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SECTION II: Newtonian Mechanics
SECTION II
Newtonian Mechanics
CIE A-Level [AS and A2]
________________________
Course Notes
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Syllabs !etails______________________
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"# $ine%atics [AS]___________________________
Content
3.1 Linear motion3.2 Non-linear motion
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) de)ine dis*lace%ent+ s*eed+ velocity and accele&ation
Sy%bol !e)inition SI
nit
,ecto&
Scala&
!is*lace%ent s Distance moved in particular direction
m Vector ,elocity v or u Velocity = change in displacement / time ms-1 Vector
S*eed v or u peed = total distance / time ms-1 calar
Accele&ation a !cceleration = change in velocity / time ms-2 Vector
(b) se '&a*hical %ethods to &e*&esent dis*lace%ent+ s*eed+ velocity and
accele&ation
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(c) )ind dis*lace%ent )&o% the a&ea nde& a velocity-ti%e '&a*h
(d) se the slo*e o) a dis*lace%ent-ti%e '&a*h to )ind the velocity
(e) se the slo*e o) a velocity-ti%e '&a*h to )ind the accele&ation
"" #$"% &'
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SECTION II: Newtonian Mechanics
(f) de&ive+ )&o% the de)initions o) velocity and accele&ation+ e.ations that
&e*&esent ni)o&%ly accele&ated %otion in a st&ai'ht line
v=u+at
s=[(u+v)/2]t
v2=u2+2ass=ut+1/2at 2
s=vt-1/2at 2
!E/I,ATION0
tart )ith de*inition o* acceleration
a = (v-u) / t
+earrange to get *irst e,uation
v = u + at
%ae de*inition o* average velocity
Ave&a'e velocity 1 s t
Ave&a'e velocity 1 (v +u)/2
%here*ore
s t 1 v 342
+earrangement gives
s = [(v + u)t]/2
%aing v = u + at and s = [(v + u)t]/2. %o eliminate v…
s = ut + 1/2at 2
%aing v = u + at and s = [(v – u)t]/2. %o eliminate t…
v2=u2+2as
These )o&%la a&e 'iven on the test *a*e&
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u &nitial velocity
v 0inal velocity
a !ccelerationt %ime
s Displacement
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(g) solve *&oble%s sin' e.ations that &e*&esent ni)o&%ly accele&ated %otion in a
st&ai'ht line+ incldin' the %otion o) bodies )allin' in a ni)o&% '&avitational )ield
withot ai& &esistance
&* a ody *alls in a vacuum near the "arths sur*ace it has an acceleration g o* )&ee-
)all
(h) &ecall that the wei'ht o) a body is e.al to the *&odct o) its %ass and the
accele&ation o) )&ee )all
'ass = related to the amount o* matter in an oecteight = *orce o* gravity e4erted on an oect 5or the *orce on a supporting scale6
eight 5N6 = mass 5g6 4 g 5ms-26 g=acceleration o* *ree *all
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(i) desc&ibe an e5*e&i%ent to dete&%ine the accele&ation o) )&ee )all sin' a )allin'
body
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(j) desc&ibe .alitatively the %otion o) bodies )allin' in a ni)o&% '&avitational )ield
with ai& &esistance
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SECTION II: Newtonian Mechanics
(k) desc&ibe and e5*lain %otion de to a ni)o&% velocity in one di&ection and a
ni)o&% accele&ation in a *e&*endicla& di&ection#
:ravitational *ield in vertical direction
v$ has no *orce acting so is constant
vV has a constant *orce acting so there is a constant acceleration
#roectile 'otion
paraolic motion
v$
v$
v$
v$
v$
v$
vV
vV
vV
vV
vV
vV
•
#araolic in asence o* air resistance• %he vertical and hori;ontal components are independent
"" #$"% &'
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6# !yna%ics [AS]____________________________
Content
(.1 Ne)tons la)s o* motion(.2 Linear momentum and its conservation
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) state each o) Newton7s laws o) %otion
NE8TON7S 9I/ST LA8(
>!n oect continues in uni*orm motion in a straight line or at rest unless a
resultant *orce acts.?
NE8TON7S SECON! LA8(
>%he rate o* change o* momentum o* an oect is proportional to the resultant
*orce )hich acts on the oect.?
NE8TON7S T:I/! LA8(
>)hen t)o odies ! and @ interactA the *orce that ! e4erts on @ is e,ual and
opposite to the *orce @ e4erts on !.?
(b)show an nde&standin' that %ass is the *&o*e&ty o) a body that &esists chan'e in%otion
'ass is a property o* a ody that resists change in motion
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SECTION II: Newtonian Mechanics
(c) desc&ibe and se the conce*t o) wei'ht as the e))ect o) a '&avitational )ield on a
%ass
eight = *orce o* gravity e4erted on an oect 5or the *orce on a supporting scale6
eight 5N6 = mass 5g6 4 g 5N/g6 g=gravitational *ield strength
(d) de)ine linea& %o%ent% as the *&odct o) %ass and velocity
'omentum = 'ass 4 velocity
p ;'%s-
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(f) &ecall and solve *&oble%s sin' the &elationshi* F = ma+ a**&eciatin' that
accele&ation and )o&ce a&e always in the sa%e di&ection
/EMEM=E/( Accele&ation is always in the di&ection o) the &esltant )o&ce
"" #$"% &'
(g) state the *&inci*le o) conse&vation o) %o%ent%
La) o* conservation o* linear momentum
>The total linea& %o%ent% o) a syste% o) inte&actin' *a&ticles &e%ains
constant *&ovided the&e is no &esltant e5te&nal )o&ce#?
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SECTION II: Newtonian Mechanics
(h) a**ly the *&inci*le o) conse&vation o) %o%ent% to solve si%*le *&oble%s
incldin' elastic and inelastic inte&actions between two bodies in one di%ension
;nowled'e o) the conce*t o) coe))icient o) &estittion is not &e.i&ed4
E@AMLE0##
(i) &eco'nise that+ )o& a *e&)ectly elastic collision+ the &elative s*eed o) a**&oach is
e.al to the &elative s*eed o) se*a&ation
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(j) show an nde&standin' that+ while %o%ent% o) a syste% is always conse&ved in
inte&actions between bodies+ so%e chan'e in ;inetic ene&'y sally ta;es *lace#
ELASTIC AN! INELASTIC Collisions0##
Inelastic Collisions a&e the no&%al sitation
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SECTION II: Newtonian Mechanics
B# 9o&ces [AS]_______________________________
Content
.1 %ypes o* *orce.2 ",uilirium o* *orces
.3 Centre o* gravity
.( %urning e**ects o* *orces
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) desc&ibe the )o&ces on %ass and cha&'e in ni)o&% '&avitational and elect&ic
)ields+ as a**&o*&iate
a&ticle 9ield E))ectncharged mass :ravitational !ttracted in direction o*
*ield line
ncharged mass "lectric *ield No e**ect
Charged mass :ravitational *ield !ttracted in direction o**ield line
#ositive charge "lectric *ield !ttracted in direction o**ield line
Negative charge "lectric *ield +epelled in oppositedirection to *ield line
(b) show an nde&standin' o) the o&i'in o) the *th&st actin' on a body in a )lid
In a )lid###
• #articles are constantly colliding )ith the sides o* the container or
immersed oect
• %hese collisions produce a *orce
• %his *orce provides the upthrust on the immersed ody
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(c) show a .alitative nde&standin' o) )&ictional )o&ces and viscos )o&ces incldin'
ai& &esistance no t&eat%ent o) the coe))icients o) )&iction and viscosity is &e.i&ed4
• 0rictional *orces are *orces that act against the direction o* motion
• Viscous *orces result *rom motion through *luids
• @oth types o* *orces are due to the interaction et)een charges on themoving oect and the material it is close to
"" #$"% &'
(d) se a vecto& t&ian'le to &e*&esent )o&ces in e.ilib&i%
(e) show an nde&standin' that the wei'ht o) a body %ay be ta;en as
actin' at a sin'le *oint ;nown as its cent&e o) '&avity
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SECTION II: Newtonian Mechanics
(f) show an nde&standin' that a co*le is a *ai& o) )o&ces that tends to
*&odce &otation only
(g) de)ine and a**ly the %o%ent o) a )o&ce and the to&.e o) a co*le
(h) show an nde&standin' that+ when the&e is no &esltant )o&ce and no
&esltant to&.e+ a syste% is in e.ilib&i%
(i) a**ly the *&inci*le o) %o%ents#
I) an obect is in e.ilib&i%+ the s% o) the cloc;wise %o%ents abot a *ivot a&e
e.al to the s% o) the anticloc;wise %o%ents#
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SECTION II: Newtonian Mechanics
D# 8o&;+ ene&'y+ *owe& [AS]__________________
Content
7.1 "nergy conversion and conservation7.2 or
7.3 #otential energyA inetic energy and internal
energy
7.( #o)er
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) 'ive e5a%*les o) ene&'y in di))e&ent )o&%s+ its conve&sion and conse&vation+ anda**ly the *&inci*le o) ene&'y conse&vation to si%*le e5a%*les
Energy Type Example
Kinetic Energy Moving objects (Car)
Gravitational PotentialEnergy
Raised objects (ater in a da!)
Chemical Energy Energ" stored in bonds (coal# oil)Strain Energy Energ" due to $e%ing o& !aterials (elastic band)
Nuclear Energy Energ" associated 'it ato!ic nuclei (issionreactors)
Internal Energy Energ" o& !aterials * +inetic &ro! ,articles !oving
,otential &ro! bondsElectrical Energy Energ" &ro! !oving carges (electricit")Light Energy Energ" &ro! Electro!agnetic 'aves (ligt# IR)
Sound Energy Energ" due to vibrating ,articles (sound)
#rinciples o* Conservation o* "nergy
• Everall the total energy o* any closed system must e constant
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SECTION II: Newtonian Mechanics
• "nergy is neither created or destroyedA it ust changes *orm
• %here is no change in the total energy o* the niverse
(b) show an nde&standin' o) the conce*t o) wo&; in te&%s o) the *&odct o) a )o&ce
and dis*lace%ent in the di&ection o) the )o&ce
or = 0orce 4 distance moved y *orce
(c) calclate the wo&; done in a n%be& o) sitations incldin' the wo&; done by a
'as that is e5*andin' a'ainst a constant e5te&nal *&ess&e( W 1 p #
This )o&%la is 'iven on the test *a*e&
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SECTION II: Newtonian Mechanics
(d) de&ive+ )&o% the e.ations o) %otion+ the )o&%la E; 1 %v2
Finetic "nergy gained y an oect is e,ual to the )or done on that oect
tart )ith v2
1 2
3 2as
+earrange to *orm as 1 2 F v2
'ultiple oth sides y mass %as 1 %2 F %v2
0=ma so 9s 1 %2 F %v2
(e) &ecall and a**ly the )o&%la E; 1 %v2
Finetic energy = energy associated )ith a moving oect
$inetic Ene&'y G4 1
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"" #$"% &'
(g) show an nde&standin' and se the &elationshi* between )o&ce and *otential
ene&'y in a ni)o&% )ield to solve *&oble%s
(h) de&ive+ )&o% the de)inin' e.ation W 1 Fs+ the )o&%la ! * 1 mgh )o& *otential
ene&'y chan'es nea& the Ea&th7s s&)ace
(i) &ecall and se the )o&%la ! * 1 mgh )o& *otential ene&'y chan'es nea& the
Ea&th7s s&)ace
(j) show an nde&standin' o) the conce*t o) inte&nal ene&'y
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SECTION II: Newtonian Mechanics
Inte&nal Ene&'y 1 Total otential Ene&'y 3 Total /ando% $inetic Ene&'y
/ando% $inetic Ene&'y 1 T&anslational $inetic Ene&'y 3 /otational $inetic
Ene&'y
T&anslational ene&'y is the energy associated )ith the )hole molecule moving in
a certain direction.
/otational ene&'y is the energy associated )ith the molecule rotation around acertain point.
otential ene&'y is the energy associated )ith intermolecular *orces.
(k) &ecall and nde&stand that the e))iciency o) a syste% is the &atio o) se)l wo&;
done by the syste% to the total ene&'y in*t
"**iciency = se*ul )or E% / %otal energy trans*erred"**iciency = se*ul energy E% / %otal energy &N
"**iciency = se*ul po)er E% / %otal po)er &N
(") show an a**&eciation )o& the i%*lications o) ene&'y losses in *&actical devices and
se the conce*t o) e))iciency to solve *&oble%s
E))iciency 1 $inetic Ene&'y Ot Che%ical Ene&'y In
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SECTION II: Newtonian Mechanics
(m) de)ine *owe& as wo&; done *e& nit ti%e and de&ive *owe& as the *&odct o)
)o&ce and velocity
#o)er = +ate at )hich "nergy is trans*erred
#o)er 56 = energy trans*erred / time taen = )or done / time taen
1 att 56 = 1 Gs-1
Power = W/t
W = Fs
Power = Fs/t
Power = Fv
(#) solve *&oble%s sin' the &elationshi*s $ 1 W/t and $ 1 Fv#
SEE AST AE/ HESTION =OO$S
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SECTION II: Newtonian Mechanics
J# Motion in a ci&cle
[A2]_____________________
Content8.1 Finematics o* uni*orm circular motion
8.2 Centripetal acceleration
8.3 Centripetal *orce
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) e5*&ess an'la& dis*lace%ent in &adians
(b) nde&stand and se the conce*t o) an'la& velocity to solve *&oble%s
(c) &ecall and se v 1 % to solve *&oble%s
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(d) desc&ibe .alitatively %otion in a c&ved *ath de to a *e&*endicla& )o&ce+ and
nde&stand the cent&i*etal accele&ation in the case o) ni)o&% %otion in a ci&cle
• 9o&ce a**lied *e&*endicla& to the velocity di&ection
• Accele&ation in di&ection o) )o&ce
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SECTION II: Newtonian Mechanics
"" #$"% &'
(e) &ecall and se cent&i*etal accele&ation a 1 % 2+ a = v2 /%
Cent&i*etal accele&ation( %he acceleration o* an oect travelling in circular motion.
Cent&i*etal accele&ation 1 ace#t%ipeta" 1 v2 /% r = radius
ace#t%ipeta" 1 r ω 2
(f) &ecall and se cent&i*etal )o&ce F 1 m% 2+ F 1 mv2 /2
Cent&i*etal )o&ce 1 %a 1 mv2 /r
1 m r ω 2
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SECTION II: Newtonian Mechanics
K# &avitational )ield [A2]_____________________
Content
9.1 :ravitational *ield9.2 0orce et)een point masses
9.3 0ield o* a point mass
9.( 0ield near to the sur*ace o* the "arth
9. :ravitational potential
Lea&nin' otco%es_____________________________________
Candidates shold be able to(
(a) show an nde&standin' o) the conce*t o) a '&avitational )ield as an e5a%*le o))ield o) )o&ce and de)ine '&avitational )ield st&en'th as )o&ce *e& nit %ass
g = gravitation *ield strengthm = test mass
units = N g-1 = ms-2
(b) &ecall and se Newton7s law o) '&avitation in the )o&% F 1 %
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SECTION II: Newtonian Mechanics
(c) de&ive+ )&o% Newton7s law o) '&avitation and the de)inition o) '&avitational )ield
st&en'th+ the e.ation g= &'% 2 )o& the '&avitational )ield st&en'th o) a *oint %ass
(d) &ecall and solve *&oble%s sin' the e.ation g= &'/% 2 )o& the '&avitational )ield
st&en'th o) a *oint %ass
(e) show an a**&eciation that on the s&)ace o) the Ea&th g is a**&o5i%atelyconstant and is called the accele&ation o) )&ee )all
!s changes in r at the sur*ace o* the "arth are small in comparison to the distanceto the center o* the "arth 5and so the center o* gravity6 g can e considered
constant.
' 1 #K< N;' 1 #K< %s-
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SECTION II: Newtonian Mechanics
' mm
0102
;ero potential energy
at in*inity
potential energy decreases as
gravitational *orce does )or-
0orce on m increases
:ravitational potential energy o* mass m=:'m
r -
This )o&%la is 'iven on the test *a*e&
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SECTION II: Newtonian Mechanics
(h) &eco'nise the analo'y between ce&tain .alitative and .antitative as*ects o)
'&avitational )ield and elect&ic )ield
IJ,,
0102
;ero potential
at in*inity potential increase
0orce on , increases
"lectric #otential "nergy o* charge , =J,
4πε0r
Elect&ic *otential ene&'y( )or done in moving a charge *rom in*inity to a point
• Hero o* potential energy is at in*inity
• #otential energy taen as a negative value
•%he )or done in moving a charge et)een t)o points in an electril *ieldis independent o* the path taen
Elect&ic *otential( "nergy per unit test charge.
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SECTION II: Newtonian Mechanics
(i) analyse ci&cla& o&bits in inve&se s.a&e law )ields by &elatin' the '&avitational
)o&ce to the cent&i*etal accele&ation it cases
:ravitational attraction = centripetal *orce
GMm
r 2
mv 2
r =
GM v 2 r =
v √= GM r v = 2 π r
T
GM = 2 π r
T 5 6
2r =
4π 2 r 3
T 2
r 3
T 2 = Constant
(j) show an nde&standin' o) 'eostationa&y o&bits and thei& a**lication#
"arths rotates once every 2(hrs.@y using r 3 / %2 the radius o* orit needed *or geostationary orit can e calculated
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SECTION II: Newtonian Mechanics
=ac;'&ond /eadin'_________________
#$K&CA :iancoli 7th editionA Chapter 2-9
se)l 8ebsites______________________
htt*(*het#colo&ado#edensi%lationscate'o&ynew
htt*(www#s-cool#co#;alevel*hysics#ht%l
htt*(www#*hysicsclass&oo%#co%%%ediainde5#c)%
htt*(www#*hys#hawaii#edtebavantnavainde5#ht%l
htt*(www#colo&ado#ed*hysics2inde5#*l
Constants___________________________
[These a&e 'iven on each test *a*e&]
http://phet.colorado.edu/en/simulations/category/newhttp://www.s-cool.co.uk/alevel/physics.htmlhttp://www.physicsclassroom.com/mmedia/index.cfmhttp://www.phys.hawaii.edu/~teb/java/ntnujava/index.htmlhttp://www.colorado.edu/physics/2000/index.plhttp://www.s-cool.co.uk/alevel/physics.htmlhttp://www.physicsclassroom.com/mmedia/index.cfmhttp://www.phys.hawaii.edu/~teb/java/ntnujava/index.htmlhttp://www.colorado.edu/physics/2000/index.plhttp://phet.colorado.edu/en/simulations/category/new