Transcript Gravity – A Familiar Force - Warren Hills Regional School District

Gravity –
A Familiar Force
Gravitational Force
• Gravitational force – an attractive force
that every object in the universe exerts on
every other object in the universe.,
Gravitational Force
Alternatively:
Gravity – mutual force of attraction
between particles of matter
• There is a gravitational attraction between
your hand and your pencil. The gravitation
attraction of the Earth is much greater, so
the pencil falls when you release it.
Newton Predicts Manmade Satellites of Earth
Newton’s Thought Experiment: If a cannon was able to launch
successive cannonballs with greater and greater initial speed, so
the horizontal distance of the ball’s travel increases, eventually
the initial speed will be great enough so that the curvature of the
Earth will cause the cannonball to continue falling without ever
landing.
Serway/Faugh –
Physics pg 230
A spacecraft in low Earth orbit must have an orbital
velocity of at least 17,450 mph. At this speed the
spacecraft will make one trip around the Earth in
about an hour and a half.
International
Space Station
Sir Isaac Newton noticed an apple fall to the
ground and reasoned that according to his
second law of motion, the acceleration of falling
bodies to the Earth is caused by a force (a force
of attraction).
Newton’s Universal Law of Gravitation
• Every body attracts every
other body in the universe
• with a force that is directly
proportional to the masses
of the two bodies
• and inversely proportional to
the square of the distance
between them.
Factors Related to
Gravitational Attraction:
• 1) Masses of bodies (The higher the mass,
the higher the amount of attraction.)
• 2) Distance between bodies (The greater
the distance, the less amount of
attraction.)
Gravitational Force Exists between any
two masses
• Gravitational force attracts all masses to each
other. It exists between any two masses
regardless of size.
• The force of attraction between desks in a
classroom is negligibly small relative to the
force between the Earth and each desk
because of the differences in mass.
Serway/Faugn Physics Text pg 231
• If the gravitational force acts between all masses,
why doesn’t the earth accelerate up toward a
falling apple?
• It does!
• But, the Earth’s acceleration is so tiny that you
cannot detect it. Earth’s mass is so large, and
acceleration is inversely proportional to mass, so the
Earth’s acceleration is negligible.
Serway/Faugn Physics Text pg 231
• A basketball has a greater acceleration toward
the Earth as well.
Gravitational Attraction between the
Earth and its moon
• The force that the moon exerts on the Earth is
equal and opposite to the force that the Earth
exerts on the moon. This relationship is an
example of Newton’s third law of motion.
Serway/Faugn Physics Text pg 231
• The gravitational force that acts on the moon is
the centripetal force that causes the moon to
move in its circular path around the Earth.
• The centripetal force on
the Earth, however, is
less obvious because the
Earth is much more
massive than the moon.
Serway/Faugn Physics Text pg 231
Gravitation and Ocean Tides
High and low tides are partly
due to gravitational force
exerted on the Earth by its
moon.
• The tides result from the difference between
the gravitational force at the earth’s surface
and at the Earth’s center.
• On the side of the Earth that
is nearest to the moon, the
moon’s gravitational force is
greater that it is at the Earth’s
center. This is because
gravitational force decreases
with distance.
Serway/Faugn Physics Text pg 234
• The water is pulled toward the moon, creating an
outward bulge.
• On the opposite side of the Earth, the gravitational
force is less than it is at the center. On this side, all
mass is still pulled toward the moon, but the water is
pulled least. This creates another outward bulge .
Serway/Faugn Physics Text pg 234
Gravity is a Field Force
• Masses create a gravitational field in space. A
gravitational force is an interaction between a
mass and the gravitational field created by
other masses. Serway/Faugn Physics Text pg 234
The gravitational field
vectors represent
Earth’s gravitational
field at each point.
Note that the field
has the same strength
at equal distances from
Earth’s center.
At any point, Earth’s
gravitational field can
be described by the
gravitational field
strength and is equal
to the gravitational
force exerted on a unit
of mass at that point
Equation for calculation of gravitational
force between two bodies:
How was the constant G obtained?
Lord Henry Cavendish determined the Universal
Gravitation Constant (constant of proportionality) in
1798. This was a nearly a century after Newton
developed his Universal Law of Gravitation.
• Cavendish using a device referred to as a torsion
balance. It involved a rigid rod about 2-feet long. Two
small lead spheres were attached to the ends of the rod
and the rod was suspended by a thin wire.
• When the rod becomes twisted, the torsion of the wire
begins to exert a torsional force that is proportional to
the angle of rotation of the rod. The more twist of the
wire, the more the system pushes backwards to restore
itself towards the original position. The Physics Classroom.com
• Cavendish had calibrated his instrument to determine
the relationship between the angle of rotation and the
amount of torsional force.
• He then brought two large lead spheres near the
smaller spheres attached to the rod. Since all masses
attract, the large spheres exerted a gravitational force
upon the smaller spheres and twisted the rod a
measurable amount. The Physics Classroom.com
• Once the torsional force balanced the
gravitational force, the rod and spheres came to
rest and Cavendish was able to determine the
gravitational force of attraction between the
masses. The Physics Classroom.com
• By measuring m1, m2, d and Fgrav, the value of G could
be determined. Cavendish's measurements resulted in
an experimentally determined value of 6.75 x 10-11 N
m2/kg2.
• Today, the currently accepted value is 6.67259 x 10-11
N m2/kg2. (The value of G is an extremely small numerical
value. Its smallness accounts for the fact that the force of
gravitational attraction is only appreciable for objects with
large mass.) The Physics Classroom.com
SAMPLE CALCULATION:
• A 0.300 kg billiard ball is placed 0.003 m from a
0.400 kg billiard ball. What is the magnitude of the
gravitational force between the them?
Billiard ball masses are relatively small compared
to large planetary masses, or star masses.
Einstein Sees Gravity Differently
It was part of his famous General Theory of Relativity, and
it offered a very different explanation from Newton’s Law
of Universal Gravitation. Einstein didn't believe gravity
was a force at all; he said it was a distortion , or curve, in
the shape of space-time, otherwise known as "the fourth
dimension" How Stuff Works .com
• NEWTON: Particles that start to move along parallel
trajectories will never meet, but are fated to remain
forever at a constant distance from one another. If
particles diverge from this behavior, it must be because
there is a forces acting to accelerate the particles, causing
them to leave the straightest possible paths and follow
curved trajectories instead. Einstein on line
• EINSTEIN: The two particles could still be moving on the
straightest possible lines - not in the plane, but on a curved
surface! There is no force making the particles deviate from the
straightest possible lines; the mere fact that the particles are
moving on a sphere means that, even if they still move as
straight as possible, their paths will converge.
What is a Black Hole?
A black hole is a region of spacetime from
which gravity prevents anything, including
light, from escaping. The theory of general
relativity predicts that a sufficiently compact
mass will usually deform spacetime to form
a black hole.
How Big Are Black Holes?
Scientists think the smallest black holes are as small as just one atom. These
black holes are very tiny but have the mass of a large mountain. Mass is the
amount of matter, or "stuff," in an object.
Another kind of black hole is called "stellar." Its mass can be up to 20 times
more than the mass of the sun. There may be many, many stellar mass
black holes in Earth's galaxy. Earth's galaxy is called the Milky Way.
The largest black holes are called "supermassive." These black holes have
masses that are more than 1 million suns together. Scientists have found
proof that every large galaxy contains a supermassive black hole at its center.
The supermassive black hole at the center of the Milky Way galaxy is called
Sagittarius A. It has a mass equal to about 4 million suns and would fit
inside a very large ball that could hold a few million Earths.
An artist's drawing a black hole named
Cygnus X-1. It formed when a large star
caved in. This black hole pulls matter
from blue star beside it.