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Unit 6: Universal Gravitation
Part 1
Everything pulls on
everything else.
Newton’s Law of Universal Gravitation
Law of Universal Gravitation:
every object attracts every other object with
a force that directly proportional to the
mass of each object and inversely
proportional to the square of the distance
between them.
Newton’s Law of Universal Gravitation
m
m
Why would you weigh
less on a mountain top?
Newton’s Law of Universal Gravitation
universal gravitational constant, G:
describes the strength of gravity in the
equation for universal gravitation
G = 6.67 × 10−11 N·m2/kg2
the units of G make the force of gravity come out in newtons
Newton’s Law of Universal Gravitation
Gravity weakens with distance. (weight decreases)
• but gravity never drops to zero
• The gravitational influence of every object,
however small or far, is exerted through all space.
Newton’s Law of Universal Gravitation
G was first measured 150 years after Newton’s discovery of
universal gravitation by a method of measuring the attraction
between two masses.
G = 6.67 × 10−11 or 0.000 000 000 0667
The extremely low value of G tells us that gravity is a
very weak force.
It is the weakest of the
four fundamental forces.
We sense gravitation only
when very large masses
are involved (like Earth).
Universal Gravitation
The Earth is round because of gravitation.
• Since everything attracts everything else,
Earth had attracted itself together
before it became solid.
• Stars, planets, moons,
are all fairly spherical
because they have
to be.
Universal Gravitation
Gravity played a role in the formation of the solar system.
a. A slightly rotating ball of interstellar gas contracted due to
mutual gravitation.
b. The rotational speed of the ball of gas increased.
c. The increased momentum caused wider paths about the
rotational axis, producing an overall disk shape.
The greater surface area of the disk promoted cooling and
clusters of swirling matter—the birthplace of planets.
Universal Gravitation
The Expanding Universe
According to current scientific understanding, the
universe originated and grew from the explosion of a
primordial fireball about 15 billion years ago.
“Big Bang” theory: the origin of the universe
was an explosion of energy as the beginning
of matter, space and time.
Gravitational Field
gravitational field:
force field that occupies the space around a
massive body so that any mass in the
field space experiences a gravitational force
We can regard the moon as in contact with the
gravitational field of Earth.
Gravitational Field
A more familiar force field is the magnetic field of a
magnet.
• Iron filings on near a magnet
reveal the shape of the
magnet’s magnetic field.
• Where the filings are close
together, the field is strong.
• Earth is a giant magnet, and
like all magnets, is
surrounded in
a magnetic
field.
Gravitational Field
Field lines can also represent the pattern of Earth’s
gravitational field.
• The field lines are closer together where the
gravitational field is stronger.
• Any mass near Earth will
be accelerated in the
direction of the field lines.
• Earth’s gravitational field
follows the inverse-square
law (it’s strongest near
Earth surface and weaker
at greater distances from
Earth).
Gravitational Field Inside a Planet
The gravitational field of Earth exists inside Earth
as well as outside.
Imagine a hole drilled completely through Earth.
Consider the kind of motion you would undergo if
you fell into such a hole.
video clip:
“Fall Through Earth”
Gravitational Field Inside a Planet
Where is max velocity?
As you fall, your
acceleration diminishes.
The pull of the mass
above partly cancels
the pull below.
You’d gain speed
moving toward the
center, and lose
speed moving away
from the center.
The trip would take
nearly 45 minutes.
Gravitational Field Inside a Planet
At the center of
Earth, your weight
would be zero,
because you would
be pulled equally
by gravity in all
directions.
Weight and Weightlessness
The force of gravity, like any force, causes
acceleration.
Objects under the influence of gravity are pulled
toward each other and accelerate.
We are almost always in contact with Earth, so we
think of gravity as something that presses us
against Earth rather than as something that
accelerates us.
Weight and Weightlessness
The sensation of weight is equal to the force that
you exert against a supporting object (the floor).
Why?
more
support
force
Why?
less
support Why no weight
in free fall?
force
Four Fundamental Forces
•
Electromagnetic
•
Nuclear (strong/weak)
m
•
Gravitational
m
Four Fundamental Forces
Electromagnetic Force
– combination of electric & magnetic forces
– only force that can attract and repel
opposite
like
 Magnets have 2 poles
(north / south)
Four Fundamental Forces
Nuclear Forces (Review from Chem)
– Strong and Weak hold the nucleus together
overcomes electric
repulsion of
positive protons
involved in radioactivity
- 100x stronger than weak
- strongest force
- shortest distance
Four Fundamental Forces
Gravitational Force
– every object in attracts every other object
– depends on mass and distance
more mass
more force
more distance
less force
– WEAKEST universal force, but …
acts over LONGEST DISTANCE
Unit 6: Electrostatics and Fields
Part 2
Electricity at rest: forces
between charges and their
behavior in materials.
Electrical Forces and Charges
What if two forces
acted on you that
were each billions of
times stronger than
gravity?
The enormous
attractive and
repulsive electrical
forces between the
charges in Earth and
the charges in your
body balance out.
Electrical Forces and Charges
Electrical forces are from subatomic particles.
(protons attract electrons,
but electrons repel other electrons)
Electrical Forces and Charges
like…repel
opposite…attract
like…repel
charge: fundamental electrical property
causing mutual attractions or repulsions
between electrons or protons.
Conservation of Charge
Electrons and protons have electric charge.
In a neutral atom, there are as many electrons
as protons, so there is no net charge.
ions
Conservation of Charge
A charged object has an imbalance
by adding or removing electrons.
Demo
Electrons are neither
created nor destroyed, but
are simply transferred from
one material to another.
This principle is known as:
conservation of
____________
of charge
charge
Conservation of Charge
think!
If you scuff electrons onto your shoes while
walking across a rug, are you negatively or
positively charged?
Answer:
You have more electrons and are negatively
charged.
Coulomb’s Law
What is this?
Newton’s Law of Universal Gravitation
(2 masses attract according to an
inverse square law)
Coulomb’s Law
Coulomb’s Law
d -distance between charges.
q1 -quantity of one charge.
q2 -quantity of another charge.
k -constant.
charge is in coulombs (C)
1 C = 6.24 × 1018 electrons
(1 C passes through a 100-W
light bulb in 1 s)
Coulomb’s Law
Coulomb’s Law
k = 9,000,000,000 N·m2/C2 (9.0 x 109 N·m2/C2)
If a pair of charges of 1 C each were 1 m apart,
the force of repulsion between the two charges
9 billion N
would be _______________.
(more than 10 times the weight of a battleship! )
Coulomb’s Law
Newton’s Law of
Universal Gravitation
Coulomb’s Law
Coulomb’s Law
think!
What is the main significance of the fact that
G in Newton’s law of gravitation is a very
small number and k in Coulomb’s law is a
very large number?
Answer:
gravity is a weak force, but…
the electrical force is enormously strong.
Coulomb’s Law
think!
How will the electrostatic force compare
when charges are twice the distance apart?
Answer:
(inverse-square law)
at twice the distance, the force will be
one fourth as much.
Quick Quiz!
1. If a neutral atom has 22 protons in its
nucleus, the number of surrounding
electrons is…
A. less than 22.
B. exactly 22.
C. more than 22.
D. unknown.
Quick Quiz.
2. When we say charge is conserved, we
mean that charge can…
A. be saved, like money in a bank.
B. only be transferred from one place to
another.
C. take equivalent forms.
D. be created or destroyed, as in nuclear
reactions.
Quick Quiz.
3. A difference between Newton’s law of
gravity and Coulomb’s law is that only one
of these…
A. is a fundamental physical law.
B. uses a proportionality constant.
C. applies the inverse-square law.
D. involves repulsive and attractive forces.
Conductors and Insulators
conductors:
materials through which electric charge flows
Metals are good conductors for the motion of
electric charges because their electrons are
“loose” in a
“sea of
electrons”
Conductors and Insulators
insulators:
poor conductors with tightly bound electrons
(rubber, glass, plastic, wood, cloth)
Charge flows more
easily through
hundreds of
kilometers of metal
wire than through
the few centimeters
of insulating
material.
Conductors and Insulators
semiconductors:
materials that can be made to act as
insulators or as conductors.
Atoms in a semiconductor hold their electrons
until given small energy boosts.
Charging by Friction and Contact
charged by friction
charged by contact
?
+ ++
+ +
+ +
Charging by Induction
charged by
induction
(no direct contact)
Charging by Induction
grounding:
allowing charges
to move off (or
onto) a conductor
by touching.
Charging by Induction
The negatively charged bottoms of clouds
induce a positive charge on Earth’s surface.
Most lightning is an
electrical discharge
between oppositely
charged parts of
clouds.
Charging by Induction
think!
Why does the negative rod in the Figure 1 have the
same charge before and after, but not when charging
takes place in the Figure 2?
Figure 1
Figure 2
Answer:
No contact was made. The transfer of charge by
contact reduced the negative charge on the rod.
Charging
In summary,
objects are electrically charged in 3 ways:
• By friction, when electrons are transferred
by rubbing from one object to another.
• By contact, when electrons are transferred
by direct contact without rubbing.
• By induction, when electrons are
gathered or dispersed by a nearby charge
without contact.
Quick Quiz!
1. Which is the predominant carrier of
charge in copper wire?
A. protons
B. electrons
C. ions
D. neutrons
Quick Quiz.
2. When you scuff electrons off a rug with
your shoes, your shoes are then…
A. negatively charged.
B. positively charged.
C. ionic.
D. electrically neutral.
Quick Quiz.
3. When a cloud that is negatively charged
on its bottom and positively charged on
its top moves over the ground below, the
ground acquires…
A. a negative charge.
B. a positive charge.
C. no charge since the cloud is
electrically neutral.
D. an electrically grounded state.
Unit 6: Electrostatics and Fields
Part 3
An electric field is a
storehouse of energy.
Electric Fields
electric field:
force field that surrounds an electric charge
An electric field has both magnitude and direction.
vector
gravitational
force field
electrostatic
force field
Electric Fields
Imagine a small positive “test charge” placed in an
electric field.
• the field (E) is strongest where force (F) on a
test charge is greatest (longest vector)
repulsive force
• test charge
gives direction
attractive force with
same magnitude,
opposite direction
Electric Field Lines
Magnitude is shown by:
a. vector length
b. distance between
field lines
VIDEO
5:57
Electric Field Lines
a. Field lines from a positive charge go to infinity.
b. For equal but opposite charges, the field lines go
from positive and to negative charge.
c. Between two oppositely charged capacitor plates,
field lines are evenly spaced.
(opposite charges)
(like charges)
inside
ring?
(oppositely charged plates)
like or opposite?
Electric Shielding
When a car is struck by lightning, the occupant inside
the car is completely safe.
The electrons shower down upon the car, repel and
spread over the outer metal surface.
The electric fields
inside the car cancel
to almost zero.
Video Clip –
Lightning Car
5:16
Electric Shielding
Shielding :
• free charges
arrange on the
surface to cancel
fields inside.
Quick Quiz !
1. An electric field has…
A. no direction.
B. only magnitude.
C. both magnitude and direction.
D. the same strength throughout.
Quick Quiz.
2. In the electric field surrounding a group of
charged particles, field strength is greater
where field lines are…
A. thickest.
B. longest.
C. farthest apart.
D. closest.
Quick Quiz.
3. Electrons on the surface of a conductor will
arrange themselves so that the electric
field…
A. inside cancels to zero.
B. follows the inverse-square law.
C. tends toward a state of minimum energy.
D. is shielded from external charges.
Electric Fields
The strength of an electric field (E) on a test
charge (q) experiencing a force (F) at a point is:
F
E=
q
VIDEO
12:12
The force (F) on a
charge (q) at a
point in an electric
field (E) is:
F = qE
• A charge of –2 C is placed in an electric field
of strength 5000 N/C.
What force is experienced by the charge?
F = qE
F = (–2)(5000) F = –10000 N
• What is the strength of an electric field that
exerts a force of 50 N on a particle with a
charge of 0.05 C?
F
E=
q
50
E=
0.05
E = 1000 N/C
Electric Field Lines
VIDEO
3:13
Electric Field Lines
#1
X
Y
+
+
-Z
Electric Field Lines
#2
Electrical Potential Energy
Objects have potential energy from location.
a. Gravitational PE of weight is transferred into KE.
b. Electrical PE of charge is transferred into KE.
Electrical Potential Energy
electrical potential energy:
PE of a charge due to its
location in an electric field.
Work is done in pushing the charge
against the electric field.
(work = energy gained by the charge)
VIDEO1
8:08
VIDEO2
3:45
If the charge is released, it will accelerate
away from the sphere as electrical PE
transforms into KE.
Electric Potential
push 1 charge against
an electric field requires
an amount of work.
push 2 charges against
the same field requires
twice as much work.
2 charges have twice the electrical PE as 1
10 charges have ten times the electrical PE
But they would both have the SAME
electrical potential energy per charge.
Electric Potential
electric potential:
electrical PE per charge
At each location the PE per charge
will be the same.
PE = 10 J
q=1C
more charge,
more electrical PE,
PE = 20 J
but…
q=2C
Electric Potential
5000
The charge is typically
less than a millionth of
a coulomb.
Therefore, the energy
is very small—about a
thousandth of a joule.
0.001 J
5000 V =
0.0000002 C
A high voltage requires great energy only if a
great amount of charge is involved.
Electric Potential
think!
With twice as much charge on one
object, is the electrical potential
energy the same or twice as great?
Is the electric potential be the same
or is it be twice as great?
Answer:
Twice as much charge has twice as much
electrical potential energy, because it takes twice
as much work to bring the object to that location.
The electric potential would be the same, because
the electric potential = 2 PE
2q
Quick Quiz!
1. The potential energy of a compressed
spring and the potential energy of a
charged object both depend…
A. only on the work done on them.
B. only on their locations in their
respective fields.
C. on their locations in their respective
fields and on the work done on them.
D. on their kinetic energies exceeding
their potential energies.
Quick Quiz.
2. How is electric potential is related to
electrical potential energy?
A. The two terms are different names for
the same concept.
B. Electric potential is the ratio of
electrical potential energy per charge.
C. Both are measured using the units of
coulomb.
D. Both are measured using only the
units of joules.