ODU Mechanics Questions o Level A Level Physics
October 4, 2022 | Author: Anonymous | Category: N/A
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Download ODU Mechanics Questions o Level A Level Physics...
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Lesmahgow High School Higher Physics Our Dynamic Universe Mechanics Pr Problems oblems Revision problems......................................................................2 Speed.....................................................................................2 ccelera!ion............................................................................" #ec!ors.................................................................................... ec!ors....................................................................................$ $ Sec!ion %& '(ua!ions o) mo!ion...................................................* '(ua!ions o) mo!ion................................................................* Mo!ion + !ime graphs.............................................................., Sec!ion 2& -orces energy and power........................................%/ 0alanced and unbalanced )orces..........................................%/ Resolu!ion o) )orces..............................................................2% 1or done ine!ic and po!en!ial energy...............................23 Sec!ion "& 4ollisions 4ollisions and e5plo e5plosions................ sions.........................................2/ .........................2/ Solu!ions................................................................................... "2 Speed..................................................................................."2 ccelera!ion.........................................................................."2 '(ua!ions o) mo!ion.............................................................."" Mo!ion+!ime graphs.............................................................."" 0alanced and unbalanced )orces.........................................."$ Resolu!ion o) )orces.............................................................."* 1or done ine!ic and po!en!ial energy..............................."* 4ollisions and e5plosions......................................................"/
1
Revision problems Speed %.
6h 6he e wor world ld do down wnhil hilll si siing ing s spee peed d !r !rial ial !!a aes es pl place ace a a!! Le Les s r rcs cs every year. Describe a me!hod !ha! could be used !o 7nd !he average speed o) !he sier over !he % m run. 8our descrip!ion should include& 9a 9a:: 9b 9b:: 9c: 9c :
any appara!us re(uired de!ails o) wha! measuremen!s need !o be !aen an e5plana!ion o) how you would use !he measuremen!s !o carry ou! !he calcula!ions.
2.
n a a!hl !hle!e e!e rrun uns s a %3 %3;; ;; m rrace ace in a !!ime ime o) " m min in $ $; ; s. 4 4alc alcula ula!e !e his average speed )or !he race.
".
2.
c car ar iis s !r !rav avel elli ling ng a a!! a s spe peed ed o o)) %3 %3=; =; m s −% .
,.
!r !rolle olley y acc acceler a!es uni) uni)orm ormly ly do down wn spaced a slop slope. e.;=3; 6 6wo wo m lligh! igh! ga!e ga!es s !he connec!ed !oelera!es a mo!ion compu!er are apar! on 7
slope. 6he speeds recorded as !he !rolley passes !he ligh! ga!es are ;=2; m s −% and ;=3; m s −% 9a: 4alc 4alcula! ula!e e !he acce accelera lera!ion !ion o) !h !he e !r !rolley olley.. 9b: 1ha 1ha!! !im !ime e does !h !he e !r !rolley olley !!a ae e !o !ra !ravel vel !h !he e ;=3 m be be!wee !ween n !he ligh! ga!es> −%
.
he helic licop op!er !er iis s ri risin sing g ve ver! r!ica ically lly a a!! a sp speed eed o) % %;=; ;=; m s when a wheel )alls oK. 6he wheel hi!s !he ground ,=;; s la!er. 4alcula!e !he heigh! o) !he helicop!er above !he ground when !he wheel came came oK. 6he eKec!s o o)) )ric!ion can be ig ignored nored..
%;. ball is !h !hro rown wn ver! ver!icall ically y upwar upwards ds )r )rom om !he ed edge ge o) a cliK as shown in !he diagram. 4 m s-1
33 m
Sea
6he 6h e eK ec ec!s !s o) )r )ric ic!i !ion on ca can n be igno ig nored red.. 9a:: 9i 9a 9i::
1h 1ha! a! is !h !he e h hei eigh gh!! o o)) !!he he ba ball ll a abo bove ve se sea a llev evel el 2 2=; =; s a a))!e !err being !hrown>
9ii: 1ha! is !he velo veloci!y ci!y o o)) !he b ball all 2=; s a) a)!er !er be being ing !!hr hrown> own> 9b: 1ha 1ha!! is !he !!o!al o!al d dis!a is!ance nce !r !ravel avelled led by !h !he e ball ))ro rom m laun launch ch !o landing in !he sea>
8
Mo!ion + !ime graphs %.
6h 6he e gr graph aph sho shows ws h how ow !!he he d disp isplac laceme emen! n! o o)) an o obBe bBec! c! va varie ries s wi wi!h !h !ime.
North
9a: 4alc 4alcula! ula!e e !he velo veloci!y ci!y o o)) !he obBe obBec! c! be be!wee !ween n ; an and d % s s.. 9b: 1ha 1ha!! is !h !he e velo veloci!y ci!y o o)) !he o obBec bBec!! be!w be!ween een 2 a and nd $ s ))ro rom m !he s!ar!> 9c: Dra Draw w !he co corr rrespo espondin nding g dis! dis!ance ance ag agains ains!! !ime g graph raph )or !h !he e movemen! o) !his obBec!. 9d: 4alc 4alcula! ula!e e !he a avera verage ge sp speed eed o) !!he he obB obBec! ec! )o )orr !he , seco seconds nds shown on !he graph. 9e: Dra Draw w !he co corr rrespo espondin nding g veloc veloci!y i!y ag agains! ains! !ime g graph raph ))or or !he movemen! o) !his obBec!.
9
2.
6h 6he e gr graph aph sho shows ws h how ow !!he he d disp isplac laceme emen! n! o o)) an o obBe bBec! c! va varie ries s wi wi!h !h !ime.
North m / t n e m e c a l p s i d
9a: 4alc 4alcula! ula!e e !he v veloc eloci!y i!y o) !!he he ob obBec! Bec! d durin uring g !he 7r 7rs! s! sec second ond )rom !he s!ar!. 9b: 4alc 4alcula! ula!e e !he v veloc eloci!y i!y o) !!he he ob obBec! Bec! b be!we e!ween en % an and d 3 s )r )rom om !he s!ar!. 9c: Dra Draw w !he co corr rrespo espondin nding g dis! dis!ance ance ag agains ains!! !ime g graph raph )or !h !his is obBec!. 9d: 4alc 4alcula! ula!e e !he a avera verage ge sp speed eed o) !!he he obB obBec! ec! )o )orr !he 3 seco seconds. nds. 9e: Dra Draw w !he co corr rrespo espondin nding g veloc veloci!y i!y ag agains! ains! !ime g graph raph ))or or !hi !his s obBec!. 9): 1ha 1ha!! ar are e !h !he e dis displac placeme emen! n! a and nd !!he he v veloc eloci!y i!y o o)) !h !he e ob obBec! Bec! ;=3 seconds a)!er !he s!ar!> 9g: 1ha 1ha!! ar are e !he di displac splaceme emen! n! and !he ve veloci loci!y !y o) !h !he e obBe obBec! c! " seconds a)!er !he s!ar!>
10
".
6h 6he e gr graph aph sho shows ws !!he he d disp isplac lacem emen! en! ag again ains! s! !!im ime e gr graph aph )o )orr !h !he e movemen! o) an obBec!.
North m / t n e m e c a l p s i d
South
9a: 4alc 4alcula! ula!e e !he velo veloci!y ci!y o o)) !he obBe obBec! c! be be!wee !ween n ; an and d 2 s s.. 9b: 4alc 4alcula! ula!e e !he v veloc eloci!y i!y o) !!he he ob obBec! Bec! b be!we e!ween en 2 an and d $ s )r )rom om !he s!ar!. 9c: Dra Draw w !he co corr rrespo espondin nding g dis! dis!ance ance ag agains ains!! !ime g graph raph )or !h !his is obBec!. 9d: 4alc 4alcula! ula!e e !he a avera verage ge sp speed eed o) !!he he obB obBec! ec! )o )orr !he $ seco seconds. nds. 9e: Dra Draw w !he co corr rrespo espondin nding g veloc veloci!y i!y ag agains! ains! !ime g graph raph ))or or !hi !his s obBec!. 9): 1ha! are !he displacemen! and !he veloci!y o) !he obBec! ;=3 s a)!er !he s!ar!> 9g: 1ha 1ha!! ar are e !he di displac splaceme emen! n! and !he ve veloci loci!y !y o) !h !he e obBe obBec! c! " seconds a)!er !he s!ar!>
11
$.
n o obBe bBec! c! s s!ar !ar!s !s ))rrom a d disp isplac lacem emen! en! o) ; m m.. 6h 6he e gr graph aph sho shows ws how !he veloci!y o) !he obBec! varies wi!h !ime )rom !he s!ar!. velocity against time
1
velocity m s
8 7 6 5 4 3 2 1 0
North
0
1
2
3
4
5
6
7
8
time / s
9a: 4alc 4alcula! ula!e e !he a accele ccelera!i ra!ion on o) !!he he ob obBec! Bec! b be!we e!ween en ; an and d % s. 9b: 1ha 1ha!! is !h !he e accel accelera! era!ion ion o o)) !he o obBec! bBec! be!w be!ween een 2 a and nd $ s )rom !he s!ar!> 9c: 4alc 4alcula! ula!e e !he d displ isplacem acemen! en! o o)) !he o obBec bBec!! 2 seco seconds nds a) a)!er !er !h !he e s!ar!. 9d: 1ha 1ha!! is !h !he e disp displacem lacemen! en! o o)) !he o obBec! bBec! , seco seconds nds a) a)!er !er !!he he s!ar!> 9e: S Se!ch e!ch !h !he e cor corre respon sponding ding dis displac placemen emen!! again agains! s! !im !ime e grap graph h )or !he movemen! o) !his obBec!.
12
3.
n o obBe bBec! c! s s!ar !ar!s !s ))rrom a d disp isplac lacem emen! en! o) ; m m.. 6h 6he e gr graph aph sho shows ws how !he veloci!y o) !he obBec! varies wi!h !ime )rom !he s!ar!.
velocity m s 1 North
South
9a: 4alc 4alcula! ula!e e !he a accele ccelera!i ra!ion on o) !!he he ob obBec! Bec! b be!we e!ween en ; an and d 2 s. 9b: 4alc 4alcula! ula!e e !he a accele ccelera!i ra!ion on o) !!he he ob obBec! Bec! b be!we e!ween en 2 an and d $ s )rom !he s!ar!. 9c: Dra Draw w !he co corr rrespo espondin nding g accel accelera! era!ion ion ag agains ains!! !im !ime e grap graph h )or !his obBec!. 9d: 1ha 1ha!! ar are e !he di displac splaceme emen! n! and !he ve veloci loci!y !y o) !h !he e obBe obBec! c! " seconds a)!er !he s!ar!> 9e: 1ha 1ha!! ar are e !he di displac splaceme emen! n! and !he ve veloci loci!y !y o) !h !he e obBe obBec! c! $ seconds a)!er !he s!ar!> 9): S Se!ch e!ch !he cor corre respon sponding ding d displ isplacem acemen! en! a again gains! s! !!ime ime grap graph h )or !he movemen! o) !his obBec!.
13
*.
6h 6he e vel veloci oci!y !y!i !ime me g grap raph h )o )orr an o obBe bBec! c! iis s sh show own n be below low..
posi!ive value indica!es a veloci!y due nor!h and a nega!ive value indica!es a veloci!y due sou!h. 6he displacemen! o) !he obBec! is ; a! !he s!ar! o) !iming. 9a:: 4a 9a 4alcu lcula! la!e e !he dis displa placem cemen! en! o o)) !he ob obBec Bec!& !& 9i 9i:: " s a)!e a)!err !i !imi ming ng s! s!ar ar!s !s 9i 9ii: i: $ s a) a)!e !err !!im imin ing g s s!a !ar! r!s s 9iii: 9ii i: * s a) a)!er !er !!im iming ing s s!ar !ar!s. !s. 9b: Dra Draw w !he c cor orre respon sponding ding a accele ccelera!i ra!ion+ on+!ime !ime g graph raph.. /.
6h 6he e g gra raph ph sh show ows s h how ow !h !he e a acc ccel eler era! a!io ion n a o) an obBec! s!ar!ing )rom res! varies wi!h !ime.
4 a -2
ms
2 0
5
10
Time / s
Draw a graph !o show how !he veloci!y o) !he obBec! varies wi!h !ime )or !he %; seconds o) !he mo!ion.
14
,.
6h 6he e gr graph aph sho shows ws !!he he v velo eloci! ci!y y o) a ba ball ll !!ha! ha! is d drrop opped ped a and nd bounces on a Noor. n upwards direc!ion is !aen as being posi!ive. C
+
Veloit! 0
D
O
time
-
E B
9a: 9 b: De s sc c r ibe ibe !!h h e velocity o) o) !he ball as represen!ed by sec!ion 4D o) !he graph. 9 c : De s sc c r ibe ibe ! h e velocity o) o) !he ball as represen!ed by sec!ion D' o) !he graph. 9d: 1ha 1ha!! happ happened ened !!o o !he ba ball ll a! !h !he e !ime rrepr epresen esen!ed !ed by p poin! oin! 0 on !he graph> 9e: 1ha 1ha!! happ happened ened !!o o !he ba ball ll a! !h !he e !ime rrepr epresen esen!ed !ed by p poin! oin! 4 on !he graph> 9): How does !he spee speed d o) !he ball imm immedia edia!ely !ely be)o be)ore re re reboun bound d )rom !he Noor compare wi!h !he speed immedia!ely a)!er rebound> 9g: S Se!ch e!ch a grap graph h o) ac acceler celera!io a!ion n agai agains! ns! !!ime ime ))or or !h !he e movemen! o) !he ball.
15
.
ba ball ll is !hr !hrown own ver! ver!icall ically y upw upwar ards ds a and nd rre!ur e!urns ns !o !he !hr !hrower ower " seconds la!er. 1hich veloci!y!ime graph represen!s !he mo!ion o) !he ball>
%;. ball is dr dropp opped ed )ro )rom m a heigh! a and nd boun bounces ces up and d down own on a horiJon!al sur)ace. 1hich veloci!y!ime graph represen!s !he mo!ion o) !he ball )rom !he momen! i! is released>
" / m s-1
" / m s-1
" / m s-1 t/s t/s
C
B
A " / m s-1
t/s
" / m s-1 t/s
0
t/s D
E
%%. Describe how yo you u could measur measure e !he accelera!ion o) a !roll !rolley ey !ha! s!ar!s )rom res! and moves down a slope. 8ou are provided wi!h a me!re s!ic and a s!opwa!ch. 8our descrip!ion should include& 9a: a di ag ram 9b:: a li 9b lis! s! o o)) !he me measu asurrem emen! en!s s !a !a en
16
9c: how y you ou w would ould use !!hese hese mea measur suremen emen!s !s !o calcu calcula!e la!e !he accelera!ion o) !he !rolley 9d: how y you ou wo would uld es es!im !ima!e a!e !h !he e unce uncer!a r!ain!i in!ies es inv involve olved d in !h !he e e5perimen!. %2. Des Describ cribe e a si!ua! si!ua!ion ion wh wher ere e a runner h has as a disp displacem lacemen! en! o) %;; m due nor!h a veloci!y o) " m s −% due nor!h and an accelera!io accelera!ion n o) 2 m s − 2 due sou!h. 8our descrip!ion should include a diagram. %". 8ou 8ou mus! Bus!i)y y your our answer. %$.
8ou mus! Bus!i)y your answer.
%3
8ou mus! Bus!i)y your answer.
17
Section 2: Forces, energy and power
0alanced and unbalanced )orces %.
S! S!a! a!e e Ae Aew! w!on onGs Gs %s %s!! L Law aw o o)) Mo Mo!i !ion on..
2.
li li)! )! o o)) ma mass ss 3 3;; ;; g !r !rave ls cable u upw pwar ards ds a!pulls a co cons! ns!an! an! sp speed eed.. 4alcula!e !he !ension inavels !he !ha! !he li)! upwards.
".
9a 9a:: )u )ull lly y lloa oade ded d o oil il !a !an ner er ha has s a ma mass ss o) 2= 2=; ; @ %;, g. g. s !he speed speed o) !he !an !aner er increases )r )rom om ; !o a s!eady ma5imum spee d o) ,.; m s − % !he )orce )rom !he propellers remains cons!an! a! ".; @ %; * A A..
3.0 x 10 6 N force from propelle pr opellers rs
2.0 x 10 8 kg
9i:
4alc 4alcula! ula!e e !h !he e ac accele celera!i ra!ion on o) !!he he !!an aner er BBus! us! as i! s s!ar! !ar!s s )rom res!. 9ii: 1ha! is !h !he e siJ siJe e o) !!he he )o )orc rce e o) )r )ric!i ic!ion on ac ac!ing !ing on !h !he e !aner when i! is !ravelling a! !he s!eady speed o) ,.; ,. ; m s −% >
9b: 1he 1hen n i!s engi engines nes ar are e s!op s!opped ped !h !he e !an !aner er !a !aes es 3; min minu!es u!es !o come !o res! )rom a speed o) ,.; m s −% . 4alcula!e i!s average decelera!ion. $.
6h 6he e gr graph aph sho shows ws h how ow !!he he s spe peed ed o) a pa para rachu chu!is !is!! va vari ries es wi wi!h !h !!im ime e a)!er having Bumped )rom an aeroplane.
0
"/ms
-1
4
D '
0
t/s
18
1i!h re)erence !o !he origin o) !he graph and !he le!!ers 0 4 D and ' e5plain !he varia!ion o) speed wi!h !ime )or each s!age o) !he parachu!is!Gs )all. 3.
6wo g girls irls push a ca carr o) mas mass s 2; 2;;; ;; g g.. 'a 'ach ch ap applies plies a )o )orce rce o) 3 3; ; A and !he )orce o) )ric!ion is *; A. 4alcula!e !he accelera!ion o) !he car.
*.
bo boy y onsa!eboard a s sa a!eb !eboar oard ri rides des up p adec sl slop ope. e. 6 6he he !o !o!al !alormly ma mass ss )rom o o)) !h !he e boy and !he isd; g. u He elera!es uni) uni)ormly %2bo my s − % !o ! o 2 m s − % in * seconds. 4alcula!e !he resul!an! )orce ac!ing on him.
/.
bo bo5 5 o) ma mass ss " "; ; g is p pull ulled ed a alon long g a rrou ough gh s sur ur)ac )ace e by a cons!an! )orce o) %$; A. 6he accelera!ion o) !he bo5 is $=; m s −2 . 9a: 4alc 4alcula! ula!e e !he m magni! agni!ude ude o) !h !he e unba unbalanc lanced ed )or )orce ce caus causing ing !he accelera!ion. 9b: 4alc 4alcula! ula!e e !he ))or orce ce o) )r )ric!io ic!ion n be!w be!ween een !h !he e bo bo5 5 and !!he he sur)ace.
,.
ca carr o) m mass ass ,; ,;; ; g iis s ac accel celera era!ed !ed ))rrom rres! es! !o % %, , m s −% in %2 seconds. 9a: 1ha 1ha!! is !h !he e siJe o o)) !he rresul esul!an! !an! ))or orce ce ac! ac!ing ing on !he ca car> r> 9b: How )ar d does oes !!he he ca carr !r !ravel avel iin n !h !hese ese % %2 2 sec seconds onds> > 9c: ! !!he he en end d o) !h !he e %2 sec seconds onds peri period od !h !he e bra brae es s ar are e ope opera!e ra!ed d and !he car comes !o res! in a dis!ance o) 3; m. 1ha! is !he siJe o) !he average )ric!ional )orce ac!ing on !he car> $
.
9 a: ro c e ! o ) mas s $ = ; @ % ; g is launched ver!ically upwards )rom !he sur)ace o) !he 'ar!h. 9b: 6he li li)! )! no now w accel accelera! era!es es upw upward ards s a! %=3 %=3; ; m s −2 . 1ha! is !he new reading on !he balance> 9c: 6he lli)! i)! !!hen hen !!rave ravels ls up upwar wards ds a! a cons cons!an! !an! speed o) 3=; 3=;; ; m −% s . 1ha! is !he new reading on !he balance> 9d: -or !he llas! as! s! s!age age o) !!he he Bour Bourney ney !he li li)! )! dec deceler elera!es a!es a! %=3; m s − 2 while going up. 4alcula!e !he reading on !he balance. %". small li)! in a ho!el is )ully lo loaded aded and has a !o!al m mass ass o) 2 23; 3; g. -or sa)e!y reasons !he !ension in !he pulling cable mus! never be grea!er !han "3;; A. 9a: 1ha 1ha!! is !!he he !e !ensio nsion n in !!he he ca cable ble w when hen !he lli)! i)! is& 9 i : a ! re s ! 9ii: mov moving ing u upwar pwards ds a! a c cons! ons!an! an! s speed peed o o)) % m s − % 9iii: moving upw upwards ards wi! wi!h h a cons!an! accele accelera!ion ra!ion o) 2 m s − 2 9iv: accelera!ing downwar downwards ds w wi!h i!h a cons!an! accelera!ion o) 2 m s − 2 . 9b: 4alc 4alcula! ula!e e !he m ma5im a5imum um pe perm rmi!!e i!!ed d upwar upward d accele accelera! ra!ion ion o) !he )ully loaded li)!. 9c: Desc Describe ribe a si!u si!ua!io a!ion n wher where e !he lli)! i)! c could ould h have ave an upw upward ard accelera!ion grea!er !han !he value in 9b: wi!hou! breaching sa)e!y regula!ions.
20
%$. pac pacage age o) ma mass ss $=;; g iis s hung )r )rom om a spri spring ng 9Aew 9Aew!on: !on: balance a!!ached !o !he ceiling o) a li)!.
3 m s-2
4 kg
6h e li 6he li)! )! is ac acce cele lera ra!i !ing ng up upwa wards rds a! "= "=;; ;; m s − 2 . 1ha! is !he reading on !he spring balance> %3. 6h 6he e gr graph aph sho shows ws ho how w !h !he e downward downward speed speed o) a li)! varies wi!h !ime.
" / m s-1 2
t/s 4 10 12 9a: 0Dra Draw w !he co corr rrespo espondin nding g accel accelera! era!ion ion ag agains ains!! !im !ime e grap graph. h. 9b: $.; g m mass ass is s suspe uspended nded ))ro rom m a spr spring ing ba balanc lance e insid inside e !he li)!. De!ermine !he reading on !he balance a! each s!age o) !he mo!ion.
%*. 6wo !r !rolleys olleys Boined b by y a s!ring a are re pull pulled ed along a )r )ric!ionless ic!ionless Na! sur)ace as shown.
2 kg
T
1 kg 24 N
9a: 4alcula!e !he accelera!ion o) !he !rolleys. 9b:: 4a 9b 4alc lcul ula! a!e e !h !he e !e !ens nsio ion n T in !he s!ring Boining !he !rolleys.
21
%/. car o) m mass ass %2 %2;; ;; g !o !ows ws a car caravan avan o o)) mas mass s %;;; g g.. 6he )ric!ional )orces on !he car and caravan are 2;; A and 3;; A respec!ively.. 6he car ac celera!es a! 2.; m s − 2 . respec!ively 9a: 4alc 4alcula! ula!e e !he )o )orce rce e e5er 5er!ed !ed by !h !he e engi engine ne o) !h !he e car car.. 9b: 1ha 1ha!! )or )orce ce does !he !!ow ow ba barr e5 e5er! er! o on n !he c carav aravan> an> 9c: 6he c car ar !h !hen en !r !ravel avels s a! a co cons! ns!an! an! sp speed eed o o)) %; m s −% . ssuming !he )ric!ional )orces !o be unchanged calcula!e& 9 i: ! h e n ne ew e eng ngin ine e ))o o rc e 9ii: !he )or )orce ce e5 e5er!e er!ed d by !!he he !o !ow w bar on !!he he ca carava ravan. n. − 9d: 6he c car ar br bra aes es an and d dece decelera! lera!es es a! 3=; m s 2 . 4alcula!e !he )orce e5er!ed by !he braes 9assume !he o!her )ric!ional )orces remain cons!an!:. %,. log o) m mass ass $;; g is s!a!ion s!a!ionary ary.. !rac!or o) mass % %2;; 2;; g pulls !he log wi!h a !ow rope. 6he !ension in !he !ow rope is 2;;; A and !he )ric!ional )orce on !he log is ,;; A. How )ar will !he log move in $ s> %. )or )orce ce o) *; A is u used sed !o p push ush !h !hree ree b bloc locs s as sho shown. wn.
60 N
A
B
C
'ach bloc has a mass o) ,=; g and !he )orce o) )ric!ion on each bloc is $=; A. 9a: 4al c ul a !e & 9i 9i:: !h !he e ac acce cele lera ra!i !ion on o) !h !he e bl bloc ocs s 9ii:: !h 9ii !he e )or )orce ce !h !ha! a! bl bloc oc e e5e 5er! r!s s on bl bloc oc 0 9iii: !he )o )orc rce e bloc 0 e e5e 5er!s r!s on b bloc loc 4. 9b: 6he pu pushin shing g )or )orce ce is !he !hen n re reduce duced d un!i un!ill !he blo blocs cs mo move ve a! cons!an! speed. 9i: 4al 4alcul cula!e a!e !h !he e v valu alue e o o)) !!his his pus pushin hing g )o )orrce. 9ii: Does !he )orce !h !ha! a! bloc e e5er!s 5er!s on bloc 0 now e(ual !he )orce !ha! bloc 0 e5er!s on bloc 4> '5plain. 2;. 2=; g g !r !rolley olley is co connec!ed nnec!ed by s!ring !o a %=; g mass a as s show shown. n. 6he 6h e be benc nch h an and d pu pull lley ey are )r )ric ic!i !ion onle less ss.. 2 kg
22
1 kg
9a: 4alc 4alcula! ula!e e !he acce accelera lera!ion !ion o) !h !he e !r !rolley olley.. 9b:: 4a 9b 4alcu lcula! la!e e !he !!ens ensio ion n in !h !he e s! s!rin ring. g.
Resolu!ion o) )orces %.
m man an pul pulls ls a gar garden den ro rolle llerr wi wi!h !h a )o )orrce o o)) 3; A. A.
50 N 30
0
FH
9a: -ind !he eKec! eKec!ive ive hor horiJon iJon!al !al )or )orce ce appli applied ed !o !he rroller oller.. 9b: Desc Describe ribe a and nd e e5pla 5plain in how !he m man an can incr increase ease !!his his eKec!ive horiJon!al )orce wi!hou! changing !he siJe o) !he )orce applied. 2.
b bar arge ge iis s dr dragg agged ed a alo long ng a can canal al a as s sh show own n be below low..
500 N 45 o
#$%&e
1ha! is !he siJe o) !he componen! o) !he )orce parallel !o !he canal> ".
!o !oy y !r !rain ain o o)) ma mass ss ; ;=2 =2; ; g iis s gi given ven a pu push sh o o)) %; A alo along ng !!he he rrail ails s a! an angle o) ";I above !he horiJon!al. 4alcula!e& 9a: !he m magni agni!ude !ude o o)) !he c comp omponen onen!! o) )o )orc rce e alon along g !he rrails ails 9b:: !he acc 9b accele elera ra!io !ion n o) !h !he e !r !rain ain..
$.
ba barg rge e o) m mas ass s %; %;;; ;; g g is pu pulle lled d by a rop ope e alo along ng a can canal al a as s shown.
23
#$%&e
40o 800 N
6he 6h e rop rope e ap appl plie ies s a )o )orce rce o) ,; ,;; ; A a! an an angl gle e o) $; $;II !o !he !h e direc!ion o) !he canal. 6he )orce o) )ric!ion be!ween !he barge and !he wa!er is %;; A. 4alcula!e !he accelera!ion o) !he barge. 3.
cr cra!e a!e o) m mass ass %; %;; ; g iis s pu pulle lled d alo along ng a rrou ough gh su sur) r)ace ace b by y !w !wo o ropes a! !he angles shown.
120 N 200 200
100 kg
120 N 9a: 6he c cra!e ra!e iis s mov moving ing a! a cons cons!an! !an! spee speed d o) %= %=; ; m s − % . 1ha! is !he siJe o) !he )orce o) )ric!ion> 9b: 6he ))or orces ces ar are e now e each ach in incre creased ased !!o o %$; A a! !he sam same e angle. ssuming !he )ric!ion )orce remains cons!an! calcula!e !he accelera!ion o) !he cra!e. *.
2 2=; =; g g b bloc loc o) wo wood od is p plac laced ed on a sl slope ope as sh show own. n.
300
6h e bl 6he bloc oc rem remai ains ns s! s!a! a!io iona nary ry.. 1h 1ha! a! are !he !h e si siJe Je an and d di direc rec!i !ion on o) !he )ric!ional )orce on !he bloc> /.
ru runw nway ay is 2=; m lo long ng a and nd rrais aised ed ; ;="; ="; m a! o one ne e end. nd. !roll !rolley ey o) mass ;=3; g is placed on !he runway. 6he !rolley moves down
24
!he runway wi!h cons!an! speed. 4alcula!e !he magni!ude o) !he )orce o) )ric!ion )ric!i on ac!ing on !he !rolley !rolley.. ,.
ca carr o) m mass ass ; ;; ; g iis s pa par red ed o on n a hi hill. ll. 6 6he he s slo lope pe o) !!he he h hill ill iis s %3I !o !he horiJon!al. 6he braes on !he car )ail. 6he car runs down !he hill )or a dis!ance o) 3; m un!il i! crashes in!o a hedge. 6he 6h e av aver erag age e )o )orce rce o) )r )ric ic!i !ion on on !he !h e ca carr as i! runs ru ns do down wn !he !h e hi hill ll is ";; A. 9a 9a:: 9b 9b:: 9c: 9c :
.
4alcula!e !he componen! o) !he weigh! ac!ing down !he slope. -ind !he accelera!ion o) !he car. 4alcula!e !he speed o) !he car Bus! be)ore i! hi!s !he hedge.
!r !roll olley ey o) m mass ass 2= 2=; ; g iis s pla placed ced on a s slo lope pe wh which ich ma maes es a an n angle o) *;I !o !he horiJon!al. 9a: s!u s!uden! den! p pushe ushes s !he !r !rolle olley y and !h !hen en re releas leases es i! so !!ha! ha! i! moves up !he slope. 6he )orce o) )ric!ion on !he !rolley is %=; A. 9i:
1h 1hy y do does es !!he he !!rroll olley ey co con!i n!inue nue !!o o mo move ve u up p !h !he e slo slope pe a)!er i! is released> 9ii: 4alc 4alcula! ula!e e !he unba unbalance lanced d )or )orce ce on !!he he !r !rolley olley as i! moves up !he slope. 9iii: 4alcula!e !!he he ra!e a! which !he !r !rolley olley loses speed as i! moves up !he slope. 9b: 6he !r !rolley olley e even! ven!uall ually y come comes s !o rres! es! !h !hen en s!a s!ar!s r!s !o m move ove down !he slope. 9i: 4al 4alcul cula!e a!e !!he he u unb nbala alance nced d )o )orrce on !!he he !!rroll olley ey as i! moves down !he slope. 9ii: 4alc 4alcula! ula!e e !he a accel ccelera! era!ion ion o o)) !he !!ro rolley lley do down wn !h !he e slo slope. pe.
25
1or done ine!ic an and d po!en!ial energy %.
sm small all b ball all o o)) ma mass ss ; ;=2 =2; ; g iis s dr drop opped ped ))ro rom m a he heigh igh!! o) $ $=; =; m above !he ground. 6he ball rebounds !o a heigh! o) 2=; m. 9a: 4alc 4alcula! ula!e e !o !o!al !al loss in ener energy gy o o)) !h !he e b ball. all. 9b: 4alcula! ula!e e sp speed eed he BBus! us!! be be)or )ore eii!! i!lea hi!s he ground ound.. 9c: 4alc 4alc 4alcula! ula!e e !he !he spee speed d o) o) !!he !!he he ball ba ball ll Bus Bus! a) a)!er !er leaves ves!!he !!he hegr ground.
2.
bo bo5 5 o) m mas ass s /; g g is p pull ulled ed al alon ong g a ho hori riJon Jon!al !al s sur) ur)ace ace b by y a horiJon!al )orce o) ; A. 6he bo5 is pulled a dis!ance o) %2 m. 6here 6h ere is a )r )ric ic!i !ion onal al )o )orce rce o) ,; A be be!w !wee een n !he !h e bo5 an and d !he !h e sur)ace. 9a: 4alc 4alcula! ula!e e !he !o!a !o!all wo wor r do done ne b by y !he pull pulling ing )o )orc rce. e. 9b: 4alc 4alcula! ula!e e !he am amoun! oun! o o)) ine ine!ic !ic ene energ rgy y gaine gained d by !he b bo5 o5..
".
bo bo5 5 o) m mas ass s 2= 2=; ; g iis s pu pulle lled d up a ))ri ric!i c!ionl onless ess slo slope pe as sh show own. n.
3'0 m
2 '0 (& 0'50 m
9a: bo5 4alc 4alcula! ula!e e !he gravi! avi!a!io a!ional po!en!i en!ial al ener energy gy gain gained ed by !h !he e when i! is gr pulled upnal !hepo! slope. 9b:: 6h 9b 6he e b bloc loc iis s n now ow rele eleas ased. ed. 9i: Us Use e co cons nserv erva!i a!ion on o o)) ene energ rgy y !o 7n 7nd d !h !he e sp speed eed o o)) !h !he e bo bo5 5 a! !he bo!!om o) !he slope. 9ii: Use a ano! no!her her m me!ho e!hod d !o c con7r on7rm m you yourr an answer swer !o 9i 9i:. :. $.
wi winch nch dri driven ven b by y a mo mo!o !orr is u used sed !o lli) i)!! a cr cra! a!e e o) m mas ass s 3; g g !hrough a ver!ical heigh! o) 2; m. 9a: 4alc 4alcula! ula!e e !he si siJe Je o) !h !he e mini minimum mum ))or orce ce re re(uir (uired ed !o li) li)!! !he cra!e. 9b: 4alc 4alcula! ula!e e !he m minim inimum um a amou moun! n! o) w wor or d done one by !he w winch inch while li)!ing !he cra!e. 26
9c: 6he p power ower o) !h !he e win winch ch is 2= 2=3 3 1 1.. 4al 4alcula cula!e !e !h !he e mini minimum mum !ime !aen !o li)! !he cra!e !o !he re(uired heigh!. 3.
!!ra rain in ha has s a co cons ns!a !an! n! sp spee eed d o o)) % %; ; m s−% over a dis!ance o) 2=; m. 6he driving )orce o) !he !rain engine is "=; @ %;$ A A.. 1ha! is !he power developed by !he !rain engine> −%
*.
n ar arrrow o) ma mass ss 22 g h has as a s spe peed ed o) "; m s as i! s!ries a −2 !arge!. 6he !ip o) !he arrow goes "=; @ %; m in!o !he !arge!. 9a: 4alc 4alcula! ula!e e !he aver average age )or )orce ce o) !he !ar !arge! ge! on !h !he e arr arrow ow.. 9b: 1ha 1ha!! is !he !!ime ime !a !ae en n )or !h !he e ar arro row w !o com come e !o rres! es! a) a)!er !er s!riing !he !arge! assuming !he !arge! e5er!s a cons!an! )orce on !he arrow>
27
Section 3: ollisions and e!plosions
%.
1h 1ha! a! iis s !h !he e mo momen men!um !um o) !h !he e ob obBec Bec!! in e each ach o o)) !h !he e )ol )ollo lowin wing g si!ua!ions> 9a:
9b:
4 m s-1
9c :
6 m s-1
20 kg
5 kg
1.5 kg 25 m s-1
2.
!r !roll olley ey o) m mass ass 2= 2=; ; g iis s !r !rave avelli lling ng w wi!h i!h a sp speed eed o o)) %= %=3 3 m s − % . 6he 6h e !ro !roll lley ey co coll llid ides es an and d s! s!ic ics s !o a s!a! s! a!io iona nary ry !ro !roll lley ey o) mas mass s 2= 2=; ; g.. g 9a:
4alc 4alcula! ula!e e !he vel veloci! oci!y y o) !he !r !rolley olleys s imm immedia! edia!ely ely a) a)!er !er !h !he e collision. 9b:: Sh 9b Show ow !!ha! ha! !h !he e co colli llisio sion n is iinel nelas! as!ic. ic.
".
!a !arg rge! e! o) ma mass ss $ $=; =; g g ha hangs ngs )r )rom om a !!re ree e by a llon ong g s!r s!ring ing.. n arrow o) mass %;; g is 7red a! !he !arge! and embeds i!sel) in !he !arge!. 6he speed o) !he arrow is %;; m s − % Bus! be)ore i! s!ries !he !arge!. 1ha! is !he speed o) !he !arge! immedia!ely a)!er !he impac!>
$.
!r !roll olley ey o) m mass ass 2= 2=; ; g iis s mo movin ving g a! a c cons ons!an !an!! sp speed eed whe when n i! collides and s!ics !o a second s!a!ionary !rolley. 6he graph shows how !he speed o) !he 2=; g !rolley varies wi!h !ime.
0.5 v /
-1
ms
0.2
0
time / s
De!ermine !he mass o) !he second !rolley !rolley..
28
3.
%". 6wo !r !rolleys olleys ini!ial ini!ially ly a! rres! es! and in con!ac! Ny apar! whe when n a plunger on one o) !hem is released. One !rolley has a mass o) 2=; g and moves oK a! a speed o) 2=; m s − % . 6he second !rolley has a mass o) "=; g. 4alcula!e !he veloci!y o) !his !rolley. %$. cue e e5er! 5er!s s an aver average age )or )orce ce o) /=;; A on a s!a!ionar s!a!ionary y snoo snooer er ball o) mass 2;; g. 6he impac! o) !he cue on !he ball las!s )or $3=; ms. 1ha! is !he speed o) !he ball as i! leaves !he cue> %3
)oo )oo!bal !balll o) ma mass ss 3; 3;; ; g is s s!a!i !a!ionar onary y. 1hen a gir girll ic ics s !he b ball all her )oo! is in con!ac! wi!h !he ball )or a !ime o) 3; ms. s a resul! o) !he ic !he ball moves oK a! a speed o) %; m s − % . 4alcula!e !he average )orce e5er!ed by her )oo! on !he ball.
%*. s!a! s!a!iona ionary ry gol) ba ball ll o) mas mass s %;; g is s!r s!ruc uc by a club club.. 6he ball moves oK a! a spe ed o) "; m s − % . 6he average )orce o) !he club on !he ball is %;; A. 4alcula!e !he !ime o) con!ac! be!ween !he club and !he ball. %/. 6he grap graph h shows how !he )orce e5 e5er!ed er!ed by a hoc hocey ey s!ic on a s!a!ionary hocey ball varies wi!h !ime.
30
/N F /N 40 N
20
0
time / ms
6h e ma 6he mass ss o) !he !h e ba ball ll is %3 %3; ; g. De!ermine !he speed o) !he ball as i! leaves !he s!ic. %,. ball o o)) mass %;; g )all )alls s )r )rom om a he heigh! igh! o) ; ;=2; =2; m o on!o n!o con concre!e. cre!e. 6he 6h e ba ball ll reb rebou ound nds s !o a he heig igh! h! o) ;= ;=%, %, m. 6h 6he e du dura ra!i !ion on o) !he !h e impac! is 23 ms. 4alcula!e& 9a: !he ch change ange iin n mom momen!u en!um m o) !!he he ba ball ll cau caused sed by !he boun bounceG ceG 9b:: !he iimp 9b mpuls ulse e on !h !he e bal balll dur during ing !!he he b boun ounce ce 9c: !he a avera verage ge un unbalan balanced ced )o )orc rce e e5 e5er!e er!ed d on !h !he e ball by !he concre!e 9d: !he a avera verage ge un unbalan balanced ced )o )orc rce e o) !he c concr oncre!e e!e on !he b ball. all. 9e: 1ha 1ha!! is in !he !!o!al o!al a avera verage ge upw upward ards s )or )orce ce on !he b ball all dur during ing impac!> %. rubbe rubberr ball o) mass $; $;=; =; g is drop dropped ped )ro )rom m a heig heigh! h! o) ;=, ;=,;; ;; m on!o !he pavemen!. 6he ball rebounds !o a heigh! o) ;=$3; m. 6he 6h e av aver erag age e )o )orce rce o) co con! n!ac ac!! be be!w !wee een n !he !h e pa pave veme men! n! an and d !he !h e ba ball ll is 2=,; A. 9a: 4alc 4alcula! ula!e e !he v veloc eloci!y i!y o) !!he he ba ball ll Bus Bus!! be) be)or ore e i! hi! hi!s s !he ground and !he veloci!y Bus! a)!er hi!!ing !he ground. 9b: 4alc 4alcula! ula!e e !he !im !ime e o) c con!a on!ac! c! b be!we e!ween en !h !he e bal balll and pavemen!. 2;. ball o o)) mass $;; g !r !ravels avels )all )alls s )ro )rom m rres! es! and hi!s !he grou ground. nd. 6he 6h e ve velo loci ci!y !y!i !ime me gr grap aph h rep repres resen en!s !s !he !h e mo mo!i !ion on o) !he !h e ba ball ll )o )orr !he !h e 7rs! %=2 s a)!er i! s!ar!s !o )all.
31
B
6 )*ee+ / m s-1 0 A
-4
C 0·6
0·8
1·2
E
time / s
D
9a: Desc Describe ribe !!he he mo mo!ion !ion o) !he ball d durin uring g sec! sec!ions ions 0 0 0 04 4 4D and D' on !he graph. 9b: 1ha 1ha!! is !h !he e !im !ime e o) con con!ac! !ac! o o)) !he b ball all w wi!h i!h !h !he e gr ground ound> > 9c: 4alc 4alcula! ula!e e !he a avera verage ge un unbala balanced nced ))or orce ce o) !h !he e gr ground ound o on n !he ball. 9d: How m much uch e ener nergy gy is llos! os! du due e !o co con!ac n!ac!! wi! wi!h h !he g gro round> und> 2%. 1a!er wi!h a spe speed ed o) 3 3; ; m s − % is eBec!ed horiJon!ally )rom a 7re hose a! a ra!e o) 23 g s−% . 6he wa!er hi!s a wall horiJon!ally and does no! rebound )rom !he wall. 4alcula!e !he average )orce e5er!ed on !he wall by !he wa!er. 22. rroc oce! e! eBe eBec!s c!s g gas as a! a ra ra!e !e o o)) 3; g s− % eBec!ing i! wi!h a cons!an! speed o) %,;; m s −% . 4alcula!e magni!ude o) !he )orce e5er!ed by !he eBec!ed gas on !he roce!. 2". Describe in de!ail an e5 e5perimen! perimen! !ha! y you ou wou would ld do !o de! de!ermin ermine e !he average )orce be!ween a )oo!ball boo! and a )oo!ball as !he ball is being iced. Draw a diagram o) !he appara!us and include all !he measuremen!s !aen and de!ails o) !he calcula!ions 2$. carried 2=; gou!. !!ro rolley lley !r !ravell avelling ing a! *= *=; ; m s −% collides wi!h a s!a!ionary %=; g !rolley. 6he !rolleys remain connec!ed a)!er !he collision. 9a: 4al c ul a !e & 9i: !h !he e vel veloci oci!y !y o) !h !he e !r !roll olleys eys BBus us!! a) a)!er !er !he col collis lision ion 9ii: !he mom momen!u en!um m g gaine ained d by !he %=; g !rolley !rolley 9iii: !he mo momen!um men!um los! by !he 2=; g !r !rolley olley.. 9b: 6he co collisi llision on las! las!s s )or ;= ;=3; 3; s. 4al 4alcula! cula!e e !he ma magni! gni!ude ude o) !!he he average )orce ac!ing on each !rolley.
32
23. 2*. Aew! Aew!onGs onGs cr cradle adle ap appar para!us a!us is us used ed !o dem demons! ons!ra!e ra!e conserva!ion o) momen!um. -our s!eel spheres each o) mass ;.% g are suspended so !ha! !hey are in a s!raigh! line. Sphere % is pulled !o !he side and released as shown in diagram
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