* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Ch 6.2 and 7 study guide-Circular Motion and Gravitation
Survey
Document related concepts
Fictitious force wikipedia , lookup
N-body problem wikipedia , lookup
Center of mass wikipedia , lookup
Classical mechanics wikipedia , lookup
Equations of motion wikipedia , lookup
Fundamental interaction wikipedia , lookup
Equivalence principle wikipedia , lookup
Work (physics) wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Classical central-force problem wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Mass versus weight wikipedia , lookup
Centripetal force wikipedia , lookup
Transcript
Name Study Guide continued 6 c. If the plane is traveling with a horizontal speed of 483 km/h when the capsule is released, what is the horizontal distance between the point at which the capsule is released and the point at which the capsule strikes the ground? Draw a diagram to help you answer the question. Section 6.2 Uniform Circular Motion In your textbook, read about uniform circular motion on page 153. Answer the following questions. Use complete sentences. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. What are the two conditions necessary for an object to be in uniform circular motion? 2. Why is a particle in uniform circular motion not moving at a constant velocity? 3. Use Newton’s laws to explain how you know that an object in uniform circular motion must be experiencing a force. 4. Use Newton’s laws to explain how you know that an object in uniform circular motion is being accelerated. Physics: Principles and Problems Chapters 6–10 Resources 11 Name 6 Study Guide continued 5. An object in uniform circular motion is at position r 1 at the beginning of a time interval and position r 2 at the end of the time interval. Write an algebraic expression that describes the object’s average velocity during this time interval. You may want to draw a diagram to help you answer the question. 6. The object described in the Question 5 has a velocity vector v1 at the beginning of the time interval and v2 at the end of the time interval. Write an algebraic expression that describes the object’s average acceleration during this time interval. In your textbook, read about uniform circular motion on page 153. Answer the following questions. Use complete sentences. 7. For each situation below, what provides the force that causes centripetal acceleration? You may want to draw a diagram to help you answer some of the questions. a. a ball on a string swinging in a circle in uniform circular motion c. a car driving in a circle in uniform circular motion d. a person on a carnival ride that has hanging baskets that are whirled around horizontally in uniform circular motion 8. What is the relationship between the centripetal acceleration of an object in uniform circular motion and the object’s velocity? 12 Chapters 6–10 Resources Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. b. a satellite moving around Earth in uniform circular motion Date Period Name CHAPTER 7 Study Guide Gravitation Vocabulary Review Write the term that correctly completes the statement. Use each term once. Kepler’s second law gravitational mass Newton’s law of universal gravitation inertial mass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. gravitational field 1. describes the amount of resistance an object has to any application of force. 2. states that an imaginary line line drawn between a planet and the Sun sweeps out equal areas in equal time periods. 3. If the of an object is increased, the gravitational force it experiences will increase as a result. 4. The region around Earth in which objects experience a force due to Earth’s gravity is called the . 5. suggests that objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. Section 7.1 Planetary Motion and Gravitation In your textbook, read about planetary motion, Kepler’s laws and Newton’s law of universal gravitation on pages 171–176. Match the name of the scientist with the correct contribution. Each name may be used more than once. Nicholas Copernicus Johannes Kepler Tycho Brahe Isaac Newton 1. was the first astronomer to propose that the Sun is the center of the solar system. 2. believed that all planets except Earth orbit the Sun. 3. used huge instruments he built himself to record the exact positions of the planets and stars. 4. used 30 years worth of observations made by other scientists and concluded that the planets orbit the Sun. 5. proposed that the force exerted on a planet by the Sun is inversely proportional to the distance between centers of the planet and the Sun. Physics: Principles and Problems Chapters 6–10 Resources 45 Name 7 Study Guide continued 6. discovered that the shape of a planet’s orbit is an ellipse. 7. was the first to theorize that the force that makes objects fall to Earth is the same force that the Sun exerts on the planets. 8. used geometry and mathematics to discover his three laws of planetary motion. Write first, second, or third in the blanks to indicate which of Kepler’s laws the statement is describing. 9. relates the motion of more than one object about a single body 10. describes the shape of the planets’ orbits 11. states that the Sun is located at one focus of a planet’s orbit 12. TA 2 r 3 A TB rB 13. states that an imaginary line drawn from a planet to the Sun will sweep out equal areas in equal time intervals In your textbook, read about Kepler’s laws and Newton’s law of universal gravitation on pages 172–176. Refer to the diagram to answer questions 14–18. Planet A t1 Sun 1 3 t2 t3 t 4 Planet B 14. The shaded portions of Planet A’s orbit represent the area swept out by an imaginary line between the Sun and the planet between times t1 and t2 and between times t3 and t4. If the area of these shaded regions is equal, what must be true about the time intervals t2 t1 and t4 t3? 15. If you know the period of both Planets A and B, what other information would you need to determine Planet A’s average distance from the Sun? 46 Chapters 6–10 Resources Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2 Name Study Guide continued 7 16. The gravitational field of the Sun exerts a force on Planet B. At which point on the orbit of Planet B is this force at its least? At which point is it greatest? 17. At point 3, Planet B is six times further from the Sun than it is at point 1. If the magnitude of the force exerted on Planet B by the gravitational field of the Sun at point 1 is F, what is the magnitude of the force at point 3? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 18. If the period of Planet A is TA and the period of Planet B is TB and Planet A’s average distance from the Sun is rA, write a formula that represents rB, Planet B’s average distance from the Sun. In your textbook, read about universal gravitation on pages 176–178. Fill in the chart with the correct values of F for each change in the system described in questions 19–23. The magnitude of the gravitational force between two masses, P and Q, is F. Change in System New Magnitude of Force 19. The mass of P is doubled. 20. The distance between the masses is doubled. 21. The mass of P is doubled and the mass of Q is tripled. 22. The entire mass of the system is increased by a factor of four. 23. The distance between the masses is halved. Physics: Principles and Problems Chapters 6–10 Resources 47 Name Study Guide 7 continued Answer the following questions. Use complete sentences or show your calculations. 24. Given the value of pi and the universal gravitational constant, what other information would you need to calculate the period of a planet orbiting the Sun? 25. Describe the balance Cavendish used to find an experimental value for the universal gravitational constant. 26. What is the gravitational force between two 1.00-kg masses that are placed 1.00 m apart? What is another name for this number? Using the Law of Universal Gravitation In your textbook, read about the orbits of planets and satellites on pages 179–180. Write the term that correctly completes the statement. 1. The motion of a projectile has both and components. 2. A projectile fired horizontally will accelerate toward Earth at a rate of . 3. If the magnitude of the component of a projectile’s motion is great enough, the projectile will fall to Earth at the same rate that Earth curves away from the projectile. 4. A projectile fired horizontally from less than 150 km above the surface of Earth will fall back to Earth no matter how fast it is traveling because of . 5. An object that falls to Earth at the same rate that Earth curves away from the object is said to be in . 48 Chapters 6–10 Resources Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Section 7.2 Name Study Guide continued 7 In your textbook, read about the motion of satellites and acceleration due to gravity on pages 180–182. For each statement below, write true or rewrite the italicized part to make the statement true. 6. The speed of a satellite orbiting Earth depends only on the mass of Earth and the mass of the satellite. 7. The equations of motion are different for objects in orbit around Earth and for planets orbiting the Sun. 8. Orbital speed and period are independent of the mass of the satellite. 9. If the radius of Earth were changed but the mass remained the same, acceleration due to gravity would not change. 10. As you move farther away from Earth’s center, acceleration due to gravity changes according to a direct relationship. 11. Even though astronauts on the space shuttle appear to be weightless, Earth’s gravitational force on the space shuttle is not zero. In your textbook, read about the gravitational field, inertial mass, and gravitational mass on pages 182–184. Answer the following questions. Use complete sentences. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 12. What units are used to measure the strength of gravitational fields? 13. In which direction does the force of Earth’s gravitational field always act? 14. Describe the difference between gravitational and inertial mass. 15. Does the inertial mass depend on the distance between objects? Explain. Physics: Principles and Problems Chapters 6–10 Resources 49 Name 7 Study Guide continued Read about Einstein and his general theory of relativity on pages 184–185. For each description on the left, write the letter of the matching term on the right. 16. the effect of mass on space a. gravitational field 17. effect of gravity on light b. general theory of relativity c. curvature 18. Einstein thought gravity was a(n) d. effect of space e. deflection 19. an object so dense that light leaving the object is bent back on itself f. black hole 20. predicts the effects of gravity 21. allows us to picture gravity acting at a distance Complete each statement by writing the correct term in the blank provided. 22. Newton’s law of universal gravitation allows us to calculate the force that exists between two bodies because of their mass. , but rather an effect of itself. 24. According to Einstein, the mass of a body changes the 25. around it. causes space to be curved, and other bodies are accelerated because of the way they follow this curved space. 26. According to Einstein’s theory of enough, any light it emits is actually bent back to the object. 50 Chapters 6–10 Resources , if an object is massive and dense Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 23. Einstein proposed that gravity is not a Date Period Name CHAPTER 7 Section 7-1 Quiz Planetary Motion and Gravitation 1. Write Kepler’s laws next to their respective numbers below. 1st 2nd 3rd Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2. Mercury is 57.9106 km from the Sun. Venus is 108.2106 km from the Sun. If Venus has a period of 224.7 Earth days, how many Earth days does it take Mercury to make one trip around the Sun? 3. The Sun has a mass of 1.991030 kg. The planet Neptune has a mass of 1.031026 kg and is 4.501012 m from the Sun. Calculate the gravitational force between the Sun and Neptune. 4. Describe the process and equipment Cavendish used to establish an experimental value for the universal gravitational constant. Physics: Principles and Problems Chapters 6–10 Resources 51 Date Period Name CHAPTER 7 Section 7-2 Quiz Using the Law of Universal Gravitation 1. Explain the conditions necessary for an object to attain and then stay in orbit around Earth. 2. What are the orbital speed (in m/s) and period (in seconds) of a satellite orbiting 350 km above the surface of Earth? Earth has a mass of 5.981024 kg and a radius of 6.38106 m. 4. Briefly explain how Einstein’s general theory of relativity accounts for gravity, both its causes and effects. In your answer, include an explanation of how the general theory of relativity differs from Newton’s law of universal gravitation. 52 Chapters 6–10 Resources Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. A satellite orbits Earth 270 km above Earth’s surface. Calculate the acceleration due to gravity at this altitude. Answer Key Chapter 6 continued Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Section 6-2 Uniform Circular Motion 1. The object must be moving in a circle with a fixed radius and the object must be moving at a constant speed. 2. While speed is a directionless quantity, velocity is a vector and therefore any change in direction indicates a change in velocity. 3. Newton’s first law states that a body moving at a constant velocity will continue moving at a constant velocity unless a force acts on that body. Since an object in uniform circular motion has a changing velocity, it must be experiencing a force. 4. Newton’s second law states that when a force acts on a mass, that force causes acceleration along the same axis that the force is applied. As shown in Question 3, an object in uniform circular motion must be experiencing a force since is has a changing velocity. Therefore, that force must be causing the object to accelerate along the same axis as the force. r2 r1 r 5. v or v t t2 t1 v2 v1 v 6. a or a t t2 t1 7. a. the string b. the force of gravity c. the force of friction between the tires and the pavement d. the chain on which the basket hangs 8. The centripetal acceleration is directly proportional to the square of the velocity. 9. The centripetal acceleration is inversely proportional to the radius of rotation. 1 10. 2 11. 4 12. 2 Physics: Principles and Problems Section 6-3 Relative Velocity 1. a. 3 m/s b. 2 m/s c. 5 m/s 2. a. 3 m/s b. 2 m/s c. 1 m/s 3. north 4. a. southwest b. vboat/water N vJohn/boat vJohn/water Section 6-1 Quiz 1. Newton’s second law states that when a force is applied to an object, the object will accelerate along the same axis that the force is applied. Assuming that air resistance is negligible, no forces act on a projectile along the horizontal axis and therefore the object has no horizontal component to its acceleration other than the initial force. 2. The force of gravity acts along the vertical axis of a projectile’s flight. This force is constant and thus the acceleration the projectile experiences along the vertical axis is constant and is equal to the acceleration due to gravity. 3. a. d vt d 235 m v 5.0 m/s t 47 s b. As the projectile travels up and then down again, it reaches its maximum height at the midway point of its path, 47 s t 24 s 2 1 1 yf at2 (9.80 m/s2)(24 s)2 2 2 2800 m Chapters 6–10 Resources 179 Answer Key Chapter 7 continued Analyze 1. See Data Table. 2. See Data Table. 3. See Data Table. Sample Calculation for Pluto: e 4/16 0.25 4. See Data Table. 5. Both foci are at the center. 6. It is very close to being a circle. 7. The comet. It looks more flattened out then the other orbits. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Conclude and Apply 1. Yes, the planets and comet travel in elliptical orbits. 2. Since the eccentricity of Earth is so small, Kepler might not have concluded that planets have elliptical orbits. 3. It travels fastest at perihelion. According to Kepler’s second law, equal areas are swept out in equal time. Since there is less area available at perihelion, the planet must move faster. vP A 10.0 1.7 4. vA P 6 .0 1 5. vA minimum velocity 3.7 km/s vP 1.7 vA 1.7 3.7 km/s 6.3 km/s Going Further 1. Collect data using dates of location of a planet. Use areas and dates to confirm the second law. 2. In order to show the third law, a computer model would have a planet actually moving so that periods and distances could be measured. Real-World Physics Students can research elliptical orbits of satellites. Encourage the students to pick one or two satellites and, if possible, plot orbit data to determine the path that each satellite takes. Physics: Principles and Problems Study Guide Vocabulary Review 1. 2. 3. 4. 5. inertial mass Kepler’s second law gravitational mass gravitational field Newton’s law of universal gravitation Section 7-1 Planetary Motion and Gravitation 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. Copernicus Brahe Brahe Kepler Newton Kepler Newton Kepler third first first third second t2 t1 t4 t3 planet B’s average distance from the Sun It is least at point 3 and greatest at point 1. 1 The magnitude of the force at point 3 is F 36 TB2rA3 rB 3 TA2 2F 1 F 4 6F 4F 4F the planet’s mean distance from the Sun as well as the mass of the Sun Chapters 6–10 Resources 185 Answer Key 25. It was a thin rod with small lead spheres at each end. The rod was suspended by a thin wire attached at its center so that the rod could spin freely. He then placed two larger lead spheres in fixed positions near the smaller spheres. The gravitational attraction between the lead spheres allowed Cavendish to obtain a value for the universal gravitational constant. m1m2 26. F G (6.671011 N·m2/kg2) r2 (1.00 kg)(1.00 kg) 6.671011 N. This (1.00 m)2 number is significant because it is equal to the value of the universal gravitational constant. Thus, the constant is defined as the value of the gravitational force between two 1.00 kg masses placed exactly one meter apart. horizontal, vertical 9.80 m/s2 horizontal air resistance orbit the radius of the satellite’s orbit. the same true would change inverse-square relationship true N/kg toward Earth’s center Gravitational mass determines the force of attraction between two masses and inertial mass determines an object’s resistance to any type of force 15. No; the inertial mass is a function of an object’s resistance to an exterior force, not to its position relative to other objects. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 186 Chapters 6–10 Resources 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. c e d f b a gravitational force; space space mass general relativity Section 7-1 Quiz Planetary Motion and Gravitation 1. 1st: The paths of the planets are ellipses with the Sun at one focus. 2nd: An imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals. 3rd: The square of the periods of two planets is equal to the cube of their respective mean TA 2 rA 3 distances from the Sun, or TB rB (224.7 d) r 2. TM TV rM 3 V 57910 km 87.8 days 108210 km 6 6 3 mSmN 3. F G (6.671011 N·m2/kg2) r2 (1.991030 kg)(1.031026 kg) (4.501012 m)2 6.771020 N 4. Cavendish used a small rod suspended at its midpoint by a thin wire. The rod had small lead spheres at either end. He then placed larger lead spheres in fixed positions near the rod. He then used the angle through which the rod turned to calculate the attractive force between the spheres and then to calculate the universal gravitational constant. Physics: Principles and Problems Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Section 7-2 Using the Law of Universal Gravitation Chapter 7 continued Answer Key Chapter 7 continued Section 7-2 Quiz Using the Law of Universal Gravitation 1. The horizontal component of the object’s velocity must be great enough that the object falls toward Earth at the same rate that Earth curves away from the moving object. For the object to remain moving fast enough to stay in orbit, the object must be more than 150 km above the surface of Earth so that air resistance does not decrease the horizontal component of the object’s velocity. GmE r 2. v (6.671011 N·m2/kg2)(5.981024 kg) (350103 m 6.38106 m) 7700 m/s Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. T 2 2 r3 GmE (350103 m 6.38106 m)3 (6.671011 N·m2/kg2)(5.981024 kg) 5500 s rE 2 3. a g (9.80 m/s2) r 6.3810 m 27010 m 6.3810 m 6 3 2 6 9.0 m/s2 4. According to the general theory of relativity, mass curves the space around it. Other bodies are then accelerated by the curvature of the space through which they might pass. Thus, gravity is not a force but an effect of space itself. Newton’s law of universal gravitation simply allows us to calculate the magnitude of the gravitational attraction between two bodies. 2. The apparent position of the star on the day of the eclipse is meaningless by itself. For Einstein’s theory to be true, light from the star must be bent by the Sun’s gravity. This means that the astronomers would observe a change in the star’s apparent position. Since, it is the change that is important and not the star’s position on any one date, the results of this experiment would have proved nothing if the star’s position had not previously been noted. 3. The experiment provided support for Einstein’s theory because the apparent position of the star changed when its light passed close to the Sun. This change in apparent position indicates that the path and direction of the light was bent, presumably by the Sun’s gravitational field. Chapter 7 Enrichment Variations in the Acceleration Due to Gravity on Earth 1. Acceleration due to gravity is less near the equator and less at higher elevations. Thus, you would find the lowest value of acceleration due to gravity at a high elevation near the equator and you would find the highest value near the North or South Pole at sea level. 2. There appears to be a stronger correlation between acceleration due to gravity and latitude. While acceleration due to gravity increases consistently with increases in latitude, the values for acceleration due to gravity in Table 1 don’t increase consistently with increases in elevation. In some cases, an increase in elevation corresponds to a decrease in acceleration due to gravity. Chapter 7 Reinforcement Gravitation 1. According to the general theory of relativity, only the Sun has enough mass to curve space and deflect the light from distant stars to any measurable degree. Physics: Principles and Problems Chapters 6–10 Resources 187