"Chapter 4 - DOC 7"
Chapter 11 – Out into space Specification Section 126.96.36.199 Out into space General learning outcomes for each section are given in the teaching notes from the CD-ROM. For information on Key Skills see the Specification section on the CD-ROM. Types: Students should demonstrate: (a) knowledge and understanding of phenomena, concepts and relationships by describing and explaining cases involving... (b) comprehension of the language and representations of physics: by making appropriate uses of the terms…; by expressing in words and vice-versa...; by sketching, plotting from data and interpreting… (c) quantitative and mathematical skills, knowledge and understanding by making calculations and estimates involving… Lesson Content Activities Homework 11.1 (a) motion in a horizontal circle and in a circular Rhythms of gravitational orbit, the heavens (b) changes of gravitational and kinetic energy, work done where the force is not along the line of motion 2 2 2 2 (c) v = r ω, a = v /r, F= mv /r, a = ω r and F = mω r 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 Activity 10S “Watching the Reading 10T “Brahe and Hamlet” Section 11.1 from the textbook, and one or more of Readings planets go round Reading 20T “Hubble” 10T, 20T, 30T. Begin with a brainstorm of how unaided Activity 20S “Retrograde Reading 30T “The problem of observations of the motions/appearance of the Sun, Moon and motion” longitude” 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 1 Lesson Content Activities Homework 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) and the phases of Venus (p36) to illustrate the heliocentric model in action. 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. Use data on planetary orbit radii and orbital periods to derive Kepler’s third law. rd Lesson 2: Strictly speaking, the teaching of Kepler’s Laws is File 30T “Planetary orbit Qs 10D “Using Kepler’s 3 law” optional, so if you are pushed for time, you could limit the work data” 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 = v /r in calculations involving 2 uniform circular motion. Recall and use the relationships v = 2Πr/T, ω = 2Πf and ω = 2π/T in calculations involving uniform circular 2 Lesson Content Activities Homework motion. Recall and use the relationship v = rω in calculations involving uniform circular motion. Recall and use the relationships a = ω r, F = mv /r, F 2 2 2 = mω r 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. Lesson 3-4: Begin with a recap of Newton’s first law, using Activity 30D “Galileo’s Qs 20W “Orbital velocities and Galileo’s “pin and pendulum” experiment (Activity 30D) and/or frictionless experiment” acceleration” the thought experiment of p36 in the BOOK. Lead into Activity 40E “Testing F = Qs 30S “Centripetal force” 2 discussion of what causes an object to follow a circular path, mv /r” Qs 40S “Circular motion- more noting that while the magnitude of the tangential velocity is Activity 60S “Driving round challenging” constant, the velocity itself is continually changing, and is in a circle” Qs 50C “Centrifuges” always centripetally directed. Derive the relationship a = v /r 2 Qs 20W “Orbital velocities Qs 70W “Radians and angular and, using v = rω, the corresponding relationship a = ω r. 2 and acceleration” speed” Discuss how Newton’s second law leads to the corresponding Qs 30S “Centripetal force” BOOK Qs p39 2 2 force relationships F = mv /r and F = mω r. Activity 40E can Qs 40S “Circular motion- 2 be used to test the relationship F = mv /r experimentally, while more challenging” Activity 60S enables circular acceleration to be modelled. Qs 50C “Centrifuges” Discuss the origin of the centripetal force in a variety of Qs 70W “Radians and situations (see BOOK p38, and get students to brainstorm angular speed” others). Mention the absence of work done in circular motion, BOOK Qs p39 as the force is perpendicular to the direction of motion. Students should be given plenty opportunity to practise using the various relationships: see BOOK questions p39 and the question sets listed right. 11.2 (a) motion in a uniform gravitational field, the gravitational field Newton’s of a point mass Gravitational (b) gravitational field, diagrams/graphs of gravitational fields 2 2 law (c) F = -GMm/r , g = F/m, g = -GM/r 3 Lesson Content Activities Homework Appreciate the thought processes that led Newton to promulgate his Law of Universal Gravitation. Recall and use the equation describing Newton’s Law 2 of Universal Gravitation: F = -Gm1m2/r . Understand how Kepler’s third law may be derived from a consideration of Newton’s Law of Universal Gravitation and the expression for centripetal force. Make calculations on satellites orbiting massive 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 Activity 70S “Variations in Activity 80S “Gravitational (NLUG) using the treatment of BOOK p40, where the Moon’s gravitational force” universes” centripetal acceleration is just the acceleration at the Earth’s Activity 80S “Gravitational Activity 90S “Gravitation with three 2 surface diluted by distance . Lead into F = -Gm1m2/r , 2 universes” bodies” illustrating the equation with Activity 70S and sample Activity 90S “Gravitation Qs 80W “Newton’s gravitational calculations. The inverse square nature of the law can be with three bodies” law” understood in terms of gravity diluting over a surface of area Qs 80W “Newton’s Qs 60C “How Cavendish didn’t 2 4пr (see BOOK p41). Discuss how the gravitational force gravitational law” determine g and Boys did” gives rise to the centripetal force. It is worthwhile showing how Qs 110S “Finding the mass Qs 90C “Are there planets around 2 Kepler’s third law arises by equating Gm 1m2/r = m2ω r, and 2 of a planet with a satellite” other stars?” inserting ω = 2п/T. Activities 80S and 90S can be used to Qs 110S “Finding the mass of a explore the nature of the gravitational force further, possibly planet with a satellite” 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. 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 2 fields g = F/m = -GM/r , to make calculations involving gravitational fields. Draw the pattern of gravitational field lines around a mass such as a planet. 4 Lesson Content Activities Homework 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 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, Activity 110S “Probing a Activity 110S “Probing a recapping work from Chapter 9 on the gravitational field at the gravitational field” gravitational field” surface of the Earth, and generalizing to any body with mass. Qs 110S “Finding the mass Qs 110S “Finding the mass of a Show the relationship between the equation for gravitational of a planet with a satellite” planet with a satellite” force and that for field, noting how they are linked through F = BOOK Qs p46 BOOK Qs p46 mg. Discuss the graphical depiction of a gravitational field, Qs 120D “The gravitational field noting that the field lines show the direction of the gravitational between the Earth and the Moon” force that acts on a mass placed in the field. Discuss the Qs 130C “Variation in g” launching of a satellite into orbit (BOOK p42), noting that the Reading 60T “Forces on real gravitational field is accelerating the satellite towards the Earth objects” always, but it remains in orbit due to high speed. It is also Reading 70T “Gravity can pull worth pointing out that objects in free fall are not weightless, things apart” but that they are being accelerated towards the centre of the Reading 100T “Supernovae and Earth. Go through the calculation of geostationary orbit radius, black holes” 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. 11.3 Arrivals (a) momentum as a vector, force as rate of change of and momentum, conservation of momentum departures (b) momentum, graphs showing force versus time for collisions etc. (c) p = mv, F = Δ(mv)/ Δ t 5 Lesson Content Activities Homework 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 etc. Lesson 9-10: Introduce momentum as the “quantity of motion” Activity 120E “Low friction Worksheet “Momentum problems” possessed by a body. Introduce the momentum equation p = collisions and explosions” on colliding basketballs. mv. The following experiments are drawn directly from the (use video camera?) Qs 140W “Change in momentum GCSE separate sciences physics “Forces and Motion” Activity 160S “Modelling as a vector” module. You should demonstrate all of the experiments collisions” Qs 160S “Collisions of spheres” qualitatively, and do or analyse a selection of them using the Worksheet “Momentum Qs 170C “Collision with spaceship video camera. Activity 160S should also be used to simulate problems” on colliding Earth” collisions, if desired for homework. basketballs Use the air track and vehicles to demonstrate the following collisions, if possible recording each collision using the 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). Data can be displayed and analysed on the iMac. 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 6 Lesson Content Activities Homework applied to collisions (BOOK p48). 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 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 Activity 180S “Crunch – Qs 150S “Impulse and momentum disintegration is possibly the most instructive) to illustrate the gently!” in collisions” principle that the change in momentum is the same for each Qs 160S “Collisions of spheres” body. Use this result to discuss the simple rule that m 1Δv1 = m2Δv2, illustrating qualitatively with the examples on p50. 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 7 Lesson Content Activities Homework further in detail. Explain the operation of a rocket in terms of action- reaction (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). Lesson 12: Blow up a balloon and let it fly across the class, Activity 170D “Testing a Qs 180S “Jets and rockets” getting students to brainstorm how it works in terms of rocket engine” Qs 190C “Getting a satellite up to conservation of momentum. Recapping the analysis of the Launch model rocket speed” disintegration on the air track (or discussion of cannon BOOK Qs p54 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 a rocket kit outside on the playing 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 BOOK p53), 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 rocket. Note that the kit rocket motors are classified according to total impulse (= thrust x burn time). 4.4 Mapping (a) work done, changes of GPE and KE, gravitational field and gravity potential of a point mass, motion in a uniform gravitational field (b) KE and GPE, gravitational field, gravitational potential, graphs showing variation of gravitational potential with distance, gravitational potential as the area under the field versus distance graph, graphs showing force as the tangent to a graph of GPE versus distance, equipotential surfaces (c) GPE change = mgh, work done = FΔs, GPE = -GMm/r, Vgrav = Egrav/m = -GM/r 8 Lesson Content Activities Homework 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). Lesson 13: To begin with, we consider only uniform fields: in Activity 210D “Gravitational Qs 200W “Pole vaulting” later lessons the treatment is extended to radial fields. While slides” (analyse data from) Qs 210S “Gravitational potential doing this lesson, you can stress that the treatment applies for energy and gravitational potential” 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 BOOK p56. 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 -1 to be 0 J kg . 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. 9 Lesson Content Activities Homework 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 of a two-body system such as Earth-Moon. Lesson 14-15: Generalise the relationships field strength = - Activity 240S Analysing data Qs 220D “Gravitational PD, field potential gradient and potential difference = area under field- from the Apollo 11 mission strength and potential” displacement graph to radial fields (p57). Introduce the to the Moon” 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 (BOOK p57) 2 how the relationship Vgrav = C – ½ v 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 p58. Although this will only appeal to the most mathematically inclined, you should at least go through it to show how the equation Vgrav = -GM/r is consistent 2 with g = GM/r . 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 10 Lesson Content Activities Homework Moon potential would look like (see p59). Activity 230S can be used to further explore the field-potential relationship. 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. Activity 250S “Variations in field and potential” Activity 260S “Probing gravitational potential” Activity 280S “Relating field and potential” 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 Activity 230S “Inferring Qs 250S “Summary questions for the Earth from a consideration of the (constant) total fields” Chapter 11” mechanical energy (TME = GPE + KE). Note that a spacecraft BOOK Qs p60 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 11 Lesson Content Activities Homework 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 Activity 290S “Setting up Qs 230D “Changing orbits” 290S on putting satellites in orbit, and Qs 230D. energetic orbits” Qs 240D Why is a black hole Qs 230D “Changing orbits” black?” Reading 120T “Comets and the Rosetta mission” Reading 130T “The Cassini- Huygens mission to Saturn” Do test on Chapter 11 BOOK Qs p62 12