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INTEGRATED SCIENCE Gravity
INTEGRATED SCIENCEGravity
I can do the following for this section 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 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 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 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 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. 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 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 DiscoveryLaw of Universal Gravitation
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.
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 Check1. According to the equation for gravity what happens
to the force between two bodies if the mass of one body is doubled?
2. What happens if instead the mass of the other body is doubled?
3. What happens if the masses of both bodies are doubled?
4. What happens if the mass of one body is doubled, and the other is tripled?
Concept Check Answers1. 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.
2. What happens if instead the mass of the other body is doubled? The force doubles also.
3. What happens if the masses of both bodies are doubled? The force is four times as much.
4. 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
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
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 Check1. 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!
a. ¼ (F=1/d2)b. 1/9c. 1/100
Concept Check2. 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
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 Check1. Light from the sun, like gravity, obeys the inverse-
square 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. ¼ as bright2. 4 times brighter
The Universal Gravitation 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 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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
Ocean Tides are a result of Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 Differencesin Gravitational Pulls
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 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.
