Transcript The Law of Universal Gravitation

The Law of
Universal
Gravitation
and
Circular
Motion
Fundamental Forces of
Nature
–Gravity
–Electromagnetism
–Strong Nuclear Force
–Weak Nuclear Force
–Contact Forces
Gravity is an attractive
force between all masses
Gravity is a field force
–Two objects’
gravitational fields
interact. The objects
don’t actually touch.
The Law of Universal
Gravitation
- Gravitational force
depends on the mass of
both objects and the
distance between their
centers of mass.
The force of gravity between
objects depends on the
distance between their centers
of mass.
The Law of Universal
Gravitation
Fg = G _m1m2_
2
r
Fg = G _m1m2_
2
r
G = 6.673 x
-11
10
2
2
N*m /kg
–G is the gravitational
constant
Philipp von Jolly developed a method of
measuring the attraction between two
masses. This allowed him to calculate
the value for G 150 years after Newton.
The value of G, 6.673 x 10-11, tells us
that gravity is a very weak force.
It is the weakest of the presently known
four fundamental forces.
We sense gravitation only when masses
like that of Earth are involved.
Can you sense the gravitational force of
the person sitting next to you?
When G was first
measured in the
1700s, newspapers
everywhere
announced the
discovery as one
that measured the
mass of Earth.
Look at our equation. See if
you can you figure out how
they did it?
Gravity and Distance:
The Inverse-Square Law
13.5
Gravity decreases according to the
inverse-square law. The force of gravity
weakens as the square of distance.
• An apple that weighs 1 N at Earth’s surface weighs only
0.25 N when located twice as far from Earth’s center.
• When it is 3 times as far, it weighs only 1/9 as much.
• But no matter how great the distance, Earth’s gravity
does not drop to zero.
• The gravitational influence of every object, however
small or far, is exerted through all space.
Gravitational Field
Earth can be thought of as being surrounded
by a gravitational field that interacts with
objects and causes them to experience
gravitational forces.
We can regard the moon as in contact
with the gravitational field of Earth.
A gravitational field occupies the space
surrounding a massive body.
A gravitational field is an example of a
force field, for any mass in the field space
experiences a force.
Electric field around a charged object is
another example.
The strength of the
gravitational field is the
acceleration due to gravity
g = G _m2_
2
r
13.7 Gravitational Field Inside a Planet
As you fall into a
hole bored through
Earth, your
acceleration
diminishes. The pull
of the mass above
you partly cancels
the pull below.
13.7 Gravitational Field Inside a Planet
In a cavity at the
center of Earth,
your weight
would be zero,
because you
would be pulled
equally by
gravity in all
directions.
Circular Motion
Aspects of Circular
Motion
–Tangential speedspeed of an object
tangent to its circular
path
Aspects of Circular
Motion
–Uniform circular
motion– when the
tangential speed is
constant
Centripetal Acceleration
–During uniform circular
motion the velocity is
changing as the
direction changes
10.2 Circular Motion and Speed
Tangential speed depends on rotational speed and
the distance from the axis of rotation.
Which part of the turntable moves faster—the outer
part where the ladybug sits or a part near the orange
center?
Centripetal Acceleration
–The acceleration of an
object directed towards
the center of its circular
motion
ac = _vt
r
2_
Force and Circular Motion
–The net force on an object in
uniform circular motion acts
towards the circles center
–Can be called centripetal
force.
Fnet = mac
Fnet = _mvt2_
r
Force and Circular
Motion
–The net force
(centripetal) is exerted
by whatever is keeping
the object in its circular
path
The force exerted on a whirling
can is toward the center. No
outward force acts on the can.
• The “string” that holds the moon
on its almost circular path is
gravity.
• Electrical forces provide the
centripetal force acting between
an orbiting electron and the atomic
nucleus in an atom.
• Anything that moves in a circular
path is acted on by a centripetal
force.
‘Centrifugal Force’
–It is not a force
–It is an effect caused by
the inertia of an object
trying to stay in straight
line motion
10.4 Centripetal and ‘Centrifugal’ Forces
The only force that is exerted on the
whirling can (neglecting gravity) is
directed toward the center of circular
motion. This is a centripetal force.
No outward force acts on the can.
10.4 Centripetal and ‘Centrifugal’ Forces
The can provides the centripetal
force necessary to hold the ladybug
in a circular path.
Centripetal force holds a car in a curved path.
a. For the car to go around a curve, there must
be sufficient friction to provide the required
centripetal force.
b. If the force of friction is not great enough,
skidding occurs.
Newton’s Ideas about
Gravitation and planetary
orbit
If you drop a stone, it will fall in a
straight-line path to the ground
below. If you move your hand, the
stone will land farther away. What
would happen if the curvature of
the path matched the curvature of
Earth?
Throw a stone at any speed and
one second later it will have
fallen 5 m below where it would
have been without gravity.
If you toss the stone
horizontally with the proper
speed, its path will match the
surface curvature of the Earth
or any other planetary body.
In the curvature of Earth, the
surface drops a vertical distance
of nearly 5 meters for every 8000
meters tangent to its surface.
Neglecting air resistance, if you
throw a ball at 8000 m/s, it
could come back around and
hit you in the head!
If the moon did not fall, it would
follow a straight-line path.
The tangential velocity of Earth
about the sun allows it to fall around
the sun rather than directly into it.
You can move the object
faster and make the orbit
elliptical.
Gravitational force and
the tides
–The interaction between
gravitational fields
creates the tides.
–Circular motion also
affects the tides
–The Sun exerts more
gravitational force on the
Earth than the Moon, but the
Moon has a greater affect on
our tides.
–The huge distance to the Sun
causes the force of the sun on
both sides of the earth to be
about the same.
– The difference in the distance of the
Moon to each side of the Earth has a
much larger affect on the pull of
Moon’s gravity.
– The Moon pulls on the side of Earth
that is closer with much more force
than the side farther away