Cambridge International AS & A Level Mathematics 9709/04 Mechanics 1 (M1 !or e"amination #rom $017 Contents Introd%ction Introd%ction ' 1 !orces and e%ilibri%m e%ilibri%m ) $ *inematics o# motion in a straight line line + ' ,e-ton.s la-s o# motion motion 10 4 nerg -or2 and 3o-er 3o-er 1$
Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
Introduction 6his scheme o# -or2 3rovides ideas abo%t ho- to constr%ct and deliver a co%rse It has been bro2en do-n into di##erent %nits o# the three s%bect areas o# 8%re Mathematics (%nits 81 8$ and 8' Mechanics (%nits M1 and M$ and 8robabilit & Statistics (%nits S1 and S$ !or each %nit there are s%ggested teaching activities and learning reso%rces to %se in the classroom #or all o# the sllab%s learning obectives 6his scheme o# -or2 li2e an other is meant to be a g%ideline o##ering advice ti3s and ideas It can never be com3lete b%t ho3e#%ll 3rovides teachers -ith a basis to 3lan their lessons It covers the minim%m re%ired #or the Cambridge International AS & A Level co%rse b%t also adds enhancement and develo3ment ideas It does not ta2e into acco%nt that di##erent schools ta2e di##erent amo%nts o# time to cover the Cambridge International AS & A Level co%rse 6he mathematical content o# Mechanics 1 in the s llab%s is detailed in the tables belo- 6he order in -hich to3ics are listed is not intended to im3l anthing abo%t the order in -hich the might be ta%ght Recommended prior knowledge *no-ledge o# the content o# Cambridge Level / Cambridge I:CS; Mathematics is ass%med Candidates -ill be e"3ected to be #amiliar -ith scienti#ic notation #or the e"3ression o# com3o%nd %nits eg ) m s 1 #or ) metres 3er second As -ell as demonstrating s2ill in the a33ro3riate techni%es candidates -ill be e"3ected to a33l their 2no-ledge in the sol%tion o# 3roblems Individ%al %estions set ma involve ideas and methods #rom more than one section o# the relevant content list Outline S%ggestions #or inde3endent st%d (I) and #ormative assessment (F) are indicated -here a33ro3riate -ithin this scheme o# -or2 6he activities in the scheme o# -or2 are onl s%ggestions and there are man other %se#%l activities to be #o%nd in the materials re#erred to in the learning reso%rce list 33ort%nities #or di##erentiation are indicated as basic/consolidation and challenging/extension 6here is the 3otential #or di##erentiation b reso%rce length gro%3ing e"3ected level o# o%tcome and degree o# s%33ort b the teacher thro%gho%t the scheme o# -or2 6imings #or activities and #eedbac2 are le#t to the %dgment o# the teacher according to the level o# the learners and si details o# #orthcoming training o33ort%nities are 3osted online
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Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
6his scheme o# -or2 is available as 8@! and an editable version in Microso#t 5ord #ormat> both are available on 6eacher S%33ort at http://teachers.cie.org.uk I# o% are %nable to %se Microso#t 5ord o% can do-nload 3en ##ice #ree o# charge #rom ---o3eno##iceorg Resources 6he %3=to=date reso%rce list #or this sllab%s incl%ding te"tboo2s endorsed b Cambridge is listed at ---cieorg%2 Endorsed textbooks have been -ritten to be closel aligned to the sllab%s the s%33ort and have been thro%gh a detailed %alit ass%rance 3rocess As s%ch all te"tboo2s endorsed b Cambridge #or this sllab%s are the ideal reso%rce to be %sed alongside this scheme o# -or2 as the cover each learning obective ebsites and !ideos 6his scheme o# -or2 incl%des -ebsite lin2s 3roviding direct access to internet reso%rces Cambridge International "aminations is not res3onsible #or the acc%rac or content o# in#ormation contained in these sites 6he incl%sion o# a lin2 to an e"ternal -ebsite sho%ld not be %nderstood to be an endorsement o# that -ebsite or the sites o-ners (or their 3rod%cts/services 6he -ebsite 3ages re#erenced in this scheme o# -or2 -ere selected -hen the scheme o# -or2 -as 3rod%ced ther as3ects o# the sites -ere not chec2ed and onl the 3artic%lar reso%rces are recommended
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Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
"# Forces and e$uilibrium %earning ob&ecti!es
'uggested teaching acti!ities
Identi# the #orces acting in a given sit%ation
6he idea o# #orces sho%ld alread be #amiliar to learners b%t it is a good idea #or o% to disc%ss them -ith the class as m%ch as time allo-s Bo% co%ld 3erha3s start -ith a brainstorm eliciting as man named #orces as 3ossible and t3es o# sit%ations in -hich the might be 3resent and allo-ing the o33ort%nit #or learners. misconce3tions to be bro%ght o%t and con#ronted 5here 3ossible 3ractical activities are also hel3#%l rein#orcing the idea that the st%d o# Mechanics is modelling real 3hsical sit%ations Bo% co%ld %se an air trac2 and slider 3%lled b a mass over a 3%lle It is 3artic%larl hel3#%l i# o% can var the angle o# elevation o# the 3%lling #orce I# an air trac2 is not available an mass on di##erent t3es o# s%r#ace is e%all %se#%l eg boo2s 3%lled b string %3 a slo3ing des2 Bo% can %se this demonstration to bring o%t ideas abo%t e%ilibri%m and motion d%e to %nbalanced #orces as -ell as normal reactions and the variable nat%re o# #rictional #orces Learners sho%ld be able to analse sit%ations -hich involve the #ollo-ing #orces -eight tension #riction normal reaction air resistance (ma2e s%re the are clear that this -ill o#ten be neglected in mathematical models that involve 3articles and the driving #orce (eg o# an engine Bo% co%ld 3rovide learners -ith a variet o# sit%ations or diagrams and as2 them to indicate the #orces and their directions
Dnderstand the vector nat%re o# #orce and #ind and %se com3onents and res%ltants
(6he a33roach to this -ill de3end on -hether or not the vector section o# %nit 81 has been covered alread @ivide the class into gro%3s then set %3 a mass on a string 3assing over a 3%lle #or each gro%3 Learners sho%ld hold this in 3lace -ith a ,e-ton meter attached to the #ree end o# the string 6he sho%ld meas%re the si
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Cambridge International AS & A Level Mathematics (9709 #rom $017
%earning ob&ecti!es
Scheme o# 5or2
'uggested teaching acti!ities
As2 #or #eedbac2 #rom each gro%3 to see -hat the have #o%nd and -hat ideas the have come %3 -ith 6his sho%ld lead nat%rall to the idea that a single #orce can be re3licated b t-o or more #orces (the idea o# com3onents r conversel that t-o or more #orces can be re3resented b their overall e##ect (the idea o# a res%ltant Sho- learners ho- to resolve a single #orce into t-o 3er3endic%lar com3onents F cos θ and F sin θ and also ho- to #ind the res%ltant o# t-o 3er3endic%lar #orces 8rovide 3lent o# these #or learners to 3ractise either as an e"ercise #or individ%al learners to do in class or inde3endentl later as this -ill be an essential s2ill thro%gho%t both Mechanics mod%les Most te"tboo2s -ill contain man %se#%l e"am3les (I) ast papers (I)(F) E%ne $01' 3a3er 41 %estion ' ,ovember $01$ 3a3er 41 %estion 4 ,ovember $01$ 3a3er 4$ %estion 4 ,ovember $014 3a3er 4$ %estion $ Dse the 3rinci3le that -hen a 3article is in e%ilibri%m the vector s%m o# the #orces acting is
Cover both a33roaches here (1 the triangle o# #orces and ($ #inding the s%m o# the com3onents o# all the #orces in a chosen direction Learners -ho are less con#ident mathematicall -ill 3robabl #ind the second a33roach more accessible as the #irst one is li2el to involve the %se o# the sine and cosine r%les Introd%ce the triangle o# #orces grad%all a#ter covering the techni%e in three #orce sit%ations -here t-o o# the #orces are 3er3endic%lar ma2ing the trigonometr more straight#or-ard It is a good idea to 3rovide e"am3les -here the given #orces are alread in e%ilibri%m and as2 learners to demonstrate that the are Also 3rovide e"am3les -here the #orces are not in e%ilibri%m and as2 learners to #ind the magnit%de and direction o# the #orce that is needed #or e%ilibri%m 6his reso%rce htt3//ta3io3org/mechanics/static/$0$/3ageF4G$)4html has good ideas #or 3ractical activities as -ell as gro%3 disc%ssion ideas and individ%al %estions #or learners ast papers (I)(F) E%ne $01$ 3a3er 4$ %estion $
Dnderstand that a contact #orce bet-een
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8lacing sim3le obects on a hori
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Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
%earning ob&ecti!es
'uggested teaching acti!ities
t-o s%r#aces can be re3resented b t-o com3onents the normal com3onent and the #rictional com3onent
balancing the -eight o# an obect As2 learners to dra- a diagram sho-ing the #orces and their directions He3eat this -ith the s%r#ace at di##erent angles o# elevation "3lain that the contact #orce can be re3resented b t-o 3er3endic%lar com3onents the normal reaction (ens%re that the signi#icance o# normal. is clear signi#ing a 3%sh. b the s%r#ace and the #rictional #orce resisting movement 3arallel to the s%r#ace
Dse the model o# a smooth. contact and %nderstand the limitations o# this model
"3lain the signi#icance o# the -ord smooth. in modelling sit%ations indicating that o% can i gnore the #rictional com3onent o# the contact #orce that resists motion 3arallel to the s%r#ace ns%re that learners %nderstand the signi#icance o# the direction o# the contact #orce ast papers (I)(F) E%ne $01' 3a3er 4$ %estion 7 (6his %estion involves motion o# an obect on a smooth s%r#ace altho%gh s2ills #rom other 3arts o# the Scheme o# 5or2 are also needed ,ovember $014 3a3er 41 %estion $ ,ovember $014 3a3er 4$ %estion 4 (6his %estion models the same sit%ation t-ice> once on a smooth s%r#ace and once on a ro%gh s%r#ace and is %se#%l to demonstrate the di##erence bet-een the t-o cases
Dnderstand the conce3ts o# limiting #riction and limiting e%ilibri%m> recall the de#inition o# coe##icient o# #riction and %se the relationshi3 F = µR or F ≤ µR as a33ro3riate
@isc%ss -h the obect does not slide %ntil a critical. angle is achieved 6his co%ld #orm the basis o# an investigation -ith di##erent obects and/or di##erent s%r#aces A similar investigation might incl%de %st a hori
Dse ,e-ton.s third la-
8resent learners -ith a variet o# sit%ations in -hich a #orce is to be identi#ied @e#ine ,e-ton.s third la- and as2 #or the e%al and o33osite #orce to each one that has been identi#ied Some t3ical cases to consider (1 the res%ltant #orce e"3erienced b a 3%lle -hen t-o connected masses are h%ng over it (a 3roblem involving strings at di##erent angles co%ld be %sed as an extension e"ercise ($ a mass in a li#t/elevator s%33orted or raised b a cable (' a to-ing. sit%ation eg car and trailer/caravan (these might be better %sed a#ter the section on ,e-ton.s La-s o# Motion has been covered
6his -ebsite htt3//---e"amsol%tionsnet/maths=revision/mechanics/statics/#riction/t%torial=13h3 has a %se#%l video t%torial s%mmarising most o# the ideas abo%t #riction in Mechanics
Bo% can #ind good notes and a #e- e"am3les and %estions here htt3//---mathcentreac%2/reso%rces/%3loaded/mc= -eb=mech$=11=$0093d#
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Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
*# +inematics o, motion in a straight line %earning ob&ecti!es
'uggested teaching acti!ities
Dnderstand the conce3ts o# distance and s3eed as scalar %antities and o# dis3lacement velocit and acceleration as vector %antities (in one dimension onl
Heiterate the di##erence bet-een scalar and vector %antities In one dimension the direction o# a vector -ill determine -hether o% %se a 3ositive or negative sign A #e- sim3le e"am3les o# this sho%ld be s%##icient Bo% sho%ld stress that negative s3eed or distance is not a33ro3riate and that %se o# these -ill be 3enalised in e"ams Also ens%re that learners %nderstand that a negative acceleration is e%ivalent to a 3ositive deceleration
S2etch and inter3ret dis3lacement=time gra3hs and velocit=time gra3hs and in 3artic%lar a33reciate that = the area %nder a velocit=time gra3h re3resents dis3lacement = the gradient o# a dis3lacement= time gra3h re3resents velocit = the gradient o# a velocit=time gra3h re3resents acceleration
A s%mmar o# the 2e 3oints #or the t-o t3es o# gra3hs -ith a #e- %estions is given here htt3//---mathcentreac%2/reso%rces/%3loaded/mc=-eb=mech1=10=$0093d#
Dse di##erentiation and integration -ith res3ect to time to solve sim3le 3roblems concerning dis3lacement velocit and acceleration (restricted to calc%l%s -ithin the sco3e o# %nit 81
6he doc%ment mentioned above (htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFch$3d# has a good e"3lanation o# the %se o# di##erentiation and integration in the conte"t o# dis3lacement velocit and acceleration It is -orth s3ending time on e"am3les that re%ire learners to #ind constants o# integration
Dse a33ro3riate #orm%lae #or motion -ith constant acceleration in a straight
6he doc%ment mentioned above (htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFch$3d# demonstrates the derivation and %se o# the #orm%lae as -ell as 3roviding %estions #or learners to tr #or themselves It
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A more com3lete disc%ssion -ith e"tensive e"am3les and %estions is at htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFch$3d# (6his incl%des the calc%l%s as3ect and the e%ations o# motion #or constant acceleration as -ell as a treatment o# the #orces involved in changing the motion o# an obect ast papers (I)(F) E%ne $01' 3a3er 4$ %estion G ,ovember $01' 3a3er 4$ %estion 7 3arts (i and (ii (later 3arts re%ire s2ills #rom other 3arts o# the Scheme o# 5or2 ,ovember $01' 3a3er 4' %estion 4
Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
%earning ob&ecti!es
'uggested teaching acti!ities
line
-o%ld be %se#%l to challenge learners to derive the #orm%lae 3erha3s giving them a #e- hints 6he co%ld start #rom the basic de#inition o# constant acceleration as the di##erence in velocities 3er second or #rom their %nderstanding o# acceleration as the gradient o# a velocit=time gra3h htt3s//---o%t%becom/-atchJvK#S7hs is a video -ith a straight#or-ard e"am3le demonstrating ver clearl the %se o# the #orm%lae (sometimes 2no-n as s%vat. e%ations named a#ter the #ive variables involved It is 3artic%larl im3ortant to ma2e it clear to learners that these #orm%lae can onl be %sed in cases -here the acceleration is constant not -here acceleration varies -ith time It is also im3ortant that learners have e"3erienced and disc%ssed the relevance o# cases -here the time has to be #o%nd #rom a %adratic e%ation giving t-o sol%tions Learners -ill bene#it #rom attem3ting a -ide variet o# %estions re%iring them to %se the e%ations o# motion and o% can #ind man s%ch %estions in te"tboo2s and at the lin2s above 8ast 3a3er %estions on this obective o#ten a33ear in %estions that also cover other obectives s%ch as the %se o# ,e-ton.s $nd la- or vertical motion %nder gravit 6his %estion a33lies onl to this obective ast papers (I)(F) E%ne $01' 3a3er 4$ %estion $
-# .ewtons laws o, motion %earning ob&ecti!es
'uggested teaching acti!ities
A33l ,e-ton.s la-s o# motion to the linear motion o# a 3article o# constant mass moving %nder the action o# constant #orces -hich ma incl%de #riction
It is essential that learners can identi# the direction o# motion and %nderstand that #orces resolved 3er3endic%lar to the motion m%st be balanced -hile the res%ltant #orce 3arallel to the motion is -hat -ill ca%se the acceleration htt3s//---2hanacademorg/science/3hsics/#orces=ne-tons=la-s/ne-tons=la-s=o#=motion has a good descri3tion o# all three o# ,e-ton.s la-s o# motion 3resented in an interesting -a and -ith tho%ght#%l %estions in %i< #orm Interested and more able learners might #ind the video here htt3//mathcentreac%2/st%dents/to3ics/mechanics/ne-ton/ -orth -atching altho%gh it deals -ith motion in t-o dimensions s%ch as orbital motion and there#ore goes beond the
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Cambridge International AS & A Level Mathematics (9709 #rom $017
%earning ob&ecti!es
Scheme o# 5or2
'uggested teaching acti!ities sco3e o# this scheme o# -or2 6here is good coverage o# this to3ic in the doc%ment mentioned above (htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFch$3d# -ith %se#%l e"ercises #or learners 3erha3s #or inde3endent st%d (I) # the 3ast 3a3er %estions that e"3lore this obective man also re%ire other obectives #or e"am3le regarding mass and -eight or motion on an inclined 3lane Nere are some -hich #oc%s largel on hori
Dse the relationshi3 bet-een mass and -eight
Bo% sho%ld ens%re that learners are #amiliar -ith the instr%ction on the #ront o# the e"am 3a3er to %se 10 ms=$ as the acceleration d%e to gravit Man learners -ill come across other val%es #or e"am3le in their st%d o# 8hsics htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFch$3d# has some good ideas #or 3ractical -or2 and disc%ssions concerning acceleration d%e to gravit and ho- to obtain the #orce o# -eight #rom a 2no-n mass ast papers 6his obective is covered e"tensivel in %estions listed %nder the vertical motion and motion on an inclined 3lane obective (see later
Solve sim3le 3roblems -hich ma be modelled as the motion o# a 3article moving verticall or on an inclined 3lane -ith constant acceleration
6his short video cli3 sho-s clearl ho- to analse the #orces on an obect moving on an inclined 3lane htt3s//---o%t%becom/-atchJvKdA4vBd-7Og
Solve sim3le 3roblems -hich ma be modelled as the motion o# t-o 3articles connected b a light ine"tensible string
Bo% -ill #ind it -orth-hile to disc%ss the signi#icance o# the modelling ass%m3tions here smooth. 3eg or 3%lle im3lies constant tension along the length o# the string and light ine"tensible string. im3lies that the connected 3articles have identical acceleration
Cambridge International AS & A Level Mathematics (9709 #rom $017
%earning ob&ecti!es -hich ma 3ass over a #i"ed smooth 3eg or light 3%lle
Scheme o# 5or2
'uggested teaching acti!ities
6his lin2 3rovides hel3#%l notes e"am3les and %estions htt3//---mathcentreac%2/reso%rces/%3loaded/mc=-eb= mech$=1$=$0093d# (I) A video t%torial -ith a clear e"am3le o# ho- to solve vertical string %estions is here htt3//---e"amsol%tionsnet/maths=revision/mechanics/dnamics/connected=3articles/vertical=strings/t%torial=13h3 6his lin2 sho-s an animation -ith e"3lanations -hen at least one o# the strings is not vertical htt3//---e"amsol%tionsnet/maths=revision/mechanics/dnamics/connected=3articles/inclined= 3lanes/animation/t%torial=13h3 It also lin2s to e"am3les o# ho- to solve these 3roblems ast papers (I)(F) E%ne $01$ 3a3er 41 %estion G E%ne $01$ 3a3er 4' %estion 7 E%ne $01' 3a3er 4' %estion 7
0# Energ12 work and power %earning ob&ecti!es
'uggested teaching acti!ities
Dnderstand the conce3t o# the -or2 done b a #orce and calc%late the -or2 done b a constant #orce -hen its 3oint o# a33lication %ndergoes a dis3lacement not necessaril 3arallel to the #orce (%se
6his lin2 gives a de#inition o# -or2 done b a #orce and a t%torial on ho- to %se this de#inition to solve 3roblems -hen the motion is hori
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Cambridge International AS & A Level Mathematics (9709 #rom $017
%earning ob&ecti!es
Scheme o# 5or2
'uggested teaching acti!ities
o# the scalar 3rod%ct is not re%ired 6his lin2 deals -ith motion on an inclined 3lane htt3//---e"amsol%tionsnet/maths=revision/mechanics/-or2=energ= 3o-er/-or2/incline/t%torial=13h3 ast papers (I)(F) E%ne $01$ 3a3er 4$ %estion 1 E%ne $01$ 3a3er 4' %estion 1 ,ovember $01$ 3a3er 4$ %estion 1 Dnderstand the conce3ts o# gravitational 3otential energ and 2inetic energ and %se a33ro3riate #orm%lae
htt3//---e"amsol%tionsnet/maths=revision/mechanics/-or2=energ=3o-er/gravitational=3otential=energ/t%torial= 13h3 has a video t%torial -hich de#ines gravitational 3otential energ and demonstrates ho- to calc%late it and htt3//---e"amsol%tionsnet/maths=revision/mechanics/-or2=energ=3o-er/2inetic=energ/t%torial=13h3 does the same #or 2inetic energ It also incl%des a derivation o# change in 2inetic energ #rom -or2 done b a #orce ast papers (I)(F) E%ne $01$ 3a3er 41 %estion ' 3arts (i and (ii ,ovember $014 3a3er 4$ %estion ) 3art (i
Dnderstand and %se the relationshi3 bet-een the change in energ o# a sstem and the -or2 done b the e"ternal #orces and %se in a33ro3riate cases the 3rinci3le o# conservation o# energ
It is a good idea to ma2e s%re that learners are clear abo%t -hich #orces are treated as e"ternal. in each sit%ation A common error is to incl%de the -eight t-ice #irst in calc%lating -or2 done as -eight " distance. and again as a change in 3otential energ 6his lin2 has a com3lete treatment o# the theor involved here -ith -or2ed e"am3les as -ell as %estions #or learners to tr htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFchG3d# (I) 6here are video t%torials here htt3//---e"amsol%tionsnet/maths=revision/sllab%ses/Inde"/3eriod= 1/Mechanics/mod%le3h3P:8 Clic2 on the lin2 to Conservation o# energ / 5or2=nerg 8rinci3le. ast papers (I)(F) E%ne $01$ 3a3er 4' %estion ) E%ne $01' 3a3er 41 %estion $ E%ne $01' 3a3er 4$ %estion $
Dse the de#inition o# 3o-er as the rate at
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htt3//---cimt3lmo%thac%2/3roects/me3res/alevel/mechanicsFchG3d# has a good e"3lanation o# the conce3t o#
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Cambridge International AS & A Level Mathematics (9709 #rom $017
Scheme o# 5or2
%earning ob&ecti!es
'uggested teaching acti!ities
-hich a #orce does -or2 and %se the relationshi3 bet-een 3o-er #orce and velocit #or a #orce acting in the direction o# motion
3o-er and the mathematical im3lications o# the de#inition 6here are -or2ed e"am3les and %estions #or learners(I) It is im3ortant to enco%rage learners to thin2 abo%t ideas s%ch as the ma"im%m velocit #or a given 3o-er -ith a given resistance 6he need to be able to %se the de#inition o# 3o-er in the conte"t o# analsing #orces ns%re that learners are clear that the 3o-er relates to the dri!ing #orce not to an o# the other e"ternal. #orces involved ast papers (I)(F) E%ne $01$ 3a3er 41 %estion ' E%ne $01$ 3a3er 4$ %estion G E%ne $01' 3a3er 41 %estion 4
Solve 3roblems involving #or e"am3le the instantaneo%s acceleration o# a car moving on a hill -ith resistance
A good clear #orce diagram is ver im3ortant #or these 3roblems nco%rage learners to label the driving #orce as P /v -herever a33ro3riate htt3//---e"amsol%tionsnet/maths=revision/mechanics/-or2=energ=3o-er/3o-er/%ni#orm=motion/t%torial=13h3 is a video t%torial that de#ines the conce3t o# 3o-er develo3s its lin2 -ith #orce and velocit and -or2s thro%gh an e"am3le o# a vehicle on an inclined 3lane htt3//---e"amsol%tionsnet/maths=revision/mechanics/-or2=energ= 3o-er/3o-er/acceleration/t%torial=13h3develo3s the 3revio%s t%torial to consider acceleration as -ell ast papers (I)(F) E%ne $01$ 3a3er 41 %estion 1 E%ne $01$ 3a3er 4' %estion 4 E%ne $01' 3a3er 4$ %estion )
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Q Cambridge International "aminations $01G ?ersion 11 D3dated $G0$1G
