Transcript 7-Universal Gravitation

Universal
Gravitation
Gravity is the way in which
masses communicate with each
other
• Newton had the insight to see that the
force on the moon has the same nature as
the force on a falling apple – they are both
pulled by earth’s gravity.
 The apple is pulled more by Earth’s gravity
because it is so close to Earth’s surface.
The Falling Moon
• Newton hypothesized that the moon
was simply a projectile circling the
earth under the attraction of gravity.
• Newton generalized his moon finding
to all objects, and stated that all
objects in the universe attract each
other.
The Falling Earth
• The planets continually fall around the sun in
closed paths, known as orbits. The planets do
not crash into the sun because they have
tangential (sideways) velocity.
Tangential velocity: the “sideways”
velocity-the component of velocity
perpendicular to the pull of gravity
 If the tangential velocity of the planets was
reduced to zero, they would move straight
towards the sun and crash into it.
 SI Unit: m/s
 Ex: The proper amount of tangential velocity
allows Earth to orbit the sun w/o flying into it
or flying off into the vacuum of space
Check Your Understanding
Since the moon is gravitationally
attracted to Earth, why does it not
simple crash into Earth?
Because the moon has enough tangential
velocity.
Family Guy Gravity Clip
http://www.mediazine.net/view/family_guy_p
eter_gravity
Newton’s Law of Universal
Gravitation
Newton’s Law of Universal Gravitation:
every object attracts every other object
with a force that for any two objects is
directly proportional to the mass of
each other.
 The greater the masses, the greater the
attraction between them; the greater the
distance between the objects, the weaker the
force of gravity.
 The force of gravity is the weakest of the
presently four known fundamental forces.
 SI Unit: Newton (N)
 Equation:
FG = G m1 m2 / d2
• FG = Force of gravity (N)
• G = universal gravitation constant (6.67 x 10-11
Nm2/kg2)
• m1 = mass of object 1 (kg)
• m2 = mass of object 2 (kg)
• d = distance (m)
Check Your Understanding
How is the gravitational force between a
pair of planets altered when the mass
of one of the planets is doubled?
Double mass = Double FG
When both masses are doubled?
Double both masses = Quadruple FG
(2)(2) = 4
Check Your Understanding
When the masses are not changed, but they
are twice as far apart?
 Increase d by 2 = Decrease in FG by ¼
1/ 22
When they are three times further apart?
 Increase d by 3 = Decrease FG by 1/9
1/32
When they are five times further apart?
 Increase d by 5 = Decrease FG by 1/25
1/52
• Because gravitational forces are the
weakest forces found in nature, the force
of attraction between you and a classmate
is unnoticeable.
• In addition to your mass, your weight also
depends on the distance from the center
of earth.
 At the top of a mountain, your mass is the
same as it is anywhere else, but your weight
is slightly less because you are further from
earth’s center.
Check Your Understanding
If there is an attractive force between all
objects, why do we not feel ourselves
gravitating toward massive buildings in
our vicinity?
Because the masses are small compared
to the mass of the earth
• The further away an object is from Earth’s
center, the less the force of gravity acting on
the object
• The force of gravity will NEVER go to ZERO!!!!
 You can never be completely weightless in space
• There is always some mass in the universe creating a
gravitational force
Check Your Understanding
What’s Wrong with These Statements??
The moon and planets are beyond the
pull of Earth’s gravity.
 All objects in the universe attract each
other.
Gravity gets stronger with altitude, as
evidenced by objects carried up a
flight of stairs feeling heavier.
 Gravity decreases with altitude because
the distance from the center of the Earth
is increased
Gravitational Fields
• A force field exerts a force on an object in its
vicinity.
– Ex: gravity, electricity, magnetism
• Field lines represent a force field.
Gravitational field: the kind of force
field that surrounds massive
objects.
 Where the lines are close together, the field
is stronger; further away, where the field
lines are farther apart, the field is weaker.
 Ex: the force of gravity exerted by Earth
• The gravitational field of earth exists inside
the earth as well as outside.
• If you were to fall from the North Pole to
the South Pole through the center of earth,
you’d lose speed moving toward the
center, and gain speed moving away from
the center.
• In a cavity at the center of Earth your weight
would be zero, because you would be pulled
equally by gravity in all directions.
• At the center of the earth, the gravitational field
strength is zero.
Check Your Understanding
Halfway to the center of Earth, would
gravity pull on you more strongly or
less strongly than at the surface of
Earth?
Less strongly
So would you weigh more or less?
Less b/c the overall net force of gravity
is less
Check Your Understanding
If you dropped a rock into a tunnel
through Earth what would happen to its
speed as it approached the center?
Speed would decrease
In the above question, what would
happen to its speed as it moved away
from the center?
Speed would increase
Weight and Weightlessness
• Objects under the influence of gravity are
pulled toward each other and accelerate.
The pressing against earth is the
sensation we interpret as weight.
• What keeps us from accelerating into the
earth is the Earth’s surface
 The force of the earth pushing back up on you
is a support force called the normal force
 A scale actually tells you your normal force,
not your weight
• If you were to weigh yourself in an elevator
accelerating up, compared to your
ordinary weight, the scale would say you
weigh more.
• If you were to weigh yourself in an elevator
accelerating down, compared to your
ordinary weight, the scale would say you
weigh less.
• If you were to weigh yourself in an elevator in free
fall, compared to your ordinary weight, you weigh
zero.
• Weightlessness is NOT the absence of gravity; it
is the absence of the normal force.
Check Your Understanding
If you are in an elevator that is accelerating
upward, will the scale say you are heavier
or lighter than normal?
 It would say you weigh more than usual b/c
your normal force is greater. The ground is
pushing up on you more, thus making the
scale have a larger reading.
Check Your Understanding
If you are in an elevator that is moving at a
constant speed upward, will the scale say
you are heavier or lighter than normal?
 Neither! Your weight would be the same as if
the elevator were standing still because there
is no acceleration, and therefore no change
in force (and no change in your weight
reading). Only when an elevator is
accelerating do you notice a difference.