motion.
Centripetal Force is the force required to keep an
object moving in a circular path (to overcome
inertia).
F = (mV2)/r
F is centripetal force (N)
m is mass moving in a circle (Kg)
V is the velocity of the moving object (m/sec2)
R is the radius of the circular path (m)
The planets are maintained in a roughly circular orbit by the force of the sun’s
gravity pulling them inward. This provides an explanation for Kepler’s second law and
leads to the following calculation.
F (gravity) = F (centripetal)
Gmsme/r2 = (meV2)/r (notice that the mass of the moving object
cancels out of the equation)
2
2
Gms/r = (V )/r
ms = V2r/G
Lets Try
(notice that although this calculation is for
the sun based on the orbit of the Earth, it
would work for the mass of any object
around which another object revolved)
V of the Earth is the circumference of its orbit divided by
365.25 days.
2πr/(365.25 x 24 x 60 x 60 sec)
2π(1.5 x 1011 m)/3.156 x 107 sec
= approx 30,000 m/sec
ms = (29,865 m/s)2 x (1.5 x 1011m) / (6.67 x
10-11 m3/kgs2)
ms = 2 x 1030 Kg
Compare to accepted value of 1.989 x 1030 Kg
Surface gravity (acceleration of dropped objects for example)
F = m1a = Gm1m2/r2
a = Gm/r2 knowing mass of Earth, we can calculate the
acceleration of gravity on Earth. (9.8 m/sec2)
The relationships between gravity, mass, acceleration and distance provide us
with a powerful tool to determine attributes of the planets and their moons.
ALL OF A SUDDEN WE CAN CALCULATE MASSES OF OBJECTS (AND WE
DON’T HAVE TO FIT THEM ON A BALANCE)!!!!!
The accepted mass of the Earth is 5.97 x 1024 Kg.
Can you demonstrate this by using the distance from the Earth to the moon 3.84 x 108 m
and its orbital period of 27.3 days.
ELECTROMAGNETIC RADIATION (LIGHT)
Intensity and Color of light
Light – electromagnetic radiation
Travels through vacuum by electric magnetic interaction
James Clerk Maxwell
Wave Particle Duality (Quantum Physics – it is what you say it is)
Photon = packet of energy
Wavelength = distance between successive crests (nm)
Frequency = number of waves in a second (Hz)
Interference and slit experiments! (Truly strange outcomes)
Speed = 300,000 km/sec and constant in a vacuum (Einstein)
c = λf
so frequency and wavelength are related
Varies in transparent media (prism) with blue slowest
Prism splits light into colors
Refraction
Bending due to different velocities
Faster = farther from normal
Slower = closer to normal
Red is longer wavelength at approx. 700nm
Blue is shorter at approx. 400nm
Calculate frequency if wavelength is 700nm
3.0 x 108 = 7.0 x 10-7 f
f = 4.2 x 1014 Hz
Parts of the spectrum outside of visible light
Infrared – heat experiment
Ultraviolet – film darkening experiment
Radio waves, x-rays, gamma rays
Gamma rays –less than 0.01nm
X-rays – 0.01-10nm
Ultraviolet – 10-400nm
Visible light – 400-700nm
Infrared – 700-150,000nm (0.7-5000microns)
Radio Waves – more than 5mm (up to 100’s of m)
Calculate frequency if wavelength is 100m
Energy of electromagnetic radiation depends on frequency/wavelength
E = hc/λ
E is energy of the photon in joules
H is planks constant 6.63 x 10-34 joule-second
C is speed of light in meters/second
λ is wavelength in meters
So since c and h (plank’s constant) are constant, longer
wavelengths have proportionally less energy than shorter ones.
(higher frequency = higher energy)
Calculate E for wavelength of 100m and 700nm
E = (6.63 x 10-34 )(3.0 x 108)/100 = 1.99 x 10-27 J
E = (6.63 x 10-34 )(3.0 x 108)/7.0 x 10-7 = 2.84 x 10-19 J
Blue has more energy than red
Wiens Law – color of max. radiation is a function of temperature
Example of stove burner (red-yellow-blue)
T = 3 x 106/λm (in degrees K, wavelength in nm of max. emission,
constant in K nm)
Sun radiates most strongly at roughly 500nm and thus
T = 3 x 106/500nm = 6000K
Creation of electromagnetic radiation
Bohr model of the atom
Nucleus with protons (+) and neutrons
Electron cloud (-)
2s, 6p, 6d etc. (periodic table)
Possible energy levels for an electron (Quantized)
Whole number multiples of wavelength (can’t cancel itself out)
Absorbs or emits electromagnetic radiation at specific wavelengths
based upon energy difference between orbits.
Each element has different energy levels and different numbers of levels
Energy = wavelength from above!!
Continuous spectrum – blackbody
Emission spectrum – bright line
Absorption spectrum – dark line
Atmospheric effects – windows versus wavelengths that are absorbed or blocked.
Short wavelengths blocked by ozone and ordinary oxygen
Ozone layer holes CFCs
Infrared absorbed by CO2 and water
Climate Change
Electric charges in upper atmosphere block completely the longest radio
waves.
Radio reflection and long distance reception
Two windows – multipart visible/infrared and big radio wave window
ALBERT EINSTEIN
Relativity
Mass and Energy are related E = mc2
E = (1.0kg) x (3.0 x 108)2 = 9 x 1016 J
Mass distorts space
Length, time, mass vary dependent on the velocity of the
observer (everything is relative).
Different model – better fit to reality (passes tests)