Gravity
Gravity
KEY TERMS
free fall terminal velocity projectile motion
OBTECTIVES
Explain that gravitational force becomes stronger as the
• Evalunie the concept that free-fall acceleration near
Earth's urface is independent of the mass of the falling object.
* Demonstrate mathematically how free-fall acceleration relates to weight.
• Describe orbital motion as a combination of two motions.
bounced al Wer the placel Wuyded the astrous who no wearines all oy spacuits bounce so easly on the moon, y
shown in Figure 1?
Law of Universal Gravitation
For thousands of years, two of the most part lina scientific que. tions housandy do objects fall toward Eatsh? and "What kon the planets in motion. in the sky?" A British scientist, Sir lace Newton (1642-1727), realized that they were two parts of the same question. Newton generalized his observations on granity in a law now known as the law of universal gravitation. The law states that all objects in the universe attract each other through gravitational force.
Universal Gravitation Equation
F = Gm, m2
This equation says that the gravitational force increases as one or both masses increase. It also says that the gravitational force decreases as the distance between the masses increases. In fact, because distance is squared in the equation, even a small increase in distance can cause a large decrease in force. The symbol G in the equation represents a constant.
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Imagine an elephant and a cat. Because an elephant has a Laget mass than a cat, does, the gravitational fonce beteen an Aphant and Earth is greater than the gravitational force tenen a cat and Earth. That is why a cat is much easier to pick up than an elephant! There is also gravitational force between the at and the elephant, but it is very small because the cat's mass znd the elephant's mass are so much smaller than Earth's mass.
The gravitational force between most objects around you is rela-mely very small.
Figure 6
The arrows indicate the gravitational force between abjects. The length of the arrows indicates the stength of the force.
INTEGRATING
BIOLOGY
Gravity plays a role in your body. Blood pressure, for exam-ple, is affected by gravity. Therefore, your blood pressure will be greater in the lower part of your body than in the upper part. Doctors and nurses take your blood pressure on your arm at the level of your heart to see what the blood pressure is likely to be at your heart.
ic force
A Gravitational force is small between objects that have small masses.
Gravitational force is larger when one or both objects have larger masses.
Figure 7
A Gravitational force rapidly becomes stronger as the distance between two objects decreases.
Gravitational force rapidly becomes weaker as the distance between two objects increases.
1.0m
2.0m
free fall the motion of a body when only the force of gravity is acting on the body
Gravitational force decreases as distance increases
Gravitational force also depends on the distance between to object, as shown in Figure 7. The force of gravity changes as the dietee between the balls changes. If the distance between the decreases to one fourth its original value. If the original distance two bal double, tongal ine Fre between them
is tripled, the gravitational force decreases to one-ninth its origi. nal value. Gravitational force is weaker than other types of forces, even though it holds the planets, stars, and galaxies together:
Free Fall and Weight
When gravity is the only force acting on an object, the object is said to be in free fall. The free-fall acceleration of an object is directed toward the center of Earth. Because free-fall acceleration results from gravity, it is often abbreviated as the letter g.
Near Earth's surface, g is approximately 9.8 m/s
Free-fall acceleration near Earth's surface is constant
In the absence of air resistance, all objects near Earth's surface accelerate at the same rate, regardless of their mass. As shown in Figure 8, the feather and the apple, dropped from the same height, would hit the ground at the same moment. In this book, we disregard air resistance for all calculations. We assume that all objects on Earth accelerate at exactly 9.8 m/s
Why do all objects have the same free-fall acceleration?
Newton's second law shows that acceleration depends on both force and mass. A heavier object experiences a greater gravitational force than a lighter object does. But a heavier object is also harder to accelerate because it has more mass. The extra mass of tional force.
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weight = mass X free-fall acceleration
W = mg
Note that because weight is a force, the SI unit of weight is ta aton, ar weighter shall apple weihat of cist is
10 kg bok have seen piot 1.0 kg x 9.8 m/3* = 9 ab
You may have seen pictures of astronauts floating in the air, so hown orbit, as . Does this mean that they dong in che acc gravity? In orbite free falls, the space shuttle, and all operienc board experience free all because of Barth's gravity. In bects the stronauts and their surroundings all accelerate at the same the Therefore,
the floor of the shuttle does not push up against the astronauts and the astronauts appear to be floating. This situation is referred to as apparent weightlessness.
Weight is different from mass
Mass and weight are easy to confuse. Although mass and weight are directly proportional to one another, they are not the same.
Mass is a measure of the amount of matter in an object. Weight is the gravitational force an object experiences because of its mass.
The weight of an object depends on gravity, so a change in an object's location will change the object's weight. For example, on
Earth, a 66 kg astronaut weighs 66 kg x 9.8 m/s = 650 N (about
150 lb), but on the moon's surface, where g is only 1.6 m/s', the astronaut would weigh 66 kg x 1.6 m/s, which equals 110 N (about 24 lb). The astronaut's mass remains the same every-where, but the weight changes as the gravitational force acting on the astronaut changes in each place.
Weight influences shape
Gravitational force influences the shapes of living things. On land, large animals must have strong skeletons to support their mass against the force of gravity. The trunks of trees serve the same function. For organisms that live in water, however, the downward force of gravity is balanced by the upward force of the water For many of these creatures, strong skeletons are unnec-sary. Because a jellyfish has no skeleton, it can drift gracefully through the water but collapses if it washes up on the beach.
ic force
Figure 9
In the low-gravity environment of the orbiting space shuttle, astronauts experience apparent weightlessness.
INTEGRATING
SPACE SCIENCE
Planets in our solar system have different masses and different diameters. Therefore,
each has its own unique value for g. Find the weight of a 58 kg person on the following planets:
Earth, where g = 9.8 m/s
Venus, where g = 8.9 m/s.
Mars, where g = 3.7 m/s
Neptune, where g =
11.0 m/s
Forces balanced: no acceleration
Force of air resistance
Force of gravity
Figure 10
When a skydiver reaches terminal velocity, the force of gravity is balanced by air resistance.
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
56 CHAPTER 11
Velocity is constant when air resistance
balances weight
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When these two forces are equal, the orien velocity, elerating and reaches its maximum velocity, which is called
the terminal velocity.
When skydivers shat a jump, their para. chutes are closed, and they are accelerated toward Barth by the fo fee of gravity. As their velocity increases, the force they experience because of air resistance increases. When air resistance and the force of gravity are equal, skydivers reach a terminal velocity of about 320 km/h (200 mih). But when they open the parachute, air resistance increases greatly. For a while, this increased air resistance slows them down. Eventually, they reach a new terminal velocity of several kilometers per hour, which allows them to land safely.
Free Fall and Motion
Skydivers are often described as being in free fall before they open their parachutes. However, that is an incorrect description, because air resistance is always acting on the skydiver. An object is in free fall only if gravity is pulling it down and no other forces are acting on it. Because air resistance is a force, free fall can occur only where there is no air—in a vacuum (a place in which is not in free fall.
there is no matter) or in space. Thus, a skydiver falling to Earl Because there is no air resistance in space, objects in space are in free fall. Consider a group of astronauts riding in a space-crat. When they are in space, gravity is the only force acting 0. the stocat and the astronaus, As a result, the spaceat and. the stronaus are in fre al. They aresul the same ace di adraion, no matter how great al falla their indied!
orbiting objects are in free fall
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As you learned earlier in this section, welsht a measure of Savitational fore themends on the mass of do me ana hec
it ances betwee planets f you traveled in space baccard tom i the stars osa planets, he gravitational force ara frou nould be almost undeletable because the distance bing on you and other objects would be great. But you would sibehueens. and so would all the other objects in the universe, Themare, gravity would stil attract you to other objects Therefore, slightly-so you would still have weight.
Astronauts "float" in orbiting spaceships, not because they are weightless but because they are in free fall. The moon stays in orbit around Earth, as in Figure 11, and the planets stay in orbit around the sun, all because of free fall. To better understand why these objects continue to orbit and do not fall to Earth, you need to learn more about what orbiting means.
Two motions combine to cause orbiting
An object is said to be orbiting when it is traveling in a circular or nearly circular path around another object. When a spaceship orbits Earth, it is moving forward but it is also in free fall toward Earth. Figure 12 shows how these two motions combine to cause orbiting.
Path of
the moon
Force of
Earth's gravity on the moon
c force
Figure 11
The moon stays in orbit around Earth because Earth's gravitational force provides a pull on the moon.
Figure 12
How an Orbit Is Formed
B
* The shuttle moves forward at a constant speed. This would be its Path if there were no gravitational pull from Earth.
B The shuttle is in free fall because gravity pulls it toward Earth. This would be its path if it were not traveling forward.
© When the forward motion combines with free fall, the shuttle follows the curve of Earth's sur-face. This is known as orbiting.
After the ball leaves the pitcher's hand, its horizontal velocity is constant.
B The ball's vertical velocity increases because gravity causes it to accelerate downward.
C The two
motions combine to form a curved
path.
Figure 13
Two motions combine to form projectile motion.
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
0
Cla
358
CHAPTER 11
Projectile Motion and Gravity
The orbit of the space shuttle around Barth is an example of
Projectile motion is the curved path an
projectile motion.
object follows when thrown, launched, or otherwise projected near the surface of Earth. The motions of leaping frogs, thrown balls, and arrows shot from a bow are all examples of projectile motion. Projectile motion has two components-horizontal and vertical. The two components are independent; that is, they have no effect on each other. In other words, the downward acceleration due to gravity does not change a projectile's horizontal motion, and the horizontal motion does not affect the downward motion. When the two motions are combined, they form a curved path, as shown in Figure 13.
Projectile motion has some horizontal motion
When you throw a ball, your hand and arm exert a force on the ball that makes the ball move forward. This force gives the ball its horizontal motion. Horizontal motion is motion that is perpendicular (90°) to Earth's gravitational field.
After you have thrown the ball, there are no horizontal force acting against the ball (if you ignore air resistance). Therefote, there are no forces to change the ball's horizontal motion. So, the horizontal velocity of the ball is constant after the ball leaco your hand, as shown in Figure 13.
lenoring air resistance allows you to simplify projectie. wotion so that you can understand the horizontal and then the them to components of projectile motion. Then, you can pus them together to understand projectile motion as a whole:
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In the absence of air resistance, gravity on Earth pull down are in prair acceleration of 9, m Faon blets that are in projectile motion, just as it does on all fling obiens. Fi are 14 shows that the d don-falling object are identical.
ward accelerations of a thrown object and ora Because objects in projectile motion accelerate downward, you should always aim above a target it you want to hit it with a thrown or propelled object.
This is why archers point their arrows above the bulls eye on a target. If they aimed an arrow directly at a bull's eye, the arrow would strike below the center of the target rather than the middle.
Figure 14
zontal push.
A The red ball was dropped without a hori-
B The yellow ball was given a horizontal push off the ledge at the same time it was dropped.
It follows a projectile-motion path.
The two balls have the same acceleration downward because of gravity. The horizontal motion of the yellow ball does not affect its vertical motion.
SECTION 2 REVIEW
SUMMARY
• Gravitational force between two masses strengthens as the masses become more massive and rapidly weakens as the distance between them increases.
> Gravitational acceleration results from gravitational force, is constant, and does not depend on mass.
Mathematically, weight = mass x free-fall accelera-
tion, or w = mg.
• Projectile motion is a combination of a downward free-fall motion and a forward horizontal motion.
State the law of universal gravitation, and use examples to explain the effect of changing mass and changing distance on gravitational force.
Explain why your weight would be less on the moon than on Earth even though your mass would not change. Use the law of universal gravitation in your explanation.
Describe the difference between mass and weight.
Name the two components that make up orbital motion, and explain how they do so.
Critical Thinking Using Newton's second law, explain why the gravitational acceleration of any object near Earth is the same no matter what the mass of the object is.
Math SkillsThe force between a planet and a spacecraft is 1 million newtons. What will the force be if the spacecraft moves to half its original distance from the planet?
Gravity
Key Terms:
Free fall
Terminal velocity
Projectile motion
Objectives:
Explain that gravitational force becomes stronger as the mass increases.
Evaluate the concept that free-fall acceleration near Earth's surface is independent of the mass of the falling object.
Demonstrate mathematically how free-fall acceleration relates to weight.
Describe orbital motion as a combination of downward motion and forward motion.
Law of Universal Gravitation:
All objects in the universe attract each other through a gravitational force.
Equation: F = G(m1*m2)/r^2
Gravitational force increases with greater masses and decreases as the distance between them increases.
Free Fall and Weight:
Free fall occurs when gravity is the only force acting on an object.
Free-fall acceleration (g) near Earth's surface is approximately 9.8 m/s² for all objects, regardless of mass.
Weight (W) is the product of mass (m) and free-fall acceleration (g): W = mg.
Differences between Mass and Weight:
Mass is a measure of the amount of matter in an object, while weight is the gravitational force on an object due to its mass.
Weight changes based on gravitational force (e.g., different planets), but mass remains constant.
Projectile Motion:
A combination of horizontal and vertical motions.
Objects in projectile motion follow a curved path influenced by gravity.
Terminal Velocity:
The constant velocity of a falling object when air resistance equals the force of gravity.
An object reaches terminal velocity when the downward force of gravity is balanced by the upward force of air resistance.
Critical Thinking Questions:
State the law of universal gravitation and discuss how changing mass and distance affects gravitational force.
Explain why weight is less on the moon than on Earth, despite unchanged mass.
Describe the two components that define orbital motion and explain their interplay.
Gravity Overview
Key Terms:
Free Fall: The motion of a body when only the force of gravity is acting upon it.
Terminal Velocity: The constant speed of a falling object when the force of air resistance equals the force of gravity.
Projectile Motion: The curved path followed by an object that is thrown, launched, or otherwise projected near the surface of the Earth.
Objectives:
Explain that gravitational force becomes stronger as mass increases.
Evaluate that free-fall acceleration near Earth's surface is independent of the mass of the falling object.
Demonstrate mathematically how free-fall acceleration (g) relates to weight (W = mg).
Describe orbital motion as a combination of downward and forward motions.
Law of Universal Gravitation:
All objects in the universe attract each other via gravitational force, governed by the equation:
F = G(m1*m2)/r^2
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Gravitational force increases with mass and decreases with distance.
Weight vs. Mass:
Weight is the force exerted by gravity on an object (W = mg).
Mass is the amount of matter in an object and remains constant regardless of location.
Key Principles:
Free Fall: All objects experience the same free-fall acceleration near Earth's surface regardless of their mass (approximately 9.8 m/s²).
Projectile Motion: Projectile motion has independent horizontal and vertical components affected by gravity, creating a curved trajectory.
Terminal Velocity: An object in free fall reaches terminal velocity when air resistance equals gravitational force, resulting in constant speed.
Critical Thinking Points:
Discuss the impact of changing mass and distance on gravitational force.
Explain the difference in weight on Earth versus the Moon, despite unchanged mass.
Define and describe the two components of orbital motion: downward gravitational pull and forward inertia.
Gravity Overview
Key Terms:
Free Fall: The motion of a body when only the force of gravity is acting upon it.
Terminal Velocity: The constant speed of a falling object when air resistance equals the force of gravity.
Projectile Motion: The curved path followed by an object that is thrown or projected near the surface of the Earth.
Objectives:
Explain how gravitational force increases with mass.
Evaluate that free-fall acceleration near Earth's surface is independent of mass.
Demonstrate how free-fall acceleration relates to weight mathematically (W = mg).
Describe orbital motion as a combination of downward and forward motions.
Law of Universal Gravitation:
All objects attract each other via gravitational force, expressed as:
F = G(m1*m2)/r²,where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between centers. Gravitational force increases with mass and decreases with distance.
Weight vs. Mass:
Weight (W) is the gravitational force on an object (W = mg), while mass is the measure of matter in an object, remaining constant regardless of location.
Key Principles:
Free Fall: All objects near Earth experience the same acceleration (approximately 9.8 m/s²).
Projectile Motion: Involves independent horizontal and vertical components influenced by gravity.
Terminal Velocity: Reached when gravitational force balances air resistance, resulting in a constant speed.
Critical Thinking Points:
Discuss the effects of changing mass and distance on gravitational force.
Explain why weight differs on Earth versus the Moon while mass remains unchanged.
Define and describe the components of orbital motion: gravitational pull and forward motion.