9.2 GRAVITATIONAL FIELD, POTENTIAL, AND ENERGY 9.4 ORBITAL MOTION HW/Study Packet

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1 9.2 GRAVITATIONAL FIELD, POTENTIAL, AND ENERGY 9.4 ORBITAL MOTION HW/Study Packet Required: READ Hamper pp HL Supplemental: Cutnell and Johnson, pp , Tsokos, pp Tsokos Questions pp #3,7,12,24,28,29 REMEMBER TO. Work through all of the example problems in the texts as you are reading them Refer to the IB Physics Guide for details on what you need to know about this topic Refer to the Study Guides for suggested exercises to do each night First try to do these problems using only what is provided to you from the IB Data Booklet Refer to the solutions/key ONLY after you have attempted the problems to the best of your ability UNIT OUTLINE I. GRAVITATIONAL POTENTIAL A. REDEFINING GRAVITATIONAL POTENTIAL ENERGY B. GRAVITATIONAL POTENTIAL DEFINED C. EQUIPOTENTIAL SURFACES D. THE GRAVITATIONAL FIELD AND POTENTIAL GRADIENT II. ESCAPE VELOCITY III. HOW THINGS MOVE IN ORBITS A. THE ROLE OF CENTRIPETAL FORCE IN SATELLITE MOTION B. KEPLER S LAWS IV. ENERGIES OF SATELLITES A. KINETIC, POTENTIAL, AND TOTAL ENERGY B. VARIATIONS OF ENERGIES WITH ORBITAL RADIUS V. WEIGHTLESSNESS IN ORBIT FROM THE IB DATA BOOKLET WHAT YOU SHOULD BE ABLE TO DO AT THE END OF THIS TOPIC State the definitions of gravitational potential energy and gravitational potential Calculate work done as a mass is moved across two points with gravitational potential difference Sketch patterns of equipotential surfaces State the relation between equipotential surfaces and gravitational field lines Understand the meaning of the term escape velocity and derive an expression for the escape velocity from a planet s surface Relate orbital motion to circular motion, and derive Kepler s Third Law Derive expressions for the KE, PE, and total energy of an orbiting satellite Solve problems of orbital motion and describe conditions that lead to weightlessness in freefall and deep space 1

2 HOMEWORK PROBLEMS: 1. A 6.0 kg mass (m 3 ) is placed between 2 other masses (m 1 = kg and m 2 = kg) as shown. All 3 masses are along a line between their centres. F 31 F 32 m 1 = kg r 31 = 3.00 m m 3 = 6.00 kg r 32 = 2.00 m m 2 = kg a) Determine the net (resultant) force on m 3. [+7.78 x 10-9 N] b) Determine the acceleration of m 3. [1.30 x 10-9 ms -2 ] c) Find the gravitational field at m 3 due to m 1 and m 2. [+1.30 x 10-9 Nkg -1 ] 2. Consider 2 points, X and Y, at distances 1.00 m and 4.00 m from a 1500 kg mass as shown. Find: a) Find the gravitational potentials at points X and Y. [X: -1.0 x 10-7 Jkg -1 Y: -2.5 x 10-8 Jkg -1 ] 4.00 m b) How much energy is needed to move a mass of 2.0 x 10 6 kg from X to Y? [0.150 J] 2

3 3. The diagram shows the equipotential surfaces near a certain non-spherical body. Calculate the potential energy of a g mass m at a) P [300 J] b) Q [250 J] c) R [250 J] What is the work that must be done on m to move it from d) P to Q? [50 J] e) Q to R? [0 J] 4. A binary star system consists of two stars with masses M 1 and M 2 rotating about a common centre. The centres of the two stars are separated by a distance R = m. The total gravitational potential due to the stars at any point along a line joining their centres is V. The graph shows how V varies with the distance x from the centre of star M1. (Values of the potential inside each star are not known.) 3

4 A particle is launched with kinetic energy E K from the surface of star with mass M 2. The particle arrives at the surface of the star of mass M 1. Use the graph to a) explain whether the kinetic energy of the particle at the surface of M 1 is less than, equal to, or larger than E K. [E K increases, so larger] b) determine the distance x at which the gravitational field strength due to the two stars is zero. [4.8 x 10 9 m] M 1 c) determine the ratio. M 2 [0.44] 5. The graph below shows the variation with distance R from the centre of a planet of the gravitational potential V. The radius R 0 of the planet = 5.0 x 10 6 m. Values of V are not shown for R < R 0. a) Use the graph to determine the magnitude of the gravitational field strength at the surface of the planet. [7.8 N kg -1 ] 4

5 b) A satellite of mass 3.2 x 10 3 kg is launched from the surface of the planet. Use the graph to determine the minimum launch speed that the satellite must have in order to reach a height of 2.0 x 10 7 m above the surface of the planet. (You may assume that it reaches its maximum speed immediately after launch.) [7.9 x 10 3 m s -1 ] 6. The mass of a planet is M and its radius is R. In order for a body of mass m to escape the gravitational attraction of the planet, determine the minimum kinetic energy of the body at the surface of the planet in terms of these variables. [GMm/r] 7. A satellite of mass m is in a circular orbit around the Earth at height R from the Earth s surface. The mass of the Earth may be considered to be a point mass concentrated at the Earth s centre. The Earth has mass M and radius R. orbit Earth mass M satellite mass m a) In terms of the given variables, determine the kinetic energy of the satellite when in orbit of height R. [GMm (4R) -1 ] R R b) The kinetic energy of the satellite in this orbit is 1.5 x J. Calculate the total energy of the satellite. [-1.5 x J] 8. Planets A and B orbit the same star. The orbital radius of planet B is four times that of planet A. Use Kepler s 3 rd Law to determine the ratio of the orbital period of planet B to the orbital period of planet A. [8] 5

6.2 ELECTRIC FORCE AND FIELD HW Study Packet

6.2 ELECTRIC FORCE AND FIELD HW Study Packet Required: READ Hamper 195-199 Tsokos, pp 280-291 SL / HL Supplemental: Cutnell and Johnson, pp 533-559 DO Tsokos p 287 #3,7,9 pp 296-297 #4,6,11,12 REMEMBER