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Chapter 12- Universal Gravitation. Do question 180, 1-4 and 7-10 after test. It was fairly apparent to people for centuries that the earth, attracted objects on earth to it. Newton knew that since the apple changed speed Gravity must be a force. - PowerPoint PPT Presentation
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Chapter 12- Universal Gravitation
Do question 180, 1-4 and 7-10after test.
It was fairly apparent to people for centuries that the earth, attracted objects on earth to it.
Newton knew that since the apple changed speedGravity must be a force
Newton knew that the moon’s velocity changed constantly and therefore there must be a force on it.
Might the earth pull on the moon just like the apple?
Can Earth’s gravity reach all the way to the moon?Where does it stop????
If the moon is falling to the earth like the apple, then WHY doesn’t it fall
Newton realized that the moon and the apple are both falling like projectiles.
Cannonballs are shot with increasing speed
They are all falling towards the earth
gravity free path
Gravity pulls the moon towards the center of the earth
providing the ___________ Forceto keep it moving in
a circle
Fg
v
CENTRIPETAL
The tangential velocity is sufficient
to keep it from falling into the earth
Fg
vThe velocity is
always perpendicular to the force of
gravity
In order to “prove” his theory he wanted to predict the acceleration of the moon and see
if it matched observation.
He knew an apple on earth accelerates at 9.8 m/s2.
But what about the moon out in space?
If both the moon and the apple were just above the surface of the earth.
Which would hit the ground first:
The massive moon or
the tiny apple?
Heavy and light objects fall at the same rate on earth, he figured the mass of the moon wouldn’t affect its acceleration
But the apple is much closer to the earth than the moon.
The apple is a distance 1 earth radius for the center of mass of the earth
The moon is 60 earth radii away.The apple is only 1.
Note: apple not to scale
Newton reasoned that gravity would get weaker the farther
away two objects are.Think of 2 magnets
For reasons we will see later,He calculated that at a distance 60 times
From the center of the earth.
9.8 m/s2
602amoon =
amoon = .0027 m/s2
After falling for 1 second on earth’s surface an apple would have fallen 4.9 m
from a gravity free path
4.9 m
Without gravity after 1 second the
moon would be here
it falls 1.4 mm eachsecond
His answer matched what we know todayBut he wasn’t sure if the distance used
should be between the centers of the objects and didn’t publish for another 20 years
What would happen if the moon
suddenly stopped
It would fall to the earth.
The fall would take about 3.5 hours
Sun
The earth is constantly falling toward the sun
If the earth lost some of its tangential velocity?
The objects in our solar system have just the right speed to stay in their orbit.
If an object is moving too slow, it falls closer to the sun. As it does it speeds up.
What makes the earth and the sun so special that they attract objects to them with an
invisible force of gravity?
They have MASS
What else has mass?
Are you attracted to the person sitting next to you?
YES!!
Its called GRAVITY
Newton didn’t discover gravity,
He discovered that anything that has mass attracts anything else that has mass.
If there was no friction on the table you could pull your pencil to you not by
magic but by gravity
NEWTON’s Universal Law of Gravitation
Fg ~m1 m2
d2
m1 m2d
Proportional to – not equal to
Distance between center of masses
This is the force of gravity on EACH Object
Fg ~m1 m2
r2
m1 m2rRemember Newton 3rd law:
When m1 exerts a force on m2 then…..
Which feels a greater FORCE from the other
The exert EQUAL but opposite forces on each other
If the mass of 1 object is doubled,Then Fg ________
Fg ~m1
r2
m1 m2r
m2
doubles
Compare the force of gravity between the earth & 1kg object
to earth & 2kg object
Fg ~m1
r2
m2
If the mass of both object is doubled,Then Fg ________
Fg ~m1
r2
m1 m2r
m2
quadruples
If the distance between them doubles,Then Fg ________
Fg ~m1
r2
m1 r
m2
is 1/4
m2
If everything attracts everything else,Why isn’t it more obvious?
The mass of the earth is HUGE!!!!!
The force between earth and a 1 kg object is only 10 NHow big will the attraction be
between two 1 kg objects?
Fg =m1 m2
r2
G
Fg ~m1
r2
m2
In order to make this an equation we need a fudge factor.
If we knew G we could calculate the force between any two objects
Fg =m1 m2
r2
G
In order to find G, both masses would need to be known. As well as the force and
distance between them.
What is so hard about this?
The force of gravity between normal objects that can be weighed is VERY weak.
How to measure?
Henry Cavendish
English chemist and physicist who was shy and absent-minded. He was terrified of women, and communicated with his female servants by notes.
G = 6.67 10-11 Nm2/kg2
Fg =m1 m2
r2
G
G = .0000000000667
A very small number because gravity is a relatively weak force
9.8 N =1kg mearth
(6,380,000 m)2
G
A 1 kg object on the surface of the earth has a force of gravity of 9.8 N between it and the earth. The radius of
the earth is 6,380,000 m.
With G known, they could find the mass of the earth
mearth = 5.98 1024 kg
Cavendish’s experiment is often said to have weighed the earth in his
experiment
5.98 1024
Phillip von JollyAround 1850
later used a simpler apparatus and got
more accurate results
What is the force of gravity between a 65 kg student sitting .50 m away from a 75 kg student?
G = 6.67 x 10 -11
What is the force of gravity between the earthand the planet mars at their closest approach
(which is 1.01x1011 m between centers of mass)
mearth = 5.98 1024 kg
mmars = 6.41 x 1023 kg
Closest approach 101.1 million kilometers
2.51 x 1016 N
What is the force of gravity between the earth and 5.0 kg object which 12,760,000 m
(2 earth radii) above the surface of the earth?
mearth = 5.98 1024 kg
rearth = 6,380,000 m
Add to questions page 180
11, 15, 16, 17, 19, 20, 21, 22
If you increase the separation of two objects by 3 times, why doesn’t Fg decrease by 3
instead of decreasing by________9
How much more pizza do you get when you go from a pizza which is 1 m in radius
to one that is 2 m
Area = r2
When a light shines it spreads out as a spheregetting dimmer as you go further
Picture a hollow sphere with the light bulb in the middle.
If the sphere was doubled in radius, the same amount of light is spread out over 4 times the area.
Area of a sphere = 4 r2
So it is 4 times dimmer
Picture a butter gun
Many things follow this law:Gravity, Light, Sound, Magnets, Radioactivity……
1 m2 m
3 m
It shoots out the same amount of butter each time
The further away, the more it can cover with 1 shot
1 inch thick
What is the distance from?
Compare weights when you are halfway up a mountain vs. at the top?
Did the distance double?
How far away from the surface of the earth would you need to be to have your
mass reduced to ¼.
rearth
rearth
Your weight is just a special case of gravitational force
Your mass also attracts the earth
Which is stronger the:Fg,you,earth
Fg,earth,you
and everything else in the universe
When you wave your hand the rest of the universe feels it
Your mass also attracts the earth
The shuttle orbits the earth at 200,000 m above it surface. How strong is gravity there?
Gravitational pull is still 94% at that height.
astronauts is space
astronauts training in an airplane
If an astronaut still has ~94% of earth’s gravity on them, why do they “feel” weightless
The feeling of weight is most closely related to the Normal Force exerted on us by the floor or
seat etc…
Still
500 N
accelerating up
600 N
accelerating down
400 N
If the cord is cut
FREE FALL
0 N
An astronaut is in Free Fall towards the Earth,Why don’t they crash?
Book problems page 18129, 32, 33
Planets and suns condensed from clouds space “dust”
Picture a square cloud of space “dust”.
Any corner gets pulled in.
Even other planets pull on the earth causing “perturbations”
The furthest “planet” Pluto was discovered because it was causing Uranus to wobble a bit in its orbit
Newton showed us that the same laws of physics on earth apply to the rest of the
universe
Two galaxies crashing
What is concerning about the fact that everything in the universe attracts
everything else?
The universe about 15,000,000,000 years ago.Then the big bang
But this is sort of like throwing a rock into the air, as it gets further up it slows
As it expands its speed slows, then
Strangely enough the universe does not seem to be slowing down as it expands, but rather
speeding up.
This is like throwing marker in the air and having it……
Move upward faster and faster instead of slowing down and coming back
1 kg
1 kg
An object is located equal distances from two 1 kg masses. Compare the magnitude
and direction of the forces it feels
Find the net force on it using the parallelogram method.
1 kg
2 kg
An object is located equal distances from a 1 kg and 2 kg masses. Compare the
magnitude and direction of the forces it feels
Find the net force on it using the parallelogram method.
Chapter 13- Gravitational Interactions
There are 2 types of forces which can pull on another object without touching it that you are familiar with.
(there are less familiar ones electric charge, strong force, weak force)
GravityMagnets
Gravity Magnets
That really bugs me.
Exert a force without contact through a vacuum
A mass creates a Force FIELD, and the field exerts a force on objects in it
Gravitational Field
Electric, Magnetic, and Gravitational Fields are FORCE FIELDS
The field is represented by imaginary field lines
The arrows point in the direction a mass would accelerate (to the center of the earth)
Where is the field strongest, close to the surface of the earth or far away?
The field lines are closest where the field is the strongest
How to measure the strength of the field?A 1 kg object on the surface feels a force of 10 NA 2 kg object at the same location in the field feels a force of 20 N.
The field isn’t any stronger, only the force on the object
Field Strength = FG
m
What is the gravitational field strength at the location of the red object
m1
m2
Field Strength = Fm
Since, F = m a
The gravitation Field Strength at a location, is just the acceleration of an object there.
m a
G m1 m2
r2
m1
m2
Field Strength = FG
m1
FG =
Field Strength = G m1
r2
Compared the acceleration due to gravity at the surface of the earth, how would the acceleration
compare on a planet that….
Field Strength = G M
r2
had twice the mass but same radiushad the same mass but 3 times radiuswas the same mass, and 1/2 as big was 5 times as massive, and 1/10 the size
What would happen if you drilled a hole through the earth and jumped in?
Would you fall?Sure, you would accelerate toward the center of mass of the earth
What would happen to the Force of gravity and your acceleration as you fell?
You are closer the CM of the
earth, but…
Some of the earth pulls
you up. Which
stronger the up or down?
Do you still
accelerate at gor
more or less
Consider this, what happens when you are at the center of the earth?
Half pulls you up,
& half pulls you down.What is the net force?
Do you stop at the center of the earth
then?
Let’s complete our journey
g
0
g/2
As you fall towards the center you speed up, but your acceleration decreases.
What happens as you pass the center of the earth?
g
0
g/2
You will begin to accelerate but which way?
g/2
g
What will your speed be when you reach the other side?
g
0
g/2
You will begin to accelerate but which way?
g/2
g
If you weren’t able to jump out???
Video link to earth hole bungee jumping
So the Net Force of Gravity (or gravitational field) increases as you get closer to the center
of mass of an object until…
IncreasingDecreasing
You get inside the object
BLACK HOLES
How do we know they are there if we can see them?
BLACK HOLES
Stars orbiting very quickly around a dark region
How do they form?
Stars “burn” hydrogenAs they run out of fuel, they start to cool.
BLACK HOLES
As they cool, the atoms slow and the star collapses under its own gravity
What happens to the mass of the star as it collapses?
What happens to the mass of a slice of bread if you squish it?
The mass of the black hole is just the same as the mass of the star that
made it (or less)!!!!
What makes them so SCARY
If they don’t have any more mass than a big star does, why is their gravitational field so
strong?
IncreasingDecreasing
Increasing
But remember the strength increases with the square of the distance. So this isn’t quite an
accurate representation
Consider a Sun and a Black hole of the same mass
Increasing
It would be a little more like this
When a sun collapses into black hole, most scientists believe it becomes infinitely small.
But let’s say that our sun collapses into a same mass black hole which is 1 trillionth the
size (109). Compare the gravitational field strength of the surface of each.
Field Strength = G M
r2
What would happen to the earth, if the sun collapsed into a black hole?
Nothing, except we would freeze!
Field Strength = G M
r2
Book problems
page 196-197#’s 1, 3-6, 8, 25-28, 30
What causes the tides?
The Fg the earth feels from the moon is not equal on all sides
59 Rearth
61 Rearth
Where is it stronger?
If the pull of gravity from the moon is stronger on your head than your feet, what is it doing to you?
Fg vs distance
Because the water is able to move around the earth it moves towards the moon.
Because the water is able to flow around the earth, it moves towards the moon.
It is the DIFFERENCE in the force of gravity on the opposite sides of the planet
which cause the tides.
Not really to scale
Which has a greater effect on the earths tides?
Sun or Moon(note the force of gravity on the earth from the sun is
MUCH stronger than from the moon)
1 m
2 m
Compare the force of gravity on opposite sides of the planet
Fg
Different by a factor of 4!!
Fg
4
3 m
2 m
Compare the force of gravity on opposite sides of the planet
Fg
Different by a factor of 2.25!!What happens to the difference in gravity as
the planets separate?
Fg
2.25
Which has a bigger impact on the earth’s tides?
Not really to scale
THE MOON because it is closer to the earth there is a greater difference on the sides of
the earth!!!!!!!
The earth spins on its axis once a day,So different parts of the earth are closest to the
moon once a day.
So how many High Tides should there be in one day
But there are actually 2 high tides and 2 Low Tides per day.
Because the earth actually has two bulges, one closest to the moon and one
furthest
What causes the other one??????
If the moon simply rotated around the earth, there would only be one
Where is the center of mass about for an earth / moon system
As the moon revolves around the earth,The earth “wobbles”
As the moon revolves around the earth,The earth “wobbles”
The inertia of the water causes it to bulge away from the moon slightly
An object that goes in a circle never speeds up even though a force is constantly
applied. Why?
Only a force that is parallel to motion can do Work
Sun
If the earth traveled in a perfect circle it would never speed up or
slow down because.
If the earth was given a extra speed it would
Sun
Get further away from the sun
Now it would start to slow
Sun
Slowest, PE- KE
Fastest, PE- KE
Fgv
Sun
F
v
FF
Which components of the forces do work on the earth?How does the other component effect the earth?Where does the force of gravity do no work on the earth?
Elliptical orbit applet
applet #2
Planet travel in elliptical orbits with the sun at one focus
Escape Velocity
The more KE is starts with the more PE it ends with (before it falls back down)
Is there a speed at which the object would never come back down?
Escape velocity is 11,200 m/s for earth
The further you get from the earth, the weaker the force of gravity gets.
At an infinite distance the force approaches zero
If you shoot an object upward and there is no friction at 11,200 m/s. It will never fall back to
earth, it will just move
Slower and slower but never stop.
Inverse Square Law
Many things follow this law:Gravity, Light, Sound, Magnets, Radioactivity……
Fg =m1 m2
r2
G
In order to predict the force of gravity between any two objects a fudge factor
was needed
In order to find it they would have to know every other variable in the equation
Why isn’t this easy.
A 1 kg object on the surface of the earth has a force of gravity of 9.8 N between it and the earth. The radius
of the earth is 6,380,000 m.What’s missing?
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