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TEACHER’S RESOURCE
TEACHER’S RESOURCE
9780176520427
ISBN
-10: 0-17-652042-2ISB
N-13: 978-0-17-652042-7
PHY12U TR.indd 1 11-11-11 10:28 AM
NEL Dynamics 1
UNIT
1 Dynamics
FUNDAMENTAL CONCEPTS BIG IDEAS CHAPTER 1
CHAPTER 2
CHAPTER 3
Matter Forces affect motion in predictable and quantifiable ways Forces acting on an object will determine the motion of that object
Energy
Systems and Interactions Many technologies that utilize the principals of dynamics have societal and environmental implications
Structure and Function
OVERVIEW Chapter 1, Kinematics, begins with a review of the equations of motion, with a focus on resolving forces in two dimensions. Students then learn about finding average and instantaneous velocity from a graph of position versus time using tangent lines and secant lines. Students also learn about average and instantaneous acceleration using tangent and secant lines on a velocity versus time graph. A focus of the unit is the key equations of motion and their derivation from graphs. These equations are used in solving problems of motion. Students study two-dimensional motion problems using three methods: scale diagrams, sine and cosine laws, and using perpendicular components. The motion of projectiles is also studied, with emphasis on the application of the equations of motion and perpendicular components. This leads to a set of equations related to the range of a projectile and the optimum conditions for maximum distance. Finally, students will learn about frames of reference and determining relative motion between frames of reference. Chapter 2, Dynamics, focuses on the causes of motion, looking at the vector analysis of forces. Students learn how to create a free-body diagram to help analyze the forces that act on an object and to assess the best approach to resolving forces into perpendicular components. Newton’s laws of motion are examined in detail, as students apply forces and the equations of motion from Chapter 1 to problems. Students learn how the forces of friction impact the motion of objects. Static and kinetic friction are studied as students apply Newton’s laws of motion. Students will gain an appreciation of the forces that exist in our everyday lives, and how the understanding of dynamics has led to technological advances in many areas. Chapter 3, Uniform Circular Motion, focuses on forces that exist as an object moves at a constant speed around a circular path. Students will study inertial and non-inertial frames of reference and learn that the frames of reference studied in Chapter 1 allow the equations of kinematics and dynamics to be applied to frames of reference that are
accelerating by using fictitious forces to help explain the behavior of objects as they move in non-inertial frames of reference. Students learn about centripetal acceleration and centripetal forces and develop related equations. The acceleration of vehicles around banked turns is studied as an application of centripetal force. The concept of friction is used to help students understand how cars can maintain their motion around banked and level curves. Applications of rotating frames of reference, such as artificial gravity and centrifuges (using centrifugal forces), and applications of uniform circular motion, such as roller coasters and improvements to athletic technology, are studied.
TEACHING NOTES • Have students look at the Key Concepts and the Starting
Points at the beginning of each chapter and at the Summary Questions in the Chapter Summary at the end of each chapter. Ask students, How could you use these two features to help you understand the ideas presented in the unit?
• This unit includes hands-on activities and has students working with scientific equipment. Review laboratory safety procedures and refer students to Appendix A1 Safety. Also review the importance of reading and checking directions before beginning an activity, thinking about the purpose of an activity or the testable question, and directing questions to other members of their group before asking you.
• You may want to use or adapt the assessment rubrics found in the Assessment Tools section on the Teacher’s Resource CD-ROM.
ENGAGE THE LEARNER
UNIT PREVIEW • Have students study the photo on page 2 of the Student
Book. Ask, What forces are acting on the athlete as she moves through the banked curve on the luge track? (Friction, air resistance, centripetal, centrifugal and
Dynamics NEL 2
gravitational forces all are acting on the athlete.) Have students brainstorm areas associated with these forces that sport science focuses on to improve the performance of the athlete. Ask, Does the choice of material of the athletic clothing help? (Smooth, tight-fitting clothing reduces resistance) and What changes to the sled could be made that would improve performance? (Lightweight materials and a more aerodynamic design would help performance.)
• Have students read the Big Ideas on page 2 of the Student Book. Ask, Why might it be important to be able to predict how forces affect motion? (Sample answer: If you can predict the effect of a force on an object, the design parameters of the object can be planned carefully for the object to be as beneficial as possible.)
UNIT TASK PREVIEW • Formulate a plan for incorporating the Unit Task into the
whole learning experience for the unit. Whenever possible, highlight ideas that relate to or might be helpful in carrying out the Unit Task. Consider the following questions to help you decide how to manage the Unit Task: – Will students begin the Unit Task early in the unit or
toward the end of the unit? – Will students work on the Unit Task as individuals, in
pairs, or in small groups? – Will you set aside class time for students to work on the
task or will students be expected to complete it on their own time?
– How will the task fit into the overall assessment plan for the unit?
• Point out the Unit Task Bookmark found within some sections (The first Unit Task Bookmark appears in Chapter 1 on page 18 of the Student Book). Explain that these icons alert students to information or procedures that may be helpful in completing the task.
• The Unit Task involves the application of forces and motion to the science of sport and games.
• For further support with the Unit Task, refer to pages 61–62 of this resource.
FOCUS ON STSE • This reading feature focuses on applying the dynamics of
motion, and gets students thinking about the application of dynamics to the winter sport of luge.
• Have students preview the title and examine the photographs that accompany the article. Ask, What do these photographs have to do with forces associated with motion? (Sample answer: To maintain a curve of a fixed radius, the athlete must maintain a fixed speed to have all forces balance. These forces include friction, the normal force, centripetal force, and friction.)
• Once students have read the feature and completed the activity, direct students again to the photograph on page 2
of the Student Book. Ask, Can you think of any factors that must be considered as engineers design better luge sleds? (Sample answer: The sled must be aerodynamic, lightweight and sturdy, yet supply enough of a frictional force that the sled can be maneuvered on the track by the athlete without too much effort.)
ARE YOU READY? • You can use the questions in this feature as a quick
review of relevant concepts and skills and as a means of assessing student understanding of them. Several years may have elapsed since students last encountered some of these concepts or skills, so in many cases it will feel like a first time introduction for students. Use this feature as an instructional opportunity and do not assume students will know the answers.
• Use student responses to identify concepts and subject areas that students may need to review.
• Should weaknesses or needs be identified, you may want to set aside time for review before students begin to work on the unit. Alternatively, you might review the targeted concepts as they present themselves in the unit.
CAREER PATHWAYS PREVIEW • Ask, What are some careers that involve an
understanding of forces and their applications? (Examples include engineering, roller-coaster design, sport science, robotics, aerospace, and military ballistics.)
• Formulate a plan for incorporating Career Pathways into the whole learning experience for the unit.
• Point out the Career Links found within some sections (The first Career Link appears in Chapter 1 on p. 12 of the Student Book.) Explain to students that at the end of each chapter, they will find a Career Pathways feature that outlines various careers requiring the study of the material in the chapter.
• For further support with Career Pathways, refer to pages 28, 44, and 59 of this resource.
DIFFERENTIATED INSTRUCTION • For each Big Idea on page 2 of the Student Book, have
students make predictions about what they think they will learn in the unit. Students may record their ideas in different ways. For example, visual learners could draw diagrams or graphic organizers; auditory learners could discuss their ideas with a partner and record their conversation.
ENGLISH LANGUAGE LEARNERS • Hand out copies of BLM 0.0-6 Science Idea Box to
students. As they work through the unit, students should use this BLM to record the key concepts and formulas of each section.
NEL Dynamics 3
Curriculum Correlation
A: Scientific Investigation Skills and Career Exploration
A1. SCIENTIFIC INVESTIGATION SKILLS SECTIONS
OVERALL EXPECTATIONS SPECIFIC EXPECTATIONS
A1. demonstrate scientific investigation skills in the four areas of skills
A1.1 formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research
1.1, 2.3.1, 2.4.1, 2.4.2. 3.3.1, 3.3.2
A1.2 select appropriate instruments and materials, and identify appropriate methods, techniques, and procedures for each inquiry
2.3.1, 2.4.1, 2.4.2, 3.3.1, 3.3.2
A1.3 identify and locate a variety of print and electronic sources that enable them to address research topics fully and appropriately
2.5, 3.6, Unit 1 Task
A1.4 apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHIMS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory and biological materials; and by using appropriate personal protection
1.5.1, 2.4, 2.3.1, 2.4.1, 2.4.2, 3.4, 3.3.1, 3.3.2, Unit 1 Task
A1.5 conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data
1.5.1, 2.4 , 2.3.1, 2.4.1, 2.4.2, 3.4 , 3.3.1, 3.3.2, Unit 1 Task
A1.6 compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams
1.5, 1.5.1, 2.4 , 2.3.1, 2.4.1, 2.4.2, 3.4 , 3.3.1, 3.3.2, Unit 1 Task
A1.7 select, organize, and record relevant information on research topics from a variety of appropriate sources, including electronic, print, and/or human sources, using suitable formats and an accepted form of academic documentation
2.5, 2.6, 3.6, Unit 1 Task
A1.8 synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data to determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory, identify sources of bias and/or error, and suggest improvements to the inquiry to reduce the likelihood of error
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.5.1, 2.3.1, 2.4.1, 2.4.2, 3.3.1, 3.3.2
A1.9 analyse the information gathered from research sources for logic, accuracy, reliability, adequacy, and bias
2.5, 2.6, 3.6, Unit 1 Task
A1.10 draw conclusions based on inquiry results and research findings, and justify their conclusions with reference to scientific knowledge
1.5, 1.5.1, 2.5, 2.6, 2.3.1, 2.4.1, 2.4.2, 3.6, 3.3.1, 3.3.2, Unit 1 Task
A1.11 communicate ideas, plans, procedures, results, and conclusions orally, in writing, and/or in electronic presentations, using appropriate language and a variety of formats
1.5, 1.5.1, 2.5, 2.6 , 2.3.1, 2.4.1, 2.4.2, 3.5, 3.6, 3.3.1, 3.3.2, Unit 1 Task
A1.12 use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.5.1, 2.3.1, 2.4.1, 2.4.2, 3.3.1, 3.3.2, Unit 1 Task
A1.13 express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.5.1, 2.3.1, 2.4.1, 2.4.2, 3.3.1, 3.3.2
4 Dynamics NEL
A2. CAREER EXPLORATION SECTION(S)
OVERALL EXPECTATIONS SPECIFIC EXPECTATIONS
A2. identify and describe careers related to the fields of science under study, and describe contributions of scientists including Canadians, to those fields
A2.1 identify and describe a variety of careers related to the fields of science under study and the education and training necessary for these careers
1.1, 1.3, 1.6, 2.1, 2.4, 2.5, 2.6, 3.3, 3.4, 3.5, 3.6
A2.2 describe the contributions of scientists, including Canadians to the fields under study
B: DYNAMICS
B1. RELATING SCIENCE TO TECHNOLOGY, SOCIETY, AND THE ENVIRONMENT SECTION(S)
OVERALL EXPECTATIONS SPECIFIC EXPECTATIONS
B1. analyse technological devices that apply the principles of the dynamics of motion, and assess the technologies’ social and environmental impact
B1.1 analyse a technological device that applies the principles of linear or circular motion
1.1, 1.2, 2.5, 2.6, 3.4, 3.5, 3.6
B1.2 assess the impact on society and the environment of technological devices that use linear or circular motion
2.5, 3.4, 3.5, 3.6
B2. DEVELOPING SKILLS OF INVESTIGATION AND COMMUNICATION SECTION(S)
OVERALL EXPECTATIONS SPECIFIC EXPECTATIONS
B2. investigate, in qualitative and quantitative terms, forces involved in uniform circular motion and motion in a plane, and solve related problems
B2.1 use appropriate terminology related to dynamics, including, but not limited to: inertial and non-inertial frames of reference, components, centripetal, period, static friction, and kinetic friction
1.3, 1.4
B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methods
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.5.1
B2.3 analyse, in qualitative and quantitative terms, the relationships between the force of gravity, normal force, applied force, force of friction, coefficient of static friction, and coefficient of kinetic friction, and solve related two-dimensional problems using free-body diagrams, vector components, and algebraic equations
2.1, 2.2, 2.3, 2.4
B2.4 predict, in qualitative and quantitative terms, the forces acting on systems of objects, and plan and conduct an inquiry to test their predictions
2.1, 2.2, 2.3, 2.4, 2.3.1, 2.4.1, 2.4.2
B2.5 analyse, in terms of qualitative and quantitative terms, the relationship between the motion of a system and the forces involved
2.1, 2.2, 2.4
B2.6 analyse, in qualitative and quantitative terms, the forces acting on and the acceleration experienced by an object in uniform circular motion in horizontal and vertical planes, and use free-body diagrams and algebraic equations to solve related problems
3.2, 3.3
B2.7 conduct inquiries into the uniform circular motion of an object, and analyse, in qualitative and quantitative terms, the relationships between centripetal acceleration, centripetal force, radius of orbit, period, frequency, mass, and speed
3.3, 3.3.1, 3.3.2
NEL Dynamics 5
B3. UNDERSTANDING BASIC CONCEPTS SECTION(S)
OVERALL EXPECTATIONS SPECIFIC EXPECTATIONS
B3. demonstrate an understanding of the forces involved in uniform circular motion and motion in a plane
B3.1 distinguish between reference systems with respect to the real and apparent forces acting within such systems
1.6, 3.1, 3.4
B3.2 explain the advantages and disadvantages of static and kinetic friction in situations involving various planes
2.4, 2.6
B3.3 explain the derivation of equations for uniform circular motion that involve the variable frequency, period, radius speed, and mass
3.2
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e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 4
: App
licat
ion
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Sum
mar
y 4:
App
licat
ion
Skills
Han
dboo
k A7
Cho
osin
g Ap
prop
riate
Car
eer
Path
way
s
Dyn
amic
s
NE
L
8 SEC
TIO
N
HA
ND
S-O
N A
CTI
VITI
ES A
ND
SK
ILLS
A
SSES
SMEN
T/EV
ALU
ATI
ON
O
PPO
RTU
NIT
IES
PRO
GR
AM
RES
OU
RC
ES
Cha
pter
2 D
ynam
ics
p. 2
9 [S
tude
nt B
ook
p. 6
0]
Min
i Inv
estig
atio
n: D
escr
ibin
g M
otio
n U
sing
N
ewto
n`s
Law
s p.
29
[Stu
dent
Boo
k p.
61]
•
Perfo
rmin
g •
Obs
ervi
ng
• Pr
edic
ting
• An
alyz
ing
• C
omm
unic
atin
g
• M
ini I
nves
tigat
ion
– O
bser
ving
effe
cts
of N
ewto
n’s
thre
e la
ws
on th
e m
otio
n of
obj
ects
in th
ree
diffe
rent
sce
nario
s •
Ass
essm
ent o
f prio
r kno
wle
dge
•
Rea
ding
and
ans
wer
ing
ques
tions
2.1
Forc
es a
nd F
ree-
Bod
y D
iagr
ams
p. 3
0 [S
tude
nt B
ook
p. 6
2]
•
Com
plet
ing
the
prac
tice
prob
lem
s •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
0.0
-2 G
raph
ic O
rgan
izer
: Com
pare
and
Con
trast
C
hart
As
sess
men
t Rub
ric 1
: Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent R
ubric
4: A
pplic
atio
n As
sess
men
t Sum
mar
y 1:
Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
4: A
pplic
atio
n
2.2
New
ton`
s La
ws
of M
otio
n p.
32 [S
tude
nt B
ook
p. 7
0]
•
Com
plet
ing
the
prac
tice
prob
lem
s •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
0.0
-4 G
raph
ic O
rgan
izer
: Con
cept
Map
BL
M 2
.2-1
New
ton’
s La
ws
of M
otio
n
BLM
2.2
-2 N
ewto
n’s
Third
Law
As
sess
men
t Rub
ric 1
: Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent R
ubric
4: A
pplic
atio
n
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Sum
mar
y 4:
App
licat
ion
2.3
App
lyin
g N
ewto
n`s
Law
s of
M
otio
n p.
33
[Stu
dent
Boo
k p.
77]
• C
ompl
etin
g th
e pr
actic
e pr
oble
ms
• C
ompl
etin
g th
e BL
M
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
BLM
2.3
-1 A
pply
ing
New
ton’
s La
ws
of M
otio
n
Asse
ssm
ent R
ubric
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 4
: App
licat
ion
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Sum
mar
y 4:
App
licat
ion
2.3.
1 O
bser
vatio
nal S
tudy
: Sta
tic
Equi
libriu
m o
f For
ces
p. 3
9 [S
tude
nt B
ook
p. 9
5]
2.3.
1 O
bser
vatio
nal S
tudy
: Sta
tic E
quili
briu
m
of F
orce
s p.
39
[Stu
dent
Boo
k p.
95]
•
Con
trollin
g Va
riabl
es
•
Perfo
rmin
g •
Obs
ervi
ng
• An
alyz
ing
• Ev
alua
ting
• C
omm
unic
atin
g
• Fo
llow
ing
safe
labo
rato
ry p
ract
ices
•
Anal
yzin
g ho
w fo
rces
of f
rictio
n an
d ot
her f
orce
s af
fect
a s
yste
m in
equ
ilibriu
m
• Pe
rform
ing
calc
ulat
ions
and
sol
ving
two
dim
ensi
onal
pro
blem
s •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
2.3
.1-1
Inve
stig
atio
n: S
tatic
Equ
ilibriu
m o
f For
ces
– D
ata
Tabl
es
BLM
2.3
.1-2
Inve
stig
atio
n: S
tatic
Equ
ilibriu
m o
f Fo
rces
– S
ampl
e D
ata
As
sess
men
t Rub
ric 7
: Obs
erva
tiona
l Stu
dy
Asse
ssm
ent S
umm
ary
7: O
bser
vatio
nal S
tudy
Se
lf-As
sess
men
t Che
cklis
t 3: O
bser
vatio
nal S
tudy
Sk
ills H
andb
ook
A2.4
Obs
erva
tiona
l Stu
dies
NE
L
Dyn
amic
s 9
SEC
TIO
N
HA
ND
S-O
N A
CTI
VITI
ES A
ND
SK
ILLS
A
SSES
SMEN
T/EV
ALU
ATI
ON
O
PPO
RTU
NIT
IES
PRO
GR
AM
RES
OU
RC
ES
2.4
Forc
es o
f Fric
tion
p. 3
5 [S
tude
nt B
ook
p. 8
4]
Min
i Inv
estig
atio
n: L
ight
from
Fric
tion
p. 3
6 [S
tude
nt B
ook
p. 8
6]
• O
bser
ving
•
Anal
yzin
g •
Com
mun
icat
ing
• M
ini I
nves
tigat
ion
– O
bser
ving
the
prod
uctio
n of
lig
ht fr
om fr
ictio
n as
a w
inte
rgre
en m
int i
s cr
ushe
d
• C
ompl
etin
g th
e pr
actic
e pr
oble
ms
• C
ompl
etin
g th
e BL
M
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
BLM
2.4
-1 F
orce
s of
Fric
tion
As
sess
men
t Rub
ric 1
: Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent R
ubric
4: A
pplic
atio
n
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Sum
mar
y 4:
App
licat
ion
Skills
Han
dboo
k A2
.1 S
kills
of S
cien
tific
Inqu
iry
2.4.
1 C
ontr
olle
d Ex
perim
ent:
Incl
ined
Pla
ne a
nd F
rictio
n p.
40
[Stu
dent
Boo
k p.
96]
2.4.
1 C
ontr
olle
d Ex
perim
ent:
Incl
ined
Pla
ne
and
Fric
tion
p. 4
0 [S
tude
nt B
ook
p. 9
6]
• H
ypot
hesi
zing
•
Con
trollin
g Va
riabl
es
•
Per
form
ing
• O
bser
ving
•
Ana
lyzi
ng
• E
valu
atin
g •
Com
mun
icat
ing
• D
evel
opin
g an
d te
stin
g a
hypo
thes
is
• Pe
rform
ing
calc
ulat
ions
to d
eter
min
e fri
ctio
nal
forc
es a
nd n
orm
al fo
rces
and
ana
lyzi
ng th
e da
ta
• F
ollo
win
g sa
fe la
bora
tory
pra
ctic
es
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
Asse
ssm
ent R
ubric
5: C
ontro
lled
Expe
rimen
t As
sess
men
t Sum
mar
y 5:
Con
trolle
d Ex
perim
ent
Self-
Asse
ssm
ent C
heck
list 1
: Con
trolle
d Ex
perim
ent
Skills
Han
dboo
k A2
.2 C
ontro
lled
Expe
rimen
ts
2.4.
2 O
bser
vatio
nal S
tudy
: Mot
ion
and
Pulle
ys
p. 4
2 [S
tude
nt B
ook
p. 9
7]
2.4.
2 O
bser
vatio
nal S
tudy
: Mot
ion
and
Pulle
ys
p. 4
2 [S
tude
nt B
ook
p. 9
7]
• P
redi
ctin
g •
Pla
nnin
g •
Con
trollin
g Va
riabl
es
•
Per
form
ing
• O
bser
ving
•
Ana
lyzi
ng
• E
valu
atin
g •
Com
mun
icat
ing
• F
ollo
win
g sa
fe la
bora
tory
pra
ctic
es
• Pl
anni
ng a
n in
vest
igat
ion
to c
alcu
late
and
then
m
easu
re th
e ac
cele
ratio
n of
a m
ovin
g m
ass
• Pr
edic
ting
valu
es
• An
alyz
ing
mea
sure
d va
lues
•
Per
form
ing
calc
ulat
ions
•
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
2.4
.2-1
Inve
stig
atio
n: M
otio
n an
d Pu
lleys
– D
ata
Tabl
es
BLM
2.4
.2-2
Inve
stig
atio
n: M
otio
n an
d Pu
lleys
–
Sam
ple
Dat
a As
sess
men
t Rub
ric 7
: Obs
erva
tiona
l Stu
dy
Asse
ssm
ent S
umm
ary
7: O
bser
vatio
nal S
tudy
Se
lf-As
sess
men
t Che
cklis
t 3: O
bser
vatio
nal S
tudy
2.5
Expl
ore
an A
pplic
atio
n in
D
ynam
ics:
Lin
ear A
ctua
tors
p.
37
[Stu
dent
Boo
k p.
91]
2.5
Expl
ore
an A
pplic
atio
n in
Dyn
amic
s:
Line
ar A
ctua
tors
p.
37
[Stu
dent
Boo
k p.
91]
•
Res
earc
hing
•
Per
form
ing
• O
bser
ving
•
Ana
lyzi
ng
• E
valu
atin
g
•
Com
mun
icat
ing
• R
esea
rchi
ng th
e di
ffere
nt ty
pes
of a
ctua
tors
and
ho
w th
ey a
re u
sed
• E
xplo
ring
the
func
tion
of a
line
ar a
ctua
tor a
nd th
e ch
arac
teris
tics
by w
hich
a li
near
act
uato
r is
clas
sifie
d •
Iden
tifyi
ng th
e ad
vant
ages
and
dis
adva
ntag
es o
f th
e us
e of
mec
hani
cal a
ctua
tors
and
how
the
use
affe
cts
soci
ety
and
the
envi
ronm
ent
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
Asse
ssm
ent R
ubric
10:
Exp
lore
an
Appl
icat
ion
As
sess
men
t Sum
mar
y 10
: Exp
lore
an
Appl
icat
ion
Se
lf-As
sess
men
t Che
cklis
t 6: E
xplo
re a
n Ap
plic
atio
n Sk
ills H
andb
ook
A4.1
Res
earc
h Sk
ills
Dyn
amic
s
NE
L
10SEC
TIO
N
HA
ND
S-O
N A
CTI
VITI
ES A
ND
SK
ILLS
A
SSES
SMEN
T/EV
ALU
ATI
ON
O
PPO
RTU
NIT
IES
PRO
GR
AM
RES
OU
RC
ES
2.6
Phys
ics
Jour
nal:
The
Phys
ics
of D
ownh
ill S
kiin
g p.
38
[Stu
dent
Boo
k p.
93]
•
Rea
ding
abo
ut th
e ph
ysic
s of
dow
nhill
skiin
g,
incl
udin
g th
e va
rious
forc
es a
ctin
g on
a s
kier
•
Iden
tifyi
ng h
ow th
e de
sign
of s
afet
y eq
uipm
ent
mus
t tak
e th
e fo
rces
act
ing
on a
dow
nhill
skie
r int
o ac
coun
t •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
0.0
-2 G
raph
ic O
rgan
izer
: Com
pare
and
Con
trast
C
hart
BL
M 0
.0-7
Gra
phic
Org
aniz
er: T
erm
Box
BL
M 0
.0-8
Rea
ding
Stra
tegi
es C
heck
list
Skills
Han
dboo
k A3
Sci
entif
ic P
ublic
atio
ns
Cha
pter
2 S
umm
ary
p. 4
3 [S
tude
nt B
ook
p. 9
8]
•
Sum
mar
y qu
estio
ns
• C
ompl
etin
g th
e BL
M
• C
hapt
er 2
Sel
f-Qui
z •
Cha
pter
2 R
evie
w
BLM
0.0
-10
Car
eers
BL
M 2
.Q C
hapt
er 2
Qui
z
Asse
ssm
ent R
ubric
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 2
: Thi
nkin
g an
d In
vest
igat
ion
Asse
ssm
ent R
ubric
4: A
pplic
atio
n As
sess
men
t Sum
mar
y 1:
Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
2: T
hink
ing
and
Inve
stig
atio
n As
sess
men
t Sum
mar
y 4:
App
licat
ion
Skills
Han
dboo
k A6
Cho
osin
g Ap
prop
riate
Car
eer
P
athw
ays
Cha
pter
3 U
nifo
rm C
ircul
ar M
otio
n p.
45
[Stu
dent
Boo
k p.
106
] M
ini I
nves
tigat
ion:
Obs
ervi
ng C
ircul
ar
Mot
ion
p. 4
5 [S
tude
nt B
ook
p. 1
07]
• P
erfo
rmin
g •
Obs
ervi
ng
• A
naly
zing
•
Com
mun
icat
ing
• M
ini I
nves
tigat
ion
– Ex
plor
ing
circ
ular
mot
ion
at
cons
tant
spe
ed
• A
sses
smen
t of p
rior k
now
ledg
e
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
Skills
Han
dboo
k A2
.1 S
kills
of S
cien
tific
Inqu
iry
3.1
Iner
tial a
nd N
on-in
ertia
l Fr
ames
of R
efer
ence
p.
46
[Stu
dent
Boo
k p.
108
]
•
Com
plet
ing
the
prac
tice
prob
lem
s •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
0.0
-2 G
raph
ic O
rgan
izer
: Com
pare
and
Con
trast
C
hart
BLM
3.1
-1 In
ertia
l and
Non
-iner
tial F
ram
es o
f R
efer
ence
As
sess
men
t Rub
ric 1
: Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
NE
L
Dyn
amic
s 1
1
SEC
TIO
N
HA
ND
S-O
N A
CTI
VITI
ES A
ND
SK
ILLS
A
SSES
SMEN
T/EV
ALU
ATI
ON
O
PPO
RTU
NIT
IES
PRO
GR
AM
RES
OU
RC
ES
3.2
Cen
trip
etal
Acc
eler
atio
n p.
47
[Stu
dent
Boo
k p.
114
]
• C
ompl
etin
g th
e pr
actic
e pr
oble
ms
• C
ompl
etin
g th
e BL
M
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
BLM
3.2
-1 T
he N
et F
orce
in U
nifo
rm C
ircul
ar M
otio
n BL
M 3
.2-2
Cen
tripe
tal A
ccel
erat
ion
As
sess
men
t Rub
ric 1
: Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent R
ubric
4: A
pplic
atio
n As
sess
men
t Sum
mar
y 1:
Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
4: A
pplic
atio
n
3.3
Cen
trip
etal
For
ce
p. 4
9 [S
tude
nt B
ook
p. 1
20]
•
Com
plet
ing
the
prac
tice
prob
lem
s •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
3.3
-1 R
esol
utio
n of
For
ces
BLM
3.3
-2 C
entri
peta
l For
ce
Asse
ssm
ent R
ubric
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 4
: App
licat
ion
Asse
ssm
ent S
umm
ary
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Sum
mar
y 4:
App
licat
ion
3.3.
1 O
bser
vatio
nal S
tudy
: Si
mul
atin
g U
nifo
rm C
ircul
ar
Mot
ion
p. 5
5 [S
tude
nt B
ook
p. 1
35]
3.3.
1 O
bser
vatio
nal S
tudy
: Sim
ulat
ing
Uni
form
Circ
ular
Mot
ion
p. 5
5 [S
tude
nt B
ook
p. 1
35]
• C
ontro
lling
Varia
bles
• P
erfo
rmin
g •
Obs
ervi
ng
• A
naly
zing
•
Eva
luat
ing
• C
omm
unic
atin
g
• A
naly
zing
gra
ph d
ata
and
calc
ulat
ing
forc
es th
at
exis
t dur
ing
unifo
rm c
ircul
ar m
otio
n •
Iden
tifyi
ng v
aria
bles
in a
ste
p of
the
proc
edur
e an
d th
e id
entif
ying
the
effe
ct c
hang
ing
the
varia
ble
has
on th
e sy
stem
•
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
3.3
.1-1
Inve
stig
atio
n: S
imul
atin
g U
nifo
rm C
ircul
ar
Mot
ion
– D
ata
Tabl
es
BLM
3.3
.1-2
Inve
stig
atio
n: S
imul
atin
g U
nifo
rm C
ircul
ar
Mot
ion
– Sa
mpl
e D
ata
As
sess
men
t Rub
ric 7
: Obs
erva
tiona
l Stu
dy
Asse
ssm
ent S
umm
ary
7: O
bser
vatio
nal S
tudy
Se
lf-As
sess
men
t Che
cklis
t 3: O
bser
vatio
nal S
tudy
Sk
ills H
andb
ook
A2.4
Obs
erva
tiona
l Stu
dies
Sk
ills H
andb
ook
A5.5
Ana
lyzi
ng E
xper
imen
tal D
ata
3.3.
2 C
ontr
olle
d Ex
perim
ent:
Ana
lyzi
ng U
nifo
rm C
ircul
ar
Mot
ion
p. 5
6 [S
tude
nt B
ook
p. 1
36]
3.3.
2 C
ontr
olle
d Ex
perim
ent:
Ana
lyzi
ng
Uni
form
Circ
ular
Mot
ion
p. 5
6 [S
tude
nt B
ook
p. 1
36]
• P
redi
ctin
g
•
Con
trollin
g Va
riabl
es
•
Per
form
ing
• O
bser
ving
•
Ana
lyzi
ng
• E
valu
atin
g •
Com
mun
icat
ing
• F
ollo
win
g sa
fe la
bora
tory
pra
ctic
es
• Pr
edic
ting
the
rela
tions
hip
betw
een
the
frequ
ency
of
rev
olut
ion
and
a va
riabl
e •
Iden
tifyi
ng th
e de
pend
ent,
inde
pend
ent,
and
cont
rolle
d va
riabl
es
• P
erfo
rmin
g ca
lcul
atio
ns a
nd g
raph
ing
expe
rimen
tal
resu
lts
• C
ompl
etin
g th
e BL
M
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
BLM
3.3
.2-1
Inve
stig
atio
n: A
naly
zing
Uni
form
Circ
ular
M
otio
n –
Dat
a Ta
bles
BL
M 3
.3.2
-2 In
vest
igat
ion:
Ana
lyzi
ng U
nifo
rm C
ircul
ar
Mot
ion
– Sa
mpl
e D
ata
As
sess
men
t Rub
ric 5
: Con
trolle
d Ex
perim
ent
Asse
ssm
ent S
umm
ary
5: C
ontro
lled
Expe
rimen
t Se
lf-As
sess
men
t Che
cklis
t 1: C
ontro
lled
Expe
rimen
t Sk
ills H
andb
ook
A2.2
Con
trolle
d Ex
perim
ents
Sk
ills H
andb
ook
A5.5
Ana
lyzi
ng E
xper
imen
tal D
Dyn
amic
s
NE
L
12SEC
TIO
N
HA
ND
S-O
N A
CTI
VITI
ES A
ND
SK
ILLS
A
SSES
SMEN
T/EV
ALU
ATI
ON
O
PPO
RTU
NIT
IES
PRO
GR
AM
RES
OU
RC
ES
3.4
Rot
atin
g Fr
ames
of R
efer
ence
p.
51
[Stu
dent
Boo
k p.
125
] M
ini I
nves
tigat
ion:
Fou
caul
t Pen
dulu
m
p. 5
2 [S
tude
nt B
ook
p. 1
28]
• P
erfo
rmin
g •
Obs
ervi
ng
• A
naly
zing
•
Com
mun
icat
ing
• M
ini I
nves
tigat
ion
– O
bser
ving
the
effe
ct o
f a
spin
ning
glo
be o
n a
wei
ght h
angi
ng fr
om a
sup
port
• C
ompl
etin
g th
e pr
actic
e pr
oble
ms
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
Asse
ssm
ent R
ubric
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 2
: Thi
nkin
g an
d In
vest
igat
ion
As
sess
men
t Sum
mar
y 1:
Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
2: T
hink
ing
and
Inve
stig
atio
n Sk
ills H
andb
ook
A2.1
Ski
lls o
f Sci
entif
ic In
quiry
3.5
Phys
ics
Jour
nal:
The
Phys
ics
of R
olle
r Coa
ster
s p.
52
[Stu
dent
Boo
k p.
131
]
•
Lear
ning
abo
ut th
e ph
ysic
s of
rolle
r coa
ster
s an
d ho
w th
ey a
re d
esig
ned
• C
ompl
etin
g th
e BL
M
• R
eadi
ng a
nd a
nsw
erin
g qu
estio
ns
BLM
0.0
-7 G
raph
ic O
rgan
izer
: Ter
m B
ox
BLM
0.0
-8 R
eadi
ng S
trate
gies
Che
cklis
t Sk
ills H
andb
ook
A3 S
cien
tific
Pub
licat
ions
3.6
Expl
ore
an Is
sue
in D
ynam
ics:
Im
prov
emen
ts in
Ath
letic
Te
chno
logy
p.
53
[Stu
dent
Boo
k p.
133
]
3.6
Expl
ore
an Is
sue
in D
ynam
ics:
Im
prov
emen
ts in
Ath
letic
Tec
hnol
ogy
p. 5
3 [S
tude
nt B
ook
p. 1
33]
• R
esea
rchi
ng
• Id
entif
ying
Alte
rnat
ives
•
Ana
lyzi
ng
• D
efen
ding
a D
ecis
ion
• C
omm
unic
atin
g
• E
valu
atin
g
• R
esea
rchi
ng in
nova
tions
in s
ports
that
impa
ct o
n pe
rform
ance
•
Com
mun
icat
ing
and
defe
ndin
g a
deci
sion
on
whe
ther
or n
ot to
com
pare
pre
viou
s re
sults
with
th
ose
aide
d by
impr
oved
tech
nolo
gy a
nd e
quip
men
t •
Com
plet
ing
the
BLM
•
Rea
ding
and
ans
wer
ing
ques
tions
BLM
0.0
-3 G
raph
ic O
rgan
izer
: Tw
o-C
olum
n Ta
ble
As
sess
men
t Rub
ric 9
: Exp
lore
an
Issu
e
Asse
ssm
ent S
umm
ary
9: E
xplo
re a
n Is
sue
Se
lf-As
sess
men
t Che
cklis
t 5: E
xplo
re a
n Is
sue
Skills
Han
dboo
k A4
Exp
lorin
g Is
sues
and
App
licat
ions
Cha
pter
3 S
umm
ary
p. 5
8 [S
tude
nt B
ook
p. 1
38]
•
Sum
mar
y qu
estio
ns
• C
ompl
etin
g th
e BL
M
• C
hapt
er 3
Sel
f-Qui
z •
Cha
pter
3 R
evie
w
BLM
0.0
-10
Car
eers
BL
M 3
.Q C
hapt
er 3
Qui
z
Asse
ssm
ent R
ubric
1: K
now
ledg
e an
d U
nder
stan
ding
As
sess
men
t Rub
ric 2
: Thi
nkin
g an
d In
vest
igat
ion
Asse
ssm
ent R
ubric
4: A
pplic
atio
n As
sess
men
t Sum
mar
y 1:
Kno
wle
dge
and
Und
erst
andi
ng
Asse
ssm
ent S
umm
ary
2: T
hink
ing
and
Inve
stig
atio
n As
sess
men
t Sum
mar
y 4:
App
licat
ion
Skills
Han
dboo
k A6
Cho
osin
g Ap
prop
riate
Car
eer
P
athw
ays
Uni
t 1 C
losi
ng
p. 6
1 [S
tude
nt B
ook
p. 1
46]
Uni
t Tas
k: A
New
Ext
rem
e Sp
ort
p. 6
1 [S
tude
nt B
ook
p. 1
46]
• U
nit T
ask
– A
New
Ext
rem
e Sp
ort
• U
nit 1
Sel
f-Qui
z •
Uni
t 1 R
evie
w
BLM
U1.
Q U
nit 1
Qui
z
Uni
t 1 T
ask
Asse
ssm
ent R
ubric
: A N
ew E
xtre
me
Spor
t U
nit 1
Tas
k As
sess
men
t Sum
mar
y: A
New
Ext
rem
e Sp
ort
Uni
t 1 T
ask
Self-
Asse
ssm
ent C
heck
list:
A N
ew
Extre
me
Spor
t
NEL Dynamics 13
Equipment and Materials The quantity of equipment and materials for activities and investigations is based on the groups suggested in the specific sections. The quantities are based on a standard class size of 32 students, broken down into groupings of two or four students. Where the term “quantity” is inappropriate—such as for a piece of tubing, masking tape, and so on—you will have to check the individual activity or investigation to obtain appropriate quantities. In the table below, “Equipment” refers to actual equipment or hardware, such as microscopes, metre sticks, glassware; and “Materials” refers to consumable items, such as chemicals, tape, water, or paper.
Unit 1: Dynamics
INVESTIGATION/ACTIVITY QUANTITY EQUIPMENT QUANTITY MATERIALS
Chapter 1 Mini Investigation: Launching Projectiles p. 15 [Student Book p. 7] Student groupings: 8 groups of 4 students
32 8 8
• eye protection • projectile launcher • ball of modelling clay, or other soft
material
1.5 Mini Investigation: Analyzing the Range of a Projectile p. 23 [Student Book p. 38] Student groupings: 16 groups of 2 students
16
• calculator
— 16
• paper • pencil
1.5.1 Observational Study: Investigating Projectile Motion p. 26 [Student Book p. 50] Student groupings: 8 groups of 4 students
8 8 8 8
• air table with sparker puck • material to support end of air table, such as a brick • metric ruler • protractor
—
• construction paper
Chapter 2 Mini Investigation: Describing Motion Using Newton’s Laws p. 29 [Student Book p. 61] Student groupings: 16 groups of 2 students
16 32
16 16
• pulley • cart (2 per group of equal mass, 1 spring-loaded) • 50 g mass • 200 g mass
—
• string
2.3.1 Observational Study: Static Equilibrium of Forces p. 39 [Student Book p. 95] Student groupings: 8 groups of 4 students
32 24 8 8
24 8 16
• eye protection • small pulley (3 per group) • circular protractor • vertical force board (or support structure) • hanger (3 per group) • 100 g mass • 200 g mass (2 per group)
8
—
• padding, such as towel or blanket
• string
2.4 Mini Investigation: Light from Friction p. 36 [Student Book p. 86] Student groupings: 8 groups of 4 students
32 8
• eye protection • pliers
—
• wintergreen mints
Dynamics NEL 14
INVESTIGATION/ACTIVITY QUANTITY EQUIPMENT QUANTITY MATERIALS
2.4.1 Controlled Experiment: Inclined Plane and Friction p. 40 [Student Book p.96] Student groupings: 8 groups of 4 students
8 8 8
• metre stick • inclined plane • protractor (optional)
—
• test object (such as running shoe, textbook, plastic block, piece of wood)
2.4.2 Observational Study: Motion and Pulleys p. 42 [Student Book p.97] Student groupings: 8 groups of 4 students
32 8 8 8 8 8 8 8 8 8
• eye protection • ticker tape timer, motion sensor,
or video camera • metre stick • protractor • stopwatch • 100 g mass • 200 g mass • 500 g mass • pulley • inclined plane from Investigation 2.4.1
— 8
• string • one object from Investigation 2.4.1
Chapter 3 Mini Investigation: Observing Circular Motion p. 45 [Student Book p. 107] Student groupings: 8 groups of 4 students
32 8 8 8 24 8
• eye protection • small eye screw • small rubber stopper • plastic tube • 50 g mass (3 per group) • alligator clip
—
• string
3.3.1 Observational Study: Simulating Uniform Circular Motion p. 55 [Student Book p.135] Student groupings: 16 groups of 2 students
16
• computer with Internet connection
—
• graphing paper or graphing software
3.3.2 Controlled Experiment: Analyzing Uniform Circular Motion p. 56 [Student Book p.136] Student groupings: 8 groups of 4 students
32 8 24 8 8 8 8 8 8
• eye protection • electronic balance or scale • small rubber stopper with centre
hole (3 per group) • hollow tube • 50 g mass • 100 g mass • 200 g mass • 250 g mass • metre stick
— — —
• 1.5 m string or fishing line • paper clip or masking tape • graph paper or graphing
software
3.4 Mini Investigation: Foucault Pendulum p. 52 [Student Book p. 128] Student groupings: 8 groups of 4 students
32 8 8
• eye protection • globe (or large ball) • 50 g mass
— — —
• wooden splint or straw • string • tape
NEL Kinematics 15
CHAPTER
1 Kinematics
PROGRAM RESOURCES Skills Handbook A2.1 Skills of Scientific Inquiry Physics 12 ExamView® Test Bank Physics 12 Online Teaching Centre
SMART Notebook lesson PowerPoint lesson
Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
TEACHING NOTES • Have students examine the Chapter Opener photograph.
Ask, Compare the paths of an acrobat fired from a cannon and a soccer ball kicked into the air. (They both follow a similar, parabolic path as they travel.)
• Ask students to relate gravity and the motion of the acrobat being fired from the cannon to the key question: How Can Two-Dimensional Motion Be Analyzed? (Gravity only affects motion in the vertical direction, but it determines how long an object will be in the air and so affects the horizontal distance an object will travel.)
• Ask students to think about what a captain would have to do to steer a cruise ship in the correct direction when a current is encountered.
ENGAGE THE LEARNER
CHAPTER INTRODUCTION • To preview the major ideas that will be explored in the
chapter, review the Key Concepts. Ask a student volunteer to read each Key Concept aloud before it is discussed. Ask prompting questions to assess students’ prior knowledge and to engage students in the topics. Examples are given: 1. What are some examples of one-dimensional and two-
dimensional situations in physics? (Sample answers: one dimensional – the motion of a train on a fixed track; two dimensional – the motion of a boat as it moves across a river with a perpendicular current)
2. What is the difference between average speed and average velocity? (Average speed is a scalar and average velocity is a vector.)
3. What is acceleration and how is it calculated? (Acceleration is the rate of change of velocity with time, calculated by dividing the change in velocity by the change in time.)
4. In everyday language, what is a component? (A component is a piece of something, or part of a whole.)
5. What is relative motion? (Relative motion is motion reported with respect to some fixed or moving object to
give a frame of reference to the motion.) Give an example of relative motion. (Sample answer: A person walking to the back of a bus as it pulls away from a stop is moving toward the back of the bus to someone sitting on the bus, but moving forward with respect to someone standing outside the bus at the stop.)
6. What is a projectile? (A projectile is an object that is thrown or launched into the air in an attempt to get it to move from one place to another.) Give some examples of projectiles. (Sample answers: a football being thrown to a receiver; an arrow being fired from a bow)
• Point out that this unit is math intensive. Throughout this chapter, students should keep a skills page to summarize the mathematical processes needed and calculator key sequences required to perform the various calculations.
• Have students complete the Starting Points questions. Ask students to save their answers for later.
• Have students complete the Mini-Investigation: Launching Projectiles.
MINI INVESTIGATION: LAUNCHING PROJECTILES
Skills: Performing, Observing, Analyzing, Communicating Purpose: Students will observe the effects of changing launch angle on the path of a projectile. Equipment and Materials (per student): eye protection; (per group): a projectile launcher or similar device; ball Student Safety • Remind students to never aim the launcher at anyone or
anything that could be damaged if struck by the ball. Notes • In this investigation, students will record observations based on
the motion of a projectile launched at a variety of launch angles. • Have students work in small groups and assign specific tasks to
each member of the group. • If a projectile launcher is not available, you could use a spring-
loaded plunger from an old board game and a ramp, or a large spring and a ruler clamped to a protractor for the set up.
• Challenge students to optimize launch conditions to get the ball to travel as far as possible. This could be a class competition.
• As an extension, have students work with their launchers to record more detailed information of launch angle and distance travelled. Once this is done, give them a fixed target, such as a trash can at a fixed distance, and have them set up their launchers so as to land the ball inside the trash can.
DIFFERENTIATED INSTRUCTION • Visual learners could outline the steps required to solve
problems using a flowchart format. Kinesthetic learners may wish to use index cards. Auditory learners may wish to discuss the steps with their peers.
• You may want to have students who are interested in computers set up a class blog, wiki, or website for posting reports, lab results, presentations, images, videos, links, and other forms of information.
Kinematics NEL
16
ENGLISH LANGUAGE LEARNERS • Have English language learners make an index card for
each vocabulary term, and for any unfamiliar terms. Cards should include a definition and sample sentence.
• You may also consider having a word wall in your classroom for new terminology as it arises in the chapter.
1.1 Motion and Motion Graphs
OVERALL EXPECTATIONS: A1; A2; B1; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.1; A1.8; A1.12; A1.13 Career Exploration: A2.1 Relating Science to Technology, Society, and the
Environment: B1.1 Developing Skills of Investigation and Communication: B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
VOCABULARY • kinematics • average velocity ( avv
)
• dynamics • secant • scalar • tangent • vector • instantaneous velocity ( v
)
• position ( d
) • instantaneous speed (v)
• displacement ( d
) • average acceleration ( ava
)
• average speed (vav) • instantaneous acceleration ( a
)
• velocity ( v
)
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 4: Application
PROGRAM RESOURCES BLM 1.1-1 Motion Graphs Physics 12 Online Teaching Centre Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Physics 12 Teacher Web Links (available on CD-ROM) Zimba, J. (2009). Force and motion: An illustrated guide to
newton’s laws. Baltimore, MD: Johns Hopkins University Press.
EVIDENCE OF LEARNING Look for evidence that students can • describe the difference between a vector and scalar • describe the difference between average and
instantaneous for both velocity and acceleration • outline the process of finding average velocity and
instantaneous velocity from a position–time graph using a secant line for average velocity and a tangent line for instantaneous velocity
• understand the correlation between the graph and characteristics of motion
SCIENCE BACKGROUND • This section is a review of grade 11U Physics; however,
the instantaneous velocity or instantaneous acceleration found using a tangent line and the average acceleration or average velocity found using a secant line will be new to most students. Students with a calculus background will have seen this in the concept of a derivative.
• Some students may ask for a calculus method for finding the velocity–time graph. If the position–time graph can be modelled with a function, the derivative of this function will generate the velocity–time function. The derivative of the velocity function (the second derivative of the initial function) will generate the acceleration function.
• In Tutorial 3, Sample Problem 1, an approximation to the time when the acceleration is at its maximum value can be found by taking the straight, sloping line segment in the velocity–time graph and determining its midpoint (as this would tend to be the point when positive acceleration to increase the velocity changes to negative acceleration to decrease the velocity). Again, for the calculus students in the class, this would be where a point of inflection occurs on the curve; so, if the function is known, find the second derivative and set this equal to zero for a more accurate result.
TEACHING NOTES
ENGAGE • To emphasize the difference between distance and
displacement, show students the segment from BBC’s Top Gear in which a Bugatti Veyron, the world’s fastest road-legal car, races a Eurofighter Typhoon jet.
• Students may need a brief review of physical quantities and graphing.
• Challenge students to verbally describe the position–time, velocity–time, and acceleration–time graphs for an everyday scenario; for example, ask, How would the motion graphs look for a car that is stopped at a stop sign, accelerates forward until it reaches 35 km/h, travels at this speed for a few seconds, and then slows to a stop at the next stop sign? (Position–time: A slight upward curve from zero to a straight line with a slope equal to the
NEL Kinematics 17
speed, followed by a downward curve that ends at a zero slope. Velocity–time: a straight, positively sloping line from 0 up to 35 km/h, followed by a horizontal line at 35 km/h, and then a straight, negatively sloping line back down to zero. There should be slight curves in the graph between the line segments of different slope values. Acceleration–time: A horizontal line above the t-axis to represent positive acceleration, then a slightly curved, rapidly decreasing line down to a horizontal line along the t-axis [when the car is moving at 35 km/h], followed by a slightly curved, rapidly decreasing line down to a horizontal line below the t-axis, representing a negative acceleration as the car slows to a stop.)
EXPLORE AND EXPLAIN • Ask, When would the magnitude of the average velocity
be equal to the average speed of an object? (When the distance covered and magnitude of the displacement are equal) When would the average and instantaneous velocity of an object be equal? (When the object experiences constant uniform motion in the interval)
• Discuss the concept of secant lines becoming a tangent line as the two points get closer together on a graph.
• Draw students’ attention to Tutorial 1 on page 10 of the Student Book and work through the sample problem with the class. Introduce the GRASS (Given, Required, Analysis, Solution, Statement) method for problem solving. Explain that using this method can help students develop problem solving and critical thinking skills.
• In Sample Problem 1, note that the average speed will always be greater than the magnitude of the average velocity, unless the magnitude of the displacement is the same as the distance (in which case the magnitudes of average velocity and speed will be equal). Since distance is independent of direction, it will be a larger value if directions change. The third side of the triangle created by the two displacements will have a magnitude less than the sum of the two given sides.
• Allow students time to answer the Practice Problems. • Draw students’ attention to Tutorial 2 on pages 12–13 of
the Student Book and work through the sample problem with the class. If students ask how to improve the accuracy of their velocity–time graph, tell them that instantaneous velocity at a variety of points on the curve can be calculated, and these velocities plotted at the instant of time for which they represent the instantaneous velocity. Alternatively, students can trace along the position–time graph with a ruler and periodically stop to calculate the slope of the ruler as they trace around the curve. This slope can then be plotted for the point in time where the ruler is in contact with the curve.
• Allow students time to answer the Practice Problems.
• Draw students’ attention to Tutorial 3 on pages 14–15 of the Student Book and work through the sample problem with the class. Remind students that any horizontal portion of a velocity–time graph indicates a zero acceleration. As well, inform students that acceleration can be negative, even when the velocity is positive. This simply means that the object is slowing down.
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS • Have students create a position–time graph to match the
acrobat shot out of the cannon in the Chapter Opener photograph. The path will be a downward pointing parabola. Then, have them create a velocity–time and acceleration–time graph for the same situation. Students should see that the velocity–time graph will be a straight line with a slope of –9.8 which crosses the x-axis at the time that matches the top of the parabola in the distance-time graph. The acceleration–time graph will be a horizontal line with a value of –9.8 to match the acceleration due to gravity of –9.8 m/s2 [up].
• Also note that if acceleration is uniform (as it is with the motion of the acrobat being shot from the cannon), the average velocity in an interval of time is exactly equal to the instantaneous velocity at the midpoint of the time interval. This can often help with the accuracy of a velocity–time graph created from a position–time graph.
• Assign BLM 1.1-1 Motion Graphs to give students more practice with motion graphs.
• Have students complete the Questions on page 16 of the Student Book.
• Full solutions are provided in the Solutions Manual.
DIFFERENTIATED INSTRUCTION • All students can work individually or in groups to design
and create an illustration, song, skit, or model that describes the difference between a scalar and its vector parallel (for example, speed and velocity).
• If possible, use a graphing calculator with a CBR range detector to create a graph of uniform motion. Have students analyze this graph to create a velocity–time graph and an acceleration–time graph for the same situation displayed on the graphing calculator.
ENGLISH LANGUAGE LEARNERS • Tell English language learners that the origin of the word
kinematics is the Greek word kinesis, meaning “motion.” • Explain that the terms speed and velocity are often used
interchangeably in everyday speech, but this practice is scientifically incorrect. The same is true of the terms distance and displacement. It is necessary to use the proper terms when dealing with the motion of objects.
Kinematics NEL
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1.2 Equations of Motion OVERALL EXPECTATIONS: A1; B1; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.8; A1.12; A1.13 Relating Science to Technology, Society, and the
Environment: B1.1 Developing Skills of Investigation and Communication: B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
VOCABULARY • free fall
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 2: Thinking and Investigation Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 2: Thinking and Investigation Assessment Summary 4: Application
PROGRAM RESOURCES BLM 0.0-4 Concept Map BLM 1.2-1 Equations of Motion Physics 12 Online Teaching Centre Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Lewin, Walter. (2011). For the love of physics: From the
end of the rainbow to the edge of time – A journey through the wonders of physics. Free Press Publishing.
EVIDENCE OF LEARNING Look for evidence that students can • identify and use the five key equations for uniformly
accelerated motion • relate the concept of free-fall motion to the acceleration
due to gravity
SCIENCE BACKGROUND • The concept of area under a curve to find displacement
given a velocity–time graph may require a review of the area formulas for rectangles, triangles, and trapezoids:
1 2
1 1 ; ;
2 2bh bh b b h ;
where h is the height, and b, b1 and b2 are the bases. Help students connect these area formulas and the equations of motion that are derived from the corresponding graphs.
• Go over the substitutions and derivation of each formula to ensure a complete understanding of the mathematics of the equations. Ensure that you are comfortable with how these formulas match the information on the graphs.
• Students will ask if they can use other combinations of equations, and the answer is yes, provided that they understand that a combination of two equations to solve a problem can lead to slight differences in final answers due to rounding errors. Indicate that it is always better to use one equation to solve for the unknown. It is quicker and eliminates the error associated with rounding.
TEACHING NOTES
ENGAGE • Challenge students to describe the process of selecting the
most appropriate motion equation to use to solve a given problem. Ask, How do we identify the equation that is needed to solve a given problem? (The choice of formula is based on the information given and asked for in the question.)
EXPLORE AND EXPLAIN • Draw students’ attention to the substitution performed on
page 17 of the Student Book, where the equation for the final velocity is substituted into the formula for the area under a trapezoid (for the displacement) to generate one of the equations for motion. Point out that all of these equations are derived in similar fashions.
• Draw students’ attention to Tutorial 1 on pages 18–19 of the Student Book and work through the sample problems with the class. In Sample Problem 1, note that the two displacements are not equal until the accelerating car has 120 m added to its displacement to account for the distance ahead of car B that car A starts. Explain that the answer had to be written in scientific notation because 70 m/s does not clearly indicate two significant digits.
• In Sample Problem 2, outline all steps of the solution as the class reads over the solution. Note that a choice for a positive direction must be made. The solution provided makes acceleration negative and the initial velocity positive, but the opposite choice is possible, and the same final answer would have been reached.
• Students may have difficulty identifying the equation that is required to solve a problem. Have them identify the variable in the question that is not asked for or given and use this missing variable and Table 1 on page 18 of the Student Book to identify the equation to use.
• Ask, What information is given when the question indicates that the object is at rest or comes to rest? (“At rest” means that the initial velocity is equal to zero, and “comes to rest” indicates that the final velocity is zero.)
NEL Kinematics 19
• Allow students time to answer the Practice Problems. • Have students complete BLM 1.2-1 Equations of Motion.
Have students work in pairs to identify which equation is needed to solve each problem before doing the work. If time permits, ask students to explain their answers and see if two different approaches could have been used to get to the same final answer.
• Draw students’ attention to Tutorial 2 on page 20 of the Student Book. Go through each step of the solution to Sample Problem 1 and ask students why the equation used was chosen from the five equations of motion. Explain that the use of 9.8 m/s2 does not factor to the number of significant digits for the final answer, as we use this value as a defined value.
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS
• Have students use dimensional and graphical analysis to derive the five equations of motion, with the assumptions of constant, uniform acceleration. For example, using slope on a velocity–time graph, we obtain this equation:
f iv va
t
,
which can be algebraically re-arranged to f iv v a t .
• Have students complete the Questions on page 21 of the Student Book.
• Full solutions are provided in the Solutions Manual.
UNIT TASK BOOKMARK • Remind students that the equations for uniformly
accelerated motion they have learned about in this section will be useful when they complete the Unit Task.
DIFFERENTIATED INSTRUCTION • Visual learners may benefit by making a concept map on
the uses and methods of choosing an equation of motion, then share their maps with a partner. (Use BLM 0.0-4 Concept Map). Students could use a journal or recording device to describe the process.
• To create student-driven learning opportunities, have students complete a project that demonstrates the topic in real life and present it to class.
• Have students choose one or two practice questions and show their work and explain it orally to their partner.
• Encourage auditory learners to discuss the steps used in problem solving with their peers.
ENGLISH LANGUAGE LEARNERS • Explain that the term free fall does not necessarily mean
that the object is falling. If a ball is thrown up into the air, as soon as it is released, it is in free fall, as it experiences motion under the influence of gravity only. Free fall does
not have to mean the object is moving back toward Earth. Have students record this on a card or key term list.
• English language learners should develop a personal math dictionary with terms, formulas, and examples.
1.3 Displacement in Two Dimensions
OVERALL EXPECTATIONS: A1; A2; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.8; A1.12; A1.13 Career Exploration: A2.1 Developing Skills of Investigation and Communication:
B2.1; B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
VOCABULARY • component of a vector
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 4: Application
PROGRAM RESOURCES BLM 1.3-1 Solving Two-Dimensional Problems Physics 12 Online Teaching Centre Physics 12 Solutions Manual Physics 12 website www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Hache, Alain. (2002). The physics of hockey. Hopkins
Fulfillment Service.
EVIDENCE OF LEARNING Look for evidence that students can • describe the process of solving two-dimensional problems
using scale diagrams, cosine and sine laws, and perpendicular components
• relate the choice of method to the ease of solution and need for accuracy in a problem
SCIENCE BACKGROUND • Students should be aware of the three most common ways
to report the direction of a vector: [N 65° E], 65° E of N and a bearing of 065° all represent the same direction.
Kinematics NEL
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• Students may ask about applications to air travel. If the altitude of the plane remains constant, the motion becomes a two-dimensional problem, but if the altitude changes, the problem becomes three-dimensional, which is beyond the scope of the course. Indicate that this could be done using components, where altitude is the only measure affected by gravity.
• In Chapter 2, Dynamics, there will be situations in which vectors will not be resolved horizontally and vertically, as the problem dictates that this would not be the best approach. This will occur when motion on an inclined plane is studied, where vectors will be resolved parallel to the ramp and perpendicular to the ramp. Remind students that when the two components are perpendicular, the first component can be in any direction, but the second needs to be perpendicular to the first.
TEACHING NOTES
ENGAGE • Challenge students to describe a situation where the scale
diagram method may be a better choice than the sine and cosine law method. If no such example is offered, ask, How would you find the resultant displacement for the following movements: 28.2 m [E 45° N] + 41.4 m [W 22° N] + 31.5 m [W 30° S]? (The scale diagram method will be easier, but may not be as accurate as an algebraic method. Using the sine and cosine law method would be much more complicated, as the diagram with three vectors does not form an easy-to-analyze triangle.)
EXPLORE AND EXPLAIN • Students may ask if the components method can be used
to work with more than two vectors. When more than two vectors are involved, this technique is the best approach to take. Many forces can act on an object, and components is the preferred method to solve such problems.
• Remind students that a resultant displacement vector does not rely on the path used to get from starting point to end point. To demonstrate this, start at a position in the room. Have students close their eyes. Relocate to a new position. Have students report your resultant displacement. They should clearly see that it is path independent of the final displacement vector.
• Draw students’ attention to Tutorial 1 on pages 24–25 of the Student Book, and work through the sample problems with the class. In Sample Problem 1, point out that scale diagrams need to be as large as possible to increase the detail and accuracy. A scale that allows for a large diagram must be chosen, and a ruler and protractor must be used. Have students practice this method by doing this question in their notebooks to see if they obtain the same
answer. Also inform students that the direction of the first displacement vector could have been given as [N 55° E]. In Sample Problem 2, the same problem is repeated, using the cosine and sine laws. Here, all students would get the same answer, if this solution were to be repeated, illustrating that this method is in general more accurate than using a scale diagram to solve a vector problem.
• Allow students time to answer the Practice Problems. • In Figure 7 on page 25 of the Student Book, students may
ask if they can resolve north first, then east (creating a triangle above the vector given). This can be done, but the contained angle to their triangle will be 53° (90° – 37°), and the sine and cosine ratios for components will be reversed. Since sin 37° = cos 53°, the final answer will be the same, regardless of which triangle is used.
• Draw students’ attention to Tutorial 2 on page 26 of the Student Book and work through the sample problem with the class. Sample Problem 1 illustrates the process of resolving vectors into perpendicular components. The check performed here only serves to verify that the components are correct. Students do not have to do this on each question once the method has been perfected.
• Allow students time to answer the Practice Problems. • Emphasize that the angle found using the sine law must
be put into context with the orientation of the diagram when reporting direction. Often, there is an angle that must either have the calculated angle added or subtracted to obtain the final direction of the resultant vector.
• Draw students’ attention to Tutorial 3 on pages 27–28 of the Student Book and work through the sample problem with the class. In Sample Problem 1, the process of resolving vectors into perpendicular components is now applied to add two displacement vectors. Point out that once the components are determined, a direction for each component pair must be chosen to be positive. For the
x-direction, the choice was to the right is positive; therefore, the x-component for the second vector is negative. For the y-direction, up is chosen to be positive, therefore the y-component of the second vector is negative.
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS • Have students complete BLM 1.3-1 Solving Two-
Dimensional Problems. Have partners choose one of the questions from BLM 1.3-1 and explain their solution.
• Have students create their own question related to their daily life or community, exchange it with a classmate, and explain their responses orally to each other.
• Have students complete the Questions on page 29 of the Student Book.
• Full solutions are provided in the Solutions Manual.
NEL Kinematics 21
DIFFERENTIATED INSTRUCTION • Auditory learners will benefit from working through the
practice problems while discussing them with a partner. • To engage kinesthetic learners, have students look at
Review Question 1 and think of their answer the following: Which method would be the best choice to solve this question? Ask students to move to the one of four corners designated for their response: scale diagram, cosine and sine laws, perpendicular components, or undecided.
ENGLISH LANGUAGE LEARNERS • Tell English language learners that the perpendicular
components method resolves vectors into two perpendicular components (that is, vectors at 90° to each other) that allow the problem to be treated as two linear problems that can be tied back together at the end using the Pythagorean theorem for magnitude and the tangent ratio for direction.
• English language learners may find it beneficial to summarize each method on an index card, and include an example if space permits.
1.4 Velocity and Acceleration in Two Dimensions
OVERALL EXPECTATIONS: A1; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.8; A1.12; A1.13 Developing Skills of Investigation and Communication:
B2.1; B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 4: Application
PROGRAM RESOURCES Physics 12 Online Teaching Centre Simulation: Ladybug Motion 2D Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Cassidy, D. (2002). Understanding physics: Student guide.
New York: Springer.
EVIDENCE OF LEARNING Look for evidence that students can • describe the difference between average velocity and
average speed in two dimensions • describe the subtraction of two vector components
[E] [W] [E] [E]A B A B
; that is, add the negative of
the vector component after the subtraction sign • recognize that the initial velocity must be subtracted from
the final velocity to find the change in velocity needed to find acceleration
SCIENCE BACKGROUND • Use the inverse tangent function between the final y-component and x-component to determine the
orientation of the vector. • Students may ask why vectors are resolved horizontally
and vertically. A two-dimensional problem is easier to solve when it is broken into linear problems, as in the case of acceleration due to gravity: the linear problems are independent, and only the vertical component experiences the acceleration due to gravity. Acceleration is not present in the horizontal direction in this situation.
• Some students may have seen a tip-to-tip method of solving a vector subtraction. A friend or tutor might show this method, or students may have found it online. For A B
this method involves drawing the first vector, then drawing the second so that the tip of the vector being subtracted is in contact with the tip of the first vector. The resultant vector is the vector that starts at the first vector and ends at the start of the second vector. Remind students that while this technique works, the preferred technique is adding the negative of the subtracted vector.
• Students may ask about acceleration not involving gravity (such as a car accelerating after being stopped at a light or a runner accelerating during a race) and how acceleration can be found in each direction. Tell them that acceleration can be done in components, but that there are less steps involved if acceleration is calculated using the total change in velocity. The change in velocity is divided by the time interval to find acceleration.
TEACHING NOTES
ENGAGE • Challenge students to explain why a car going around a
curve at a uniform speed can be accelerating. Ask, How is there acceleration if the speed of the car is constant? (The direction of the speed (i.e., the velocity) is changing, so even though the speed is constant, the change in direction will result in a change in velocity.)
Kinematics NEL
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• Ask students to describe a situation where the perpendicular components method would be better than the sine and cosine law method. If no example is offered, ask, How would you find the resultant displacement for the following movements: 35 m/s [N 20° E] + 27 m/s [N 50° W] + 18 m/s [N 65° W]? (Perpendicular components would be the easier method. Trying to use the sine and cosine law method would be much more complicated, as the diagram with three vectors does not form an easy-to-analyze triangle. Two triangles must be used and solved if the sine and cosine law method were used.)
EXPLORE AND EXPLAIN • Draw students’ attention to Tutorial 1 on pages 31–32 of
the Student Book and work through the sample problem with the class. In Sample Problem 1, the displacements in the x- and y-directions are found using the perpendicular component method. The displacement in the x-direction for the two vectors is in the same direction, so the components are added; they are in opposite directions in the y-direction, hence subtracted. Point out that when finding the average speed, the total distances are added, without reference to the direction of the position vectors to which distances were associated.
• Allow students time to answer the Practice Problems. • Draw students’ attention to Tutorial 2 on pages 33–34 of
the Student Book and work through the sample problem with the class. In Sample Problem 1, there is no scalar equivalent to acceleration, so this is purely a vector question. Once again, components are used, but here the final velocity and initial velocity are subtracted, due to the nature of acceleration being the difference in velocity over the interval of time that the velocity changed.
• As a class, have students develop a way to use the sine and cosine method to find the resultant displacement of the three vectors given in the ENGAGE section above. Have half the class use this method and the other half use the perpendicular components method to check the work. Students will see that the perpendicular components method is quicker, and possibly more accurate, as it does not involve rounding until the end of the solution.
• Ask, Which method is quicker and more accurate? Why? (Using the perpendicular components method is quicker and more accurate. The problem becomes two linear problems that do not require multiple steps and rounding until the end of the solution, when the Pythagorean theorem and tangent ratio are used to find magnitude and direction.)
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS • Have students perform an Internet search on the
acceleration of some high-performance vehicles and relate the method of reporting this acceleration (i.e., 0 to
60 in 2.4 s) to the proper physics calculation of acceleration.
• Have students pair up, choose a question from each set of Practice Problems, and explain the process they chose to solve the question.
• Have students complete the Questions on page 35 of the Student Book.
• Full solutions are provided in the Solutions Manual.
UNIT TASK BOOKMARK • Remind students that what they have learned about
acceleration in two dimensions in this section will be useful when they complete the Unit Task.
DIFFERENTIATED INSTRUCTION • If Practice Problems were discussed in pairs as
suggested above, have the pair of students summarize the best approach on a piece of paper and leave it on the desk. Have all students do a Gallery Walk, moving from desk to desk, reading the summaries and adding comments or additional information. When they return to their desk, the pair can read any additions and/or comments made to their solution and discuss.
ENGLISH LANGUAGE LEARNERS • During the Gallery Walk, ensure that English language
learners are paired with a student who can help them understand the summaries at each station.
1.5 Projectile Motion OVERALL EXPECTATIONS: A1; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.6, A1.8; A1.10; A1.11; A1.12; A1.13 Developing Skills of Investigation and Communication:
B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
VOCABULARY • projectile • range ( xd )
• projectile motion SKILLS Performing Analyzing
Communicating
NEL Kinematics 23
EQUIPMENT AND MATERIALS per student: • paper and pencil • calculator
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 2: Thinking and Investigating Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 2: Thinking and Investigating Assessment Summary 4: Application
PROGRAM RESOURCES BLM 1.5-1 Projectile Motion BLM 1.5-2 Projectile Motion Problems Skills Handbook A2.2 Controlled Experiments Physics 12 Online Teaching Centre
Simulation: Speed of Projectiles Launched at Different Angles
Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Physics 12 Teacher Web Links (available on CD-ROM) Unterman, N. A. (2001). Amusement park physics:
A teachers guide (2nd Ed.). Portland, ME: Walsh Publishing.
EVIDENCE OF LEARNING Look for evidence that students can • describe the motion of a projectile using words and using
equations • relate the components of projectile motion to a direction
involving the acceleration due to gravity and a direction that experiences no acceleration, and explain how the equations of motion allow for these components to be incorporated into the problem
SCIENCE BACKGROUND • While most of the concepts of this section are intuitive, be
sure to have a strong understanding of Figure 2 on page 37 of the Student Book, which shows that the vertical components of the motions of the two objects are equal. This, however would not be the case if the velocity of the object had an upward or downward component initially (as this would affect the vertical component of motion, as was seen in the previous section).
• Be sure to go over the rearrangement of the equations of motion to derive the range equation before you attempt to present it to the class. This is an important equation and should be one that your students are comfortable with, both in its use and derivation. A review of the trig identity
2sin cos sin 2 may be needed. This can be verified by selecting a variety of angles and checking; proving the identity may not be needed. Students may have already seen this proof in mathematics class.
POSSIBLE MISCONCEPTIONS Identify: Students might not understand that an object that is thrown straight up and then returns to the point from where it was thrown is still parabolic in its motion. Clarify: An explanation of what parabolic motion is considered in physics is a must to eliminate this confusion, as parabolic motion is usually understood as motion or trajectory in the shape of a parabola, not a straight line. The reason we call this a parabolic motion is due to the function that yields a graph in the shape of the parabola due to the y = vt – 1/2 gt2 equation. Emphasize that a graph of the motion where the horizontal axis is not distance, but time, will show the parabolic nature of the motion. Throw a ball into the air and catch it while stationary, then repeat the same throw, but move to the right as if you were moving in time to show that the path is still parabolic. Ask students to think about the position of the ball over time in each photograph of a time-lapse series of photos. There are many online video clips of such motion that will help here. Ask What They Think Now: Ask, Why is the motion of an object thrown straight up in the air still parabolic? (The object is in free fall, and so it is affected by the acceleration due to gravity, which causes parabolic motion.)
TEACHING NOTES
ENGAGE • Challenge students to describe the effect of wind on
calculations of projectile motion. Ask, How would you incorporate the velocity of the wind in the motion of a projectile? (Assuming a constant wind parallel to the ground, the effect of the wind would be on the horizontal component of the velocity, not on the vertical. Therefore, it would not affect the time the projectile is in the air, only where it ultimately lands. This can be determined by first calculating the horizontal component of the velocity, incorporating the wind, and then using the time the projectile is in the air to determine the range.)
• You could have students use online simulations to explore and practice concepts in projectile motion.
EXPLORE AND EXPLAIN • Have students complete Mini Investigation: Analyzing
the Range of a Projectile.
MINI INVESTIGATION: ANALYZING THE RANGE OF A PROJECTILE
Skills: Performing, Analyzing, Communicating Equipment and Materials (per group): paper and pencil; calculator
Kinematics NEL
24
Purpose: Students will examine and calculate the relationship between time of flight, maximum height, and range for a variety of launch angles to find trends in the calculated values. Notes • Have students work in pairs. Pair students with complementary
abilities in order for the pair to be productive. • Before students carry out the investigation, have each pair
present a drawing representing a projectile and the vectors that act on it as it moves through the air.
• After students carry out the investigation, ask the following: How does the value of 25 m/s affect the results? How would changing this value to 30 m/s affect the results?
• Stress the need to be able to resolve vectors into perpendicular vectors for this section. Doing so allows for the independent application of acceleration to the vertical component of velocity. The horizontal component is unaffected by this acceleration.
• Draw students’ attention to Tutorial 1 on pages 39–40 of the Student Book and work through the sample problems with the class. In Sample Problem 1, the object has no initial vertical velocity; therefore, the equation to find the time the object is in the air only involves a square root. Here, the negative root is ignored. In Sample Problem 2, a separate set of motion equations is used due to the fact that this problem involves an object with an initial vertical velocity that is not zero. The height that the golf ball reaches must first be calculated to then be able to determine the velocity of the ball when it lands. Note that in both cases the sign (positive or negative) assigned to measurement is essential in solving these equations.
• Ask, How are these sample problems similar to problems done in Section 1.2? (In both cases, the choice of equations to use requires the identification of what is given and what one is asked to find in the questions.)
• Allow students time to answer the Practice Problems. • Take the time to go over the derivation of the range
equation. Remind students that 2sin cos sin 2 is a trigonometric identity developed mathematically, and is simply used here, not proven or developed.
• Draw students’ attention to Tutorial 2 on page 42 of the Student Book and work through the sample problem with the class. In Sample Problem 1, the range equation is used to find the time that the ball will stay in the air. This could have been found using methods investigated in Tutorial 1, but the range equation allows for this value to be calculated quickly. Once this time is found, it is applied to the horizontal component of velocity (where there is no acceleration) to find the range of the ball. Note here that the object must come back to the same height from where it was launched.
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS • Have students complete BLM 1.5-1 Projectile Motion.
• Students can also complete BLM 1.5-2 Projectile Motion Problems, which includes problems involving the analysis of Figure 2 on page 37 of the Student Book.
• Have students come up with examples of parabolic motion, such as a soccer ball or football being kicked.
• Have students complete Investigation 1.5.1. Applicable teaching notes start on page 26 of this resource.
• Have students complete the Questions on page 43 of the Student Book.
• Full solutions are provided in the Solutions Manual.
UNIT TASK BOOKMARK • Remind students that what they have learned about
projectile motion in this section will be useful when they complete the Unit Task.
DIFFERENTIATED INSTRUCTION • Have students choose a problem from the Tutorials and
organize the information in a T-chart. On the left side, they list the information given. On the right, they then list how the given information is used to solve the problem.
• Have students in small groups act out scenarios involving projectile motion, such as the situations described in the problems and investigation. Have them discuss the effects of launch angle on the distance the projectile will travel.
ENGLISH LANGUAGE LEARNERS • Divide students into five groups, and have each group
find as many meanings as possible for the word range—including the scientific meaning from this lesson—and write a sentence for each meaning.
1.6 Relative Motion OVERALL EXPECTATIONS: A1; A2 B2; B3
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.8; A1.12; A1.13 Career Exploration: A2.1 Developing Skills of Investigation and Communication:
B2.2 Understanding Basic Concepts: B3.1 The full Overall and Specific Expectations are listed on pages 3–5.
VOCABULARY • frame of reference • relative velocity
NEL Kinematics 25
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 4: Application
PROGRAM RESOURCES Physics 12 Online Teaching Centre Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Kirkland, K. (2007). Force and motion. New York: Facts on
File Publishing.
EVIDENCE OF LEARNING Look for evidence that students can • describe the motion of an object in different ways based
on the frame of reference in which the motion is being observed
• relate the frame of reference to the mathematical operation required on the vectors to obtain the correct relative velocity
SCIENCE BACKGROUND • Frames of reference can often be thought through
logically before any equations are used. The use of subscripts can get confusing, so be sure that you have a firm grasp of the use of these subscripts before presenting the material to the class. Items such as the wind being described as the velocity of the air relative to the ground (in other words, relative to the surface of Earth) is AEv
.
• Draw on past experiences you may have had in terms of air travel to reason why a plane takes longer to get somewhere when flying into the wind. The jet stream has a seasonal pattern in that the path of the jet stream changes over time. However, if a trip only lasts a week or two, the jet stream will be relatively constant. As a result, it has a positive effect in one direction of travel and a negative effect in the opposite direction.
POSSIBLE MISCONCEPTIONS Identify: Students might not understand that the motion of an object is dependent on the frame of reference only when the frame of reference changes. Clarify: Emphasize that, from the frame of reference of the car, a ball tossed into the air in the back of a car moving at 35 km/h behaves exactly as it would if the car were stopped at a red light. However, if you were to observe the same motion from the sidewalk as the car went by, you would not just see the ball move up and down, it would also be moving forward. In both cases the ball is moving in a parabolic path, but described differently based on the frame of reference.
Explain that changing a frame of reference is useful when the motion of an object is to be described in a moving frame of reference. For example, as a space shuttle orbits Earth, (i.e., a moving frame of reference), the way the Canadarm needs to move to launch a satellite is best described in a frame of reference where the shuttle is not moving. Ask What They Think Now: Ask, What must be done when a relief package is being dropped from the air and must land at a specific point on the ground? (The people responsible for launching the package must plan for the package to be moving forward with the same velocity as the plane when it is dropped, so it must be dropped well before the plane is over the landing point. This type of problem was looked at in Section 1.5.)
TEACHING NOTES
ENGAGE • Challenge students to describe the different possible
frames of reference for a motorboat moving under the power of the wind, a motor, and the current. Ask, How would you describe the motorboat’s motion if you were
(a) on a float in the water? (b) on a sailboat in the water? (c) on a second boat with the same motor power? (d) on the shore?
(The boat would appear to be moving (a) due to the wind and the motor; (b) due to the motor only; (c) due to the wind only; and (d) due to all three.)
EXPLORE AND EXPLAIN • Draw students’ attention to Tutorial 1 on pages 45–48 of
the Student Book and work through the sample problems with the class. In Sample Problem 1, point out that relative motion in a linear direction simply requires a direction to be chosen as positive. Once this is done, velocities can either be added (if in the same direction) or subtracted (if in opposite directions) to obtain the relative velocity. Outline the use of subscripts to help identify each velocity in the frame of reference in which it is measured. In Sample Problem 2, relative motion is looked at in two dimensions and at right angles. This is similar to components studied earlier; to find the relative velocity, the Pythagorean theorem and tangent ratio can be used to find the magnitude and direction of the resultant velocity. In Sample Problem 3, the driver of the boat wants to end up on the opposite side of the river, and so must aim the boat into the current slightly to allow the current to push the boat back to the opposite side of the river. Again, point out the subscripts and use of the sine ratio and magnitude to find the speed and heading of the boat. Finally, in Sample Problem 4, relative motion is determined using components for a two-dimensional problem. Go over each step of this solution to ensure a
Kinematics NEL
26
full understanding of the process. This will serve as a review for the material from Section 1.4.
• Allow students time to answer the Practice Problems.
EXTEND AND ASSESS • Have students make up a relative-motion question based
on their past experience, exchange it with another student, and check each other’s work and reasoning.
• Have students complete the Questions on page 49 of the Student Book.
• Full solutions are provided in the Solutions Manual.
DIFFERENTIATED INSTRUCTION • Students in groups can create an illustration, song, skit, or
model that describes relative motion. If time permits, allow groups to present their work to the class.
• Students can select a real-life event and describe the motion using pictures, graphs, or short videos.
ENGLISH LANGUAGE LEARNERS • Tell students that the word relative can mean someone
who is associated with a person based on marriage or birth, but in the context of motion, relative means with respect to some other moving body or reference point.
1 Investigations 1.5.1 Observational Study: Investigating Projectile Motion OVERALL EXPECTATIONS: A1; B2
SPECIFIC EXPECTATIONS Scientific Investigation Skills: A1.4; A1.5; A1.6; A1.8; A1.10; A1.11; A1.12; A1.13 Developing Skills of Investigation and Communication:
B2.2 The full Overall and Specific Expectations are listed on pages 3–5.
SKILLS Controlling Variables Analyzing Performing Evaluating Observing Communicating
EQUIPMENT AND MATERIALS per group: • air table with spark puck • material to support one end of the air table, such as bricks • construction paper • metric ruler • protractor
ASSESSMENT RESOURCES Assessment Rubric 7: Observational Study Assessment Summary 7: Observational Study Self-Assessment Checklist 3: Observational Study
PROGRAM RESOURCES Skills Handbook A2.4 Observational Studies Skills Handbook A5 Math Skills Physics 12 Online Teaching Centre Physics 12 Solutions Manual Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Goff, John Eric. (2009). Gold medal physics: The science of
sports. Johns Hopkins Fulfillment Service.
EVIDENCE OF LEARNING Look for evidence that students can • follow safe laboratory practices • use mathematical processes to calculate velocities and
change in velocity and acceleration from the three different types of motion demonstrated on the air table
• relate the calculated acceleration to the acceleration due to gravity
SCIENCE BACKGROUND • A 10 Hz frequency on the spark timer means 10 sparks
occur every second. The time between consecutive sparks is thus 0.10 s. This time is used to determine velocity after a displacement measurement is taken between two sparks. When this is done in several locations, the acceleration between these velocities can be determined.
• In the first two motion sets, the sparks should align in a similar pattern to that seen in Figure 2 in Section 1.5.
TEACHING NOTES
STUDENT SAFETY
Review the following safety rules with students: • Do not touch the surface of the air table when the spark generator is
on, as you will get a shock. • Keep the pucks in contact with the carbon paper on the air table
when the generator is on, and keep the angle of elevation small.
• Have students work in small groups of up to four members. Give each member a particular responsibility: setting up the equipment; releasing the puck (to ensure consistency); in charge of the spark timer and ensuring that marks are being made on the construction paper; and overseeing the investigation and troubleshooting.
• If time permits, the three scenarios should be repeated once for each group member, so that each has their own sheet of construction paper on which to perform their
NEL Kinematics 27
calculations. Or, have students pair up to analyze the motion. Be sure each group member fully understands what calculations must be done.
• Students should draw between 6 and 10 velocity vectors for each type of motion and determine acceleration for each. This will allow for a more accurate result, as any outliers can be identified once calculations are performed.
• Have students share their answers to the Analyze and Evaluate and Apply and Extend questions with members of their group and then with the class.
PURPOSE • The purpose of this investigation is for students to analyze
two-dimensional projectile motion using an air table. This will strengthen their understanding of the equations associated with two-dimensional motion.
EQUIPMENT AND MATERIALS • Demonstrate the path the air puck needs to take in each
part of the procedure. Practice the motion of the release prior to having your class set up this investigation.
• Be sure all equipment is working and that the spark timer marks the construction paper with dots large enough to be seen. This may require an adjustment of the sparker wire in the channel of the puck itself. Sometimes this wire is too far up the channel to spark on the paper. Note the optimum distance of this wire as you practice in case this must be adjusted for a group as the investigation is being performed. Also be sure of the air plow to reduce the friction as much as possible. This will be a source of error if too much friction exists.
• If bricks are not available to prop up one end of the table, students’ textbooks can be used.
• Some students may ask what would happen if the puck were launched so that it had a downward component to its velocity. This could be done, but the space on the table is limited and they may not get enough data to effectively perform the calculations.
PROCEDURE • Place the bricks under one end of the air table and
determine the angle of incline as accurately as possible (using either trigonometry or a protractor). Be sure to inform students that this angle is extremely important to the investigation.
• With the spark timer not running, practice generating three scenarios: 1. No initial velocity in the x- or y-direction (i.e., the puck
is simply released) 2. A positive x-direction velocity, but no y-direction
velocity (i.e., the puck is pushed horizontally) 3. A positive x- and y-direction velocity (i.e., the puck is
pushed upward at an angle)
This should be done several times to ensure that the motion is repeatable.
• These scenarios are to then be repeated with the spark timer on, using a separate piece of construction paper for each motion. The direction of motion should clearly be marked on the construction paper to ensure that the calculations are not inverted or reversed. If the sparks are too light, have students go over the sparks with a pen or marker to ensure that all marks can be seen. This will be essential when the measurements must be taken.
OBSERVATIONS • The equation a = g sin will allow students to compare
their results to the actual value of the acceleration on the air table. It is for this reason that the angle of incline of the air table was so important.
• Remind students to record values carefully on the construction paper and organize calculations so that all data is clear and easy to understand. Students must calculate velocities and change in velocities and accelerations for multiple data values; they should use a chart to help organize and summarize calculations.
• Full solutions are provided in the Solutions Manual.
DIFFERENTIATED INSTRUCTION • Visual learners will benefit from seeing the experiment as
it occurs to help put the meaning of the dots into perspective. Have them create the same vectors as in steps 8 and 9 to help with their comprehension.
• Allow students to display and illustrate their results using any method or format they choose. Visual learners will benefit from seeing other students’ results posted.
ENGLISH LANGUAGE LEARNERS • Have English language learners work with other students
to help them follow the investigation. Have them define the terms random error and systematic error and list an example of each before doing the investigation.
CHAPTER
1 Summary
ASSESSMENT RESOURCES Assessment Rubric 1: Knowledge and Understanding Assessment Rubric 4: Application Assessment Summary 1: Knowledge and Understanding Assessment Summary 4: Application
Kinematics NEL
28
PROGRAM RESOURCES BLM 1.Q Chapter 1 Quiz BLM 0.0-10 Careers Skills Handbook A6 Choosing Appropriate Career Pathways Physics 12 ExamView® Test Bank Physics 12 Online Teaching Centre Physics 12 website
www.nelson.com/onseniorscience/physics12u
RELATED RESOURCES Kirkland, Kyle. (2007). Force and motion. Facts on File
Publishing. Zimba, Jason. (2009). Force and motion: An illustrated
guide to newton’s laws. Hopkins Fulfillment Service.
SUMMARY QUESTIONS • Ask three to five questions that will prompt students to
recall each Key Concept. Have students explain and support their responses.
1. What is the difference between distance and displacement? (Distance is a scalar and displacement is a vector, which means it has a magnitude and a direction.)
2. Describe the techniques that can be used to solve a two-dimensional problem. (In scale drawings, each vector is drawn according to the vector magnitude and scale in the correct direction. Each subsequent vector is added to the end of the previous in the same manner. Once all vectors have been drawn, the resultant is the vector that originates at the start of the first vector drawn and ends at the end of the last vector drawn. This vector is measured and the scale is applied and a protractor used to find the angle. Sine and cosine laws: The vectors do not need to be drawn exactly to scale, as the triangle created can be solved using the cosine law for magnitude and the sine law for direction. The angle found using the sine law must be at the start of the resultant vector and must be applied to the situation in the diagram to properly identify the angle in the direction. The perpendicular components method resolves each vector into two components that are perpendicular to each other. The problem becomes two linear problems. These are solved independently and then combined at the end using the Pythagorean theorem for magnitude and the tangent ratio for direction.)
3. How are components used in the motion of a projectile? (The velocity of the projectile is resolved into a horizontal and vertical component. The vertical component allows for the calculation of the time the projectile will be in the air, and this time can then be used to determine the horizontal distance the projectile will travel.)
4. When studying relative motion, what must be done to vectors to change the frame of reference? (Vectors must
either be added or subtracted (based on the direction that each velocity vector points in the frame of reference of interest) for the relative velocity to be determined. This can be done using subscripts to keep track of the relative frame of reference each measurement is taken with respect to.)
5. In the investigation on projectile motion, what angle gave the maximum range? How does the range equation prove that this angle gives the maximum range? (A 45° angle gives the maximum range. In the range equation, sin 2 gives a value of 1 when the angle of 45° is used. The sine function has a maximum value of 1, so when this value is obtained, the range is a maximum value.)
• Have students develop a graphic organizer to help sort the Key Concepts into an easy-to-follow format.
• Have students answer the Starting Points questions again and compare their answers with those they wrote at the beginning of the chapter.
• Have students complete the questions found in the Chapter Self-Quiz and Chapter Review in the Student Book. Full solutions are provided in the Solutions Manual.
• Have students complete BLM 1.Q Chapter 1 Quiz for an additional review of the material.
CAREER PATHWAYS • Provide students with a copy of BLM 0.0-10 Careers to
complete as they work on the Career Pathways and select a career that relates to the study of kinematics, projectile motion, and relative motion.
• Advise students that this is just a small sample of the careers that require an understanding of kinematics equations. Almost any career in the field of physics will require an understanding of kinematics.
• Remind students that they will most likely change thoughts several times on their occupational choice, which is normal.
• Discuss the types of careers listed in the Student Book and add any additional careers you may wish to include. If time permits, have students present their findings on educational pathways for these careers to the class.
DIFFERENTIATED INSTRUCTION • You may want to have students who are interested in
computers set up a class blog, wiki, or website for posting reports, investigation results, presentations, images, videos, links, and other forms of information.
ENGLISH LANGUAGE LEARNERS • Have English language learners review the index cards
they have made for vocabulary terms.
Blackline Master 1.1-1
BLM 1.1-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.1-1 Motion Graphs The velocity–time graph represents the motion of an object over a time interval.
Use graphical analysis to answer the following questions. 1. What is the object’s displacement relative to its starting position after 6.0 s? 2. Determine the object’s (a) average velocity (b) average speed during the first 6.0 s 3. Compare the object’s acceleration during the first 2.0 s with its acceleration between 6.0 s and 10.0 s. 4. Plot the corresponding position–time graph representing the same motion. 5. Plot the corresponding acceleration–time graph representing the same motion.
Blackline Master 1.2-1
BLM 1.2-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.2-1 Equations of Motion Equations of motion are useful in calculating quantities without the need to graph the information. Identifying the equation to be used is the key to this process. In any question, you must identify the quantities given and the quantity asked for in order to determine which equation is to be used. Table 1 on page 18 of your textbook will help in this process. Example
A small child slides down a hill on a toboggan with a constant acceleration of 2.0 m/s2. If the child’s motion starts from rest, calculate
(a) the child’s velocity after 4.0 s.
(b) how far the toboggan will have moved in this interval of time. Solution
(a) Given: i 0v
; 22.0 m/sa
; t = 4.0 s
Required: fv
Analysis: We are not given the displacement, so we will use f iv v a t
.
Solution: f i
2
f
0 (2.0 m/s [down the hill])(4.0 s)
8.0 m/s [down the hill]
v v a t
v
Statement: The child’s velocity after 4.0 s is 8.0 m/s [down the hill].
(b) Given: i 0v
; 22.0 m/sa
; t = 4.0 s
Required: d
Analysis: We can use i
1
2d v t a t
. We could use other equations, but they would rely on our answer to
part (a), and in case this solution in incorrect, we should revert to the given information.
Solution: i
2 2
1
21
(0)(4.0 s) (2.0 m/s [down the hill])(4.0 s)2
16 m [down the hill]
d v t a t
d
Statement: The toboggan will have moved 16 m in 4.0 s.
Blackline Master 1.2-1
BLM 1.2-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.2-1 Equations of Motion (continued) Practice Questions
1. A skier starts down a run that is 125 m long with an initial velocity of 4.0 m/s. The slope of the run causes the skier to accelerate at 1.1 m/s2. What will be the velocity of the skier at the end of this run?
2. A sprinter starts from rest and accelerates at a uniform rate of 1.2 m/s2 down the track.
(a) What will be the velocity of the sprinter after 15 s? (b) How far will the sprinter have travelled in this interval of time?
Blackline Master 1.2-1
BLM 1.2-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.2-1 Equations of Motion (continued)
3. A dart leaves the barrel of a blow tube at a velocity of 15 m/s. The length of the barrel of the blow tube is 0.50 m.
(a) Assume that the dart is uniformly accelerated. What is the average velocity inside the barrel of the blow tube?
(b) How long is the dart in the barrel after it starts to move?
4. A ball is carried up in a hot-air balloon at a rate of 9.0 m/s, and when it reaches a height of 80.0 m above
the ground, the ball is released. How long will it take the ball to hit the ground?
Blackline Master 1.3-1
BLM 1.3-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.3-1 Solving Two-Dimensional Problems Solving two-dimensional problems can be done in any one of three methods. Scale diagrams can be used. A ruler and protractor must be used, and a scale must be chosen that will allow the diagram to be as large as possible in order to reduce error. You will get an answer that is close to your classmates, but may not be exactly the same. Scale diagrams tend to be a little less accurate than the other two methods. See Tutorial 1: Sample Problem 1: Vector Addition by Scale Diagram on page 24 of your textbook. Sine and cosine laws can be used as an algebraic method. The accuracy is better than a scale diagram and your result will be exactly the same as the results of your classmates. However, this method becomes more difficult to use when more than two vectors are combined.
Sine law: sin sin sin
a b c
A B C Cosine law: 2 2 2 – 2 cosa b c bc A
See Tutorial 1: Sample Problem 2: Vector Addition Using the Cosine and Sine Laws on pages 24–25 of your textbook. Perpendicular components are a second algebraic method that can be used. This involves resolving all vectors into perpendicular components (usually a north–south, east–west orientation or an x-axis, y-axis arrangement). The problem then becomes two independent linear problems that can be combined at the end, using the Pythagorean theorem for the resultant magnitude and the tangent ratio for the direction. This method should be used when more than two vectors must be combined. See Tutorial 2: Sample Problem 1: Determining Vector Components Using Trigonometry on page 26 of your textbook. Practice Questions
1. A clock has a 12 cm long second hand. Determine the average velocity of this hand in moving from the 3 to the 12 on the clock face. [Hint: A good diagram may help here.]
2. Use the sine and cosine law method to find the resultant velocity if a small plane moving at airspeed of 201
km/h [E 50° N] encounters a wind blowing at 50.0 km/h from the west. [Hint: A wind from the west means that the wind is blowing east.]
3. A dog walks 600.0 m [E 47° N], then 500.0 m [N 38° W], then 300.0 m [W 29° S], and finally 400.0 m [S
13° E]. Use components to find the resultant displacement of the dog.
Blackline Master 1.5-1
BLM 1.5-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.5-1 Projectile Motion 1. A ball is thrown downward from the top of building with a speed of 18.0 m/s at an angle of 30.0° to the
horizontal.
(a) What are the horizontal and vertical components of the velocity the instant the ball is thrown?
(b) What are the horizontal and vertical components of the velocity 1.00 s after being thrown?
2. A golf ball is hit with an initial velocity of 32.5 m/s at an angle of 65° to the ground. The ball lands at a
point that is 6.31 m higher than from where it was hit.
(a) How long is the ball in the air?
Blackline Master 1.5-1
BLM 1.5-1 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.5-1 Projectile Motion (continued)
(b) How far does the ball travel horizontally before hitting the ground?
(c) Determine the velocity of the golf ball just before it hits the ground.
3. A soccer goal keeper kicks the ball, giving it an initial velocity of 27 m/s at a 70.0° angle to the horizontal. If we ignore air resistance,
(a) what will be the ball’s maximum height?
(b) how long will the ball be in the air?
(c) what is the range?
Blackline Master 1.5-2
BLM 1.5-2 Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ 1.5-2 Projectile Motion Problems
Figure 1 The two balls reach the lowest position at the same instant, even though one ball was dropped and the other was given an initial horizontal velocity. Both balls had an initial vertical velocity of zero, and both experienced free fall.
Projectile motion is best understood when the horizontal and vertical components of an object’s motion are considered independently. A projectile follows a parabolic trajectory to the ground. Once the projectile is in motion, only the force of gravity acts on the object (assuming no other forces are acting). Thus, the force of gravity is the net force and acts vertically downward. According to Newton’s second law of motion, the object’s acceleration is also vertically downward and equals 9.8 m/s2. The vertical motion of a projectile consists of a uniform downward acceleration in the vertical plane and uniform motion (constant velocity) in the horizontal plane. Since no forces act horizontally, there is no horizontal acceleration. Figure 1 shows two balls as they fall to the ground. The ball on the left falls vertically downward, while the ball on the right is projected and has some horizontal motion. The horizontal component of the ball on the right’s motion is uniform. Both balls become progressively farther apart as the balls fall and are aligned horizontally. This indicates that both balls are experiencing the same vertical acceleration due to gravity. The time interval between images is constant in this stroboscopic photograph.
Question Look at Figure 1. The last image occurs 11 images after the first image. The vertical distance between the 12 images was 0.50 m. The horizontal distance travelled by the ball on the right across the 12 images was 25 cm. Determine:
(a) the flash rate of the stroboscope.
(b) the projection speed of the ball on the right. Assume that the acceleration of gravity is 9.8 m/s2.
Blackline Master 1.Q
BLM 1.Q Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ Chapter 1 Quiz Answer the questions on a separate piece of paper if necessary. Indicate whether each statement is true or false. If the statement is false, rewrite it to make it true.
1. Velocity is simply speed with a direction.
________________________________________________________________________________________
________________________________________________________________________________________ 2. The area under a velocity–time graph gives the total displacement.
________________________________________________________________________________________
________________________________________________________________________________________ 3. The magnitude of the average velocity is always less than the average speed in the same interval of time.
________________________________________________________________________________________
________________________________________________________________________________________
Fill in the blanks.
4. The least accurate method used in vector addition is _________________. The most accurate and easiest to use method is ____________________.
5. The study of motion that considers only trajectory, displacement, velocity, and acceleration is called ______________.
6. Average velocity is the slope of a __________ line on a position–time graph and instantaneous velocity is
the slope of a __________line on a position–time graph.
Match each term on the left with the most appropriate description on the right.
7. ____ (a) velocity (i) the straight-line distance and direction of an object from a reference point
____ (b) speed (ii) the change in position divided by the time interval
____ (c) position (iii) the total distance divided by the time interval
____ (d) displacement (iv) the change in position of an object
Blackline Master 1.Q
BLM 1.Q Copyright © 2012 by Nelson Education Ltd.
NAME: _______________________________________________ DATE: _____________________ Chapter 1 Quiz (continued) Write a short answer to each question. For numerical questions, provide a full solution. 8. Give an example of motion where there would be a non-zero average speed, but a zero average velocity. 9. A boat accelerates from 8.0 m/s to 11 m/s at a rate of 0.50 m/s2. How far does the boat travel during the
period of time that the acceleration is occurring? Assume that the forward direction is positive. 10. A whale travels 20.0 km [E 25° N] and then moves 45.0 km [N 40.0° W]. What is the total displacement
of the whale? 11. You stand at the edge of a cliff overlooking a river at its base. The cliff is 295 m high and the distance
from the base of the cliff to the other side of the river is 82.0 m. If you throw a rock with a horizontal velocity of 12.7 m/s, does the rock land on the other side of the river? Show all work.
12. A person is walking to the back of a bus at 1.1 m/s as the bus moves forward at 12.2 m/s. What velocity
does this person appear to have to a person standing on the side of the road?