Transcript r earth - mrbernabo

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
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
v
Fg
Gravity pulls the
moon towards the
center of the earth
providing the
CENTRIPETAL Force
___________
to keep it moving in
v
Fg
The tangential
velocity is sufficient
to keep it from
falling into the earth
The 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 jus
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.
2
9.8
m/s
amoon =
602
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
it Without
falls 1.4 mm
gravity
each
after 1second
second the
moon would be here
His answer matched what we know today
But he wasn’t sure if the distance used
should be between the centers of the objects
and didn’t publish for another 20 years
ItWhat
would
would
fall to
happen
the earth.
if the moon
The
suddenly
fall would
stopped
take about
3.5 hours
The earth is constantly falling toward the sun
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
m1
m2
d
Distance between center of masses
Fg ~
m1 m2
2
d
Proportional to – not equal to
This is the force of gravity on EACH Object
m1
m2
r
Remember Newton 3rd law:
When m1 exerts a force on m2 then…..
Fg ~
m1 m2
2
r
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,
doubles
Then Fg ________
m1
r
m1 m2
Fg ~
r2
m2
Compare the force of gravity between the
earth & 1kg object
to
earth & 2kg object
m1 m2
Fg ~
r2
If the mass of both object is doubled,
quadruples
Then Fg ________
m1
r
m1 m2
Fg ~
r2
m2
If the distance between them doubles,
is 1/4
Then Fg ________
m1
r
m1 m2
Fg ~
r2
m2
If everything attracts everything else,
Why isn’t it more obvious?
The mass of the earth is HUGE!!!!!
The
between
earth andbe
Howforce
big will
the attraction
abetween
1 kg object
only
10 N
two is
1 kg
objects?
m 1 m2
Fg ~ 2
r
In order to make this an equation we
need a fudge factor.
Fg =
G m1 m2
2
r
If we knew G we could calculate the force between any two objects
The
In order
forcetooffind
gravity
G, both
between
masses
normal
wouldobjects
need
tothat
be can
known.
be weighed
As wellisasVERY
the force
weak.
and
distance between them.
How to measure?
What is so hard about this?
Fg =
G m1 m2
2
r
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
-11
10
2
2
Nm /kg
G = .0000000000667
A very small number because gravity is a relatively weak force
Fg =
G m1 m2
2
r
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
9.8 N =
G 1kg mearth
(6,380,000
2
m)
Cavendish’s experiment is often
said to have weighed the earth in his
experiment
5.98 1024
mearth = 5.98
24
10
kg
Phillip von Jolly
Around 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 earth
and 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 =
2
pr
When a light shines it spreads out as a sphere
getting 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.
a sphere
=
So itArea
is 4 oftimes
dimmer
4 p r2
Picture a butter gun
It shoots out the same amount of butter each time
The further away, the more it
can cover with 1 shot
1 inch thick
1m
2m
3m
Many things follow this law:
Gravity, Light, Sound, Magnets, Radioactivity……
What is the distance from?
What happens to your weight as you
climb a mountain?
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
Your mass also attracts the earth
and everything else in the universe
When you wave your hand the rest of
the universe feels it
The shuttle orbits the earth at 200,000 m above
it surface. How strong is gravity there?
Let’s put things to scale
6,380 km
Shuttle
6,580 km
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…
600 N
500 N
400 N
Still
accelerating up
accelerating
down
If the cord is cut
FREE FALL
An astronaut is in Free Fall towards the Earth,
Why don’t they crash?
Book problems page 181
29, 32, 33
Why did all planets turn out pretty round?
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
An object
is located
equal
Find the
net force
on itdistances
using thefrom
two 1 kg masses.
Compare
the magnitude
parallelogram
method.
and direction of the forces it feels
1 kg
1 kg
An object
located
equal
from a 1
Findisthe
net force
ondistances
it using the
kg and
2 kg masses.method.
Compare the
parallelogram
magnitude and direction of the forces it feels
2 kg
1 kg
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)
Gravity
Magnets
Gravity
Magnets
Exert a force without
contact through a vacuum
That really bugs me.
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
arrows
field
is
represented
the direction
bywhere
imaginary
a to
mass
The
Where
field
is lines
thepoint
field
areinclosest
strongest,
close
the
field
the
would
accelerate
(to
lines
the or
center
the earth)
surface
of
isfield
the
the earth
strongest
farofaway?
AA
1How
kg
2 kg
object
toobject
measure
onatthe
the
the
surface
same
strength
location
feelsofathe
force
infield?
theoffield
10 N
feels a force of 20 N.
The field isn’t any stronger, only the force on
the object
What is the gravitational field strength at the
location of the red object
Field Strength =
m1
m2
FG
m
Since, F = m a
Field Strength =
mFa
m
The gravitation Field Strength at a location,
is just the acceleration of an object there.
Field Strength =
FG
m1
G m1 m2
FG =
r2
m1
m2
G m1
Field Strength = r2
Compared the acceleration due to gravity at the
surface of the earth, how would the acceleration
compare on a planet that….
had
was
hadthe
5the
twice
times
same
same
the
asmass
mass,
mass
massive,
but
but
and3same
and
1/2
times
as
1/10
radius
radius
bigthe size
Field Strength =
GM
r2
Sure,What
you wouldWould
accelerate
happen
youif fall?
you
toward
drilled
the acenter
hole
through
of mass
the earth
of theand
earth
jumped in?
What would happen to the Force of gravity
and your acceleration as you fell?
Do
Some
You
youof
are
still
the
earth
closerpulls
the
accelerate
at g
CM
you
the
orofup.
earth,
Which
but…
more
stronger
or the
up or
down?
less
Consider this, what happens when you are at
the center of the earth?
Do
Half
youpulls
stop
at you
the center
up,
&
of half
the earth
pulls
youthen?
down.
What is the
net force?
Going back what happened to the acceleration
half way down?
g
g/2
?
0
As
What
youhappens
fall
towards
as you
thepass
center
you
center
speed
of the
up,
Let’s
complete
our the
journey
but your acceleration
earth? decreases.
g
g/2
0
What
You will
willbegin
your to
speed
accelerate
be when
butyou
which
reach
way?
the
other side?
g
g/2
0
g/2
g
You will
If you
begin
weren’t
to accelerate
able to jump
but which
out???way?
g
g/2
0
g/2
g
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…
You get inside the object
Decreasing
Increasing
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?
As they run
Stars
out“burn”
of fuel,
hydrogen
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?
The
of tothe
hole
is just
the
Whatmass
happens
theblack
mass of
a slice
of bread
if you
squish
it? star that
same as the
mass
of the
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?
Consider a Sun and a Black hole
of the same mass
Decreasing
Increasing
But remember the strength
increases with the square of the
distance. So this isn’t quite an
accurate representation
Increasing
It would be a little more like this
Increasing
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 =
GM
r2
What would happen to the earth, if the
sun collapsed into a black hole?
Field Strength =
GM
r2
Nothing, except we would freeze!
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?
The Fg the earth feels from the moon is not
equal on all sides
Fg vs distance
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.
Which
has
a
greater
effect
on
the
earths
It is the DIFFERENCE in the force of
tides?
gravity on the opposite sides of the planet
Sun
or
Moon
which
cause
the
tides.
(note the force of gravity on the earth from the sun is
MUCH stronger than from the moon)
Not really to scale
Compare the force of gravity on opposite sides
of the planet
Fg
Fg
4
1m
2m
Different by a factor of 4!!
Compare the force of gravity on opposite sides
of the planet
Fg
Fg
2.25
2m
3m
Different by a factor of 2.25!!
What happens to the difference in gravity as
the planets separate?
THE
MOON
it is closer
to earth’s
the earth
Which
has abecause
bigger impact
on the
there is a greater difference
on the sides of
tides?
the earth!!!!!!!
Not really to scale
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
What causes
the earth
the other
actually
one??????
has two
bulges, one closest to the moon and one
furthest
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
BrainPop tides movie
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
If the earth traveled in a perfect
circle it would never speed up or
slow down because.
Sun
If the earth was given a extra speed it would
Now it would start to slow
Sun
Get further away from the sun
Slowest, PE- KE
v
Fg
Sun
Fastest, PE- KE
Which
How
components
does
other
ofofthe
component
forcesdo
dono
effect
work
the
ononthe
earth?
earth?
Where
does
thethe
force
gravity
work
the
earth
v
F
F
Sun
F
Elliptical orbit applet
applet #2
Planet travel in elliptical orbits
with the sun at one focus
Is
The
there
more
a speed
KE isatstarts
which
with
thethe
object
morewould
PE it never
ends
with (before
come back
it fallsdown?
back down)
Escape Velocity
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.
Escape velocity is 11,200 m/s for earth
Inverse Square Law
Many things follow this law:
Gravity, Light, Sound, Magnets, Radioactivity……
totopredict
of gravity
AInIn
1order
kg
object
theforce
surface
oftothe
order
findon
it the
they
would
have
between
any
two objects
ain
fudge
factor
know
every
variable
the of
equation
earth
has
a other
force
of gravity
9.8 N
was needed
between it and the earth. The radius
Why isn’t this easy.
of the earth is 6,380,000 m.
What’s missing?
Fg =
G m1 m2
2
r