Transcript Chapter 4

Chapter 4
Making Sense of the Universe:
Understanding Motion, Energy, and
Gravity
Describing Motion
• Speed: How Fast.
• Velocity: How fast in which direction.
• Acceleration: How fast and in which
direction velocity changes.
Sometimes, acceleration is a
constant
• Example: Acceleration due to gravity is
constant near the surface of the Earth.
• Since it is a constant, the acceleration due to
gravity is given the special symbol g.
• For the earth, g = 9.8 m/s/s or
approximately 10 m/s/s.
When Acceleration = g, we have
Free Fall Motion.
V = 0m/s
g
t = 0 seconds
Notice that the V arrow gets
longer while the g arrow does
not. It remains constant in
length and direction.
V(t) = V(0) + g(t)
V(2sec) = 0 + (10m/s2)(2s)
V(2sec) = 20m/s
g
V=?
t = 2 seconds
Gravitational Acceleration Near the
Surface of the Earth.
On the Earth, the
acceleration due to
gravity is ~ 10m/s2
(9.8 m/s2).
Momentum and Force
• Momentum = Mass x velocity
• Force = (Change in Momentum)/(Change in time).
m
V
p – linear
momentum
p = mV
Example: If m = 10kg and V = 10m/s (East)
P = (10kg)(10m/s) = 100 kg m/s (East)
Mass and Weight
• Mass : Amount of matter a body possesses.
• Weight : Force of gravity acting on the mass.
• Apparent weight = Net force that acts on the
mass.
Weight is not the same as mass.
The man’s weight changes, but his mass remains constant.
Free-fall, Weightlessness, and Orbit
• Free-Fall- the condition of an accelerating
mass when the acceleration = g.
• Weightless- If the only force acting is that
due to gravity, and there is no reaction force
from a floor, for example, pushing up
against you, then one is in a state of free-fall
and experiences weightlessness.
Astronauts are in a prolonged period of
weightlessness when they are in orbit
Weightlessness
Newton’s Cannon
• The faster the cannonball is shot, the farther it goes
before hitting the ground.
• If it goes fast enough, it will continually “fall around”
or orbit, the Earth.
• With a fast enough speed, it may escape the Earth’s
gravity altogether.
• Escape velocity – The minimum velocity needed to
escape from the gravitational field of a moon, planet
or star.
Newton’s Three Laws of Motion
• 1) Law of Inertia: In the absence of a net
force, the motion of an object remains
constant.
• 2) Net Force = Rate of change of momentum.
– Momentum = mass x velocity
• 3) For every force, there is always an equal and
opposite reaction force.
Conservation of Linear Momentum and
Conservation of Angular Momentum
• Conservation of Linear Momentum:
– In the absence of a net external force, linear
momentum remains constant.
• Conservation of Angular Momentum:
– In the absence of a net torque (twisting force),
the total angular momentum of a system
remains constant.
Newton’s Law of Universal Gravitation
• Every mass attracts every other mass through
the force called gravity.
• The force of attraction is directly
proportional to the product of their masses.
• The force of attraction decreases with the
square of the distance between the mass
centers. This is called an inverse square
law.
The Gravitational Force Fg
The “Why” of Kepler’s Laws, and More
• Newton found that Kepler’s first two laws apply not
only to planets, but to any object going around another
object under the force of gravity.
• He found that orbits do not have to be bound orbits as
they are with elliptical orbits.
Unbound (hyperbolic) orbits are also possible.
• Newton found that Kepler’s third law could be
generalized in a way that allows us to calculate the
mass of one or both orbiting objects.
Tides
• The tidal bulges face toward and away from
the moon because of the difference in the
strength of the gravitational attraction in
parts of the Earth at different distances from
the Moon.
• There are two daily high tides at any
location on Earth, as it rotates through the
two tidal bulges.
• Tides also
depend on tidal
forces from the
Sun, which are
about 1/3 as
strong as the
moon’s.
Highest high
tides.
Lowest low
tides.
Tidal Friction causes three important effects
1. It causes the Earth’s rotation to gradually
slow down, resulting in a longer day.
2. It makes the Moon move gradually away
from the Earth (The Moon has a slight
tangential component to its acceleration
vector)
3. Synchronous rotation is a natural
consequence of tidal friction.
Tangential
acceleration
Radial acceleration
It can be shown, by conservation of
angular momentum, that the radial
distance of the moon must increase
as the rotation rate of the Earth
decreases by tidal friction.
Pluto-Charon system – another example
of synchronous rotation
Orbital Energy and Escape Velocity
• A comet in an unbound
orbit of the Sun, passes
near Jupiter.
• The comet loses some of
its orbital energy to
Jupiter, which changes
the comet’s path to a
bound orbit around the
Sun.
unbound
orbit
bound
orbit
• The escape velocity is
the velocity necessary
for an object to
completely escape the
gravity of a large body
such as a moon, planet
or star.
v escape 
2 GM
R
G = 6.67 x 10-11 m3/kg s2
M = Mass of the planet
• The escape velocity of
the Earth = 11 km/s
R = Radius of the planet
Matter and Energy in Everyday Life
• Matter:
– Matter is simply material, such as rocks, water,
or air.
– Mass is the amount of matter an object has.
• Energy:
– In physics, energy is defined as the ability to do
work.
– Generally two types of energy:
• 1) Kinetic
• 2) Potential
• We measure energy in calories, Joules,
electron volts, along with many other units.
• A typical adult consumes about 2500
calories of energy each day from the food
they eat.
• In science and internationally, the favored
unit of energy is the joule. This is because
the joule can be written in the fundamental
units of kg, m, and sec.
• 1 calorie = 4,184 joules. So 2500 calories
used daily by a typical adult ~ 10 x 106 J
(10million joules)
• Whenever matter is moving, it has energy of
motion, or kinetic energy.
• Kinetic Energy = Energy of motion.
• Potential Energy = Usually energy of position, but
can also be regarded as stored energy.
– Gasoline has stored chemical potential energy which is
converted to kinetic energy of the car.
• Radiative Energy = Energy of light
(electromagnetic energy).
A Scientific View of Energy
v
m
We can calculate the kinetic energy of any
moving object with a very simple formula:
KE = ½ mv2
m:
v:
KE:
Mass of the object.
Speed of the object.
Kinetic energy measured in Joules.
Thermal Energy
• The energy contained within a substance as
measured by its temperature is often called
thermal energy.
• Thermal energy represents the collective
kinetic energy of the many individual
particles moving within a substance.
Temperature and Heat
Lower Temperature
Higher Temperature
Same Temperature,
but less thermal
energy.
Same Temperature,
and more thermal
energy.
Types of Potential Energy
• Gravitational Potential Energy
– The amount of gravitational potential energy
released as an object falls depends on its mass, the
strength of gravity, and the distance it falls.
– GPE = mgh.
• Mass-Energy
E = mc2
– A small amount of mass represents a huge amount
of energy.
Conservation of Energy
• A fundamental principle in science is that,
regardless of how we change the form of
energy, the total quantity of energy never
changes. This principle is called the:
Law of Conservation of Energy
The Material World
• Matter can exist in different phases.
• Solid
• Liquid
• Gas
What is Matter?
• Today, we know that all ordinary matter is composed of
atoms.
• Each different type of atom corresponds to a different
chemical element.
• Atoms can form molecules which can then form a number
of different material substances.
• Some molecules consist of two or more atoms of the same
element.
O2 – molecular oxygen
O – atomic oxygen
H2 – molecular hydrogen
H – atomic hydrogen
Atomic Structure
• A small dense nucleus lies at the center of an
atom.
• The nucleus is made up of protons and
neutrons.
• The nucleus is surrounded by particles called
electrons.
• The properties of an atom depend primarily
on the amount of electrical charge.
(protons and electrons)
Terminology
• atomic number: The number of protons in
an atom.
• atomic mass: The combined number of
protons and neutrons in an atom.
• isotope: Sometimes, the same element can
have more than the usual number of neutrons.
We call this an isotope.
– A proton and a neutron form an isotope of
hydrogen called deuterium.
Summary of Atomic Structure
Finally, at
Evaporation begins
with the
Phases
of
Matter
–
example:
water
production
of
steam
(water
vapor).
100 C (STP),
o
the water
molecules
have enough
thermal
energy to
break free
from oneanother.
The water remains
a liquid over a
large temperature
range.
As the temperature increases, the water
becomes a liquid (liquid water)
Below 0oC (32oF), water is a solid (ice)
Ref: PJ Brucat
(University of Florida)
Ions and Ionization
• The loss of one or more electrons (electrons are
negatively charged) leaves the remaining atom
with a net positive charge.
• Such charged atoms are called ions.
• The process of stripping electrons from atoms is
called ionization.
• At high temperatures, the atoms of a hot gas can
become ionized, creating a plasma phase of
matter.
Energy in Atoms
• Atoms contain electric potential energy in the
distribution of their electrons around their
nuclei.
• Consider the hydrogen atom, which is the
simplest atom.
Ionization
When the atom
contains the smallest
amount of electric
potential energy, we
say that the atom is
in the ground state.
If the electron gains
energy, it becomes
“smeared out” over a
greater volume.
If the electron gains
enough energy, it
can escape the atom
completely and we
have an ionized
atom.
The Discovery of the Quantum World
• The most surprising aspect of atoms was the
discovery that only particular energy transitions
can occur for the electron.
• This was the beginning of Modern Physics
(1910 – 1935) and a theory of Quantum
Mechanics was developed.
I’m
Continuous!
Classical System
Any height is
possible
I’m
Quantized!
Quantum System
Only discrete
“Quantized” step
heights are possible.
Energy Levels for H atom
Blue Light
Red Light
End of Section