Transcript Potential Energy

The Veil Nebula: a large,
expanding cloud resulting from
the explosion of a massive star
(a supernova remnant). Life
owes its existence to elements
created in these massive stars
and returned to space in these
explosions to form new stars
and planets.
Light from the original
supernova explosion likely
reached Earth over 5,000
years ago. Also known as the
Cygnus Loop, the Veil Nebula
now spans nearly 3 degrees or
about 6 times the diameter of
the full Moon.
Homework #2 has been posted
Questions 1-16 are multiple choice. Answers
to these questions are due on Oncourse by
5:00 pm, Wednesday, September 22.
Questions 17 – 20 require short written
answers. These are due by the beginning of
class on Thursday, September 23.
The Activities page of the class website now
has a number of out-of-class activities posted.
These activities count towards the activity
points earned towards the final grade.
Two models of the Universe
Geocentric
Heliocentric
A hallmark of science
is that
theories are testable
Which model more accurately depicts nature?
 Both make predictions for the apparent motions of
the Sun, planets and stars.
 The Heliocentric model, with modifications
incorporating Kepler’s Laws, gives more accurate
predictions
 But, the Geocentric model might be made more
accurate through appropriate modifications.
 Need additional predictions that clearly differentiate
between the two models. (need tests)
Contemporary with Kepler was
Galileo Galilei (1564-1642),
the “founder of experimental science”
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First person known to point a
telescope at the sky
He wanted to connect the
physics understood on earth
with objects in the heaven
His work got him in trouble with
the Church and led to his house
arrest for many years.
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
 Moons of Jupiter (Heavenly bodies existed
which did not orbit the earth)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
 Moons of Jupiter (Heavenly bodies existed
which did not orbit the earth)
 Phases of Venus: the two models of the
Universe made two very different predictions.
Phases of
Venus
Galileo’s observation of the phases of Venus was the final
evidence that buried the geocentric model.
Geocentric
Heliocentric
No gibbous or full phases!
All phases are seen!
Galileo observed all phases!
With Galileo’s observations, the revolution
begun by Copernicus was nearly complete…
 The structure of the universe had been totally
changed.
 The motions of the planets were understood, at least
from a geometrical perspective.
 Earth was no longer a “special” place in the universe.
 The crowning achievement was yet to come discovering the laws of nature and that naturally led to
the newly determined structure.
Sir Isaac Newton (1642-1727)
Invented calculus
Invented the reflecting
telescope
Connected gravity and
planetary forces
Universal Law of Gravitation
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
This force is always attractive and it
applies to ALL objects possessing mass!
Orbital Paths from Law of Gravitation
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Extending Kepler’s Law #1, Newton
found that ellipses were not the only
orbital paths.
All orbits are “conic sections”
– ellipse (bound)
– parabola (unbound)
– hyperbola (unbound)
Orbital Paths from Law of Gravitation
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Extending Kepler’s Law #1, Newton
found that ellipses were not the only
orbital paths.
All orbits are “conic sections”
– ellipse (bound)
– parabola (unbound)
– hyperbola (unbound)
Orbital motion takes place around
the center of mass
The Center of Mass
In Kepler's Laws, the Sun is fixed at a point in space (a
focus of an ellipse) and the planet revolves around it.
Why is the Sun privileged?
Kepler had mystical ideas about the Sun, endowing it
with almost god-like qualities that justified its special
place.
Newton demonstrated that the the Sun does not occupy
a privileged postion and in the process he modified
Kepler's 3rd Law.
The center of mass is familiar to anyone who has ever played
on a see-saw. The fulcrum point at which the see-saw will
exactly balance two people sitting on either end is the center
of mass for the two persons.
m1d1 = m2d2
Newton realized that in the planet-Sun system the
planet does not orbit around a stationary Sun (a planet
exerts as much gravitational force on the Sun as the
Sun does on a planet). F = Gm m /d2
g
1
2
 Instead, Newton proposed that both the planet and
the Sun orbited around the common center of mass for
the planet-Sun system.
 This led Newton to modify Kepler's 3rd Law.
Recall Kepler’s 3rd law: P2 / a3 = constant
Newton’s Version of Kepler’s Third Law
2
2
3
P = 4 a / G (m1 + m2)
G is known as the universal gravitational constant.
If you can measure the orbital period of two objects (P)
and the distance between them (a), then you can calculate
the sum of the masses of both objects (m1 + m2).
A Universe of Matter and Energy
What is matter?
What is energy?
Matter – material such as rocks,
water, air; “stuff” composed of
atoms
Energy – makes or has the
potential to make matter move!
The history of the universe, including biological
organisms, is based upon the interplay between
matter and energy.
Three Basic Types of Energy
• kinetic
– energy of motion
• potential
– stored energy; e.g., chemical,
gravitational, electrical, etc.
• radiative
– energy transported by light
(electromagetic radiation)
Conservation of
Energy
Fundamental law of
nature
Energy can be neither
created nor destroyed
It can change form or be
exchanged between objects.
K.E.
The total energy content of
the Universe was determined
in the Big Bang and remains
the same today.
P.E.
R.E.
Kinetic Energy (K.E.):
energy of motion
K.E. = 1/2 mv2
(m is mass, v is velocity)
On the microscopic level:
temperature
is a measure of the
average kinetic energy
of particles within a substance
Temperature Scales
Temperature vs. Heat
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lower T
higher T
same T
Temperature is the average
kinetic energy.
Heat (thermal energy) is the
total kinetic energy.
less heat
more heat
Sound waves are a form of kinetic energy on
a microscopic level
(organized vibration of molecules)
Applying what we’ve learned -
pizza vs. soup
caution in the kitchen
Potential Energy:
Energy that is “stored” within an
object and that has the potential of
being released in a different form
Gravitational Potential Energy
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gravitational potential energy is
the energy which an object stores
due to its ability to fall
g
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It depends on:
–
–
–
m
the object’s mass (m)
the strength of gravity (g)
the distance which it can fall (d)
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P.E. = mgd
d
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gravitational potential energy
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P.E. = mgd
g
Mass-Energy Potential Energy
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mass-energy: energy is stored in
matter itself
this mass-energy is what would
be released if an amount of mass,
m, were converted into energy
E = mc2
[ c = 3 x 108 m/s
is the speed of light]
Chemical Potential Energy
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Chemical potential energy:
energy stored chemical bounds
There are many additional
examples of potential energy. e.g.,
stretched springs, …
Energy, while
conserved, can be
transformed from one
type of energy to
another
Potential
Kinetic
Potential
Kinetic
Kinetic
Potential
Orbits & Energy
Uphill
Maximum
Potential
Energy
Maximum
Kinetic
Energy
Downhill