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Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Gravity Objectives Explain that gravitational force becomes stronger as the masses increase and rapidly becomes weaker as the distance between the masses 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 two motions. Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Bellringer Recall that weight is defined as a measure of the gravitational force exerted on an object. Use knowledge you have about gravity to answer the questions in the following situations: 1. Elvis is a student whose mass is 70 kg. On Earth’s surface, Elvis weighs about 690 N. Suppose Elvis could stand on the surface of the following bodies in the solar system. In the blanks provided, match Elvis’ weight with the letter of the appropriate body. (Note that Earth has a mass of 6.0 x 10 24 kg.) Planet Elvis’ weight a. Jupiter (m = 1.9 x 10 27 kg)780 N _______ b. Venus (m = 4.9 x 10 24 kg) 113 N _______ c. Neptune (m = 1.0 x 10 26 kg) 260 N _______ d. Mercury (m = 3.3 x 10 23 kg) 1800 N _______ e. Earth’s moon (m = 7.4 x 10 22 kg) 620 N _______ Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Bellringer, continued 2. Suppose Elvis is in orbit around Venus at a distance twice as far from the planet’s center as the surface of Venus is. Would you expect his weight to be greater than, less than, or equal to his weight on the surface of the planet? Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Law of Universal Gravitation Sir Isaac Newton (1642–1727) generalized his observations on gravity in a law now known as the law of universal gravitation. Universal Gravitation Equation m 1 and m 2 are the masses of the two objects d is the distance between the two objects G is a constant Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Law of Universal Gravitation, continued All matter is affected by gravity. Two objects, whether large or small, always have a gravitational force between them. When something is very large, like Earth, the force is easy to detect. Gravitational force increases as mass increases. Gravitational force decreases as distance increases. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Free Fall and Weight Free fall is the motion of a body when only the force of gravity is acting on the body. Free-fall acceleration near Earth’s surface is constant. If we disregard air resistance, all objects near Earth accelerate at 9.8 m/s 2. Freefall acceleration is often abbreviated as the letter g, so g = 9.8 m/s 2. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Free Fall and Weight, continued Weight is equal to mass times free-fall acceleration. weight = mass  free-fall acceleration w = mg Weight is different from mass. Mass is a measure of the amount of matter in an object. Weight is the gravitational force an object experiences because of its mass. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Free Fall and Weight, continued Weight influences shape. Gravitational force influences the shape of living things. Velocity is constant when air resistance balances weight. 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 is called the terminal velocity. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Free Fall and Motion Orbiting objects are in free fall. The moon stays in orbit around Earth because Earth’s gravitational force provides a pull on the moon. Two motions combine to cause orbiting. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Projectile Motion and Gravity Projectile motion is the curved path an object follows when thrown, launched, or otherwise projected near the surface of Earth. Projectile motion applies to objects that are moving in two dimensions under the influence of gravity. Projectile motion has two components—horizontal and vertical. The two components are independent. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Projectile Motion and Gravity, continued Projectile motion has some horizontal motion. Horizontal motion is motion that is perpendicular (90º) to Earth’s gravitational field. The horizontal velocity is constant. Projectile motion also has some vertical motion. The vertical motion is the same as downward free- fall motion. Section 2 Gravity Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 3 Newton’s Third Law Objectives Explain that when one object exerts a force on a second object, the second object exerts a force equal in size and opposite in direction on the first object. Show that all forces come in pairs commonly called action and reaction pairs. Recognize that all moving objects have momentum. Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Bellringer You have learned that forces account for changes in the motion of objects. Using what you have learned, explained what happens in the following situation: An ice skater holding a basketball is standing on the surface of a frozen pond. The skater throws the ball forward. At the same time, the skater slides on the ice in the opposite direction. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Bellringer, continued 1. Is the force on the ball greater than, less than, or equal to the opposite force on the skater? 2. Is the acceleration of the ball greater than, less than, or equal to the acceleration of the skater? (Hint: Remember Newton’s Second Law.) 3. Explain your answers. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Action and Reaction Forces Newton’s third law of motion states that for every action force, there is an equal and opposite reaction force. Forces always occur in action-reaction pairs. Action-reaction force pairs are equal in size and opposite in direction. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Action and Reaction Forces, continued Force pairs do not act on the same object. When one object exerts an action force on a second object, the second object exerts a reaction force on the first object. Equal forces don’t always have equal effects. For example, the action force of Earth pulling on an object and causing it to fall is much more obvious than the equal and opposite reaction force of the falling object pulling on Earth. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Momentum Momentum is a quantity defined as the product of the mass and velocity of an object. momentum = mass  velocity p = mv Moving objects have momentum. For a given velocity, the more mass an object has, the greater its momentum is. Likewise, the faster an object is moving, the greater its momentum is. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Math Skills Momentum Calculate the momentum of a 6.00 kg bowling ball moving at 10.0 m/s down the alley toward the pins. 1. List the given and unknown values. Given: mass, m = 6.00 kg velocity, v = 10.0 m/s down the alley Unknown: momentum, p = ? kg m/s (and direction) Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Math Skills, continued 2. Write the equation for momentum. momentum = mass x velocity p = mv 3. Insert the known values into the equation, and solve. p = mv = 6.00 kg  10.0 m/s p = 60.0 kg m/s down the alley Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Momentum, continued Force is related to change in momentum. When you force an object to change its motion, you force it to change its momentum. Momentum is conserved in collisions. The law of conservation of momentum states that the total amount of momentum in an isolated system is conserved. Conservation of momentum explains rocket propulsion. Section 3 Newton’s Third Law Chapter 11

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Momentum, continued Momentum is transferred. When a moving object hits a second object, some or all of the momentum of the first object is transferred to the second object. Momentum can be transferred in collisions, but the total momentum before and after a collision is the same. Action and reaction force pairs are everywhere. Section 3 Newton’s Third Law Chapter 11