Download Scheme of work, chapter 11

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.
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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
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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.
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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
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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.
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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).
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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
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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