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1 CHAPTER 12 2 Gravity SECTION Forces KEY IDEAS As you read this section keep these questions in ind: What is free fall? How are weight and ass related? How does gravity affect the otion of objects? What Is Gravity? Have you ever seen ovie footage of the Apollo astronauts walking on the oon? If so, you ay have seen the bouncing up and down in their large spacesuits. Why could the astronauts jup so high on the oon? The answer is that gravity is weaker on the oon 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 ain parts: 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 asses 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, ass, and distance. Universal Gravitation Equation READING TOOLBOX Suarize As you read this section, underline the ain ideas in each paragraph. When you finish reading, ake an outline of the section using the ideas you underlined. 1. Identify On what two factors does the strength of the gravitational force between two objects depend? The gravitational force between two objects The asses of the two objects F = G A constant called the universal gravitational constant 1 2 d 2 The distance between the two objects Interactive Reader 255 Forces
2 2. Suarize How do the asses of objects affect the gravitational force between the? How Does Mass Affect Gravitational Force? Look back at the equation describing the law of universal gravitation. Notice that the two asses, 1 and 2, are ultiplied together on the right side of the equation. Therefore, the gravitational force between two objects increases as the asses of the objects increase. Gravitational force is weak between objects that have sall asses. 3. Infer The gravitational force between the sun and Earth is larger than the force between the sun and the oon. What do you think is the reason for this? 4. Explain Why is the gravitational force between the botto two balls saller than that between the top two balls? Iagine an elephant and a cat standing on Earth. Earth s gravity pulls on the elephant and the cat. The elephant has a larger ass 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 uch larger ass than either the elephant or the cat. Therefore, the gravitational force between the elephant and the cat is very sall copared to Earth s gravitational force on the. How Does Distance Affect Gravitational Force? Look again at the equation for the law of universal gravitation. Notice that distance is in the denoinator on the right side of the equation. Therefore, as the distance between two objects increases, the gravitational force between the decreases. Gravitational force is stronger when one or both of the objects have ore ass. d 2 Gravitational force is strong between objects that are close together. Gravitational force decreases as the distance between two objects increases. 2d Interactive Reader 256 Forces
3 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 sall asses, or both. Therefore, Earth s gravitational force affects objects on Earth ost significantly. Gravitational forces fro other objects are usually sall enough to ignore. 5. Explain Why don t you feel a gravitational force between you and your desk? What Is Free Fall? Iagine dropping a ball. It will fall toward the ground because Earth s gravitational force acts on it. Reeber Newton s second law of otion: 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 sae free-fall acceleration. Recall that acceleration depends on both force and ass. 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 ore ass. 6. Define What is free fall? 7. Identify Why do the two balls have the sae free-fall acceleration, even though they have different asses? The gravitational force on the larger ball is twice as great as the force on the saller ball. However, the larger ball has a larger ass, so it is harder to accelerate. Therefore, both balls have the sae free-fall acceleration. Interactive Reader 257 Forces
4 8. Define What is air resistance? AIR RESISTANCE AND TERMINAL VELOCITY You ay have seen objects falling through the air at different rates. For exaple, a piece of paper falls ore slowly than a ball. This ay see to contradict the stateent that all objects have the sae free-fall acceleration. However, free fall happens when gravity is the only force that acts on an object. On Earth, objects fall through the atosphere. The gases in the atosphere 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 otion: if no unbalanced forces act on an object, the object s otion 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 terinal velocity. 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.) When the skydiver first jups out of the plane, gravitational force is uch larger than the force of air resistance. Therefore, she accelerates downward. 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 terinal velocities. Interactive Reader 258 Forces
5 What Is Weight? Think back to the astronauts on the oon. The oon s ass is uch saller than Earth s ass. Therefore, objects near the oon experience a saller gravitational force than objects near Earth. The astronauts could jup very high on the oon because the gravitational force on the was sall. Another way to say this is the astronauts weighed less on the oon. Weight is the gravitational force on an object. Reeber that Earth s gravity is the ain gravitational force we feel at Earth s surface. Therefore, on Earth, the weight of an object is the sae as Earth s gravitational force on the object. The oon is very far fro Earth. When astronauts walk on the oon, Earth s gravitational force on the is very weak. The oon s gravitational force is the ain force acting on the astronauts. On the oon, the weights of the astronauts were saller than on Earth. To jup into the air, you ust push yourself up with a force greater than your weight. If your weight is saller, you need less force to jup into the air. On the oon, the astronauts only weighed one-sixth of what they weighed on Earth. Therefore, they needed less force to jup into the air. You ay 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 see to be weightless because they are in free fall. The astronauts and the space shuttle are falling toward Earth with the sae acceleration. This is why the astronauts appear to float. 10. Define What is weight? 11 Explain Why can an object never be truly weightless? Astronauts in orbit on the space shuttle see to float in idair. This is because the astronauts and the space shuttle are both in free fall. Interactive Reader 259 Forces
6 12. Copare How is weight different fro ass? 13. Apply Concepts A sall can of soup has a ass of about 400 g. What would its ass be on the oon? THE DIFFERENCE BETWEEN MASS AND WEIGHT Many people confuse ass and weight. Reeber that ass is the aount of atter in an object. Mass is easured in kilogras (kg). In contrast, weight is a force. Like all forces, weight is easured in newtons (N). The weight of an object will change if the gravitational force on it changes. For exaple, an astronaut with a ass of 66 kg weighs about 650 N (about 150 lb) on Earth. On the oon, the astronaut has the sae ass, 66 kg, because he contains the sae aount of atter. However, his weight is saller: only about 110 N (about 25 lb). The table below shows how the weights of soe objects would be different on the oon. Object Mass Weight on Earth Weight on the oon Apple 100 g 1 N (0.225 lb) 0.16 N (0.04 lb) Elephant 5,000 kg 49,000 N (11,025 lb) Train locootive 25,000 kg 245,000 N (55,125 lb) 8,000 N (1,800 lb) 40,000 N (9,000 lb) Math Skills 14. Calculate An object has a ass of 2,000 kg. What is its weight on Earth? Show your work. CALCULATING WEIGHT You can use the equation for Newton s second law of otion to calculate the weight of an object. Recall the equation for Newton s second law of otion: F = a Reeber that free-fall acceleration is the acceleration of an object because of gravity. Also, reeber that weight is the force on an object because of gravity. Therefore, you can rewrite the equation like this: weight = ass free-fall acceleration w= g On Earth, the free-fall acceleration, or g, is about 9.8 /s 2. Therefore, the weight of an object is equal to its ass in kilogras ultiplied by 9.8 /s 2. On the oon, free-fall acceleration is about 1.6 /s 2. How Does Gravity Affect Moving Objects? Iagine 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. Interactive Reader 260 Forces
7 PROJECTILE MOTION A thrown baseball shows projectile otion. Projectile otion is the curved path followed by any object that is thrown or launched near Earth s surface. Gravity causes these objects to ove along curved paths. All objects in projectile otion are oving in two directions: horizontally and vertically. These two otions cobine to give the object its curved path. However, the horizontal and vertical otions do not affect each other. You can see this in the figure below. 15. Identify What causes a thrown baseball to follow a curved path? This ball has no horizontal otion. It does not fall along a curved path. This ball was pushed off the ledge. It is oving both horizontally and vertically. The otions cobine to for a curved path. The downward acceleration on both balls is the sae. The horizontal otion of the light-colored ball does not affect its vertical otion. 16. Copare 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 oon orbiting Earth. An orbit is a circular or oval-shaped path that one object follows as it oves around another object in space. For exaple, the oon orbits Earth, and Earth orbits the sun. Gravity controls the orbits of all of the objects in the universe. A space shuttle orbiting Earth ay see very different fro a baseball falling to the ground after you throw it. However, both are exaples of projectile otion. The space shuttle in the figure below is oving forward, or horizontally. Earth s gravity is pulling the shuttle down, or vertically, toward Earth. These two otions cobine to produce the curved orbit of the shuttle. 2 Earth s gravity pulls the shuttle downward. If it were not oving horizontally, the shuttle would fall straight down to Earth s surface. 1 The shuttle oves forward at a constant speed. If Earth s gravity did not pull on it, the shuttle would ove away fro the planet. 3 The horizontal and vertical forces on the shuttle cobine to produce a curved path. This path is called an orbit. 17. Identify How would the shuttle s otion change if there were no gravitational force between it and Earth? Interactive Reader 261 Forces
8 Section 2 Review SECTION VOCABULARY free fall the otion of a body when only the force of gravity is acting on the body projectile otion the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth; the otion of objects that are oving in two diensions under the influence of gravity terinal velocity the constant velocity of a falling object when the force of air resistance is equal in agnitude and opposite in direction to the force of gravity weight a easure 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 atosphere, would a falling object ever reach terinal velocity? Explain your answer. 2. Calculate Fill in the blank spaces in the table below. Free-fall acceleration on Earth is 9.8 /s 2. On the oon, free-fall acceleration is 1.6 /s 2. Object Mass (kg) Weight on Earth (N) Weight on the oon (N) Bowling ball 5 8 Textbook 19.6 Large dog 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 see to float? 5. Identify What two kinds of otion cobine to produce projectile otion? Interactive Reader 262 Forces
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