Download Scheme of work for chapter 9

Chapter 9 – Computing the next move (18 lessons including test)
Lesson
9.1
What’s
the
next
move?
Content
Sports physics, air traffic control, predicting collisions
Activities
Homework
Activity 30S ‘Will the aircraft
collide?’
Activity 40S ‘Perspectives on
relative velocity’
Activity
25P
‘Remote
measurements on distance’
Activity 10S ‘Reconstructing a
flight’
Exam
questions
on
relative velocity
Activity 50E ‘Tracking
aircraft paths by drawing’
Qs 10S ‘Calculated steps’
Qs p193
UP Jan. 07 Q10

Review addition of vector components to give resultant
vectors.
 Calculate relative velocity of two objects by vector
subtraction.
 Use vector subtraction procedure to calculate if two
aircraft are on a collision course.
 Explain principles and practice of radar tracking of
moving aircraft.
 Calculate position and bearing of an aircraft from
successive radar pulse measurements.
Lesson 1: Begin with a recap of addition of velocity and
displacement vectors to give resultant velocity and resultant
displacement, as discussed earlier in Chapter 8. Introduce how
humans track moving objects when trying to catch a ball
(p190), leading into a discussion of how radar is used to track
aircraft and avoid collisions. Discuss how to determine whether
two aircraft are on a collision course using the procedure
outlined on p192. Illustrate this by demonstrating Activity 30S
and/or Activity 40S with the default conditions.
‘Try these’ p193 question 7 is an excellent example of how to
compute bearing and position from radar measurements. See
also Understanding Processes Jan. 07 Q10.
9.2 Speeding
up,
slowing
down
UP Jan. 07 Q10
Acceleration, predicting more complex motions, moving along
parabolas

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Explore the relationship between acceleration, velocity
and displacement using software modelling activities.
A. M. James, Matthew Arnold School, Oxford
1
Lesson
Content
 Describe the chain of velocity vectors and
displacements for a body undergoing uniform
acceleration, with constant time interval between
measurements.
 Explain the above in terms of addition of constant
velocity increment in each successive time interval.
 Know that acceleration is determined by measuring
the gradient of a velocity time graph.
Lesson 2: Using sequences from Multimedia Motion CD ROM
and/or air track, show how the displacement in each
successive time interval increases during accelerated motion:
no need for analysis at this stage. Now demonstrate, or have
students do, Activity 70S, varying the acceleration, and noting
the effect on the individual displacement vectors. Discuss what
is meant by uniform acceleration, relating to the examples just
viewed, and go through the computation rules for uniform
acceleration, as per p195. Now have students explore this
further using Activity 60S.
Activities
Homework
Sequences from Multimedia Motion
CD ROM
Activity
60S
‘Introducing
acceleration’
Activity 70S ‘Calculating a flight’

Explore the relationship between acceleration, velocity
and displacement using software modelling activities.
 Know that the velocity-time graph for a body
undergoing uniform acceleration is a straight line.
 Know that acceleration is determined by measuring
the gradient of a velocity time graph.
 Know that distance gone equals area under a velocitytime graph.
 Calculate average speeds from velocity-time graphs
using either measurement of distance gone or
determination of midpoint of v-t graph.
Lesson 3: Use Activity 80S to explore the relationship
between displacement, velocity and acceleration graphically
for a body undergoing uniform acceleration. Students should
vary the acceleration and see the effect it has on the graphs.
Consider also how to determine the distance gone (and hence
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A. M. James, Matthew Arnold School, Oxford
Activity 80S ‘Constant acceleration
with graphs’
Activity 100S ‘Acceleration from
graphs’
Qs 10M ‘Displacementtime graph’
Qs 40M ‘Accelerationtime graphs’
2
Lesson
Content
average speed) by measuring the area under the v-t graph,
and also how the midpoint of the v-t graph gives the average
speed.
As extension work, Activity 100S gives students the
opportunity to analyse the velocity-time graph for a complex
motion, to determine the accelerations at various times.
Activities
Homework
Qs 30S ‘Coping with
graphs’
Qs
50S
‘Calculating
accelerated steps’
UP G492 Specimen Q3, Q5; June
08 Q3; Jan. 08 Q1
Qs
60S
‘Uniform
acceleration’
Qs 70S ‘Braking distance
and the Highway Code’
Qs 100E ‘Slowing down a
bicycle’
Qs p209
Multimedia Motion CD ROM clips
Activity 140E ‘Rolling a marble on a
parabola’
Activity 130D ‘A thrown tennis ball
Qs p203
Qs
110S
archery’

Appreciate how to derive the kinematic equations v =u
+ at, s = ½ (u+v)t, s = ut + ½ at2, v2 = u2 + as.
 Use the kinematic equations v =u + at, s = ut + ½ at2,
v2 = u2 + as to solve motion problems.
 Recall and use the kinematic equation, s = ½ (u+v)t to
solve motion problems.
Lesson 4: Go through the derivation of the kinematic
equations, as per p197-198. Make sure that sample
calculations are included: see ‘Try these’ p203 and the
problem sets listed. The equation s = ut + ½ at2 also follows
from graphical considerations of the area under a v-t graph.
Three of the equations are provided on the formula sheet, the
fourth, s = ½ (u+v)t, is not. This last equation is simply
displacement = average velocity x time, and also follows from
graphical considerations. It may be useful to use the ‘suvat’
procedure as a way of identifying which equation should be
used.

Know that an objected projected in a gravitational field
follows a parabolic path.
 Analyse parabolic motion in terms of independent
horizontal and vertical velocity components.
 Solve numerical problems involving parabolic motion
using kinematic motion equations.
 Record (x,y,t) data for a projectile motion.
Lesson 5: This section could be introduced by showing the
“monkey and hunter” game and related animations from the
Albemarle teacher resources at
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A. M. James, Matthew Arnold School, Oxford
‘Accurate
3
Lesson
Content
http://waowen.screaming.net/revision/force&motion/mandh.htm
http://physics.k12albemarle.org/teacher .
You could also demonstrate this experiment. Stress the
independence of horizontal and vertical motions, and the exact
correspondence of the vertical component of motion of a
horizontally-projected object with that of one dropped vertically.
Use Activity 150S (4th model) and/or Albemarle resources to
show how an object projected horizontally in a gravitational
field follows a parabolic path. Discuss how to analyse the
motion in this case using p206, stressing the independence of
horizontal and vertical motions, and the fact that they are only
linked by time. Relate observations to theory.
Now using either Multimedia Motion, Activity 140E (or selfrecorded version) or Activity 130D demonstrate that a
projectile fired at an angle follows a parabolic path. Students
can now either try analysing a projectile sequence from
Multimedia Motion or self-recorded clip to produce (x,y) data
for the projectile as a function of time.
 Explore parabolic motion of projectiles using software
modelling activities.
 Explain parabolic trajectory in terms of addition of
changing vertical velocity vector to successive
calculated velocities.
 Analyse (x,y,t) data from parabolic projectile motion to
determine initial velocity magnitude and direction.
Lesson 6: Students use Activity 150S (models 1-3) to show
how the parabolic motion of an object projected at an angle to
the horizontal arises from addition of downwards-increasing
velocity increment to each successive calculated velocity. Go
through how to analyse the (x,y,t) data from previous lesson to
obtain initial vertical and horizontal velocity (range = vhoriz x t,
vvert from solution of v2 = u2 + 2as) and therefore the initial
velocity magnitude and direction. Note that there is a sheet
called ‘Projectiles help sheet’ which may be useful here,
although it and the accompanying diagram sheet approach
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A. M. James, Matthew Arnold School, Oxford
Activities
follows a parabolic path’
‘Monkey and hunter’ experiment
(see also Activity 170D)
Albemarle
resources
from
http://physics.k12albemarle.org/teacher
Homework
Activity 150S ‘Modelling parabolic
motion’
Activity 174E/File 120L ‘Finding the
range of projectiles’
Multimedia Motion CD ROM
Qs p203
Qs 80S ‘Throwing a ball’
4
Lesson
Content
projectile motion from the perspective of horizontal and vertical
velocity components added to give a resultant, rather than the
changing vertical velocity component being added to the
overall velocity vector to give the resultant. It is also worthwhile
at least demonstrating the software part of Activity 174E to
show how the parabola is affected by changes to the initial
velocity.
Activities
Homework
UP Jan. 08 Q9; Jan. 07 Q6
Qs
60S
‘Uniform
acceleration’
Qs 70S ‘Braking distance
and the Highway Code’
Qs 100E ‘Slowing down a
bicycle’
Worksheet ‘The bouncing
ball’
Exam
questions
on
projectile motion
Qs 80S ‘Throwing a ball’
Qs
110S
‘Accurate
archery’
Qs 90S ‘A slide’
Qs 100D ‘Uncertainties in
measuring g’
Qs 110D ‘Variation in
braking distance with
road conditions’
Qs 120D ‘Variation in
braking distance between
cars’
Qs p203

Develop problem solving skills using the kinematic
equations of motion, including projectiles.
Lesson 7: Practise problem solving. Qs 100D, 110D, 120D are
good for experimental uncertainties and ‘plot and look’.
9.3
Forces
change
Projectile motion, achieving prediction in more complex
situations
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A. M. James, Matthew Arnold School, Oxford
5
Lesson
velocities
Content
Activities
Homework

Explore the relationship between force, mass and
acceleration experimentally.
Lesson 8: Recap GCSE work on Newton’s second law,
showing how F = ma is derived from FΔt = Δmv. Use a frictioncompensated ramp, a dynamics trolley, pulley, cord, set of
masses and light gates. Sample results are provided on
worksheet trolley light gates data. Another version using a
single light gate and a single card with a notch is described in
Activity 200E. As a simpler alternative, use a dynamics trolley
with ticker timer on slopes of varying angles, and plot the
acceleration obtained from the ticker tape graph against sine
of the slope angle to get g (see also lesson 10).
 Recall and use the equation F = ma (Newton 2) in
solving problems.
 Know that F in the equation above is the resultant
force.
 Calculate the resultant force on a body from a
knowledge of the magnitudes and directions of all the
forces acting upon it.
Lesson 9: Explore F = ma using Activity 220S. Emphasise that
the force in this equation is a resultant force, using Qs 120M140M to give students practice in determining resultant forces
(could be homework). Discuss how resultant forces can
change velocity of an object in a variety of ways, as per p207.
Ramp, trolley, pulley, cord, set of
50 g and 100 g masses, light gates
Activity 200E ‘Acceleration and
resultant force using a light gate’
Activity 220S ‘Force, mass and
acceleration’
Qs
120M
‘Adding
forces
graphically’
Qs 130M ‘A loading problem’
Qs 140M ‘Landing an aircraft’
Qs 150S ‘Lifting a car’
Qs
160S
‘Newton’s
second law’
UP G492 Specimen Q6; June 08
Q6; Jan. 07 Q8; June 08 Q10; Jan.
08 Q4


25/06/2017 10:17 AM
Determine experimentally the acceleration due to
gravity.
Know that the weight of a body is obtained by
multiplying its mass by the gravitational field strength
(W = mg).
A. M. James, Matthew Arnold School, Oxford
6
Lesson
Content
 Use W = mg and F = ma to explain why bodies of
different mass fall at the same rate.
Lesson 10: Determine the acceleration due to gravity (using
Activity 120E, 130E or the ‘Measuring g’ timer kit). Discuss the
relationship between mass and weight, as per p206-207, and
therefore explain in terms of F = ma why objects of different
mass fall at the same rate. You could do a ‘Measuring g’
circus, with different groups trying different methods as listed in
Activity 130E.
Activities
Homework
Activity 120E ‘Measuring the
acceleration of free fall’
Activity 130E ‘Measuring g in lots of
different ways’
‘Measuring g’ electronic timer
experiment
Data from the ‘Measuring
g’ experiment can be
used in the data analysis
coursework activity.
Reading
10T
‘The
mysteries of mass’
Qs 180M ‘F=ma: some
tricky problems!’

Explore air resistance experimentally and using
software modelling activities.
Lesson 11: Optional, so omit if behind schedule. Explore
motion in resistive media by doing Activity 260E, and then
modelling with Activity 270S. In Activity 270S, it is helpful to
adapt the model so that k is a variable. Set k to 1.0.
 Explore air resistance experimentally and using
software modelling activities.
 Know that the air resistance force is made up of two
components, depending on velocity and velocity2.
 Explain why an object reaches a terminal velocity
when falling through air, in terms of resultant forces
and F = ma.
Lesson 12: Explore the effects of air resistance on the motion
of a body using Activity 280S, and, as extension work, Activity
290S. Strictly speaking, this lesson is optional, but it is a very
good way of showing the connection between resultant force,
acceleration and velocity.
9.4 Transport
engineering
Activity 260E ‘Falling cupcakes’
Activity 270S ‘Balancing forces on
cupcakes’
Activity
280S
‘Modelling
resistance’
Activity 290S ‘Throwing in air’
air
Qs 190D ‘Cycling through
air’
Qs p208
UP June 07 Q10
Transport using flows of energy for a purpose, controlling
energy flows to optimize transport properties.
 Investigate energy transfer in balls bouncing from
surfaces
 Appreciate how to derive the expressions kinetic
energy = ½ mv2 and gravitational potential energy =
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A. M. James, Matthew Arnold School, Oxford
7
Lesson
Content
mgh from work = force x displacement.
 Recall and use the expressions KE = ½ mv2 and
ΔGPE = mgh in solving problems involving energy
exchanges.
 Know that when energy exchange takes place, some
of the energy is dissipated as heat.
Lesson 13-14: A good place to start is with the experiments on
rebounding balls, showing students how to calculate the
energy transferred as heat and sound by a consideration of PE
before and after a bounce.
Derive the expression KE = ½ mv2 energy from a consideration
of W = Fs. Alternatively, you could use v2 = u2 + 2as as a
starting point.
Now show how W = Fs gives rise to ΔGPE = mgh for an object
raised in a uniform gravitational field. Show how GPE is
changed into KE when an object falls under gravity (no
resistive forces). The consistency with the kinematic equations
of motion can also be shown.
 Explore experimentally the relationship between
braking force and braking distance, and between
speed and braking distance.
 Explain the relationships in terms of KE of vehicle =
braking force x braking distance.
Lesson 15: Students investigate the relationship between
braking distance and force using Activity 340E. This can be
extended to investigating the effect of speed on braking
distance. Discuss findings in terms of the relationship KE of
vehicle = braking force x braking distance.
 Explain why vehicles have a maximum speed in terms
of balanced driving and resistive forces, and in terms
of energy flows.
 Appreciate how to derive the relationship power =
force x velocity.
 Use the equation power = force x velocity to solve
problems involving motion and energy exchanges,
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A. M. James, Matthew Arnold School, Oxford
Activities
Homework
Activity 320E ‘Good on the
rebound’
Activity 330E ‘Poor on the rebound’
Qs 200E ‘A bouncing ball’
Qs
210E
‘Landing
heavily’
Qs 220S ‘A skateboarder’
Qs 260S ‘Rolling up and
down slopes’
UP Jan. 07 Q2; G492 Specimen
Q8
Activity 340E ‘Stripping away
kinetic energy’
Activity 375E ‘Modelling braking
distance’
8
Lesson
Content
including, for the more able, motion up a slope.
Lesson 16-17: Begin by posing the question as to why every
vehicle must have a maximum speed, leading to the
conclusion that resistive forces increase with speed, and no
further acceleration is possible when the resistive forces
balance the driving force provided by the engine. Now get
students to explain why streamlining increases the maximum
speed, in terms of resistive forces (lesson 13 may help). Now
reintroduce the arguments in terms of energy instead of force,
and have students do Activity 360S.
Go through the treatment on p214, to explain maximum speed
in terms of engine power = resistive forces x velocity.
Finish with a consideration of energy flows in motion uphill, by
considering ‘Try these’ question 7 on p215 and/or some of the
examples in the problem sets listed on the right.
Do Chapter 9 test.
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A. M. James, Matthew Arnold School, Oxford
Activities
Homework
Activity 360S ‘Energy flows and
motion’
Qs 230S ‘Power and
cars’
Qs 240W ‘Along the flat
and up the hill’
Qs 280S ‘Working out
with a cycle’
Qs 270D ‘Retarding a
cyclist’
Qs p215
UP June 07 Q6
Qs p217
9