Chapter 6 SUMMARY Unit 2 Key Expectations analyze the factors affecting the motion of isolated celestial objects and calculate the gravitational potential energy for each system (6.1, 6.2, 6.3) analyze isolated planetary and satellite motion, and describe the motion in terms of the forms of energy and energy transformations that occur (e.g., calculate the energy required to propel a spacecraft from Earth s surface out of Earth s gravitational field, and describe the energy transformations that take place; calculate the kinetic energy and gravitational potential energy of a satellite in a stable orbit around a planet) (6.1, 6.2, 6.3) Key Terms gravitational field Kepler s laws of planetary motion escape speed escape energy binding energy black hole event horizon singularity Schwartzschild radius Key Equations g G M r 2 (6.1) v G rm (6.2) r C S 3 T 2 for the Sun (6.2) C S G MS for the Sun (6.2) 4p 2 C G M r 4p2 3 T 2 in general (6.2) E g GM m (6.3) r E g GM r 2 m GM r 1 m (6.3) v 2G M r escape speed (6.3) MAKE a summary Draw an Earth-Moon system diagram. Add a geosynchronous satellite (Figure 1) on the side of Earth opposite the Moon. Beyond the geosynchronous satellite, add a space probe, moving away from Earth, that has just enough energy to escape Earth s gravitational attraction. Show as many key expectations, key terms, and key equations as possible on your diagram. Figure 1 Gravitation and Celestial Mechanics 297
Chapter 6 SELF QUIZ Write numbers 1 to 10 in your notebook. Indicate beside each number whether the corresponding statement is true (T) or false (F). If it is false, write a corrected version. 1. At a particular location, the gravitational field around a celestial body depends only on the mass of the body. 2. If both the radius and mass of a planet were to double, the magnitude of the gravitational field strength at its surface would become half as great. 3. The speed of a satellite in a stable circular orbit around Earth is independent of the mass of the satellite. 4. In the Sun s frame of reference, the Moon s orbit around Earth appears as an epicycle. 5. In a typical high-school physics investigation, the Evidence is to the Analysis as Kepler s work was to Tycho Brahe s work. 6. In Figure 1, where the path distances d 1 and d 2 are equal, the speeds along those path segments are equal. Write numbers 11 to 26 in your notebook. Beside each number, write the letter corresponding to the best choice. For questions 11 to 19, refer to Figure 2. (a) y (d) y x x (b) y (e) y x x (c) y x d 2 Sun Figure 2 The first variable named in each of questions 11 to 19 corresponds to the y-variable on one of these graphs; the second variable named corresponds to the x-variable. d 1 Figure 1 direction of motion of planet 7. When calculating Kepler s third-law constant for Earth, the value is larger for the Moon than for an Earth-bound satellite because the Moon is much farther away. 8. The gravitational potential energy of the Earth-Moon system is inversely proportional to the square of the distance between the centres of the two bodies. 9. As a space probe travels away from Earth, its change in gravitational potential energy is positive, even though its gravitational potential energy is negative. 10. As you are working on this problem, your escape energy is greater than your binding energy. 11. The y-variable is the magnitude of the gravitational field strength at a point above a planet s surface; x is the planet s mass. 12. The y-variable is the magnitude of the gravitational field strength at a point above a planet s surface; x is the distance to the centre of the planet. 13. The y-variable is the speed of a satellite in a stable circular orbit around a planet; x is the mass of the planet. 14. The y-variable is the speed of a satellite in a stable circular orbit around a planet; x is the distance to the centre of the planet. 15. The y-variable is the area swept out by a line joining a planet to the Sun; x is the time interval during which that line is swept out. 16. The y-variable is the average radius of a planet s orbit; x is the period of revolution of the planet s motion around the Sun. 298 Chapter 6 An interactive version of the quiz is available online. GO www.science.nelson.com
Unit 2 17. The y-variable is the cube of the average radius of a planet s orbit; x is the square of the period of revolution of the planet s motion around the Sun. 18. The y-variable is the kinetic energy of a space probe that was given enough energy to escape Earth s gravitational field; x is the distance from Earth s centre. 19. The y-variable is the gravitational potential energy of a space probe that was given enough energy to escape Earth s gravitational field; x is the distance from Earth s centre. 20. The law that allows us to determine Earth s mass is (a) Kepler s first law of planetary motion (b) Kepler s second law of planetary motion (c) Kepler s third law of planetary motion (d) Newton s law of universal gravitation (e) Newton s second law of motion 21. If the distance between a spacecraft and Saturn increases by a factor of three, the magnitude of Saturn s gravitational field strength at the position of the spacecraft (a) decreases by a factor of 3 (b) increases by a factor of 3 (c) decreases by a factor of 9 (d) increases by a factor of 9 (e) decreases by a factor of 3 22. Satellite S 1 is moving around Earth in a circular orbit of radius four times as large as the radius of the orbit of satellite S 2. The speed of S 1, v 1, in terms of v 2 equals (a) 16v 2 (b) v 2 (c) 2v 2 (d) 0.5v 2 (e) none of these 23. If the mass of the Sun were to become half its current value, with Earth maintaining its same orbit, the time interval of one Earth year would (a) remain the same (b) decrease by a factor of 2 (c) increase by a factor of 2 (d) increase by a factor of 2 (e) decrease by a factor of 2 24. A satellite in geosynchronous orbit has a period of revolution of (a) 1.5 h (b) 1.0 h (c) 24 h (d) 365.26 d (e) none of these 25. Figure 3 shows the path of a comet around the Sun. The speeds at the four positions shown are v A, v B, v C, and v D. Which statement is true? (a) v A > v B v D > v C (b) v A < v B v D < v C (c) v A > v B > v C > v D (d) v A < v B < v C < v D (e) none of these A 26. A certain planet has Earth s mass, but only onequarter its diameter. The escape speed from this planet in terms of Earth s escape speed v E is (a) v E Sun Figure 3 (b) 1 2 v E (c) 1 4 v E (d) 4v E (e) 2v E D B comet s direction C An interactive version of the quiz is available online. GO www.science.nelson.com Gravitation and Celestial Mechanics 299
Chapter 6 REVIEW Understanding Concepts 1. If a rocket is given a great enough speed to escape from Earth, could it also escape from the Sun and, hence, the solar system? What happens to the artificial Earth satellites that are sent to explore the space around distant planets, such as Neptune? 2. Assuming that a rocket is aimed above the horizon, does it matter which way it is aimed for it to escape from Earth? (Neglect air resistance.) 3. Determine the elevation in kilometres above the surface of Uranus where the gravitational field strength has a magnitude of 1.0 N/kg. 4. Ganymede, one of Jupiter s moons discovered by Galileo in 1610, has a mass of 1.48 10 23 kg. What is the magnitude of Ganymede s gravitational field strength at a point in space 5.55 10 3 km from its centre? 5. Determine the total gravitational field strength (magnitude and direction) of the Earth and Moon at the location of the spacecraft in Figure 1. Moon 2.30 10 5 km 90.0 spacecraft Earth 3.07 10 5 km Figure 1 6. Mercury has both a surface gravitational field strength and a diameter 0.38 times the corresponding Earth values. Determine Mercury s mass. 7. A satellite in a circular orbit around Earth has a speed of 7.15 10 3 m/s. Determine, in terms of Earth s radius, (a) the distance the satellite is from Earth s centre (b) the altitude of the satellite 8. Tethys, one of Saturn s moons, travels in a circular orbit at a speed of 1.1 10 4 m/s. Calculate (a) the orbital radius in kilometres (b) the orbital period in Earth days 9. Using the mass of the Sun and the period of revolution of Venus around the Sun, determine the average Sun- Venus distance. 10. A 4.60-kg rocket is launched directly upward from Earth at 9.00 km/s. (a) What altitude above Earth s surface does the rocket reach? (b) What is the rocket s binding energy at that altitude? 11. Titan, a moon of Saturn discovered by Christian Huygens in 1655, has a mass of 1.35 10 23 kg and a radius of 2.58 10 3 km. For a 2.34 10 3 -kg rocket, determine (a) the escape speed from Titan s surface (b) the escape energy of the rocket 12. A rocket ship of mass 1.00 10 4 kg is located 1.00 10 10 m from Earth s centre. (a) Determine its gravitational potential energy at this point, considering only Earth. (b) How much kinetic energy must it have at this location to be capable of escaping from Earth s gravitational field? (c) What is its escape speed from Earth at this position? 13. Calculate the gravitational potential energy of the Sun-Earth system. 14. Determine the escape speeds from (a) Mercury (b) Earth s Moon 15. A neutron star results from the death of a star about 10 times as massive as the Sun. Composed of tightly packed neutrons, it is small and extremely dense. (a) Determine the escape speed from a neutron star of diameter 17 km and mass 3.4 10 30 kg. (b) Express your answer as a percentage of the speed of light. 16. A solar-system planet has a diameter of 5.06 10 4 km and an escape speed of 24 km/s. (a) Determine the mass of the planet. (b) Name the planet. 17. A proton of mass 1.67 10 27 kg is travelling away from the Sun. At a point in space 1.4 10 9 m from the Sun s centre, the proton s speed is 3.5 10 5 m/s. (a) Determine the proton s speed when it is 2.8 10 9 m from the Sun s centre. (b) Will the proton escape from the Sun? Explain why or why not. 18. Explain this statement: A black hole is blacker than a piece of black paper. 19. Determine the Schwartzschild radius of a black hole equal to the mass of the entire Milky Way galaxy (1.1 10 11 times the mass of the Sun). 300 Chapter 6
Unit 2 Applying Inquiry Skills 20. Table 1 provides data concerning some of the moons of Uranus. Table 1 Data of Several Moons of the Planet Uranus for Question 20 Moon Discovery r average T (Earth C U (km) days) (m 3 /s 2 ) Ophelia Voyager2(1986) 5.38 10 4 0.375? Desdemona Voyager2(1986) 6.27 10 4 0.475? Juliet Voyager2(1986) 6.44 10 4 0.492? Portia Voyager2(1986) 6.61 10 4 0.512? Rosalind Voyager2(1986) 6.99 10 4?? Belinda Voyager 2 (1986)? 0.621? Titania Herschel (1787) 4.36 10 5?? Oberon Herschel (1787)? 13.46? (a) Copy the table into your notebook. Determine Kepler s third-law constant C U for Uranus using the data for the first four moons. (b) Find the average of the C U values of your calculations in (a). (c) Use another method to determine C U. Do the values agree? (d) Complete the missing information for the last four moons listed. (e) Explain why some of the moons were discovered so much earlier than others. 21. It is beneficial to develop skill in analyzing a situation to determine if the given information or the answer to a question makes sense. Consider the following problem: Determine the radius of the orbit of a satellite travelling around Earth with a period of revolution of 65 min. (a) Do you think this problem makes sense? Why or why not? (b) Calculate a numerical answer to the problem. (c) Does the numerical answer make sense? Why or why not? (d) Why would this skill be valuable to a research physicist? 22. Figure 2 shows the energy relationships for a rocket launched from Earth s surface. (a) Determine the rocket s mass. (b) What is the escape energy of the rocket (to three significant digits)? (c) Determine the launch speed given to the rocket. (d) What will the rocket s speed be at a very large distance from Earth. E (10 10 J) 12 10 8 6 4 2 0 2 4 6 8 10 12 Figure 2 r E kinetic energy 2r E 3r E 4r E 5r E gravitational potential energy Making Connections 23. When the Apollo 13 spacecraft was about halfway to the Moon, it developed problems in the oxygen system. Rather than turning the craft around and returning directly to Earth, mission control decided that the craft should proceed to the Moon before returning to Earth. (a) Explain the physics principles involved in this decision. (b) Describe at least one major risk of this decision. Extension 24. Two remote planets consist of identical material, but one has a radius twice as large as the other. If the shortest possible period for a low-altitude satellite orbiting the smaller planet is 40 min, what is the shortest possible period for a similar low-altitude satellite orbiting the larger one? Give your answer in minutes. Sir Isaac Newton Contest Question 25. A certain double star consists of two identical stars, each of mass 3.0 10 30 kg, separated by a distance of 2.0 10 11 m between their centres. How long does it take to complete one cycle? Give your answer in seconds. Sir Isaac Newton Contest Question Separation Distance 26. We owe our lives to the energy reaching us from the Sun. At a particular planet, the solar energy flux E (the amount of energy from the Sun arriving per square metre per second) depends on the distance from the Sun to the planet. If T is the period of that planet in its journey around the Sun, that is, the length of its year, calculate how E depends on T. Sir Isaac Newton Contest Question Gravitation and Celestial Mechanics 301
Chapter7 SUMMARY Key Expectations state Coulomb s law and Newton s law of universal gravitation, and analyze and compare them in qualitative terms (7.2) apply Coulomb s law and Newton s law of universal gravitation quantitatively in specific contexts (7.2) define and describe the concepts and units related to electric and gravitational fields (e.g., electric and gravitational potential energy, electric field, gravitational field strength) (7.2, 7.3, 7.4, 7.5, 7.6) determine the net force on, and the resulting motion of, objects and charged particles by collecting, analyzing, and interpreting quantitative data from experiments or computer simulations involving electric and gravitational fields (e.g., calculate the charge on an electron, using experimentally collected data; conduct an experiment to verify Coulomb s law and analyze discrepancies between theoretical and empirical values) (7.2, 7.5, 7.6) describe and explain, in qualitative terms, the electric field that exists inside and on the surface of a charged conductor (e.g., inside and around a coaxial cable) (7.3) explain how the concept of a field developed into a general scientific model, and describe how it affected scientific thinking (e.g., explain how field theory helped scientists understand, on a macro scale, the motion of celestial bodies and, on a micro scale, the motion of particles in electric fields) (7.3) analyze and explain the properties of electric fields and demonstrate how an understanding of these properties can be applied to control or alter the electric field around a conductor (e.g., demonstrate how shielding on electronic equipment or on connecting conductors [coaxial cables] affects electric fields) (7.3) analyze in quantitative terms, and illustrate using field and vector diagrams, the electric field and the electric forces produced by a single point charge, two point charges, and two oppositely charged parallel plates (e.g., analyze, using vector diagrams, the electric force required to balance the gravitational force on an oil drop or on latex spheres between parallel plates) (7.3, 7.5) compare the properties of electric and gravitational fields by describing and illustrating the source and direction of the field in each case (7.3, 7.6) apply quantitatively the concept of electric potential energy in a variety of contexts, and compare the characteristics of electric potential energy with those of gravitational potential energy (7.4, 7.6) Key Terms induced charge separation law of conservation of charge Coulomb s law coulomb field theory field of force electric field electric potential electric potential difference electric potential energy Key Equations q 2 F E kq 1 r2 (7.2) k 9.0 10 9 Nm 2 /C 2 Coulomb s law (7.2) k q1 r2 (7.3) E E kq 1 q 2 (7.4) r V kq 1 r (7.4) E q V for charged plates V r (7.4) e 1.602 10 19 C elementary charge (7.5) q Ne (7.5) MAKE a summary There are many different concepts and equations in this chapter that are closely related to each other. List all the equations in this chapter and show how they are related. Identify which quantities in your equations are vectors, which of your equations apply to point charges, and which equations apply to parallel plates. Give an application for each equation, and discuss any principles or laws from other chapters that are related to them. 376 Chapter 7
Chapter 7 SELF QUIZ Unit 3 Write numbers 1 to 6 in your notebook. Indicate beside each number whether the corresponding statement is true (T) or false (F). If it is false, write a corrected version. 1. If a charge q exerts a force of attraction of magnitude F on a charge 2q, then the charge 2q exerts a force of attraction of magnitude 2F on the charge q. 2. The only difference between electric and gravitational forces is that the electric force is larger. 3. The electric field at the surface of a conductor in static equilibrium is perpendicular to the surface of the conductor. 4. Electric field lines indicate the path that charged particles will follow near another charged object. 5. It is safe to stay in your car during a lightning storm because the tires act as insulators. 6. The acceleration experienced by two small charges as they start from rest and move apart is inversely proportional to the square of the distance between them. Write numbers 7 to 13 in your notebook. Beside each number, write the letter corresponding to the best choice. 7. When comparing the force of attraction between an electron and a proton due to the electric force and gravity, it can be concluded that (a) the gravitational force is a lot stronger (b) the electric force is a lot stronger (c) the two types of forces are the same (d) they cannot be compared (e) the electric force is slightly stronger 8. The electric force on each of two small charged spheres due to the other sphere has a magnitude of F. The charge on one sphere is doubled, and the distance between the centres of the spheres is tripled. The magnitude of the force on each small charged sphere is (a) 2F (c) 2 F 2F (e) 3 9 (b) F 3 (d) F 9 9. The magnitude of the electric field due to a small charged object is 12 N/C at a distance of 3.0 m from the charge. The field 6.0 m away from the charge is (a) 36 N/C (c) 6.0 N/C (e) 3.0 N/C (b) 12 N/C (d) 4.0 N/C 10. Which diagram in Figure 1 represents the net electric field between two charged parallel plates if a neutral conducting sphere is placed between the plates? (a) (b) (c) (d) (e) none of these (a) + + + + + + + + (c) + + + + + + Figure 1 (b) + + + + + + (d) + + + + + + + + + + + + + + + 11. A neutral charged conductor is placed near a positively charged object. The electric field inside the neutral conductor is (a) perpendicular to the surface (b) zero (c) directed toward the negative charge (d) stronger than the electric field at the surface of the conductor (e) none of these 12. A mass has a charge on it. Another small mass with a positive charge is moved away from the first mass, which remains at rest. As the distance increases, what happens to the gravitational potential energy E g and the electric potential energy E E? (a) E g decreases and E E decreases (b) E E either decreases or increases, depending on the unknown sign of charge, and E g decreases (c) E g decreases and E E increases (d) E E decreases or increases, depending on the unknown sign of charge, and E g increases (e) E g increases and E E decreases 13. Two isolated electrons starting from rest move apart. Which of the following statements is true as the distance between the electrons increases? (a) The velocity increases and the acceleration is constant. (b) The velocity increases and the acceleration decreases. (c) The velocity decreases and the acceleration is constant. (d) The velocity increases and the acceleration increases. (e) The velocity is constant and the acceleration is constant. An interactive version of the quiz is available online. GO www.science.nelson.com Electric Charges and Electric Fields 377
Chapter7 REVIEW Understanding Concepts 1. One of the children in Figure 1 is touching an electrostatic generator. (a) Why does the hair of the child touching the electrostatic generator stand on end? (b) Why does the hair of the other child likewise stand on end? (c) Are the children grounded? Explain your answer. Figure 1 Two children holding hands; one is touching an electrostatic generator. 2. In a chart, compare similarities and differences between Newton s law of universal gravitation and Coulomb s law. 3. Coulomb s law may be used to calculate the force between charges only under certain conditions. State the conditions, and explain why they are imposed. 4. Two small, oppositely charged conducting spheres experience a mutual electric force of attraction of magnitude 1.6 10 2 N. What does this magnitude become if each sphere is touched with its identical, neutral mate, the initially neutral spheres are taken far away, and the separation of the two initially charged spheres is doubled? 5. What is the distance between two protons experiencing a mutually repelling force of magnitude 4.0 10 11 N? 6. One model of the structure of the hydrogen atom consists of a stationary proton with an electron moving in a circular path around it. The orbital path has a radius of 5.3 10 11 m. The masses of a proton and an electron are 1.67 10 27 kg and 9.1 10 31 kg, respectively. (a) Calculate the electrostatic force between the electron and the proton. (b) Calculate the gravitational force between them. (c) Which force is mainly responsible for the electron s circular motion? (d) Calculate the speed and period of the electron in its orbit around the proton. 7. Two point charges, +4.0 10 5 C and 1.8 10 5 C, are placed 24 cm apart. What is the force on a third small charge, of magnitude 2.5 10 6 C, if it is placed on the line joining the other two, (a) 12 cm outside the originally given pair of charges, on the side of the negative charge? (b) 12 cm outside the originally given pair of charges, on the side of the positive charge? (c) midway between the originally given pair of charges? 8. Explain why we use a small test charge to detect and measure an electric field. 9. If a stationary charged test particle is free to move in an electric field, in what direction will it begin to travel? 10. Why is it safer to stay inside an automobile during a lightning storm? (Hint: It is not due to the insulating rubber tires.) 11. Three small, negatively charged spheres are located at the vertices of an equilateral triangle. The magnitudes of the charges are equal. Sketch the electric field in the region around this charge distribution, including the space inside the triangle. 12. A small test charge of +1.0 mc experiences an electric force of 6.0 10 6 N to the right. (a) What is the electric field strength at that point? (b) What force would be exerted on a charge of 7.2 10 4 C located at the same point, in place of the test charge? 13. What are the magnitude and direction of the electric field strength 1.5 m to the right of a positive point charge of magnitude 8.0 10 3 C? 14. What are the magnitude and direction of the electric field strength at point Z in Figure 2? q 1 = 2.0 10 5 C q 2 = 8.0 10 6 C 60.0 cm 30.0 cm X Y Z Figure 2 + 378 Chapter 7
Unit 3 15. A ping-pong ball of mass 3.0 10 4 kg hangs from a light thread 1.0 m long, between two vertical parallel plates 10.0 cm apart (Figure 3). When the potential difference across the plates is 420 V, the ball comes to equilibrium 1.0 cm to one side of its original position. 1.0 m 1.0 cm 10.0 cm Figure 3 (a) Calculate the electric field strength between the plates. (b) Calculate the tension in the thread. (c) Calculate the magnitude of the electric force deflecting the ball. (d) Calculate the charge on the ball. 16. If two points have the same electric potential, is it true that no work is required to move a test charge from one point to the other? Does that mean that no force is required, as well? 17. How much work is required to move a charged particle through an electric field if it moves along a path that is always perpendicular to an electric field line? How would the potential change along such a path? 18. A charge of 1.2 10 3 C is fixed at each corner of a rectangle 30.0 cm wide and 40.0 cm long. What are the magnitude and direction of the electric force on each charge? What are the electric field and the electric potential at the centre? 19. Calculate the electric potential 0.50 m from a 4.5 10 4 C point charge. 20. A 1.0 10 6 C test charge is 40.0 cm from a 3.2 10 3 C charged sphere. How much work was required to move it there from a point 1.0 10 2 cm away from the sphere? 21. How much kinetic energy is gained by an electron that is allowed to move freely through a potential difference of 2.5 10 4 V? 22. How much work must be done to bring two protons, an infinite distance apart, to within 1.0 10 15 m of each other, a distance comparable to the width of an atomic nucleus? (The work required, while small, is enormous in relation to the typical kinetic energies of particles in a school lab. This shows why particle accelerators are needed.) 23. What is the magnitude of the electric field between two large parallel plates 2.0 cm apart if a potential difference of 450 V is maintained between them? 24. What potential difference between two parallel plates, at a separation of 8.0 cm, will produce an electric field strength of magnitude 2.5 10 3 N/C? 25. Most experiments in atomic physics are performed in a vacuum. Discuss the appropriateness of performing the Millikan oil drop experiment in a vacuum. 26. Assume that a single, isolated electron is fixed at ground level. How far above it, vertically, would another electron have to be so that its mass would be supported against gravitation by the force of electrostatic repulsion between them? 27. An oil droplet of mass 2.6 10 15 kg, suspended between two parallel plates 0.50 cm apart, remains stationary when the potential difference between the plates is 270 V. What is the charge on the oil droplet? How many excess or deficit electrons does it have? 28. A metallic table tennis ball of mass 0.10 g has a charge of 5.0 10 6 C. What potential difference, across a large parallel plate apparatus of separation 25 cm, would be required to keep the ball stationary? 29. Calculate the electric potential and the magnitude of the electric field at a point 0.40 m from a small sphere with an excess of 1.0 10 12 electrons. 30. An electron is released from rest at the negative plate in a parallel plate apparatus kept under vacuum and maintained at a potential difference of 5.0 10 2 V. With what speed does the electron collide with the positive plate? 31. What potential difference would accelerate a helium nucleus from rest to a kinetic energy of 1.9 10 15 J? (For a helium nucleus, q = +2e.) 32. An electron with a speed of 5.0 10 6 m/s is injected into a parallel plate apparatus, in a vacuum, through a hole in the positive plate. The electron collides with the negative plate at 1.0 10 6 m/s. What is the potential difference between the plates? Electric Charges and Electric Fields 379
33. Four parallel plates are connected in a vacuum as in Figure 4. An electron, essentially at rest, drifts into the hole in plate X and is accelerated to the right. The vertical motion of the electron continues to be negligible. The electron passes through holes W and Y, then continues moving toward plate Z. Using the information given in the diagram, calculate (a) the speed of the electron at hole W (b) the distance from plate Z to the point at which the electron changes direction (c) the speed of the electron when it arrives back at plate X 4.0 cm 4.0 cm 4.0 cm X W Y Z 3.0 10 2 V 5.0 10 2 V Figure 4 34. Two a particles, separated by an enormous distance, approach each other. Each has an initial speed of 3.0 10 6 m/s. Calculate their minimum separation, assuming no deflection from their original path. 35. An electron enters a parallel plate apparatus 10.0 cm long and 2.0 cm wide, moving horizontally at 8.0 10 7 m/s, as in Figure 5. The potential difference between the plates is 6.0 10 2 V. Calculate (a) the vertical deflection of the electron from its original path (b) the velocity with which the electron leaves the parallel plate apparatus Build your own versorium. Charge several objects and try your device. Also try it on an operating television screen. Examine the effect of turning the television off and on while keeping your versorium near the screen. Write a short report on your findings. 37. Design an experiment that can be used to test the properties of conductors in electric fields. You may use either or both of the following as is convenient: a probe that can detect electric fields; a charged neutral object attached to an insulating rod. 38. The electric field of Earth always points toward Earth. The magnitude of the field strength varies locally from as low as 100 N/C in fair weather to 20 000 N/C in a thunderstorm. A field mill measures the local electric field strength. In this device, the lower plate, parallel to the ground, is connected to Earth through an ammeter. The upper plate can be moved horizontally, and it, too, is connected to Earth. (a) When the mill is arranged as in Figure 6(a), what kind of charge is on the surface of Earth and on each plate? (Hint: Examine the field lines.) (b) What will the ammeter show when you move the upper plate rapidly over the lower plate, as in Figure 6(b)? Explain your answer. (c) What will the ammeter show when the upper plate is quickly pushed away from the lower plate? Explain your answer. (d) What will the ammeter show if the upper plate is attached to a motor and is rotated in a circle, passing periodically over the lower plate? (e) How is the ammeter reading related to the magnitude of the electric field of Earth? (a) (b) 8.0 10 7 m/s 10.0 cm 2.0 cm + 6.0 10 2 V Figure 5 Applying Inquiry Skills 36. A versorium is a device that detects the presence of an electric charge on an object. The device consists of any convenient material (e.g., a straw or a long strip of folded paper) balanced on a needle or tack with some sort of base, such as modelling clay. The straw will rotate if a charged object is brought close to one end. A Figure 6 A field mill is used to detect the magnitude of Earth s electric field. 39. You place a circular conductor near a charged plate in oil with suspended rayon fibres, as in Figure 7. The configuration assumed by the fibres indicates the geometry of the electric field. Explain what conclusions this demonstration suggests regarding the nature of electric fields (a) near the surfaces of conductors and (b) inside conductors. A 380 Chapter 7
Appendix D 7. 2.4 m 8. (a) and (b) 0.34 9. (a) 3.5 10 5 J (c) 1.2 10 3 kg (d) 0.61 10. (a) 2.0 10 2 J (b) 1.8 10 2 J (c) 2.0 10 2 J Section 4.5 Questions, pp. 218 219 5. 0.042 m 6. 1.8 N 7. 229 N 8. 2.0 10 2 m 9. (a) 0.962 [down]; 3.33 m/s 2 [down] (b) 0.151 m 10. 6.37 m/s 11. (a) 91 N/m (b) 0.40 J 12. 2.0 10 1 N/m 13. 0.38 m 14. 0.14 m 15. (b) 0.10 m (c) 1.0 10 3 N/m (d) 9.1 m/s 17. 6.4 10 4 N/m 18. 7.8 10 2 m Chapter 4 Self Quiz, p. 225 1. T 9. F 2. F 10. (c) 3. F 11. (c) 4. F 12. (e) 5. T 13. (d) 6. T 14. (e) 7. T 15. (a) 8. F 16. (d) Chapter 4 Review, pp. 226 229 9. (a) 49.1 J (b) 49.1 J 10. 32 11. (a) 1.29 10 3 J (b) 1.29 10 3 J (c) 8.14 10 3 J 12. 5.6 m 13. 8.90 m/s 14. (a) 2.5 10 12 J (b) 3 10 3 people 15. (a) 2.9 10 2 J (b) 2.9 10 2 J (c) 2.9 10 2 J 16. (a) 9.2 m/s 17. (a) 29 m/s (b) 29 m/s 18. (a) 2.3 10 2 N; 1.3 10 2 N (b) 1.4 m/s (c) 2.0 10 2 J 19. 1.0 10 4 m/s 20. 8.40 m/s 21. 42 J 22. (a) 239 N/m (b) 35.9 N (c) 2.69 J; 10.8 J 23. 0.32 m 24. 0.21 kg 25. (a) 0.053 J (b) 0.50 m/s (c) 0.33 m/s (d) 0.053 J 32. (a) 19.8 m/s (b) 20.4 m/s 34. (a) 1.12 mg (b) 1.12 mgy 35. 0.079 m 36. 0.019 J 37. 2.0 m 38. 8.4 m/s 39. 12 units Chapter 5 Section 5.1 Questions, p. 238 3. (a) 77 Ns [E] (b) 1.1 Ns [forward] (c) 3.5 10 2 Ns [down] (d) about 0.12 Ns [S] 4. 2.4 m/s [W] 5. 1.6 10 4 N [W] 6. (a) 0.66 kgm/s [left] (b) 0.66 Ns [left] 7. (a) 1.1 kgm/s [backward] (b) 1.1 Ns [backward] (c) 0.45 N [backward] 8. 1.8 m/s [backward] 9. 3.0 m/s [N] 10. (a) 11 kgm/s [up] (b) 1.7 10 3 N [up] Section 5.2 Questions, pp. 244 245 5. 1.9 m/s in the original direction of cart s velocity 6. 5.8 m/s [N] 7. 4.95 m/s [E] 8. (a) 2.34 10 4 kgm/s [W]; 2.34 10 4 kgm/s [E] (c) zero 9. 82 kg 10. 0 m/s Section 5.3 Questions, p. 253 4. 3.1 m/s forward and 0.4 m/s backward 5. m 2 6. 11 m/s 7. (b) (m m v M) (d) h 2g (m m2 v 2 M) 2 (e) v (m m M) 2gh (f) 6.6 10 2 m/s Section 5.4 Questions, pp. 258 259 2. 66 from the initial direction of the neutron s velocity 3. 55 kg 4. 1.7 m/s [47 S of E] 5. (a) 0.22 kg (b) 1.3 10 4 J Chapter 5 Self Quiz, pp. 267 268 1. F 9. T 17. (b) 2. T 10. F 18. (c) 3. F 11. (e) 19. (a) 4. F 12. (d) 20. (d) 5. T 13. (d) 21. (a) 6. T 14. (d) 22. (d) 7. F 15. (e) 8. F 16. (d) Chapter 5 Review, pp. 269 271 7. 8.1 10 2 kgm/s; 7.9 10 2 kgm/s 8. 25 m/s 9. 3.2 10 5 N [E] 10. (a) 1.7 Ns [horizontally] (b) 28 m/s [horizontally] 11. 1.00 m/s 12. 0.619 km/s 13. 1.90 10 2 m/s [toward Jupiter] 15. 0.08 m/s [N] for the 253-g car; 1.88 m/s [N] for the 232-g car 16. (b) 3.0 m/s; 4.0 m/s 17. 0.561 18. 3.00 m/s [W] 19. (a) 2.3 m/s (b) 2.5 m/s 20. (a) 0.80 m/s (b) 7.8 N 21. 3.4 10 3 km/h 22. 2.0 m/s [22 S of W] (See Table 1 below.) 31. (a) v 1 v m1 m2) l(m 1 m ; 2 2mv v 2 (m 1 m l 2) (b) v 1 0; v 2 v l (c) v 1 v l; v 2 2v l v l (d) v 1 v l; v 2 2m m 1 2 32. 3.4 10 2 m Chapter 6 Section 6.1 Questions, p. 277 2. (a) 3.99 10 3 N [toward Earth s centre] (b) 1.77 m/s 2 [toward Earth s centre] 3. 7.3 10 2 N/kg [toward Earth s centre] 4. (a) 3.0 10 6 m (b) 2.8 10 3 N 5. 11.2 N/kg 6. (a) 0.61 m/s 2 [toward Earth s centre] Table 1 Data for Question 22 (Chapter 5 Review) Component 1 2 3 Mass 2.0 kg 3.0 kg 4.0 kg (b) 2.9 10 2 N [toward Earth s centre] 7. (a) 2.6 10 3 km (b) 0.24 N 8. 0.75 r E Section 6.2 Questions, p. 284 4. 1.8 10 8 s 5. 1.6 times 6. 4.0 10 1 h 7. 9.2 10 6 m Section 6.3 Questions, p. 294 3. (a) 1.7 10 10 J (b) 5.4 10 3 m/s 4. 1.4 10 9 J 5. (a) 1.18 10 11 J (b) 5.88 10 10 J (c) 5.88 10 10 J (d) 7.74 10 3 m/s 6. (a) 3.03 10 10 J (b) 1.52 10 10 J (c) 1.52 10 10 J (d) 94% 7. (a) 6.18 10 5 m/s (b) 4.37 10 4 m/s 8. 1.68 10 3 m/s 9. 5.22 M S 11. (a) 8.86 mm Chapter 6 Self Quiz, pp. 298 299 1. T 10. F 19. (e) 2. T 11. (a) 20. (c) 3. T 12. (d) 21. (c) 4. T 13. (c) 22. (d) 5. F 14. (d) 23. (c) 6. F 15. (a) 24. (c) 7. F 16. (c) 25. (a) 8. F 17. (a) 26. (e) 9. T 18. (d) Chapter 6 Review, pp. 300 301 3. 5.1 10 4 km 4. 0.318 N/kg 5. 4.23 10 3 N/kg [1.26 from the spacecraft-to-earth line] 6. 3.3 10 23 kg 7. (a) 1.22 r E (b) 0.22 r E 8. (a) 3.1 10 5 km (b) 2.1 d 9. 1.08 10 11 m 10. (a) 1.21 10 4 km (b) 9.92 10 7 J 11. (a) 2.64 10 3 m/s (b) 8.17 10 9 J 12. (a) 3.99 10 8 J (b) +3.99 10 8 J (c) 2.82 10 2 m/s 13. 5.33 10 33 J Final Velocity 1.5 m/s [N] 2.5 m/s [E] 2.0 m/s [22 S of W] A B C D Answers 783
14. (a) 4.23 km/s (b) 2.37 km/s 15. (a) 2.3 10 8 m/s (b) 77% of the speed of light 16. (a) 1.1 10 26 kg 17. (a) 1.7 10 5 m/s 19. 3.2 10 14 m 20. (a) and (b) 1.48 10 14 m 3 /s 2 (c) 1.49 10 14 m 3 /s 2, yes (d) 0.557 d, 1.48 10 14 m 3 /s 2 ; 7.52 10 4 km, 1.48 10 14 m 3 /s 2 ; 8.67 d, 1.48 10 14 m 3 /s 2 ; 5.84 10 5 km, 1.48 10 14 m 3 /s 2 ; See also completed Table 1 below. 22. (a) 1.6 10 3 kg (b) 1.0 10 11 J (c) 1.2 10 4 m/s (d) 5.0 10 3 m/s 24. 40 min 25. 7.9 10 7 s 26. E kt 4 3 Unit 2 Self Quiz, pp. 304 306 1. F 11. F 21. (e) 2. T 12. F 22. (d) 3. F 13. T 23. (c) 4. F 14. F 24. (a) 5. T 15. (c) 25. (c) 6. F 16. (c) 26. (a) 7. F 17. (a) 27. (d) 8. F 18. (d) 28. (d) 9. F 19. (e) 10. F 20. (c) 29. (a) Galileo Galilei (b) Johannes Kepler (c) James Prescott Joule (d) Tycho Brahe (e) Robert Hooke (f) Karl Schwartzschild 30. (a) work (b) force constant of a spring (c) impulse (d) force (e) thermal energy (f) mass of Earth 31. completely inelastic collision; equals; completely inelastic collision 32. zero 33. singularity; Schwartzschild radius 34. (a) A (b) E 35. (e), (g), (h), (j), (k), (d), (b), (a), (m) Unit 2 Review, pp. 307 311 9. 11 m 10. (a) 1.0 10 1 J (b) 2.0 10 1 J (c) 2.0 m/s [W] 11. (a) 10.0 kg (b) 2.50 10 3 N [E] 12. 71 kgm/s 13. 0.60 m 14. (a) 1.00 10 2 J (b) 8.00 10 2 J (c) 0.671 m/s 17. 31 N 18. 3.8 kg 19. (a) 2.7 J (b) 0.60 m/s [W] (c) 1.6 J (d) 2.2 10 2 N/m 20. 0.20 m 21. (a) 0.42 m/s [left] (b) 0.87 m/s [left] (c) 0.38 m/s [left] 22. 2.8 s 23. 1.6 kg 24. 2 3 m 25. 11 m/s [37 S of E] 26. (a) 9.1 m/s [26 N of W] (b) 31% 27. 4.9 m/s [12 W of N] 31. 8.06 m/s 2 32. 0.69 g 33. 5.95 10 3 N/kg [toward the centre of the Sun] 34. (a) 6.16 a (b) 1.62 10 4 m/s 35. (a) 1.74 10 14 m 3 /s 2 (b) 1.09 10 8 m (c) 8.42 10 4 km 36. 1.90 10 27 kg 37. (a) 4.23 10 3 m/s (b) 2.12 10 3 m/s (c) 3.67 10 3 m/s (d) 2.39 10 19 J Table 1 Data of Several Moons of the Planet Uranus (for question 20 Chapter 6 Review) Moon Discovery r average (km) T (Earth days) C U (m 3 /s 2 ) Ophelia Voyager2 (1986) 5.38 10 4 0.375 1.48 10 14 Desdemona Voyager2 (1986) 6.27 10 4 0.475 1.48 10 14 Juliet Voyager2 (1986) 6.44 10 4 0.492 1.48 10 14 Portia Voyager2 (1986) 6.61 10 4 0.512 1.48 10 14 Rosalind Voyager2 (1986) 6.99 10 4 0.556 1.48 10 14 Belinda Voyager2 (1986) 7.52 10 4 0.621 1.48 10 14 Titania Herschel (1787) 4.36 10 5 8.66 1.48 10 14 Oberon Herschel (1787) 5.85 10 5 13.46 1.48 10 14 38. (a) 2.4 10 2 m 41. (a) 2.8 10 2 N/m 43. (a) 2.3 10 2 J; 2.1 10 2 J (b) 8.5 10 3 N 46. (a) 2.9 10 41 kg (b) 1.5 10 11 stars 47. 0.26 m/s [right] for both balls 48. (a) 0.80 m/s [N] (b) 0.64 J (c) 1.6 N [S] (d) 4.8 10 2 J 49. 3.4 10 2 m 50. (a) 744 N/m; 15.3 kg (c) 2.3 kg 52. 2.4 10 2 N Chapter 7 Section 7.2 Questions, pp. 335 336 3. 4.5 10 2 N 4. (a) 2.67 10 14 N (b) 3.6 10 4 N (d) 3.6 10 4 N, 3.6 10 3 m/s 2 (e) 3.6 10 4 N, 3.6 10 3 m/s 2 5. 1.3 10 4 C 6. 3.9 10 6 C 7. 0.20 N [right], 1.94 N [right], 2.14 N [left] 8. 2.2 N, 1.4 N 9. on the line joining them, 0.67 m from the 1.6 10 5 C 10. 55 N/m 13. (a) 5.7 10 13 C Section 7.4 Questions, pp. 358 359 1. 4.3 10 9 C 2. 0.40 7. 4.0 10 5 m 8. (a) 3.6 10 2 J (b) 1.0 10 4 V, 3.3 10 4 V, 2.8 10 3 V 9. (a) 1.1 10 6 C (b) 7.1 10 5 N/C Section 7.5 Questions, p. 364 1. (a) 1.1 10 14 (b) 0, 1.1 10 5 V (c) 1.2 N 2. (b) 2.9 10 8 3. (a) 1.9 10 18 C (b) 12 4. 1.7 10 15 C 5. (a) 8.4 (b) 0.50 N 8. (a) 4.5 10 5 C (c) 1.6 10 18 kg Section 7.6 Questions, p. 371 1. (a) 2.1 10 7 m/s (d) 4.8 10 5 m/s 2. (a) 1.0 10 18 J (b) 1.9 10 6 m/s (c) 1.6 cm 3. (a) 4.5 10 6 m 4. 7.7 10 12 J 5. (a) 1.8 10 3 m (b) 2.7 10 5 m/s (c) 5.1 Chapter 7 Self Quiz, p. 377 1. F 6. T 11. (b) 2. F 7. (b) 12. (b) 3. T 8. (e) 13. (b) 4. F 9. (e) 5. F 10. (e) Chapter 7 Review, pp. 378 381 4. 1.0 10 3 N 5. 2.4 10 9 m 6. (a) 8.2 10 8 N (b) 3.6 10 47 N (d) 2.2 10 6 m/s, 1.5 10 16 s 7. (a) 21 N away from negative charge (b) 59 N toward positive charge (c) 91 N toward positive charge 12. (a) 6.0 N/C [right] (b) 4.3 10 3 N [left] 13. 3.2 10 7 N/C [right] 14. 5.8 10 5 N/C [right] 15. (a) 4.2 10 3 N/C (b) 2.9 10 3 N (c) 2.9 10 5 N (d) 6.9 10 9 C 18. 2.1 10 5 N [55 up from the left], 0, 1.7 10 8 V 19. 8.1 10 6 V 20. 43 J 21. 4.0 10 15 J 22. 2.3 10 13 J 23. 2.3 10 4 N/C 24. 2.0 10 2 V 26. 5.1 m 27. 4.7 10 19 C, 3 electrons 28. 49 V 29. 3.6 10 3 V, 9.0 10 3 N/C [toward sphere] 30. 1.3 10 7 m/s 31. 5.9 10 3 V 32. 68 V 33. (a) 1.0 10 7 m/s (b) 1.6 cm, to the left (c) 0 m/s 34. 1.6 10 14 m 35. (a) 0.41 cm (b) 8.0 10 7 m/s [4.7 up from the right] 45. (a) 1.0 mm (b) 1.5 10 3 m Chapter 8 Section 8.2 Questions, pp. 402 403 2. 1.5 10 12 N [up] 3. 8.4 10 4 m 784 Appendix D