Transcript I can do the following for this section

INTEGRATED SCIENCE
Gravity
I can do the following for this section
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I can explain Newton’s idea that the moon falls
toward the earth like an apple does.
I can explain why the moon does not fall into the
Earth and the planets do not fall into the sun.
I can explain the significance of an inverse-square
law.
I can explain how the moon causes the ocean tides.
The legend of the falling apple
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Legend says that Isaac Newton was sitting under
and apple tree when he made the connection that
changed the way we see the world.
Newton didn’t discover gravity, he discovered that
gravity is universal.
Newton realized the earth’s gravity affects other
objects
The fact of the falling moon
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If an apple (or anything else drops from rest) it falls
in a vertical straight line path.
Consider the following if a apple falls from the
back of an apple tree on a truck at rest, the apple
falls straight downward.
If the apple falls from a moving tree on the back of
a truck the apple falls in a curved path
The fact of the falling moon
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The faster the truck moves the wider the curved
path of the falling apple
If an object moves fast enough so that its curved
path matches the earth’s curvature, it becomes a
satellite.
The fact of the falling moon
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As the moon traces out its orbit around the earth, it
maintains tangential velocity (a velocity parallel to the
earths surface)
Newton realized the moon’s tangential velocity kept it
falling around the earth instead directly into it.
Newton further realized that the moon’s path around
the earth is similar to the paths of the planets around
the sun.
The falling moon.
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As The link below is a short video on how the moon
falls around the earth.
http://www.teachersdomain.org/asset/ess05_vid_moonorbit/
Concept Check
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If the tangential velocity of the moon were zero
how would the moon move (tangential velocity
makes the moon fall around the earth)?
True or False the moon is constantly falling.
Newton’s Grandest Discovery
Law of Universal Gravitation
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Newton realized that everything pulls on everything
else in a in simple way—only involving mass and
distance
The law of Universal Gravitation says that every
mass attracts every other mass with a force that is
directly proportional to the product of the two
interacting masses.
Law of Universal Gravitation
The force is
inversely
proportional
to the square
of the
distance
separating
them.
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Force ~ Mass1 X Mass2
Distance2
m1 and m2 are masses, d is the distance between
their centers.
Thus the greater the mass (m1 & m2) the greater the
force of attraction between them.
The greater the distance between them the weaker
the force of attraction.
Concept Check
1.
2.
3.
4.
According to the equation for gravity what happens to the
force between two bodies if the mass of one body is
doubled?
What happens if instead the mass of the other body is
doubled?
What happens if the masses of both bodies are doubled?
What happens if the mass of one body is doubled, and
the other is tripled?
Concept Check Answers
1.
2.
3.
4.
According to the equation for gravity what happens to the
force between two bodies if the mass of one body is
doubled? The force doubles.
What happens if instead the mass of the other body is
doubled? The force doubles also.
What happens if the masses of both bodies are doubled?
The force is four times as much.
What happens if the mass of one body is doubled, and
the other is tripled? The force is six times as much.
Gravity and Distance:
The Inverse-Square Law
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Gravity gets dimmer the same way a light gets dimmer
as you move farther from it.
The intensity of light gets less as the inverse square of
the distance.
This is the inverse-square law.
It holds for ALL phenomena where something from a
localized spreads out uniformly throughout the
surrounding space
Insert Figure 7.4
Insert Figure 7.5
Gravity and Distance:
The Inverse-Square Law
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The greater the distance from the earth’s center, the less the
gravitational force on the object.
Example: Suppose the distance from the center of the
earth is roughly 4,000 miles. If you climbed a 4,000 mile
ladder on the surface of the earth, you would weigh only
¼ as much as you did on the earth surface. (Because you
are twice the distance from the earth’s surface.) Space
Station 217 miles above Earth Why do they say you are
weightless on it?
Insert Figure 7.8
Concept Check
How much does the force of gravity change
between the Earth and a receding rocket when the
distance between them is (a) doubled? (b)
Tripled? (c) Ten times as much?
Answers on Click!
1.
a.
b.
c.
¼ (F=1/d2)
1/9
1/100
Concept Check
2. Consider an Apple at the top of a tree. The apple is
pulled by Earth’s gravity with a force of 1N (Newton).
If the tree were twice as tall, would the force of
gravity be only ¼ as strong? Defend you answer.
Answers on Click!
2. No, because the twice as tall apple tree is not twice as far from the earth’s center. The
taller tree would have to be nearly 4,000 miles tall for the gravity to be ¼ N. For a
decrease in weight by 1 percent, an object must be raised nearly 4 times the height of Mt.
Everest. So as a practical matter we disregard the effects of everyday changes in
elevation for gravity. The apple has practically the same weight at the top of the tree as
at the bottom.
Gravity and Distance:
The Inverse-Square Law
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Summary
No matter how far away from Earth, the Earth’s
gravitational force approaches, but never reaches
zero!
Earth’s gravity may be overwhelmed by nearer or
more massive objects in space but its attraction is
always there through all of space.
Concept Check
Light from the sun, like gravity, obeys the inversesquare law. If you were on a planet twice as far as
from the sun, how bright would the sun look?
2.
How bright would the sun look if you were on a planet
twice as close to the sun?
Answers on Click!
1.
1.
2.
¼ as bright
4 times brighter
The Universal Gravitation
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The universal law of gravitation can be written as an
exact equation when the universal constant of gravitation,
G is used.
Force =G Mass1 X Mass2
Distance2
The units of G makes the force come out in newtons.
G = 6.67 x 10-11 N.m2/kg2
This is an extremely small number thus showing that gravity
is a very weak force when compared to electrical forces.
The Universal Gravitation
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The large net gravitational force we feel as weight
is because of the enormity of atoms in planet Earth
pulling on us.
A 1-kilogram mass at earth’s surface has a
gravitational force exerted on it of 9.8 newtons.
Ocean Tides are a result of Differences
in Gravitational Pulls
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Imagine a ball of Jell-O. If you exerted the same amount
of force on every part of the ball the ball would remain
spherical.
But if you pull harder on one side of the ball than the other
the ball would stretch. This what happens to the Earth.
The pull affects the oceans more than the land.
The pull on average makes a bulge of about 1 meter on the
ocean.
Ocean Tides are a result of Differences
in Gravitational Pulls
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Newton was the first to show that tides are caused
by differences in the gravitational pull by the moon
on the Earth’s opposite side.
Since Gravitational force gets weaker with distance,
the gravitational force between the earth and moon
is stronger on the side of the earth nearer to the
moon than on the opposite side of the earth.
Ocean Tides are a result of Differences
in Gravitational Pulls
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The nearest side of earth to the moon has a bulge
of water as does the opposite side.
Because of the earth’s rotation, it causes 2 sets of
ocean tides per day (2 high tides and two low
tides).
Ocean Tides are a result of Differences
in Gravitational Pulls
Ocean Tides are a result of Differences
in Gravitational Pulls
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The sun also contributes to ocean tides, but its about
half as effective as the moon.
The sun does pull about 180 times harder on the
earth than the moon, so why does aren’t tides 180
times greater due to the sun?
Ocean Tides are a result of Differences
in Gravitational Pulls
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The moon appears in the same position in the sky
every 24 hours and 50 minutes.
This makes the two high tide cycles is actually on a
24 hour and 50 minute cycle.
This means the tides do not occur at the same time
each day.
Ocean Tides are a result of Differences
in Gravitational Pulls
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Neap Tides occur when the moon is halfway
between a new moon or a full moon. (sun and moon
are at a 90o angle to each other!)
The gravitational forces partially cancel each other
out.
The result it lower than normal high tides and higher
than normal low tides
Ocean Tides are a result of Differences
in Gravitational Pulls
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Spring Tides occur when the earth, moon, and sun
all line up. The sun and the moon’s gravitational
force causes higher than normal high tides and
lower than normal low tides.
Spring tides have nothing to do with spring
season!
Spring tides occur at new or full moons.
Ocean Tides are a result of Differences
in Gravitational Pulls
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Why are there no tides on lakes? (Answer on click)
Answer: No part of the lake is significantly closer to the
moon, so there is no significant difference in the pull on the
lake to create a bulge of water, (so there is no pile up of
water).
This also holds true for the human body. A 1-kilogram
watermelon held above your head causes more microtides
than the moon over your head! (The moon has no influence
on humans, there has been numerous studies on this)
Ocean Tides are a result of Differences
in Gravitational Pulls
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The part of the earth beneath the crust is molten-fluid.
This causes Earth tides (actual rises and falls in the
Earth’s crust)
Earth tides are much smaller than ocean tides.
There are also atmospheric tides (which regulates the
cosmic rays that reach the earth’s surface).
The following are factors that affect tides: the tilt of
the Earth’s axis, interfering landmasses, and fiction with
the ocean bottom.
Gravitation is Universal
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We all know the Earth is round, but why is it round?
The reason is because everything attracts everything
else, all parts of the earth have attracted themselves
together as much as they can!
Any corners of the earth have been pulled in, making
a sphere. (same applies for the moon & stars).
Rotational effects make the earth bulge slightly at the
equator.