Transcript r - s3.amazonaws.com

PHSX 114, Friday, September
19, 2003
• Reading for today: Chapter 5 (5-8 -- 5-10)
• Reading for next lecture (Mon.): Review
Chapters 4 and 5
• Homework for today's lecture: Chapter 5,
question 18; problems 39, 43, 53, 78
Other announcements
• Exam #2 is Wed., covers Chapters 4 and 5
• Review and equation sheets are posted on
the web
• Monday's class will be review
Weightlessness and
Apparent weight
•Astronauts in orbit are “weightless”,
yet they are in Earth’s gravity
• in orbit, they are falling with
downward acceleration g
• “apparent weight” is zero
Apparent weight
•
•
•
•
•
•
•
•
•
Scale reads the force w
ΣF=ma= w – FG
Elevator example
FG=mg doesn't change with elevator's acceleration
If a=0 (elevator has constant speed), w = FG
If a>0 (elevator accelerating upward), w > FG
If a<0 (elevator accelerating downward), w < FG
If a=-g (freefall), w=0 (-mg = w – mg)
example
Your turn
Find the apparent weight of a 100 kg object if
the elevator is accelerating upward with
a=3.0 m/s2.
• Answer: 1280 N
(in kg: 131 kg=1280N / 9.8 m/s2)
• ma= w – FG; w=ma+mg=m(a+g)=
(100kg)(3.0 + 9.8 m/s2)=1280 N
Gravity, one of the four
fundamental forces of nature
•
•
•
•
1. gravity
2. electromagnetism
3. strong nuclear force
4. weak nuclear force
Gravity, one of the four
fundamental forces of nature
• Gravity is the weakest of the four
• Gravity is the least understood of the four
(at a microscopic level)
• Gravity is the most obvious of the four -all you need is mass
Review: Newton's law
of universal
gravitation
r
m1
• F = Gm1m2/r2
• r is the distance separating the two objects
• G is the gravitational constant,
G= 6.67 x 10-11 N-m2/kg2
• Force is attractive, direction is along line
joining the two objects
m2
Universal gravity
• Same force that makes an apple
fall, keeps the Moon in orbit
• Note: the apple falls toward the
center of the Earth (r is distance to
the center)
• 17th century philosophical
breakthrough -- terrestrial and
celestial objects obey the same
rules
r
Newton's gravity in historical context
• Law of gravity explains planetary motion, final
nail in the coffin of the Earth-centered universe
• Copernicus (1473-1543) has idea that planets
orbit the Sun (radical! blasphemous!)
• Tycho Brahe (1546-1601) Danish astronomer
gets $$ from the king, builds observatory. 20
years of precise (1/60 of a degree)
measurements of planetary positions.
Newton's gravity in historical context
• Johannes Kepler (1571-1630) inherits data,
deduces three laws of planetary motion
• Isaac Newton (1642-1727) explains Kepler's
laws with universal gravitation (had to invent
calculus to do so)
Kepler's first law of planetary
motion
• The path of each planet is an ellipse with the
Sun at one focus.
• Not perfect circles! Radical!
• Using calculus, can show you get an elliptical
orbit from a 1/r2 central force
• An ellipse is the locus of points such that the
sum of the distances from the two foci is
constant. (When the two foci are in the same
spot, you have a circle.)
Kepler's second law of
planetary motion
• An imaginary line joining any planet to the
Sun sweeps out equal areas in equal periods
of time.
• This means the planet moves faster when it
is closer to the Sun.
• Explained by angular momentum
conservation (Chapter 8)
Kepler's third law of planetary
motion
• The square of the period of any planet is
proportional to the cube of the planet's mean
distance from the Sun.
• The period (T) is the time an object takes to
complete one cycle of its motion. (For a planet, T
is the time to complete one orbit.)
• T12/ r13 = T22/ r23= constant (see data for our solar
system)
Your turn
• Imagine two planets orbiting another star.
Planet 1 has T1= 1 year and r1= 1.5 x 108 km.
If planet 2 has r2= 3.0 x 108 km, find T2.
• T12/ r13 = T22/ r23 =>
T2= T1(r2/ r1)3/2 =
(1 year)( 3.0 x 108 km/1.5 x 108 km)3/2 =
(1 year)(2) 3/2 = 2.83 years
Kepler's third law and circular
orbits
• For a circular orbit, straightforward to show
T2/ r3= constant and the constant is 4π2/(GM),
where M is the mass of the body being orbited
(the Sun in Kepler's case)
• Circular orbit examples