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Announcements
Evening observing Tonight-Thursday. Bring
your blue tickets to the roof (elevator to
5th floor, then stairs), wear a jacket,
9-10pm!
HW #2 was due last night: if you forgot,
finish soon for partial credit!
Finish Chapter 4, read Chapter 5.1 for next
time.
Tuesday, September 21, 2010
Last Time
Kepler’s Three laws explain the motion of
the planets:
Planets move in an ellipse with the sun at
one focus
Planet–Sun line sweeps out equal areas in
equal time (moves faster when closer!)
Period and distance (semi-major axis) are
related: P2=A3
Tuesday, September 21, 2010
Last Time
Speed: rate an object moves
Velocity: Speed and direction
acceleration: change in the speed
and/or direction.
Tuesday, September 21, 2010
Gravity, Energy,
and Motion
Tuesday, September 21, 2010
Momentum and Force
momentum = mass x velocity
Anything in motion (velocity≠0) has
momentum associated with it
A net force changes momentum, which means
an acceleration (change in velocity)
a change in momentum can result from a
change in the direction of motion.
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
1)
2)
3)
4)
A car coming to a stop
a bus speeding up
An elevator moving at a constant speed
A car rounding a corner at a constant
speed
5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
✓ 1)
2)
3)
4)
A car coming to a stop
a bus speeding up
An elevator moving at a constant speed
A car rounding a corner at a constant
speed
5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
✓ 1) A car coming to a stop
✓ 2) a bus speeding up
3) An elevator moving at a constant speed
4) A car rounding a corner at a constant
speed
5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
✓ 1) A car coming to a stop
✓ 2) a bus speeding up
✕ 3) An elevator moving at a constant speed
4) A car rounding a corner at a constant
speed
5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
✓
✓
✕
✓
1)
2)
3)
4)
A car coming to a stop
a bus speeding up
An elevator moving at a constant speed
A car rounding a corner at a constant
speed
5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Thought Question
Is there a net force at work? (✓/✕)
✓
✓
✕
✓
1)
2)
3)
4)
A car coming to a stop
a bus speeding up
An elevator moving at a constant speed
A car rounding a corner at a constant
speed
✓ 5) A planet orbiting the Sun at a constant
speed
Tuesday, September 21, 2010
Force and Momentum
We say a force
causes a
transfer of
momentum.
Tuesday, September 21, 2010
Describing Motion
speed = rate at which an
object moves.
Distance/Time
example: 10 m/s
velocity = speed +
direction.
example: 10 m/s due West
Tuesday, September 21, 2010
The Acceleration Due to
Gravity
All falling objects
accelerate at the
same rate (not
counting air
resistance)
independent of
mass.
On Earth, g ≈ 10 m/
s2: speed increases
10 m/s with each
falling second
10 m/s per second
or 10 m/s2 = 22 mph/s
Tuesday, September 21, 2010
Gravity
The acceleration due
to gravity is the
same for any object
on the surface of
the earth.
Hammer and feather
fall at the same rate
(neglecting air
resistance).
Tuesday, September 21, 2010
Force and Momentum
We say a force
causes a
transfer of
momentum.
Tuesday, September 21, 2010
the difference between
mass and weight
mass - The amount of matter in an object
weight - The force that acts upon an
object
The amount of matter (number of atoms)
in you never changes but your weight
depends on how strong gravity is at your
location.
Tuesday, September 21, 2010
What is the
difference between
mass and weight?
A
B
C
D
The moon has weaker gravity than
the Earth. On the Moon:
A) you weigh the same, but your mass is
less
B) you weigh less, but your mass is the
same
C) You weigh more, but your mass is the
same
D) you weigh more, and your mass is
more
Tuesday, September 21, 2010
What is the
difference between
mass and weight?
A
B
C
D
The moon has weaker gravity than
the Earth. On the Moon:
A) you weigh the same, but your mass is
less
✪ B) you weigh less, but your mass is the
same
C) You weigh more, but your mass is the
same
D) you weigh more, and your mass is
more
Tuesday, September 21, 2010
What is the
difference between
mass and weight?
A
B
C
D
The moon has weaker gravity than
the Earth. On the Moon:
A) you weigh the same, but your mass is
29 lbs
less
✪ B) you weigh less, but your mass is the
same
C) You weigh more, but your mass is the
same
D) you weigh more, and your mass is
more
Tuesday, September 21, 2010
What is the
difference between
mass and weight?
A
B
C
D
The moon has weaker gravity than
the Earth. On the Moon:
A) you weigh the same, but your mass is
less
✪ B) you weigh less, but your mass is the
same
C) You weigh more, but your mass is the
same
D) you weigh more, and your mass is
more
Tuesday, September 21, 2010
Units of Mass/Force
Tuesday, September 21, 2010
English
Metric
Force
Pounds
Newtons
Mass
Slugs
Kilogram
back to... Sir Isaac
Newton
English scientist, 1642–1727
Greatest scientist ever?
Light, motion, gravity
Newtonian physics dominated
until Einstein.
Invented calculus to help
solve a different problem.
Tuesday, September 21, 2010
How did Newton
change our view
of the Universe?
Realized that the same physical laws
that operate on Earth also operate in
the heavens.
We can therefore use the laws of
physics to understand the universe!
Tuesday, September 21, 2010
Newton’s Three Laws of Motion
I. An object remains at rest or moves
at a constant velocity unless a net
force acts to change its direction or
speed.
The Apollo command module keeps
moving even without firing its
engines
Tuesday, September 21, 2010
Newton’s Three Laws of Motion
II. If an object is acted on by a net
force, then this force changes the
momentum of the object, accelerating
it in the direction of the force.
Force = mass x acceleration
F = ma
Give me F, and I will tell you
how an object moves (a).
Tuesday, September 21, 2010
Newton’s Three Laws of Motion
III. For every force, there is always
and equal and opposite reaction
force
The Space Shuttle is
propelled upward with a
force equal and opposite to
the force with which the gas
is expelled out the rockets
Tuesday, September 21, 2010
A
B
C
D
Why does a rocket accelerate?
A) The exhaust pushes on the air,
causing it to move forward.
B) It is propelled forward as its
exhaust is sent backwards.
C) Force of will
Tuesday, September 21, 2010
A
B
C
D
Why does a rocket accelerate?
A) The exhaust pushes on the air,
causing it to move forward.
✪ B) It is propelled forward as its
exhaust is sent backwards.
C) Force of will
Tuesday, September 21, 2010
Weightlessness
Sense of weight
comes from Newton’s
3rd law.
Earth’s gravity pulls
you down, but the
floor pushes back
with the same force:
we feel weight!
You are “weightless”
anytime you are
freely falling.
Tuesday, September 21, 2010
Weightless
Astronauts
A
B
C
D
An astronaut is weightless because:
A)
B)
C)
D)
Tuesday, September 21, 2010
The ship’s rockets holds them up
There is no gravity in space
They are constantly in free fall
They are not attracted to the Earth
Weightless
Astronauts
A
B
C
D
An astronaut is weightless because:
A)
B)
C)
D)
Tuesday, September 21, 2010
The ship’s rockets holds them up
There is no gravity in space
They are constantly in free fall
They are not attracted to the Earth
Weightless
Astronauts
A
B
C
D
An astronaut is weightless because:
A)
B)
✪ C)
D)
Tuesday, September 21, 2010
The ship’s rockets holds them up
There is no gravity in space
They are constantly in free fall
They are not attracted to the Earth
Weightless
Astronauts
A
B
C
D
An astronaut is weightless because:
A)
B)
✪ C)
D)
The ship’s rockets holds them up
There is no gravity in space
They are constantly in free fall
They are not attracted to the Earth
See Interactive Fig. 4.4
Tuesday, September 21, 2010
Aboard an Airforce Training Airplane
Tuesday, September 21, 2010
Law’s of
Conservation
Newton’s laws are really deeper statement
about nature: “conservation laws”.
Conservation of Momentum.
Conservation of Angular Momentum.
Conservation of Energy.
Tuesday, September 21, 2010
Conservation of
Angular Momentum
Angular momentum is a special kind of
“circling or rotating momentum”.
Law: The total angular momentum of a
system cannot change unless it interacts
with something (i.e., gives up or receives
angular momentum)
Tuesday, September 21, 2010
Tuesday, September 21, 2010
Angular Momentum
Since angular
momentum is
conserved...
Angular momentum
in an orbiting planet
does not change.
Conservation of
angular momentum
Explains Kepler’s
2nd law!!!
Tuesday, September 21, 2010
Angular Momentum
Since angular
momentum is
conserved...
Angular momentum
in an orbiting planet
does not change.
Conservation of
angular momentum
Explains Kepler’s
2nd law!!!
Tuesday, September 21, 2010
Angular Momentum
Since angular
momentum is
conserved...
Angular momentum
in an orbiting planet
does not change.
Tuesday, September 21, 2010
Angular Momentum
Since angular
momentum is
conserved...
Angular momentum
in an orbiting planet
does not change.
Conservation of
angular momentum
Explains Kepler’s
2nd law!!!
Tuesday, September 21, 2010
Newton’s laws of
Gravity
Every mass attracts every other mass.
Strength of attraction is directly
proportional to the product of their masses
The strength of that attraction is
inversely proportional to the square of the
distance between them.
Tuesday, September 21, 2010
Examples
M1 M2
FG = G
d2
Double Mass #2:
new
FG
M1 (2M2 )
=G
=
2F
G
2
d
2
Tuesday, September 21, 2010
Examples
M1 M2
FG = G
d2
Double the
distance:
Fnew
G
=G
2
Tuesday, September 21, 2010
M1 M2
(2d)
2
M1 M2
1
=G
=
F
G
2
4d
4
Examples
The force of gravity between the Earth
and an apple is given by,
MEarth Mapple
FG = G
2
REarth
Newton’s Second Law: F = ma
FG = mapple aapple
Give me F, and I will tell you
how an object moves (a).
Gravity causes an apple to fall
(accelerate) from a tree
Tuesday, September 21, 2010
Explaining Kepler’s
Laws
Newton’s laws of motion and gravity
together explain Kepler’s laws of
planetary motion.
Newton’s laws work everywhere: not just
for planets orbiting the sun, but satellites
orbiting planets, etc.
Newton’s version of Kepler’s third law is an
improvement: you can calculate the mass of
the object being orbited!
Tuesday, September 21, 2010
How does Newton’s Law of
Gravity Extend Kepler’s Laws?
Newton also showed
that Kepler’s Laws
apply to all orbiting
objects, including
moons, stars, galaxies.
Ellipses are not the
only orbit possible
bound: ellipses
unbound: parabola
hyperbola
Tuesday, September 21, 2010
How does Newton’s Law of
Gravity Extend Kepler’s Laws?
The same thing that
causes apples to fall to
the Earth keeps the
planets in orbit around
the Sun
Newton was the first to show that
the laws of physics work in the
heavens.
Tuesday, September 21, 2010
Newton’s Version of
Kepler’s Third Law
If a small object orbits a large object, and
you can measure the smaller objects orbital
period and average distance from the larger
object, then you can measure the mass of the
larger object.
Measure the mass of the Sun using the
Earth
Measure the mass of the Earth from
observations of satellites
Measure the mass of Jupiter from its moons
Tuesday, September 21, 2010
Thought Question:
The gravity of the Earth pulls on you
and your gravity pulls on the Earth
Is the force you exert on the Earth,
larger, smaller, or the same as the
force the Earth exerts on you?
Tuesday, September 21, 2010
Thought Question:
The gravity of the Earth pulls on you
and your gravity pulls on the Earth
Is the force you exert on the Earth,
larger, smaller, or the same as the
force the Earth exerts on you?
The same!
Tuesday, September 21, 2010
Myou MEarth
FG = G
d2
How does gravity
cause tides?
Tuesday, September 21, 2010
Newton gives the
answer!
M1 M2
FG = G
d2
Tuesday, September 21, 2010
Tides vary with the
phase of the moon.
“Spring” tides are the
most extreme because
the gravity of the Sun
and moon combine.
Tuesday, September 21, 2010
Conservation of
Energy
A fundamental law of physics is that energy
must be conserved.
Energy can:
1) Transfer from one object to another
2) Change forms
Total amount stays the same!
Tuesday, September 21, 2010
Basic Types of Energy
Basic types:
Kinetic(motion)
Radiative(light)
Potential (stored)
Energy can change
types, but not be
destroyed.
Tuesday, September 21, 2010
Units of Energy
In the U.S., we are used to the Calorie.
(a typical adult needs 2,500 Calories)
Scientists use the joule.
1 Calorie = 4,184 joules
( a typical adult needs to eat 10 million
joules of energy a day)
Tuesday, September 21, 2010
Kinetic Energy
Kinetic Energy is energy due to motion.
Tuesday, September 21, 2010
Gravitational
Potential Energy
Potential Energy
On Earth it depends on:
1) mass of the object
2) strength of gravity
3) how far an object can
fall
Tuesday, September 21, 2010
Potential vs. Kinetic
The total energy
of the ball is
conserved (kinetic
+potential) but the
ball’s energy can
shift between
kinetic and
potential
Tuesday, September 21, 2010
Mass-Energy
2
E=mc
Einstein found that
mass itself is a form
of energy
A small amount of
matter can be
converted into a large
amount of energy
Tuesday, September 21, 2010
Examples of
2
E=mc
Hiroshima and Nagasaki
bombs fueled by an ounce
of matter
New York City could be run
for a month with a newspaper
A baseball’s worth could keep a car going
at 65 m.p.h for 5,000 years
As Electricity, the energy in an ounce of
matter is worth $70 million!
Tuesday, September 21, 2010
Reminders
Evening observing at brooks observatory
Tonight through Thursday night. Come to
the roof of this building at 9-10pm.
Weather permitting.
HW #3 available on MasteringAstronomy
Tuesday, September 21, 2010