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Name: ______________________________________________ Period: _______ Physics Unit II: Forces Subunit C: Inverse-Square Laws Equations Variables, Constants, Units Solar System Data Name Mass (kg) Radius (m) Distance from Sun (m) Sun 1.99 x 1030 696 x 106 ---- Mercury 3.30 x 10 2.44 x 10 5.79 x 10 Venus 4.87 x 1024 6.05 x 106 1.08 x 1011 Earth 5.98 x 1024 6.37 x 106 1.50 x 1011 Mars 6.42 x 1023 3.40 x 106 2.28 x 1011 Jupiter 1.90 x 1027 71.5 x 106 7.78 x 1011 Saturn 5.69 x 1026 60.3 x 106 1.43 x 1012 Uranus 8.66 x 1025 25.6 x 106 2.87 x 1012 Neptune 1.03 x 1026 24.8 x 106 4.50 x 1012 Pluto 1.50 x 1022 1.15 x 106 5.91 x 1012 23 6 10 Earth’s Moon Mass 7.40 x 1022 kg Radius 1.75 x 106 m Distance from Earth 3.80 x 108 m Elementary Particles Object Mass (kg) Electrical Charge (C) Proton 1.672 x 10-27 +1.602 x 10-19 Neutron 1.674 x 10-27 0 Electron 9.11 x 10-31 -1.602 x 10-19 Unit II: Forces Subunit D: Inverse-Square Laws Objectives By the time we finish the labs and related materials in this unit, you should be able to: 1. Use Newton’s Law of Universal Gravitation to describe the relationships between the Gravitational Force, Mass, and Distance between any two objects. 2. Use Newton’s Law of Universal Gravitation to calculate the gravitational force between objects and gravitational field strength of a planet. 3. Using Newton’s Law of Universal Gravitation and previous equations, calculate gravitational field strengths and orbital velocities. 4. Use Coulomb’s Law to describe the relationships between the Electrical Force, Mass, and Distance between any two objects. 5. Use Coulomb’s Law to calculate the electrical force. 6. Explain the difference between the force between two like charges and the force between two unlike charges. 7. List the ways that charge can be transferred, and differentiate between conductors and insulators. 8. Draw graphs of inverse square functions. 9. Draw force diagrams for objects experiencing gravitational and electrical forces. 10. Draw field lines that show the direction of the force on a test mass or charge. Unit II-D: Inverse-Square Laws Worksheet 1 1. The universal part of Newton's law of universal gravitation means that A) the amount of gravitational forces is the same for all objects. B) the acceleration caused by gravity is the same for all objects. C) the force of gravity acts between all objects. 2. According to Newton's gravitation law, the force of gravitational attraction between a planet and an object located upon the planet's surface depends upon _____. Choose all that apply. A) the radius of the planet B) the mass of the planet C) the mass of the object D) the volume of the object E) ... nonsense! None of these variables affect the force of gravity. 3. The more massive that an object is, the ______ (more, less) that the object will be attracted to Earth. 4. The more massive the Earth is, the ______ (more, less) that another object will be attracted to Earth. 5. The greater that Earth's radius is, the ______ (more, less) that another object will be attracted to Earth. 6. In the mathematical form of Newton's law of universal gravitation, the symbol G stands for A) gravity B) the acceleration of gravity C) the gravitational constant 7. Orbiting astronauts on the space shuttle do not have weight in space because A) there is no gravity in space B) there is no air resistance in space C) there are no scales in space D) the food is terrible and they work all the time E) ... nonsense! The astronauts do have weight in space. TRUE or FALSE: 8. _______ The value of G (in the equation above) is an enormously large number; that explains why (at least in part) the force of gravitational attraction between the Sun and the very distant Earth is such a large number. 8. _______ Two lab partners attract each other with a gravitational force. However, it is impossible to calculate such a force since it is only an unproven theory. 10. _______The notion that any two objects attract each other gravitationally is a theory. There is no empirical evidence for such a notion. 11. ______ Gravity is zero on the way to the moon. Astronauts are weightless in the shuttle. Use Newton's gravitational law in a conceptual manner in order to fill in the following blanks. 12. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two objects' centers is doubled, then the new force of attraction is ______ N. 13. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two objects' centers is tripled, then the new force of attraction is ______ N. 14. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two objects' centers is halved, then the new force of attraction is ______ N. 15. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two objects' centers is decreased by a factor of three, then the new force of attraction is ______ N. 16. Two objects gravitationally attract with a force of 18.0 N. If the distance between their centers is decreased by a factor of four, then the new force of attraction is ______ N. 17. Two objects gravitationally attract with a force of 18.0 N. If the mass of one of the objects is doubled and the distance between their centers is doubled, then the new force of attraction is ______ N. 18. Two objects gravitationally attract with a force of 18.0 N. If the masses of both of the objects are doubled and the distance between their centers is doubled, then the new force of attraction is ______ N. 19. Two objects gravitationally attract with a force of 18.0 N. If the masses of both of the objects are tripled and the distance between the two objects' centers is doubled, then the new force of attraction is ______ N. Unit II-D: Inverse-Square Laws Worksheet 2 1. Calculate Earth’s gravitational force on a space shuttle with a mass of 9.48 x 104 kg: A) at the Earth’s surface. B) 6.37 x 106 m away from the Earth’s surface. How many times smaller is it here? C) 1.274 x 107 m away from the Earth’s surface. How many times smaller is it here? 2. John claims that there is a strong attraction force between him and a fellow student, Jan. If John’s mass is 75 kg, Jan’s is 60 kg, and they sit 0.5 m apart, how much gravitational force attracts these two students? 3. A) Using Newton’s law of Universal Gravitation, find the force of attraction between you (say you weigh about 150 lbs., which would give you a mass of 68 kg) and the Earth. B) Now find the force of gravity on you using Fg = mg. How does this compare to your answer from part A? 4. A) Find the gravitational force between the Earth and the Sun. B) How much would the Earth “weigh” on the surface of the Sun? (remember r = total distance from center to center!) 5. A) Find the gravitational force between the Earth and the moon. B) How much would the moon “weigh” on the surface of the Earth? 6. Mercury is very close to the Sun, but is very small. Jupiter is far from the Sun, but is very large. Calculate the Sun’s gravitational force on each to determine which is greater. 7. An astronaut stands on a newly discovered planet, whose mass is unknown. He pulls his trusty bathroom scale out of his rover, and finds that he weighs 1200 N. From his orbit, he approximated the radius of the new planet to be 12 x 106 m. If he has a mass of 100 kg when fully suited, what is the mass of this new planet? Unit II-D: Inverse-Square Laws Worksheet 3 1. Calculate the strength of Earth’s gravitational field at its surface using Newton’s laws. 2. The asteroid Ceres has a mass of 7.0 x 1020 kg and a radius of 500 km. Find the gravitational field strength at the surface of Ceres. 3. One planet whose radius is 1.2 x 107 m has a gravitational acceleration of 18 m/s2. What is the mass of this planet? 4.Calculate the gravitational field strength at the surface of each object in the solar system listed in the table below. Solar System Data Name Mass (kg) Radius (m) Sun 1.99 x 1030 696 x 106 Mercury 3.30 x 1023 2.44 x 106 Gravitational Field Strength (N/kg or m/s2) Venus 4.87 x 1024 6.05 x 106 Earth 5.97 x 1024 6.38 x 106 Mars 6.42 x 1023 3.40 x 106 Jupiter 1.90 x 1027 71.5 x 106 Saturn 5.69 x 1026 60.3 x 106 Uranus 8.66 x 1025 25.6 x 106 Neptune 1.03 x 1026 24.8 x 106 Pluto 1.50 x 1022 1.15 x 106 Unit II-D: Inverse-Square Laws Worksheet 4 Vocabulary Matching. A) Charge B) Charging by conduction C) Charging by induction D) Conductors E) Conservation of charge F) Coulomb G) Electrostatics H) Elementary charge I) Grounding J) Insulators K) Neutral 1. _______ Materials through which charges will not move easily. 2. _______ The study of electrical charges that can be collected and held in one place. 3. _______ Touching an object to Earth to eliminate excess charge. 4. _______ The magnitude of the charge of a single electron. 5. _______ Separating the charges in an object without touching the object. 6. _______ Materials such as metals that allow charges to move about easily. 7. _______ An object that has positive and negative charges exactly balanced. 8. _______ Giving a neutral body a charge by touching it with a charged body. 9. _______ The net electrical charge in an isolated system never changes. 10. _______ The standard metric unit of charge. 11. _______ The property of an object that causes electrical forces. Multiple Choice. 12. An electrically neutral atom is an atom which A) does not have any protons or electrons B) has more neutrons than the sum of all its protons and electrons C) has a balance of protons and electrons (the same number of each) D) has a balance of neutrons and electrons (the same number of each) E) has a balance of protons, electrons and neutrons (the same number of each) 13. An electrically charged atom (sometimes referred to as an ion) can be distinguished from an electrically neutral atom in that the charged atom (ion) A) does not have any neutrons B) has lost one or more of its neutrons C) either has a proton or an electron present somewhere within it D) has a different number of neutrons than the sum of its electrons and protons E) has an imbalance of protons and electrons (unequal numbers of these) 5. TRUE or FALSE: Conductors cannot be charged by frictional rubbing. Explain your answer. 6. A balloon is charged by rubbing it with animal fur. It is then pressed against a wooden cabinet. The balloon and cabinet attract, seeming to defy the force of gravity. This attraction is best explained by ____. a. induction charging of the wood b. frictional charging of the wood c. polarization of wood molecules d. polarization of balloon molecules 14. A balloon is charged by rubbing it with animal fur. It is then pressed against a wooden cabinet. The balloon and cabinet attract, seeming to defy the force of gravity. 7. The above effect (in question # 6) is most often noticed of ____. a. conductors b. insulators c. charged objects This attraction is best explained by A) induction charging of the wood C) polarization of wood molecules Physics Classroom, 2009 of balloon molecules B) frictional charging of the wood D)© The polarization Page 7 15. Complete the following statements to illustrate your understanding of the three types of charge interactions: A) Oppositely-charged objects __________________________ B) Like-charged objects ____________________________ C) A charged object and a neutral object ________________________________ Staticwill Electricity 8. A negatively balloon is brought near a neutral conducting 16. A negatively charged balloon is brought nearcharged a neutral conducting sphere sphere as shown in the diagram at the right. The presence of the as shown in the diagram at the right. Thecharged presence of the charged balloon will balloon will cause something to happen in the sphere. Static Electricity Which of the following would you expect to occur? N ame: Select all that cause something to happen in the Nsphere. Which of the following would you apply. Static Electricity ame: a. Electrons in the sphere will move to the balloon. expect to occur? Select all that apply. b. Protons in the sphere will move to and the balloon. I nsulators, Conductors Polarization c. Electrons in the sphere will move to the left side. A) Electrons inI the sphere will move to the balloon. the sphere will move to the right Classroom: side. Lesson 1d.of Electrons the Staticin Electricity chapter at The Physics nsulators, ConductorsRead andfrom Polarization Protons in the sphere will move to the left side. http://www.physicsclassroom.com/Class/estatics/u8l1d.html B) from Protons spherechapter willatmove toClassroom: the e.f.balloon. Read Lesson 1 ofin the the Static Electricity The Physics Protons in the sphere will move to the right side. http://www.physicsclassroom.com/Class/estatics/u8l1e.html C) Electronshttp://www.physicsclassroom.com/Class/estatics/u8l1d.html in the sphere will Mmove to9.the left side. The process of inducing the movement of charge OP Connection: Static Electricity: preface to sublevels 5 - 7 within the sphere (referring to question # 8) causes http://www.physicsclassroom.com/Class/estatics/u8l1e.html positive and side. negative charge to be separated. This is known as ____. D) Electrons in the sphere will move to the right M OP Connection: Static Electricity: preface to sublevels 5-7 a. grounding b. charging c. polarization d. induction 1. Insulators are different than conductors in that insulators ____. E) Protons in the sphere will move tonotthe left side. a. do contain electrons or protons b. do not contain any charge 1. Insulators are different than conductors in that insulatorsc.____. Charged rods are placed a neutral conducting sphere, have a 10. weaker affinityrubber for electrons d. near do not allow charge to freely movecausing a redistribution of charge do not containin electrons protons b. domove not contain charge on the spheres. F)a.Protons the orsphere will toanythe right side.Which of the diagrams below depict the proper distribution of charge on the c. have a weaker affinity for electrons 2. d. do not chargethrough to freely moveList spheres? all thatcan apply. 2. allow Materials which electrons move readily are classified as _____. a. conductors b. insulators c. semi-conductors Materials through which electrons can move readily are classified as _____. a. conductors b. insulators c. 3. semi-conductors The diagram at the right shows a metal sphere attached to the top of an insulating stand. The metal sphere contains an excess of electrons and is thus charged. A student holds various objects in her The diagram at the right shows a metal sphere attached to the and top of an insulating stand. metalWhich of the following objects below would allow charge hand touches the object to theThe sphere. sphere contains an excess of electrons and is thus charged. A student holds in the her object to the sphere? to throw it when thevarious studentobjects touches 11. In the above situation (question # 10), the conducting sphere is ____. List all that apply. hand and touches the object to the sphere. Which of the a. following a plasticobjects straw below would allow charge b. a piece of paper a. charged b. polarized c. uncharged (neutral) to throw it when the student touches the object to the sphere? c. a steel house key d. a metal paper clip a. a plastic straw b. a piece e. of paper a strip of aluminum foil c. a steel house key d. a metal paper clip12. A physics teacher fills a buret with water and opens the valve, producing a steady stream of water falling vertically to the sink. e. a strip of aluminum foil 4. Consider these two spheres. They have both Then the teacher rubs a rubber balloon with animal fur and holds been charged. In one case the charge is isolated The stream is observed to deflect from its usual 4. Consider these two spheres. They have both it near theinstream. three distinct locations; in the other case, the towards the balloon. Explain what is causing the been charged. In one case the charge is isolatedvertical flow excess charge is even distributed about the of the water stream. in three distinct locations; in the other case, thedeflectionsurface of the sphere. Which one of these spheres excess charge is even distributed about the is made of an insulating material and which is surface of the sphere. Which one of these spheres made of a conducting material? Label which is is made of an insulating material and which is which and support your answer with an made of a conducting material? Label which is explanation. which and support your answer with an explanation. 17. Consider these two spheres. They have both been charged. In one case the charge is 3.isolated in three distinct locations; in the other case, the excess charge is evenly distributed about the surface of the sphere. Which one of these spheres is made of an insulating material and which is made of a conducting material? Label which is which and support your answer with an explanation. 13. A physics teacher charges a balloon negatively by rubbing it with animal fur. The balloon is TRUE or FALSE: then placed next to a wooden cabinet and adheres to the whatrubbing. is Conductors cannot be cabinet. charged Explain by frictional TRUE or FALSE: happening at the particle level to cause such a Explain your answer. Conductors cannot be charged by frictional rubbing. gravity-defying phenomenon. Add to the blownup view of the diagram to assist in your Explain your answer. explanation. 5. 5. 6. 6. A balloon is charged by rubbing it with animal fur. It is then pressed against a wooden cabinet. The balloon and cabinet attract, seeming to defy the force of A balloon is charged by rubbing it with animal fur. It is gravity. then pressed a is best explained by ____. Thisagainst attraction wooden cabinet. The balloon and cabinet attract, seeming defy the charging force of of the wood a. to induction b. frictional charging of the wood gravity. This attraction is best explained by ____. c. polarization of wood molecules d. polarization of balloon molecules a. induction charging of the wood b. frictional charging of the wood c. polarization of wood molecules d. polarization balloon molecules 7. ofThe above question # 6) is most ©effect The (in Physics Classroom, 2009often noticed of ____. a. conductors b. insulators c. charged objects The above effect (in question # 6) is most often noticed of ____. a. conductors b. insulators c. charged objects 18. Considering the previous question, why is your car a SAFE place to be during a thunderstorm? (and don’t give me the rubber wheels excuse!!!) 7. © The Physics Classroom, 2009 © The Physics Classroom, 2009 Page 8 Page 7 Page 7 Unit II-D: Inverse-Square Laws Worksheet 5 Alteration in the Quantity of Charge 1. Two charged objects have a repulsive force of .080 N. If the charge of one of the objects is doubled, then what is the new force? 2. Two charged objects have a repulsive force of .080 N. If the charge of both of the objects is doubled, then what is the new force? Alteration in the Distance between Charged Objects 3. Two charged objects have a repulsive force of .080 N. If the distance separating the objects is doubled, then what is the new force? 4. Two charged objects have a repulsive force of .080 N. If the distance separating the objects is halved, then what is the new force? Alteration in both the Quantity of Charge and the Distance 5. Two charged objects have a repulsive force of .080 N. If the charge of one of the objects is doubled, and the distance separating the objects is doubled, then what is the new force? 6. Two charged objects have a repulsive force of .080 N. If the charge of both of the objects is doubled and the distance separating the objects is doubled, then what is the new force? 7. Two charged objects have an attractive force of .080 N. If the charge of one of the objects is halved and the distance separating the objects is doubled, then what is the new force? 8. A balloon with a charge of 4.0 x 10-5 C is held a distance of 0.10 m from a second balloon having the same charge. Calculate the magnitude of the repulsive force. 9. Calculate the electrical force (in Newtons) exerted between a 0.022 kg balloon with a charge of -2.6 μC and a wool sweater with a charge of +3.8 μC; the separation distance is 0.75 m. (NOTE: a μC or microCoulomb is a unit of charge; 10-6 C) 10. Suppose that two equally charged spheres attract each other with a force of -0.492 N ("-" means attractive) when placed a distance of 0.03 m from each other. Determine the charge of the spheres. Unit II-D: Inverse-Square Laws Worksheet 6 1. A +5.0 μC charge and a -6.0 μC charge experience an attractive force of -0.72 N. Determine their separation distance. 2. The electron and proton of a hydrogen atom are separated on the average by a distance of about 5.3 x 10-6 m. Find the magnitudes of the electric force and the gravitational force that each particle exerts on the other. 3. A positive charge of 3.6 x 10-5 C and a negative charge of -2.4 x 10-5 C are 0.034 m apart. What is the electric force between the two particles? Is it attractive or repulsive? 4. What is the electrostatic force between a pair of balloons, each having -5.0 x 10-6 C of charge, when they are 0.3 m apart? Is the force attractive or repulsive? 5. Two charges of +4.2 x 10-8 C are separated by 0.46 m. What is the magnitude of the electrical force acting on each object? Is the force attractive or repulsive? 6. Two objects exert a force of 4.2 N on each other. The distance between the objects is 0.36 m. The charge on one object is 2.8 x 10-9 C. What is the charge on the second object? 7. A negative charge of 2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.2 m. What force exists between the charges? Is this force of repulsive or attractive? 8. Two positive charges are located 2 cm apart. Charge qA is +2 x 10-9 C and charge qB is +3 x 10-9 C. Calculate the electrical force between them. Is the force attractive or repulsive? 9. A +4.5 x 10-6 C charge is located 3.2 m from a -2.8 x 10-6 C. Find the magnitude of the electrostatic force by one charge on the other. Unit II-D: Inverse-Square Laws Worksheet 7 Multiple Choice. 1. The _____ of a charged object exerts force on other objects. A) charge B) electric field C) voltage D) mass 2. The direction and strength of a field are depicted by A) spokes B) field lines C) vector lines D) tangents 3. Only ____ electric potential can be measured. A) points of B) absolute values of C) differences in D) attractions between 4. The strength of the force on a mass in a gravitational field depends on A) the direction of the field. C) the magnitude of the field. B) the size of the mass D) both B and C. 5. The strength of the force on a charge in an electric field depends on A) the direction of the field. C) the magnitude of the field. B) the size of the charge D) both B and C. 6. As a field becomes stronger, the field lines should be drawn A) thicker. B) thinner. C) closer together. D) farther apart. 7. Consider the electric field lines shown in the diagram below. From diagram, it is apparent that object A is ____ and object B is ____. A) +, + B) -, C) +, D) -, + the Short Answer. 8. Describe two ways in which gravitational forces are like electrical forces. 9. Describe one major difference between gravitational and electrical forces. 10. Both gravitational and electrical forces act over distances. Which force is greater over the distance between the Earth and the Sun? Which force is greater over the distance between two oxygen atoms in a water molecule? 11. Several electric field line patterns are diagrams. Which of these patterns are Explain what is wrong with all incorrect shown in the incorrect? diagrams. 12. Consider the electric field lines drawn at the left for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest. Smallest 1. ____ 2. ____ 3. ____ 4. ____ 5. ____ Largest 13. For the diagram at right, use your of electric field lines to identify the objects in the following configurations. understanding charges on the Static Electricity 14. Draw the electric field lines for the following configurations of charges in the diagram below. Place arrows upon your electric field lines. < Ranking: < < Ranking: < 4. Draw the electric field lines for the following configurations of charges. Place arrows upon your electric field lines. © The Physics Classroom, 2009 Page 18 Unit II-D: Inverse-Square Laws Review Worksheet 1. What happens to the force between two objects when A) the mass of one object is doubled? B) both charges are halved? C) the distance between them is tripled? D) both masses are doubled and the distance between them is doubled? 2. Which way do field lines point around A) a small mass? B) a large mass? C) a positive charge? D) a negative charge? 3. How is the gravitational force related to the mass of an object? How is the electrical force related to the charge of an object? 4. How are the long-range forces such as the gravitational force and the electrical force related to the distance between objects? Sample Problems. Show your work! 5. What is the force of attraction between two pencils, each with a mass of 0.020 kg that are 0.05 m apart? 6. A newly discovered planet whose radius is 8.2 x 106 m has a gravitational acceleration of 14 m/s2. What is the mass of this planet? 7. The International Space Station is in an approximately circular orbit at an average altitude of 400 km above the Earth. A) Find the acceleration due to gravity on the ISS at this altitude. B) The ISS is reported to have a mass of about 370 metric tons (1 metric ton = 1000 kg). Find the “weight” of the ISS at this altitude. 8. What is the electrostatic force between a pair of electrons when they are 0.01 m apart? Is the force attractive or repulsive? 9. Two charged objects are 0.4 m apart. The charge on one object is 2.8 x 10-9 C and the charge on the second object is 5.2 x 10-6 C. What is the force between the charges? 10. Use the diagram below to answer the following questions about charge QA and QB. A) Charge QA is _________ (positive / negative). B) Charge QB is _________ (positive / negative). C) Which charge is stronger, QA or QB? ________