Download Chp 12-2 Gravity Interactive Guide

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CHAPTER 12
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SECTION
2 Gravity
KEY IDEAS
As you read this section keep these questions in mind:
• What is free fall?
• How are weight and mass related?
• How does gravity affect the motion of objects?
What Is Gravity?
Have you ever seen movie footage of the Apollo astronauts walking on the moon? If so, you may have seen
them bouncing up and down in their large spacesuits.
Why could the astronauts jump so high on the moon? The
answer is that gravity is weaker on the moon than it is on
Earth.
Gravity is a force that pulls objects together. Sir Isaac
Newton described the law of universal gravitation,
which has three main parts:
READING TOOLBOX
Summarize As you read this
section, underline the main
ideas in each paragraph.
When you finish reading,
make an outline of the
section using the ideas you
underlined.
1. Every object in the universe pulls with a gravitational
force on every other object.
2. The strength of the gravitational force between
two objects depends on the masses of the objects.
3. The strength of the gravitational force between
two objects depends on the distance between the
objects.
Newton developed an equation that shows these relationships between gravitational force, mass, and distance.
Universal Gravitation Equation
1. Identify On what two factors does the strength of the
gravitational force between
two objects depend?
The masses of
the two objects
The gravitational
force between
two objects
F=G
READING CHECK
m1m2
d2
A constant called the
universal gravitational
constant
The distance
between the
two objects
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Gravity continued
How Does Mass Affect Gravitational Force?
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2. Summarize How do the
masses of objects affect the
gravitational force between
them?
Look back at the equation describing the law of universal gravitation. Notice that the two masses, m1 and m2,
are multiplied together on the right side of the equation.
Therefore, the gravitational force between two objects
increases as the masses of the objects increase.
m
m
Gravitational force is weak between objects
that have small masses.
m
2m
Gravitational force is stronger when one or
both of the objects have more mass.
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3. Infer The gravitational
force between the sun and
Earth is larger than the force
between the sun and the
moon. What do you think is
the reason for this?
Imagine an elephant and a cat standing on Earth.
Earth’s gravity pulls on the elephant and the cat. The
elephant has a larger mass than the cat does. Therefore,
the gravitational force between Earth and the elephant is
greater than between Earth and the cat. This is one reason it is easier to pick up a cat than an elephant.
There is also a gravitational force between the elephant and the cat. However, Earth has a much larger
mass than either the elephant or the cat. Therefore, the
gravitational force between the elephant and the cat is
very small compared to Earth’s gravitational force on
them.
How Does Distance Affect Gravitational
Force?
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4. Explain Why is the
gravitational force between
the bottom two balls smaller
than that between the top
two balls?
Look again at the equation for the law of universal
gravitation. Notice that distance is in the denominator on
the right side of the equation. Therefore, as the distance
between two objects increases, the gravitational force
between them decreases.
m
m
Gravitational force is strong
between objects that are close
together.
d
m
Gravitational force decreases as the distance
between two objects increases.
m
2d
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Gravity continued
THE STRENGTH OF EARTH’S GRAVITATIONAL FORCE
Earth’s gravitational force pulls every object toward
Earth’s center. All other objects in the universe also pull
on the objects on Earth. However, other objects are very
far away, have very small masses, or both. Therefore,
Earth’s gravitational force affects objects on Earth most
significantly. Gravitational forces from other objects are
usually small enough to ignore.
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5. Explain Why don’t you
feel a gravitational force
between you and your desk?
What Is Free Fall?
Imagine dropping a ball. It will fall toward the ground
because Earth’s gravitational force acts on it. Remember
Newton’s second law of motion: an unbalanced force
that acts on an object causes the object to accelerate.
Therefore, Earth’s gravity causes the ball to accelerate
toward the ground.
When Earth’s gravity is the only force acting on an
object, the object is in free fall. During free fall, objects
accelerate toward Earth’s center. The acceleration caused
by Earth’s gravity is called free-fall acceleration.
All objects have the same free-fall acceleration. Recall
that acceleration depends on both force and mass. A
heavy object experiences a greater gravitational force
than a lighter object. However, it is harder to accelerate a
heavy object than a lighter one because the heavy object
has more mass.
READING CHECK
6. Define What is free fall?
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7. Identify Why do the two
balls have the same free-fall
acceleration, even though
they have different masses?
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The gravitational force on the larger ball is twice as great as the force on the
smaller ball. However, the larger ball has a larger mass, so it is harder to
accelerate. Therefore, both balls have the same free-fall acceleration.
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Gravity continued
AIR RESISTANCE AND TERMINAL VELOCITY
READING CHECK
8. Define What is air
resistance?
You may have seen objects falling through the air at
different rates. For example, a piece of paper falls more
slowly than a ball. This may seem to contradict the statement that all objects have the same free-fall acceleration.
However, free fall happens when gravity is the only force
that acts on an object.
On Earth, objects fall through the atmosphere. The
gases in the atmosphere produce friction on the object.
This friction is called air resistance. It acts in a direction
opposite that of the gravitational force.
As an object falls through the air, air resistance
increases. If the object falls far enough, the air resistance
on the object will equal the gravitational force on the
object. Then, there will be no unbalanced forces acting
on the object.
Recall Newton’s first law of motion: if no unbalanced
forces act on an object, the object’s motion will not
change. Therefore, when the force of air resistance balances the gravitational force, the object will no longer
accelerate. Instead, it falls at a constant velocity called its
terminal velocity.
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'PSDFPGBJS
SFTJTUBODF
9. Infer What would happen
to the skydiver’s velocity if
she opened her parachute?
Explain your answer.
(Hint: Air resistance increases
as the area of an object
increases.)
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SFTJTUBODF
(SBWJUBUJPOBM
GPSDF
When the skydiver first jumps out of
the plane, gravitational force is much
larger than the force of air resistance.
Therefore, she accelerates downward.
(SBWJUBUJPOBM
GPSDF
When the force of air resistance
equals the gravitational force, the
skydiver stops accelerating. She
falls at a constant velocity.
The gravitational force and the force of air resistance
are different on different objects. Therefore, different
objects can have different terminal velocities.
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Gravity continued
What Is Weight?
Think back to the astronauts on the moon. The moon’s
mass is much smaller than Earth’s mass. Therefore,
objects near the moon experience a smaller gravitational
force than objects near Earth. The astronauts could jump
very high on the moon because the gravitational force on
them was small. Another way to say this is the astronauts
weighed less on the moon.
Weight is the gravitational force on an object.
Remember that Earth’s gravity is the main gravitational
force we feel at Earth’s surface. Therefore, on Earth, the
weight of an object is the same as Earth’s gravitational
force on the object.
The moon is very far from Earth. When astronauts
walk on the moon, Earth’s gravitational force on them
is very weak. The moon’s gravitational force is the main
force acting on the astronauts. On the moon, the weights
of the astronauts were smaller than on Earth.
To jump into the air, you must push yourself up with a
force greater than your weight. If your weight is smaller,
you need less force to jump into the air. On the moon, the
astronauts only weighed one-sixth of what they weighed
on Earth. Therefore, they needed less force to jump into
the air.
You may have heard that astronauts are “weightless”
in space. However, this is not true. Because gravity exists
everywhere in space, an object has weight everywhere
in space. Astronauts in the space shuttle seem to be
weightless because they are in free fall. The astronauts
and the space shuttle are falling toward Earth with the
same acceleration. This is why the astronauts appear to
float.
READING CHECK
10. Define What is weight?
READING CHECK
11 Explain Why can an
object never be truly
“weightless”?
Astronauts in orbit on the space shuttle
seem to float in midair. This is because
the astronauts and the space shuttle are
both in free fall.
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Gravity continued
THE DIFFERENCE BETWEEN MASS AND WEIGHT
READING CHECK
12. Compare How is weight
different from mass?
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13. Apply Concepts A small
can of soup has a mass of
about 400 g. What would its
mass be on the moon?
Many people confuse mass and weight. Remember that
mass is the amount of matter in an object. Mass is measured in kilograms (kg). In contrast, weight is a force.
Like all forces, weight is measured in newtons (N).
The weight of an object will change if the gravitational
force on it changes. For example, an astronaut with
a mass of 66 kg weighs about 650 N (about 150 lb) on
Earth. On the moon, the astronaut has the same mass,
66 kg, because he contains the same amount of matter.
However, his weight is smaller: only about 110 N (about
25 lb). The table below shows how the weights of some
objects would be different on the moon.
Object
Mass
Weight on
Earth
Weight on
the moon
Apple
100 g
1 N (0.225 lb)
0.16 N (0.04 lb)
Elephant
5,000 kg
49,000 N
(11,025 lb)
8,000 N
(1,800 lb)
Train locomotive
25,000 kg
245,000 N
(55,125 lb)
40,000 N
(9,000 lb)
CALCULATING WEIGHT
Math Skills
14. Calculate An object has
a mass of 2,000 kg. What is
its weight on Earth? Show
your work.
You can use the equation for Newton’s second law of
motion to calculate the weight of an object. Recall the
equation for Newton’s second law of motion:
F = ma
Remember that free-fall acceleration is the acceleration of an object because of gravity. Also, remember
that weight is the force on an object because of gravity.
Therefore, you can rewrite the equation like this:
weight = mass free-fall acceleration
w = mg
On Earth, the free-fall acceleration, or g, is about
9.8 m/s2. Therefore, the weight of an object is equal to its
mass in kilograms multiplied by 9.8 m/s2. On the moon,
free-fall acceleration is about 1.6 m/s2.
How Does Gravity Affect Moving Objects?
Imagine throwing a baseball in a straight, horizontal
line. What happens to the baseball? It does not travel in
a straight line for very long. Instead, it follows a curved
path through the air until it hits the ground. This is
because gravity pulls the baseball toward the ground.
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Gravity continued
PROJECTILE MOTION
A thrown baseball shows projectile motion. Projectile
motion is the curved path followed by any object that is
thrown or launched near Earth’s surface. Gravity causes
these objects to move along curved paths.
All objects in projectile motion are moving in two
directions: horizontally and vertically. These two motions
combine to give the object its curved path. However, the
horizontal and vertical motions do not affect each other.
You can see this in the figure below.
READING CHECK
15. Identify What causes a
thrown baseball to follow a
curved path?
This ball has no
horizontal motion. It
does not fall along a
curved path.
This ball was pushed off the ledge.
It is moving both horizontally and
vertically. The motions combine to
form a curved path.
The downward acceleration on both balls is the same. The horizontal motion of the
light-colored ball does not affect its vertical motion.
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16. Compare If the dark colored ball reached the ground
after 5 seconds, how long did
it take the light colored ball
to reach the ground?
ORBITS
You have probably heard people talk about the space
shuttle or the moon orbiting Earth. An orbit is a circular
or oval-shaped path that one object follows as it moves
around another object in space. For example, the moon
orbits Earth, and Earth orbits the sun. Gravity controls
the orbits of all of the objects in the universe.
A space shuttle orbiting Earth may seem very different from a baseball falling to the ground after you throw
it. However, both are examples of projectile motion. The
space shuttle in the figure below is moving forward, or
horizontally. Earth’s gravity is pulling the shuttle down, or
vertically, toward Earth. These two motions combine to
produce the curved orbit of the shuttle.
1 The shuttle moves
forward at a constant
speed. If Earth’s gravity did not pull on it,
the shuttle would move
away from the planet.
3 The horizontal and vertical
2 Earth’s gravity pulls the shuttle downward. If
it were not moving horizontally, the shuttle
would fall straight down to Earth’s surface.
forces on the shuttle combine to produce a curved
path. This path is called
an orbit.
EHHDBG@<EHL>K
17. Identify How would the
shuttle’s motion change if
there were no gravitational
force between it and Earth?
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Section 2 Review
SECTION VOCABULARY
free fall the motion of a body when only the
force of gravity is acting on the body
projectile motion the curved path that an object
follows when thrown, launched, or otherwise
projected near the surface of Earth; the motion
of objects that are moving in two dimensions
under the influence of gravity
terminal velocity the constant velocity of a falling object when the force of air resistance is
equal in magnitude and opposite in direction
to the force of gravity
weight a measure of the gravitational force
exerted on an object; its value can change with
the location of the object in the universe
1. Apply Concepts If Earth had no atmosphere, would a falling object ever reach
terminal velocity? Explain your answer.
2. Calculate Fill in the blank spaces in the table below. Free-fall acceleration on
Earth is 9.8 m/s2. On the moon, free-fall acceleration is 1.6 m/s2.
Object
Mass (kg)
Bowling ball
5
Weight on Earth (N) Weight on the
moon (N)
8
Textbook
Large dog
19.6
50
3. Identify In the space below, write the equation for the law of universal
gravitation. Explain what each variable in the equation represents.
4. Explain Why do astronauts in orbit in the space shuttle seem to float?
5. Identify What two kinds of motion combine to produce projectile motion?
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