Section 2. Mechanics Course Notes

8/18/2019 Section 2. Mechanics Course Notes

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A-Level Course Notes: PHYSICS

SECTION II: Newtonian Mechanics

SECTION II

Newtonian Mechanics

CIE A-Level [AS and A2]

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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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(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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(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_____________________________________


(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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(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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(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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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_____________________________________


(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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(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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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_____________________________________


(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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• "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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(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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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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(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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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_____________________________________


(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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"" #$"% &'

(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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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_____________________________________


(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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(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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' 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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(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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(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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=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

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Section 2. Mechanics Course Notes