Gravitational Fields Review 2.1 Exploration of Space Be able to: o describe planetary motion using Kepler s Laws o solve problems using Kepler s Laws o describe Newton s Law of Universal Gravitation o solve problems involving Newton s Law of Universal Gravitation o calculate gravitational potential energy using Newton s Law of Universal Gravitation o solve escape velocity and binding energy problems 2.2 Low Earth Orbit Be able to: o calculate g using Newton s Law of Universal Gravitation o outline Newton s thought experiment regarding satellite motion o use Newton s Law of Universal Gravitation and circular motion to describe the motion of a satellite o solve problems involving satellite motion o define microgravity and describe conditions under which it can be produced
Problems 1. Comet Halley returns every 76 years. Find the average distance of the comet from the sun. (2.67 10 () m) 2. You wish to launch a satellite that will remain above the same spot on Earth s surface. This means the satellite must have a period of exactly one day. Calculate the radius of the circular orbit this satellite must have. Hint: The moon also circles Earth and both the moon and the satellite will obey Kepler s third law. The moon is 3.8 10 8 m from Earth and its period is 27.33 days. (4.19 10. m) 3. The mass of an electron is 9.1 10 31 kg. The mass of a proton is 1.7 10 27 kg. They are about 1.0 10 10 m apart in a hydrogen atom. What gravitational force exists between the proton and electron of a hydrogen atom? (1.03 10 01. N) 4. Two 1.00 kg masses have their centers 1.00 m apart. What is the force of attraction between them? (6.67 10 11 N ) 5. If the centers of Earth and the moon are 3.9 10 8 m apart, the gravitational force between them is about 1.9 10 20 N. What is the approximate mass of the moon? (7.25 10 )) kg) 6. What would be the value of g, acceleration of gravity, if Earth s mass was double its actual value, but its radius remained the same? If the radius was doubled, but the mass remained the same? If both the mass and radius were doubled? (19.6 m / s 2, 2.45 m / s 2, 4.9 m / s 2 ) 7. A satellite is placed in a circular orbit with a radius of 1.0 10 7 m and a period of 9.9 10 3 s. Calculate the mass of Earth. Hint: Gravity supplies the needed centripetal force for such a satellite. Scientists have actually measured the mass of Earth this way. (6.0 10 24 kg ) 8. Calculate the period of Earth s moon if the radius of orbit was twice the actual value of 3.9 10 8 m. (77.3 days) 9. Use your Table of Useful Planetary Data to find the speed and period of a satellite that would orbit Mars 175 km above its surface. (3433 m/s, 6598 s or 1.83 h) 10. A space vehicle, launched as a lunar probe, arrives at the upper limit of Earth s atmosphere. At this point, its kinetic energy is 5.0 10 9 J and its gravitational potential energy is 6.4 10 9 J. What is its binding energy? (1.4 10 9 J ) 11. Calculate the escape velocity from our solar system (i.e. from the surface of the sun). (616479 m/s)
12. The space shuttle ejects a 1200 kg booster tank so that the tank is momentarily at rest at an altitude of 2000 km. Neglecting atmospheric effects, determine: a) how much work must be done on the booster by the force of gravity in returning it to Earth s surface. ( 1.79 10 (7 J) b) the velocity with which it strikes Earth s surface. (5463 m/s) 13. A 500 kg satellite is in circular orbit 200 km above Earth s surface. Calculate a) the gravitational potential energy of the satellite. ( 3.03 10 10 J ) b) the kinetic energy of the satellite. (1.52 10 10 J ) c) its binding energy. ( +1.52 10 10 J ) 14. A rocket, of mass 1.00 10 4 kg is located 1.00 10 10 m from Earth s center. a) Determine its gravitational potential energy at this point, considering only Earth. ( 3.99 10 8 J ) b) How much kinetic energy must it have, at this point, to be capable of escaping from Earth s gravitational field? ( > 3.99 10 8 J ) c) What is the escape velocity from Earth, at this point? (282 m/s) 15. The mass of the moon is approximately 6.7 10 22 kg, and its radius is 1.6 10 6 m. With what velocity must an object be projected from the moon s surface in order to rise to an altitude equal to the moon s radius? (1671 m/s)
2.3 Electric and Magnetic Fields Electric and Magnetic Fields Review Be able to: o solve vector problems involving Coulomb s Law o calculate electric field intensity o due to a single point charge o due to multiple point charges o between parallel plates o sketch electric fields o around a point charge (positive or negative) o between like charges o between unlike charges o between parallel plates o calculate electric potential energy o calculate potential difference o solve problems involving charges moving parallel to an electric field o solve problems for charges moving perpendicular to an electric field (using kinematics of projectile motion) o calculate magnetic field intensity ( B) around a current carrying wire o calculate the magnitude of the force on a moving charged particle in a magnetic field o solve circular motion problems involving a charge moving in a magnetic field o apply the various right hand rules o solve problems based on cathode ray tubes and mass spectrometers
Review Problems 1. Two charges, q 1 and q 2, are separated by a distance, d, and exert a force on each other. What new force will exist if d is doubled? ( F 4 ) 2. Two charges, q 1 and q 2, are separated by a distance, d, and exert a force on each other. What new force will exist if q 1 and q 2 are both doubled? ( 4F ) 3. Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4.0 10 5 N. What is the new force if the distance between the charges is doubled? (1.0 10 5 N ) 4. An electric force of 2.5 10 4 N acts between two equally-charged spheres which are 2.0 cm apart. Calculate the force acting between the spheres if the charge on one of the spheres is doubled and the spheres move to a 5.0 cm separation. (8.0 10 5 N ) 5. Two identical charges are 3.00 cm apart. Find the charge on each of them if the force of repulsion is 4.0 10 7 N. ( ±2.0 10 10 C ) 6. A charge of 4.0 10 5 C is attracted by a second charge with a force of 350 N when the separation is 10.0 cm. Calculate the size of the second charge. ( 9.7 10 6 C ) 7. Three particles are placed on a straight line. The left particle has a charge of +4.6 10 6 C, the middle particle has a charge of 2.3 10 6 C, and the right particle has a charge of 2.3 10 6 C. The left particle is 12 cm from the middle particle and the right particle is 24 cm from the middle particle. Find the total force on the middle particle. ( 7.4 N [ left]) 8. The left particle in the problem above is moved directly above the middle particle, still 12 cm away. Find the force on the middle particle. (6.7 N [7.1 W of N]) 9. A positive test charge of 6.5 10 6 C experiences a force of 4.5 10 5 N. What is the magnitude of the electric field intensity? ( 6.9 N / C ) 10. It takes 8.00 mj to move a charge of 4.00 µc from point A to point C in an electric field. What is the potential difference between the two points? (2000 V) 11. How much work is required to move a positive charge of 2.5 µc between two points that have a potential difference of 60 V? (1.5 10 23 J) 12. A cloud has a potential difference relative to a tree of 900 MV. During a lightning storm, a charge of 100 C travels through this potential difference. How much work is done on this charge? (9.00 10 10 J )
13. A constant electric field of 750 N / C is between a set of parallel plates. What is the potential difference between the parallel plates if they are 1.5 cm apart? (11.25 V) 14. What is the electric field intensity between two large parallel plates 2.0 cm apart, if a potential difference of 450 V is maintained between them? (22500 V/m) 15. What potential difference applied between two parallel plates will produce an electric field strength of 2.5 10 3 N / C, if the plates are 8.0 cm apart? (200 V) 16. How far apart are two parallel plates if a potential difference of 600 V produces an electric field intensity of 1.2 10 4 N / C between them? (0.05 m) 17. An oil drop, of mass 2.6 10 15 kg, is suspended between two parallel plates 0.50 cm apart, and remains stationary when the potential difference between the plates is 270 V. What is the charge on the oil drop, and how many excess or deficit electrons does it have? ( 4.7 10 19 C, ±3 electrons) 18. A metallic ping-pong 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? ( 49 V ) 19. An electron is released from rest adjacent to the negative plate in a parallel plate apparatus. A potential difference of 500 V is maintained between the plates, and they are in a vacuum. With what speed does the electron collide with the positive plate? (1.33 10 ; m/s) 20. An electron, of mass 9.1 10 31 kg with a velocity of 5.0 10 6 m / s is injected into a parallel plate apparatus through a hole in the positive plate. It moves across the vacuum between the plates, colliding with the negative plate at 1.0 10 6 m / s. What is the potential difference between the plates? ( 68 V) 21. A proton is moving to the right in a magnetic field whose direction is up the page. What is the direction of the force exerted by the magnetic field upon the proton? 22. An electron beam moving horizontally away from you is deflected toward the right after passing through a certain region of space that contains a constant magnetic field. What is the direction of the magnetic field? 23. A beam of electrons moving left at 3.0 10 7 m / s passes at right angles to a uniform magnetic field that is directed down the page and in which the magnetic field strength is 2.0 10 4 T. What force acts upon each electron in the beam? (9.6 10 16 N [ into the page])
24. Electrons, moving at 8.5 10 7 m / s, pass through crossed magnetic and electric fields undeflected. What is the size of the magnetic field if the electric field is 4.0 10 4 N / C? (4.7 10 23 T) 25. An electron is moving at 2.0 10 8 m / s in a constant magnetic field. How strong should the magnetic field be to keep the electron moving in a circle of radius 0.50 m? (0.0023 T) 26. A beam of electrons, moving at 2.0 10 8 m / s, passes at right angles to a uniform magnetic field of 41 mt. What is the radius of the circular path in which this beam will travel through the magnetic field? (0.028 m) 27. An unknown particle is accelerated by a potential difference of 150 V. The particle then enters a magnetic field of 50.0 mt, and follows a curved path with a radius of 9.80 cm. What is the ratio of q m? (1.25 10 7 C / kg ) 28. A beam of doubly-ionized oxygen atoms is accelerated by a potential difference of 232 V. The oxygen then enters a magnetic field of 75.0 mt, and follows a curved path with a radius of 8.3 cm. What is the mass of the oxygen atom? (2.67 10 2AB kg) 29. A hydrogen ion is accelerated through an accelerating potential of 100 V and then through a magnetic field of 50.0 mt to standardize the mass spectrometer. What is the radius of curvature if the mass of the ion is 1.67 10 27 kg? (0.029 m)