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Chapter 11 – Out into space Lesson 11.1 Rhythms of the heavens (19 lessons including test) Content Scene setting Elliptical motion of planets, and energy changes associated with them Circular motion: F perpendicular to v Radians and w Explain observations of the motion of planets, stars, the Moon and the seasons in terms of the heliocentric model of the solar system. Appreciate the simplification resulting from the replacement of the geocentric model by the heliocentric one. Explain the retrograde motion of Mars and the phases of Venus in terms of the heliocentric model. Lesson 1: In advance of this lesson, students should read Section 11.1 from the textbook, and one or more of Readings 10T, 20T, 30T. Begin with a brainstorm of how unaided observations of the motions/appearance of the Sun, Moon and stars, the seasons etc. are explicable in terms of the accepted model of the solar system. Some students will not even be aware of how the stars move at night, so some time may need to be spent in eliminating misconceptions. Discuss the historical development of our understanding of motion in the solar system, from Ptolemy via Copernicus to Tycho Brahe and Kepler, stressing how the heliocentric model makes calculation and explanation of motions much simpler. Demonstrate or have students run Activity 10S. Use the examples of the retrograde motion of Mars (Activity 20S) to illustrate the heliocentric model in action. 30/06/2017 3:55 AM Activities Homework Activity 10S “Watching the planets go round Activity 20S “Retrograde motion” Celestia solar system model downloaded from www.shatters.net Reading 10T “Brahe and Hamlet” Reading 20T “Hubble” Reading 30T “The problem of longitude” Appreciate how Kepler’s first law led to precise fitting of planetary orbit data. Appreciate the origin of Kepler’s second law in terms of kinetic and potential energy exchanges. A. M. James, Matthew Arnold School, Oxford 1 Lesson Content Use data on planetary orbit radii and orbital periods to derive Kepler’s third law. Lesson 2: Strictly speaking, the teaching of Kepler’s Laws is optional, so if you are pushed for time, you could limit the work of this lesson, and spend more time on the work of lesson 1. It is worthwhile considering Kepler’s laws as they are revisited later in the chapter. Discuss Kepler’s work showing that planets followed elliptical, not circular orbits (Kepler’s first law), and discuss qualitatively Kepler’s second law in terms of KE/PE exchanges. You could mention comets as orbiting bodies with orbits so elliptical that they are only close to the Sun for a short time during each orbital pass. Students can now try to obtain Kepler’s third law for themselves using the data in File 30T. Know that a body describing uniform circular motion is being accelerated towards the centre of its motion. Know the meaning of the terms centripetal acceleration and centripetal force. Know the meaning of the terms angular speed and radian measure. Use the relationship a = v2/r in calculations involving uniform circular motion. Recall and use the relationships v = 2Πr/T, ω = 2Πf and ω = 2π/T in calculations involving uniform circular motion. Recall and use the relationship v = rω in calculations involving uniform circular motion. Recall and use the relationships a = ω2r, F = mv2/r, F = mω2r in calculations involving uniform circular motion. Know that for a body describing uniform circular motion, there must be an agent providing the centripetal force. Identify the origin of the centripetal force for a range of situations involving circular motion. 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activities Homework File 30T “Planetary orbit data” Celestia solar system model Qs 10D “Using Kepler’s 3rd law” Reading 40T ‘Kepler’s second law and angular momentum’ 2 Lesson 11.2 Newton’s Gravitational law Content Lesson 3-4: Begin with a recap of Newton’s first law, using Galileo’s “pin and pendulum” experiment (Activity 30D) and/or the thought experiment of p35. Lead into discussion of what causes an object to follow a circular path, noting that while the magnitude of the tangential velocity is constant, the velocity itself is continually changing, and is always centripetally directed. Derive the relationship a = v2/r and, using v = rω, the corresponding relationship a = ω2r. Discuss how Newton’s second law leads to the corresponding force relationships F = mv2/r and F = mω2r. Activity 40E can be used to test the relationship F = mv2/r experimentally, while Activity 60S enables circular acceleration to be modelled. Discuss the origin of the centripetal force in a variety of situations (see p39, and get students to brainstorm others). Mention the absence of work done in circular motion, as the force is perpendicular to the direction of motion. Students should be given plenty opportunity to practise using the various relationships: see questions p40 and the question sets listed right. F Activities Activity 30D “Galileo’s frictionless experiment” Activity 40E “Testing F = mv2/r” Activity 60S “Driving round in a circle” Qs 20W “Orbital velocities and acceleration” Qs 30S “Centripetal force” Qs 40S “Circular motionmore challenging” Qs 50C “Centrifuges” Qs 70W “Radians and angular speed” Qs student book p40 Homework Qs 20W “Orbital velocities and acceleration” Qs 30S “Centripetal force” Qs 40S “Circular motion- more challenging” Qs 50C “Centrifuges” Qs 70W “Radians and angular speed” Qs student book p40 RFCWU Jan. 08 Q4 Gm1m2 r2 Force field Geostationary orbit Radial g Appreciate the thought processes that led Newton to promulgate his Law of Universal Gravitation. Recall and use the equation describing Newton’s Law of Universal Gravitation: F = -Gm1m2/r2. Understand how Kepler’s third law may be derived from a consideration of NLUG and the expression for centripetal force. Make calculations on satellites orbiting massive 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford 3 Lesson Content bodies to determine, for example, the mass of the massive body, the orbital period, the orbital radius. Lesson 5-6: Introduce Newton’s Law of Universal Gravitation (NLUG) using the treatment of p41, where the Moon’s centripetal acceleration is just the acceleration at the Earth’s surface diluted by distance2. Lead into F = -Gm1m2/r2, illustrating the equation with Activity 70S and sample calculations. The inverse square nature of the law can be understood in terms of gravity diluting over a surface of area 4пr2 (see p42). Discuss how the gravitational force gives rise to the centripetal force. It is worthwhile showing how Kepler’s third law arises by equating Gm 1m2/r2 = m2ω2r, and inserting ω = 2п/T. Activities 80S and 90S can be used to explore the nature of the gravitational force further, possibly setting for homework if time is limited. In the second session, students should do problem solving, using, for example, Qs 80W, Qs 110S, and/or Activities 80S and 90S. 30/06/2017 3:55 AM Activities Homework Activity 70S “Variations in gravitational force” Activity 80S “Gravitational universes” Activity 90S “Gravitation with three bodies” Qs 80W “Newton’s gravitational law” Qs 110S “Finding the mass of a planet with a satellite” Celestia Activity 80S “Gravitational universes” Activity 90S “Gravitation with three bodies” Qs 80W “Newton’s gravitational law” Qs 60C “How Cavendish didn’t determine g and Boys did” Qs 90C “Are there planets around other stars?” Qs 110S “Finding the mass of a planet with a satellite” Qs 10W ‘Testing for an inverse square law’ RFCWU G494 Specimen Q8; June 07 Q7; Jan. 07 Q5 Know that a gravitational field is a region in space where a mass feels a force due to another mass. Know the meaning of the term gravitational field strength. Recall and use the equation for radial gravitational fields g = F/m = -GM/r2, to make calculations involving gravitational fields. Draw the pattern of gravitational field lines around a mass such as a planet. Sketch the variation in gravitational field strength with distance from a body. Sketch the variation in total gravitational field strength with distance from the surface of the Earth to the surface of the Moon, identifying key features. Make calculations on satellites orbiting massive A. M. James, Matthew Arnold School, Oxford 4 Lesson 11.3 Arrivals and departures Content bodies to determine, for example, the mass of the massive body, the orbital period, the orbital radius. Lesson 7-8: Introduce the concept of the gravitational field, recapping work from Chapter 9 on the gravitational field at the surface of the Earth, and generalizing to any body with mass. Show the relationship between the equation for gravitational force and that for field, noting how they are linked through F = mg. Discuss the graphical depiction of a gravitational field, noting that the field lines show the direction of the gravitational force that acts on a mass placed in the field. Discuss the launching of a satellite into orbit (p43-44), noting that the gravitational field is accelerating the satellite towards the Earth always, but it remains in orbit due to high speed. It is also worth pointing out that objects in free fall are not weightless, but that they are being accelerated towards the centre of the Earth. Go through the calculation of geostationary orbit radius, and then get students to do Qs 110S (could be homework), if not done so already. Students can carry out Activity 110S which uses Apollo data to determine the variation in field strength with distance from the Earth to the Moon. Alternatively, just use display material 100O as a basis for discussion, and do Activity 110S for homework. Display material 120O illustrates the variation of the field strength from the Earth to the Moon, which can be explored quantitatively using Qs 120D. Momentum Elastic and inelastic collisions Energy conservation qualitatively Know the meaning of the term momentum, and how to calculate it using p = mv. Know that momentum is conserved in collisions, disintegrations, explosions etc. Investigate experimentally the principle of conservation of momentum. Use the principle of conservation of momentum to do calculations on collisions, disintegrations, explosions 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activities Homework Activity 110S “Probing a gravitational field” Qs 110S “Finding the mass of a planet with a satellite” Qs student book p47 Activity 110S “Probing a gravitational field” Qs 110S “Finding the mass of a planet with a satellite” Qs student book p47 Qs 120D “The gravitational field between the Earth and the Moon” Qs 130C “Variation in g” Reading 60T “Forces on real objects” Reading 70T “Gravity can pull things apart” Reading 100T “Supernovae and black holes” 5 Lesson Content etc. Lesson 9-10: Introduce momentum as the “quantity of motion” possessed by a body. Introduce the momentum equation p = mv. The following experiments are drawn directly from the GCSE separate sciences physics “Forces and Motion” module. You should demonstrate all of the experiments qualitatively, and do or analyse a selection of them using the video camera. Activity 160S should also be used to simulate collisions, if desired for homework. Use the air track and vehicles to demonstrate the following collisions, if possible recording each collision using digital camera: (1) elastic collision (equal masses); (2) elastic collision (light + heavy); (3) coalescence (equal masses); (4) coalescence (light + heavy); (5) disintegration (light + heavy and/or light + light). Alternatively, you could show the relevant clips from the Multimedia Motion CD. Some of the collisions could be pre-recorded if necessary, and you could get different groups to analyse different collisions, pooling results later. Get students to analyse the data from some of the experiments to elucidate/confirm the principle of conservation of momentum, noting that momentum has direction as well as magnitude. Where possible, follow up the analysis of each collision with a numerical question (see question sets right) based on the type of collision considered, and try to relate each collision to a “real world” situation, for example the recoil of a gun when fired. Discuss briefly Galilean invariance as applied to collisions. 30/06/2017 3:55 AM Activities Homework Activity 120E “Low friction collisions and explosions” Activity 130E ‘Newton’s cradle’ Activity 140E ‘kicking a football’ Activity 160S “Modelling collisions” Worksheet “Momentum problems” on colliding basketballs Reading 80T ‘Starting with momentum’ Worksheet “Momentum problems” on colliding basketballs. Qs 140W “Change in momentum as a vector” Qs 160S “Collisions of spheres” Qs 170C “Collision with spaceship Earth” Reading 90T ‘Sling shotting spacecraft’ Know that the change in momentum of one body in a collision is equal and opposite to that of the other body. Know the meaning of the term impulse (= change in momentum = force x time). Explain, in terms of FΔt = change in momentum, how and why the contact time is maximized in ball/racquet A. M. James, Matthew Arnold School, Oxford 6 Lesson Content Activities sports. Explain, in terms of FΔt = change in momentum, how and why the impact force is minimized in vehicle collisions. Calculate the change in momentum from a force versus time graph. Sketch how the force versus time graph changes when, say, the impact time is increased. Lesson 11: Analyse data from one of the collisions (the disintegration is possibly the most instructive) to illustrate the principle that the change in momentum is the same for each body. Use this result to discuss the simple rule that m 1Δv1 = m2Δv2, illustrating qualitatively with the examples on p51. Introduce the term impulse, defining it simply as the change in momentum as discussed above. Show how F = ma gives rise to FΔt = change in momentum, and discuss the usefulness of this equation in sport, where maximizing the force and/or contact time (follow through) leads to a large momentum change for the ball/puck. Show how the change in momentum can be computed from a force versus time graph, as the area under the graph. Discuss situations where we desire to minimize the force by increasing the time over which it acts, such as parachutists landing, crumple zones on cars. Stress that the area under the force-time graph will be the same, as the momentum change is the same, but the force is reduced if the contact time is increased: show this graphically. Activity 180S explores this further in detail. Explain the operation of a rocket in terms of actionreaction (Newton 3). Apply the relationship F = change in momentum/time to calculate the thrust of a rocket. Apply the relationship F = change in momentum/time, and the principle of conservation of momentum to determine the motion of a rocket-powered vehicle (moving either horizontally or vertically). 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activity 180S gently!” Homework “Crunch – Qs 150S “Impulse and momentum in collisions” Qs 160S “Collisions of spheres” 7 Lesson 4.4 Mapping gravity Content Lesson 12: Blow up a balloon and let it fly across the class, getting students to brainstorm how it works in terms of conservation of momentum. Recapping the analysis of the disintegration on the air track (or discussion of cannon recoiling on firing cannon ball) may be helpful. Discuss the action-reaction pair of forces involved: balloon exerts force on gas, and gas exerts force on balloon. You could also demonstrate one of the rocket kits out on the field, possibly with video recording of the take-off against a scale, so that the initial acceleration can be determined. Go through the analysis of momentum conservation for a rocket ejecting hot gases (see p54 of student book), although note that this analysis only applies for horizontal motion. Go through a calculation to determine the initial acceleration of a rocket launched vertically, possibly using data from the kit. Note that the kit rocket motors are classified according to total impulse (= thrust x burn time). Gravitational potential in both uniform and radial fields g Activities Activity 170D “Testing a rocket engine” Launch model rocket RFCWU Jan. 08 Q9; June 07 Q5 Homework Qs 180S “Jets and rockets” Qs 170C ‘Collision with spaceship Earth’ Qs 190C “Getting a satellite up to speed” Qs student book p55 V r Energy conservation quantitatively Recall and use the equation ΔGPE = mgΔh for objects moving in uniform gravitational fields. Know that gravitational potential is defined as GPE per unit mass. Sketch field lines and corresponding equipotential lines for a uniform gravitational field. Determine gravitational field strength in a uniform field from a plot of potential versus displacement (slope of graph). Determine force from a plot of GPE versus displacement (slope of graph) Determine gravitational potential difference from a plot of field strength versus displacement (area under graph). 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford 8 Lesson Content Lesson 13: To begin with, we consider only uniform fields: in later lessons the treatment is extended to radial fields. While doing this lesson, you can stress that the treatment applies for situations close to the Earth’s surface where the gravitational field strength does not change significantly with height. Recap GCSE/AS work on the equation ΔGPE = mgΔh (weight x height = gravitational force x vertical distance). Define gravitational potential as GPE per unit mass, and discuss the field and corresponding potential energy pictures as per p57. Discuss the graphical relationship between field and potential (field strength = -potential gradient), and similarly potential difference = area under field versus displacement graph. These relationships are best understood if specific numerical examples are considered (see Qs 210S). At this stage it is acceptable to set the potential at the Earth’s surface to be 0 J kg-1. If time permits, you could analyse data collected in Activity 210D, or set this for homework. Analyse spacecraft data to show that gravitational potential varies with 1/r. Use the equation Vgrav = -GM/r to calculate potentials of radial fields. Appreciate that a 1/r potential is consistent with an inverse square gravitational field. Determine gravitational field strength in a uniform field from a plot of potential versus displacement (slope of tangent). Determine force from a plot of GPE versus displacement (slope of tangent) Determine gravitational potential difference from a plot of field strength versus displacement (area under graph). Compute energy changes for a body moving in a radial gravitational field, using Vgrav = -GM/r and the fact that KE + GPE = a constant. Sketch and interpret graphs for the combined potential 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activities Activity 190D ‘Exploring potential with a tennis ball’ Activity 210D/270D “Gravitational slides” (analyse data from) Activity 220S ‘Storing energy with gravity’ Homework Qs 200W “Pole vaulting” Qs 210S “Gravitational potential energy and gravitational potential” 9 Lesson Content of a two-body system such as Earth-Moon. Lesson 14-15: Generalise the relationships field strength = potential gradient and potential difference = area under fielddisplacement graph to radial fields (p58). Introduce the problem of calculating energy changes etc. in a radial field, one that is not uniform. Explore the variation in gravitational potential and field using Activity 240S, which uses Apollo 11 data. Alternatively and more succinctly, show (p58-59) how the relationship Vgrav = C – ½ v2 arises, and then get students to verify that the Apollo 11 data on p58 gives a 1/r variation of potential with distance. To further illustrate how a 1/r potential gives rise to an inverse square field, go through the treatment at the top of p59. Although this will only appeal to the more mathematically inclined, you should at least go through it to show how the equation Vgrav = -GM/r is consistent with g = GM/r2. Discuss, in at least qualitative terms, the energy changes experienced by Apollo 11 returning to Earth, in terms of falling down a potential well whose slope gives the field strength and hence the acceleration. (A large filter funnel with a marble, or better still a rubber sheet helps to illustrate this point.) You should also consider what a graph of the combined Earth plus Moon potential would look like (see p60). Activity 230S can be used to further explore the field-potential relationship. Activities Homework Activity 240S Analysing data from the Apollo 11 mission to the Moon” Qs 220D “Gravitational PD, field strength and potential” RFCWU June 08 Q8; Jan. 07 Q8 Use modelling software to trace equipotentials in a radial field, probe variation in gravitational potential from motion data, explore the link between field strength and potential gradient. Lesson 16: Software activities 250S, 260S and 280S. 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activity 250S “Variations in field and potential” Activity 260S “Probing gravitational potential” Activity 280S “Relating field and potential” 10 Lesson Content Activities Homework Know that, with no forces other than gravity acting, the total mechanical energy for a body in a gravitational field equals its KE plus its GPE. Explain correctly the term escape velocity. Calculate the escape velocity for a planet given its mass and radius. Calculate the speed of arrival of a meteorite at the Earth, from a knowledge of its initial speed, distance from Earth, and the mass and radius of the Earth. Explain the slingshot effect for speeding up spacecraft. Lesson 17: Discuss how to calculate the escape velocity from the Earth from a consideration of the (constant) total mechanical energy (TME = GPE + KE). Note that a spacecraft could “escape” at any speed, but the “escape velocity” corresponds to the speed that needs to be reached if the craft is going to coast to infinity, slowing to a halt as it does so. Consider also the situation where meteorites etc. arrive at the Earth: equivalent to the escape situation run in reverse. You can extend this treatment to situations where the initial speed and distance of the meteorite from the Earth are known, not just assuming it starts from infinity with zero speed. Activity 230S can also be used to show the changes in GPE and KE, the total energy remaining constant. Discuss the slingshot technique for speeding up spacecraft (see Reading 90T). Understand the interplay of KE, GPE and other factors in determining how best to launch a satellite into a particular orbit. Lesson 18: Optional, do if time permits. Students do Activity 290S on putting satellites in orbit, and Qs 230D. 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Activity fields” 230S “Inferring Qs 250S “Summary questions for Chapter 11” Qs student book p61 RFCWU Jan. 08 Q8 Activity 290S “Setting up energetic orbits” Qs 230D “Changing orbits” Qs 230D “Changing orbits” Qs 240D Why is a black hole black?” Reading 120T “Comets and the Rosetta mission” 11 Lesson Content Activities Chapter 11 test 30/06/2017 3:55 AM A. M. James, Matthew Arnold School, Oxford Homework Reading 130T “The CassiniHuygens mission to Saturn” Reading 110W ‘Gravitational potential due to a spherical mass’ Qs student book p63 12