odu mechanics questions o level a level physics

8/16/2019 ODU Mechanics Questions o level a level physics

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Lesmahgow High SchoolHigher Physics

Our Dynamic UniverseMechanics Problems

Revision problems......................................................................2

Speed.....................................................................................2ccelera!ion............................................................................"

#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 and e5plosions.........................................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


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Revision problems

Speed

%. 6he world downhill siing speed !rial !aes place a! Les rcs

every year. Describe a me!hod !ha! could be used !o 7nd !heaverage speed o) !he sier over !he % m run. 8our descrip!ion

should include&

9a: any appara!us re(uired

9b: de!ails o) wha! measuremen!s need !o be !aen

9c: an e5plana!ion o) how you would use !he measuremen!s !o

carry ou! !he calcula!ions.

2. n a!hle!e runs a %3;; m race in a !ime o) " min $; s. 4alcula!e

his average speed )or !he race.

".

9speed o) ligh! ? "=; @ %;, m s −%:.

$. 6he dis!ance be!ween London and Aew 8or is $,;; m. plane

!ravels a! an average speed o) Mach %=" be!ween London and

Aew 8or.

4alcula!e !he !ime !o !he neares! minu!e )or !his Bourney. 9Mach

% is !he speed o) sound. 6ae !he speed o) sound !o be "$; m s

−%:.

3. 6he graph shows how !he speed o) a girl varies wi!h !ime )rom

!he ins!an! she s!ar!s !o run )or a bus.

2 8 18

5

10

15v

(ms )-1

t (s)

P Q

R

O

She s!ar!s )rom s!and s!ill a! O and Bumps on !he bus a! C.

-ind&

9a: !he s!eady speed a! which she runs9b: !he dis!ance she runs

2


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9c: !he increase in !he speed o) !he bus while !he girl is on i!

9d: how )ar !he bus !ravels during CR

9e: how )ar !he girl !ravels during OR.

*. ground!oair guided missile s!ar!s )rom res! and accelera!es a!

%3; m s−2

)or 3 s. 1ha! is !he speed o) !he missile 3 s a)!erlaunching>

/. n s!on Mar!in has an accelera!ion o) * m s−2 )rom res!. 1ha!

!ime does i! !ae !o reach a speed o) "; m s −%>

,. car is !ravelling a! a speed o) "$ m s −%. 6he driver applies !he

braes and !he car slows down a! a ra!e o) %3 m s −2. 1ha! is !he

!ime !aen )or !he speed o) !he car !o reduce !o $ m s −%>

ccelera!ion

%. sa!eboarder s!ar!ing )rom res! goes down a uni)orm slope and

reaches a speed o) , m s −% in $ s.

9a: 1ha! is !he accelera!ion o) !he sa!eboarder>

9b: 4alcula!e !he !ime !aen )or !he sa!eboarder !o reach a

speed o) %2 m s −%.

2.

9b: 6he cyclis! main!ains !his cons!an! accelera!ion. 1ha! is his

speed a)!er a )ur!her 2=; s>

9c: How long a)!er he s!ar!s !o accelera!e does he reach a speed

o)

2, m s −%>

". s!uden! se!s up !he appara!us shown !o 7nd !he accelera!ion o)

a !rolley down a slope.

3


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Clock1

Clock3

Clock2

Light gates

Leng!h o) card on !rolley ? 3; mm

6ime on cloc % ? ;=%; s 9!ime !aen )or card !o in!errup! !op

ligh! ga!e:

6ime on cloc 2 ? ;=;3 s 9!ime !aen )or card !o in!errup! bo!!om

ligh! ga!e: 6ime on cloc " ? 2=3; s 9!ime !aen )or !rolley !o !ravel be!ween

!op and bo!!om ligh! ga!e:

Use !hese resul!s !o calcula!e !he accelera!ion o) !he !rolley.

#ec!ors

%. car !ravels 3; m due nor!h and !hen re!urns "; m due sou!h.

6he whole Bourney !aes 2 hours.

4alcula!e&

9a: !he !o!al dis!ance !ravelled by !he car

9b: !he average speed o) !he car

9c: !he resul!an! displacemen! o) !he car

9d: !he average veloci!y o) !he car.

2. girl delivers newspapers !o !hree houses E 8 and F as shown

in !he diagram.

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She s!ar!s a! E and wals direc!ly )rom E !o 8 and !hen !o F.

9a: 4alcula!e !he !o!al dis!ance !he girl wals.

9b: 4alcula!e !he girlGs 7nal displacemen! )rom E.

9c: 6he girl wals a! a s!eady speed o) % m s −%

.9i: 4alcula!e !he !ime she !aes !o ge! )rom E !o F.

9ii: 4alcula!e her resul!an! veloci!y.

5

Y

Z

30 m

40 m

N

X


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". -ind !he resul!an! )orce in !he )ollowing e5ample&

8 No

30

8 N

8 N

2 N

6 N

3 N

a) b) c)

3 N

4 N

$. S!a!e wha! is mean! by a vec!or (uan!i!y and scalar (uan!i!y.

ive !wo e5amples o) each.

3. n orien!eer runs 3 m due sou!h !hen $ m due wes! and !hen 2

m due nor!h. 6he !o!al !ime !aen )or !his is % hours. 4alcula!e!he average speed and average veloci!y o) !he orien!eer )or !his

run.

*. )oo!ball is iced up a! an angle o) /;I a! %3 m s −%.

4alcula!e&

9a: !he horiJon!al componen! o) !he veloci!y

9b: !he ver!ical componen! o) !he veloci!y.

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Section 1: Equations of motion

'(ua!ions o) mo!ion

%. n obBec! is !ravelling a! a speed o) ,=; m s −%

.

!his

%; s>

2. car is !ravelling a! a speed o) %3=; m s −%.

uni)ormly a! *=; m s −2 and !ravels a dis!ance o) 2;; m while

accelera!ing. 4alcula!e !he veloci!y o) !he car a! !he end o) !he

2;; m.

". ball is !hrown ver!ically upwards !o a heigh! o) $; m above i!s

s!ar!ing poin!. 4alcula!e !he speed a! which i! was !hrown.

$. car is !ravelling a! a speed o) ";=; m s −%.

%=,; m s −2 un!il i! comes !o res!.

while slowing down. 1ha! !ime does i! !ae !o !ravel !he 23; m>

3. s!one is !hrown wi!h an ini!ial speed 3=; m s −% ver!ically down a

well. 6he s!one s!ries !he wa!er *; m below where i! was!hrown.

4alcula!e !he !ime !aen )or !he s!one !o reach !he sur)ace o) !he

wa!er.

6he eKec!s o) )ric!ion can be ignored.

*. !ennis ball launcher is ;=*; m long. !ennis ball leaves !he

launcher a! a speed o) "; m s −%.

9a: 4alcula!e !he average accelera!ion o) !he !ennis ball in !helauncher.

9b: 4alcula!e !he !ime !he ball accelera!es in !he launcher.

/.

,. !rolley accelera!es uni)ormly down a slope. 6wo ligh! ga!esconnec!ed !o a mo!ion compu!er are spaced ;=3; m apar! on !he

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slope. 6he speeds recorded as !he !rolley passes !he ligh! ga!es

are ;=2; m s −%

and ;=3; m s −%

9a: 4alcula!e !he accelera!ion o) !he !rolley.

9b: 1ha! !ime does !he !rolley !ae !o !ravel !he ;=3 m be!ween

!he ligh! ga!es>

. helicop!er is rising ver!ically a! a speed 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 oK. 6he eKec!s o) )ric!ion can be ignored.

%;. ball is !hrown ver!ically upwards )rom !he edge o) a cliK as

shown in !he diagram.

33 m

Sea

4 m s-1

6he eKec!s o) )ric!ion can be ignored.

9a: 9i: 1ha! is !he heigh! o) !he ball above sea level 2=; s a)!er

being !hrown>

9ii: 1ha! is !he veloci!y o) !he ball 2=; s a)!er being !hrown>

9b: 1ha! is !he !o!al dis!ance !ravelled by !he ball )rom launch

!o landing in !he sea>

8


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". 6he graph shows !he displacemen! agains! !ime graph )or !he

movemen! o) an obBec!.

9a: 4alcula!e !he veloci!y o) !he obBec! be!ween ; and 2 s.

9b: 4alcula!e !he veloci!y o) !he obBec! be!ween 2 and $ s )rom

!he s!ar!.

9c: Draw !he corresponding dis!ance agains! !ime graph )or !his

obBec!.9d: 4alcula!e !he average speed o) !he obBec! )or !he $ seconds.

9e: Draw !he corresponding veloci!y agains! !ime graph )or !his

obBec!.

9): 1ha! are !he displacemen! and !he veloci!y o) !he obBec! ;=3

s a)!er !he s!ar!>

9g: 1ha! are !he displacemen! and !he veloci!y o) !he obBec! "

seconds a)!er !he s!ar!>

11

North

South

d i s p l a c e m e n t / m


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$. n obBec! s!ar!s )rom a displacemen! o) ; m. 6he graph shows

how !he veloci!y o) !he obBec! varies wi!h !ime )rom !he s!ar!.

9a: 4alcula!e !he accelera!ion o) !he obBec! be!ween ; and % s.

9b: 1ha! is !he accelera!ion o) !he obBec! be!ween 2 and $ s

)rom !he s!ar!>

9c: 4alcula!e !he displacemen! o) !he obBec! 2 seconds a)!er !he

s!ar!.

9d: 1ha! is !he displacemen! o) !he obBec! , seconds a)!er !he

s!ar!>

9e: Se!ch !he corresponding displacemen! agains! !ime graph)or !he movemen! o) !his obBec!.

12

velocity against time

0

1

2

3

4

5

6

78

0 1 2 3 4 5 6 7 8

time / s

North

velocity m s 1


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3. n obBec! s!ar!s )rom a displacemen! o) ; m. 6he graph shows

how !he veloci!y o) !he obBec! varies wi!h !ime )rom !he s!ar!.

9a: 4alcula!e !he accelera!ion o) !he obBec! be!ween ; and 2 s.

9b: 4alcula!e !he accelera!ion o) !he obBec! be!ween 2 and $ s

)rom !he s!ar!.

9c: Draw !he corresponding accelera!ion agains! !ime graph )or

!his obBec!.

9d: 1ha! are !he displacemen! and !he veloci!y o) !he obBec! "seconds a)!er !he s!ar!>

9e: 1ha! are !he displacemen! and !he veloci!y o) !he obBec! $

seconds a)!er !he s!ar!>

9): Se!ch !he corresponding displacemen! agains! !ime graph

)or !he movemen! o) !his obBec!.

13

North

South

velocity m s 1


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*. 6he veloci!y!ime graph )or an obBec! is shown below.

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: 4alcula!e !he displacemen! o) !he obBec!&

9i: " s a)!er !iming s!ar!s

9ii: $ s a)!er !iming s!ar!s

9iii: * s a)!er !iming s!ar!s.

9b: Draw !he corresponding accelera!ion+!ime graph.

/. 6he graph shows how !he accelera!ion a o) an obBec! s!ar!ing

)rom res! varies wi!h !ime.

Draw a graph !o show how !he veloci!y o) !he obBec! varies wi!h

!ime )or !he %; seconds o) !he mo!ion.

14

0 5 10

Time / s

2

4a

m s-2


15/40


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. ball is !hrown ver!ically upwards and re!urns !o !he !hrower "

seconds la!er. 1hich veloci!y!ime graph represen!s !he mo!ion

o) !he ball>

%;. ball is dropped )rom a heigh! and bounces up and down 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>

%%. Describe how you could measure !he accelera!ion o) a !rolley

!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 diagram

9b: a lis! o) !he measuremen!s !aen

16

0

A

D

B C

E

" / m s-1 " / m s-1 " / m s-1

" / m s-1 " / m s-1

t / s

t / s

t / s

t / s

t / s


17/40

9c: how you would use !hese measuremen!s !o calcula!e !he

accelera!ion o) !he !rolley

9d: how you would es!ima!e !he uncer!ain!ies involved in !he

e5perimen!.

%2. Describe a si!ua!ion where a runner has a displacemen! o) %;; m

due nor!h a veloci!y o) " m s −%

due nor!h and an accelera!ion o)2 m s −2 due sou!h. 8our descrip!ion should include a diagram.

%". 8ou mus! Bus!i)y your answer.

%$. 8ou mus! Bus!i)y your

answer.

%3 8ou mus! Bus!i)y your answer.

17


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Section 2: Forces, energy and power

0alanced and unbalanced )orces

%. S!a!e Aew!onGs %s! Law o) Mo!ion.

2. li)! o) mass 3;; g !ravels upwards a! a cons!an! speed.

4alcula!e !he !ension in !he cable !ha! pulls !he li)! upwards.

". 9a: )ully loaded oil !aner has a mass o) 2=; @ %;, g.

s !he speed o) !he !aner increases )rom ; !o a s!eady

ma5imum speed o) ,.; m s −% !he )orce )rom !he propellers

remains cons!an! a! ".; @ %;* A.

3.0 x 106 Nforce from propellers

2.0 x 108 kg

9i: 4alcula!e !he accelera!ion o) !he !aner Bus! as i! s!ar!s

)rom res!.

9ii: 1ha! is !he siJe o) !he )orce o) )ric!ion ac!ing on !he

!aner when i! is !ravelling a! !he s!eady speed o) ,.; m

s −%>

9b: 1hen i!s engines are s!opped !he !aner !aes 3; minu!es

!o come !o res! )rom a speed o) ,.; m s −%. 4alcula!e i!s

average decelera!ion.

$. 6he graph shows how !he speed o) a parachu!is! varies wi!h !ime

a)!er having Bumped )rom an aeroplane.

18

0

4 D

'

" / m s-1

0t / s


19/40

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 girls push a car o) mass 2;;; g. 'ach applies a )orce o) 3;

A and !he )orce o) )ric!ion is *; A. 4alcula!e !he accelera!ion o)!he car.

*. boy on a sa!eboard rides up a slope. 6he !o!al mass o) !he boy

and !he sa!eboard is ; g. He decelera!es uni)ormly )rom %2 m

s −% !o

2 m s −% in * seconds. 4alcula!e !he resul!an! )orce ac!ing on him.

/. bo5 o) mass "; g is pulled along a rough sur)ace by a

cons!an! )orce o) %$; A. 6he accelera!ion o) !he bo5 is $=; m s −2.

9a: 4alcula!e !he magni!ude o) !he unbalanced )orce causing !he

accelera!ion.

9b: 4alcula!e !he )orce o) )ric!ion be!ween !he bo5 and !he

sur)ace.

,. car o) mass ,;; g is accelera!ed )rom res! !o %, m s −% in %2

seconds.

9a: 1ha! is !he siJe o) !he resul!an! )orce ac!ing on !he car>9b: How )ar does !he car !ravel in !hese %2 seconds>

9c: ! !he end o) !he %2 seconds period !he braes are opera!ed

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>

. 9a: roce! o) mass $=; @ %;$ g is launched ver!ically upwards

)rom !he sur)ace o) !he 'ar!h.

!hrus! o) /=; @ %;3 A.

9i: Draw a diagram showing all !he )orces ac!ing on !he

roce! Bus! a)!er !aeoK.

9ii: 4alcula!e !he ini!ial accelera!ion o) !he roce!.

9b: s !he roce! rises !he !hrus! remains cons!an! bu! !he

accelera!ion o) !he roce! increases. ive !hree reasons )or

!his increase in accelera!ion.

9c: '5plain in !erms o) Aew!onGs laws o) mo!ion why a roce! can

!ravel )rom !he 'ar!h !o !he Moon and )or mos! o) !he

Bourney no! burn up any )uel.

19


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21/40

%$. pacage o) mass $=;; g is hung )rom a spring 9Aew!on:

balance a!!ached !o !he ceiling o) a li)!.

3 m s-24 kg

6he li)! is accelera!ing upwards a! "=;; m s −2. 1ha! is !he reading

on !he spring balance>

%3. 6he graph shows how !he downward speed o) a li)! varies wi!h

!ime.

9a: Draw !he corresponding accelera!ion agains! !ime graph.

9b: $.; g mass is suspended )rom a spring balance inside !he

li)!. De!ermine !he reading on !he balance a! each s!age o)

!he mo!ion.

%*. 6wo !rolleys Boined by a s!ring are pulled along a )ric!ionless Na!

sur)ace as shown.

2 kg 1 kg

24 NT

9a: 4alcula!e !he accelera!ion o) !he !rolleys.

9b: 4alcula!e !he !ension T in !he s!ring Boining !he !rolleys.

21

2

0 4 10 12

" / m s-1

t / s


22/40


23/40

9a: 4alcula!e !he accelera!ion o) !he !rolley.

9b: 4alcula!e !he !ension in !he s!ring.

Resolu!ion o) )orces

%. man pulls a garden roller wi!h a )orce o) 3; A.

300

50 N

FH

9a: -ind !he eKec!ive horiJon!al )orce applied !o !he roller.

9b: Describe and e5plain how !he man can increase !his

eKec!ive horiJon!al )orce wi!hou! changing !he siJe o) !he

)orce applied.

2. barge is dragged along a canal as shown below.

o45

500 N

1ha! is !he siJe o) !he componen! o) !he )orce parallel !o !he

canal>

". !oy !rain o) mass ;=2; g is given a push o) %; A along !he rails

a! an angle o) ";I above !he horiJon!al.

4alcula!e&

9a: !he magni!ude o) !he componen! o) )orce along !he rails

9b: !he accelera!ion o) !he !rain.

$. barge o) mass %;;; g is pulled by a rope along a canal as

shown.

23

#$%&e


24/40

6he rope applies a )orce o) ,;; A a! an angle o) $;I !o !he

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. cra!e o) mass %;; g is pulled along a rough sur)ace by !wo

ropes a! !he angles shown.

100 kg

120 N

120 N

200

200

9a: 6he cra!e is moving a! a cons!an! speed o) %=; m s −%. 1ha! is

!he siJe o) !he )orce o) )ric!ion>

9b: 6he )orces are now each increased !o %$; A a! !he same

angle. ssuming !he )ric!ion )orce remains cons!an!

calcula!e !he accelera!ion o) !he cra!e.

*. 2=; g bloc o) wood is placed on a slope as shown.

300

6he bloc remains s!a!ionary. 1ha! are !he siJe and direc!ion o)

!he )ric!ional )orce on !he bloc>

/. runway is 2=; m long and raised ;="; m a! one end. !rolley o)

mass ;=3; g is placed on !he runway. 6he !rolley moves down

24

40o

800 N

#$%&e


25/40

!he runway wi!h cons!an! speed. 4alcula!e !he magni!ude o) !he

)orce o) )ric!ion ac!ing on !he !rolley.

,. car o) mass ;; g is pared on a hill. 6he slope o) !he hill is

%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 average )orce o) )ric!ion on !he car as i! runs down !he hill is

";; A.

9a: 4alcula!e !he componen! o) !he weigh! ac!ing down !he

slope.

9b: -ind !he accelera!ion o) !he car.

9c: 4alcula!e !he speed o) !he car Bus! be)ore i! hi!s !he hedge.

. !rolley o) mass 2=; g is placed on a slope which maes an

angle o) *;I !o !he horiJon!al.

9a: s!uden! pushes !he !rolley and !hen releases i! so !ha! i!

moves up !he slope. 6he )orce o) )ric!ion on !he !rolley is %=;

A.

9i: 1hy does !he !rolley con!inue !o move up !he slope

a)!er i! is released>

9ii: 4alcula!e !he unbalanced )orce on !he !rolley as i!

moves up !he slope.

9iii: 4alcula!e !he ra!e a! which !he !rolley loses speed as i!

moves up !he slope.

9b: 6he !rolley even!ually comes !o res! !hen s!ar!s !o move

down !he slope.

9i: 4alcula!e !he unbalanced )orce on !he !rolley as i!

moves down !he slope.

9ii: 4alcula!e !he accelera!ion o) !he !rolley down !he slope.

25


26/40

1or done ine!ic and po!en!ial energy

%. small ball o) mass ;=2; g is dropped )rom a heigh! o) $=; m

above !he ground. 6he ball rebounds !o a heigh! o) 2=; m.

9a: 4alcula!e !o!al loss in energy o) !he ball.

9b: 4alcula!e !he speed o) !he ball Bus! be)ore i! hi!s !he ground.

9c: 4alcula!e !he speed o) !he ball Bus! a)!er i! leaves !he

ground.

2. bo5 o) mass /; g is pulled along a horiJon!al sur)ace by a

horiJon!al )orce o) ; A. 6he bo5 is pulled a dis!ance o) %2 m.

6here is a )ric!ional )orce o) ,; A be!ween !he bo5 and !he

sur)ace.

9a: 4alcula!e !he !o!al wor done by !he pulling )orce.

9b: 4alcula!e !he amoun! o) ine!ic energy gained by !he bo5.

". bo5 o) mass 2=; g is pulled up a )ric!ionless slope as shown.

9a: 4alcula!e !he gravi!a!ional po!en!ial energy gained by !he

bo5 when i! is pulled up !he slope.

9b: 6he bloc is now released.

9i: Use conserva!ion o) energy !o 7nd !he speed o) !he bo5a! !he bo!!om o) !he slope.

9ii: Use ano!her me!hod !o con7rm your answer !o 9i:.

$. winch driven by a mo!or is used !o li)! a cra!e o) mass 3; g

!hrough a ver!ical heigh! o) 2; m.

9a: 4alcula!e !he siJe o) !he minimum )orce re(uired !o li)! !he

cra!e.

9b: 4alcula!e !he minimum amoun! o) wor done by !he winchwhile li)!ing !he cra!e.

26

2 '0 (&

3'0 m

0'50 m


27/40

9c: 6he power o) !he winch is 2=3 1. 4alcula!e !he minimum

!ime !aen !o li)! !he cra!e !o !he re(uired heigh!.

3. !rain has a cons!an! speed o) %; m s−% over a dis!ance o) 2=;

m. 6he driving )orce o) !he !rain engine is "=; @ %;$ A.

1ha! is !he power developed by !he !rain engine>

*. n arrow o) mass 22 g has a speed o) "; m s−% as i! s!ries a

!arge!. 6he !ip o) !he arrow goes "=; @ %;−2 m in!o !he !arge!.

9a: 4alcula!e !he average )orce o) !he !arge! on !he arrow.

9b: 1ha! is !he !ime !aen )or !he arrow !o come !o res! a)!er

s!riing !he !arge! assuming !he !arge! e5er!s a cons!an!

)orce on !he arrow>

27


28/40

Section 3: ollisions and e!plosions

%. 1ha! is !he momen!um o) !he obBec! in each o) !he )ollowing

si!ua!ions>

9a: 9b: 9c:

2. !rolley o) mass 2=; g is !ravelling wi!h a speed o) %=3 m s −%.

6he !rolley collides and s!ics !o a s!a!ionary !rolley o) mass 2=;

g.

9a: 4alcula!e !he veloci!y o) !he !rolleys immedia!ely a)!er !he

collision.

9b: Show !ha! !he collision is inelas!ic.

". !arge! o) mass $=; g hangs )rom a !ree by a long s!ring. 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!>

$. !rolley o) mass 2=; g is moving a! a cons!an! speed when 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.

De!ermine !he mass o) !he second !rolley.

28

0

0.5

0.2

v / m s-1

time / s

5 kg

4 m s-1

1.5 kg

6 m s-120 kg

25 m s-1


29/40

3. collides headon wi!h ano!her vehicle o) mass %=2 g !ravelling a!

2=; m s −% in !he opposi!e direc!ion. 6he vehicles loc !oge!her on

29


30/40

impac!. De!ermine !he speed and direc!ion o) !he vehicles a)!er

!he collision.

%;. 7rewor is launched ver!ically and when i! reaches i!s

ma5imum heigh! i! e5plodes in!o !wo pieces. One piece has a

mass o) 2;; g and moves oK wi!h a speed o) %; m s −%

. 6he o!herpiece has a mass o)

%2; g. 1ha! is !he veloci!y o) !he second piece o) !he 7rewor>

%%. 6wo !rolleys ini!ially a! res! and in con!ac! move apar! when a

plunger on one !rolley is released. One !rolley wi!h a mass o) 2

g moves oK wi!h a speed o) $ m s −%. 6he o!her moves oK wi!h a

speed o) 2 m s−% in !he opposi!e direc!ion. 4alcula!e !he mass o)

!his !rolley.

%2. man o) mass ,; g and woman o) mass 3; g are sa!ing on

ice. ! one poin! !hey s!and ne5! !o each o!her and !he woman

pushes !he man. s a resul! o) !he push !he man moves oK a! a

speed o) ;=3 m s −%. 1ha! is !he veloci!y o) !he woman as a resul!

o) !he push>

%". 6wo !rolleys ini!ially a! res! and in con!ac! Ny apar! when 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 hasa mass o) "=; g. 4alcula!e !he veloci!y o) !his !rolley.

%$. cue e5er!s an average )orce o) /=;; A on a s!a!ionary snooer

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!ball o) mass 3;; g is s!a!ionary. 1hen a girl ics !he ball

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!ionary gol) ball o) mass %;; g is s!ruc by a club. 6he ball

moves oK a! a speed 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 graph shows how !he )orce e5er!ed by a hocey s!ic on a

s!a!ionary hocey ball varies wi!h !ime.

30


31/40

6he mass o) !he ball is %3; g.

De!ermine !he speed o) !he ball as i! leaves !he s!ic.

%,. ball o) mass %;; g )alls )rom a heigh! o) ;=2; m on!o concre!e.

6he ball rebounds !o a heigh! o) ;=%, m. 6he dura!ion o) !he

impac! is

23 ms. 4alcula!e&

9a: !he change in momen!um o) !he ball caused by !he bounceG

9b: !he impulse on !he ball during !he bounce

9c: !he average unbalanced )orce e5er!ed on !he ball by !he

concre!e

9d: !he average unbalanced )orce o) !he concre!e on !he ball.

9e: 1ha! is in !he !o!al average upwards )orce on !he ball during

impac!>

%. rubber ball o) mass $;=; g is dropped )rom a heigh! o) ;=,;; mon!o !he pavemen!. 6he ball rebounds !o a heigh! o) ;=$3; m.

6he average )orce o) con!ac! be!ween !he pavemen! and !he ball

is 2=,; A.

9a: 4alcula!e !he veloci!y o) !he ball Bus! be)ore i! hi!s !he

ground and !he veloci!y Bus! a)!er hi!!ing !he ground.

9b: 4alcula!e !he !ime o) con!ac! be!ween !he ball and

pavemen!.

2;. ball o) mass $;; g !ravels )alls )rom res! and hi!s !he ground.

6he veloci!y!ime graph represen!s !he mo!ion o) !he ball )or !he

7rs! %=2 s a)!er i! s!ar!s !o )all.

31

0

F /N

40 N

20 time / ms


32/40

9a: Describe !he mo!ion o) !he ball during sec!ions 0 04 4D

and D' on !he graph.

9b: 1ha! is !he !ime o) con!ac! o) !he ball wi!h !he ground>

9c: 4alcula!e !he average unbalanced )orce o) !he ground on !he

ball.

9d: How much energy is los! due !o con!ac! wi!h !he ground>

2%. 1a!er wi!h a speed o) 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. roce! eBec!s gas a! a ra!e 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 e5perimen! !ha! you would do !o de!ermine

!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

carried ou!.

2$. 2=; g !rolley !ravelling a! *=; m s −% collides wi!h a s!a!ionary

%=; g !rolley. 6he !rolleys remain connec!ed a)!er !he collision.

9a: 4alcula!e&

9i: !he veloci!y o) !he !rolleys Bus! a)!er !he collision

9ii: !he momen!um gained by !he %=; g !rolley

9iii: !he momen!um los! by !he 2=; g !rolley.

9b: 6he collision las!s )or ;=3; s. 4alcula!e !he magni!ude o) !he

average )orce ac!ing on each !rolley.

32

B6

-4

0·6 0·8

1·2A

C

D

E time / s

)*ee+ /

m s-1

0


33/40


34/40

3. 9a: 3 m s −%

9b: "3 m

9c: %; m s −%

9d: %;; m

9e: %"3 m

*. /3; m s −%

/ 3 s

,. 2 s

ccelera!ion

%. 9a: 2 m s −2

9b: * s

2. 9a: 2=; m s −2

9b: 2$ m s −%

9c: *=; s

". ;=2; m s −2

"ectors

%. 9a: ,; m

9b: $; m h−%

9c: 2; m nor!h

9d: %; m h−% nor!h

2. 9a: /; m

9b: 3; m bearing ;"/

9c: 9i: /; s9ii: ;=/% m s −% bearing ;"/

". 9a: *=, A bearing ;//

9b: %%=" A bearing ;$3

9c: *=$ A bearing %2

3. verage speed ? %% m h−%

verage veloci!y ? 3 m h−% bearing 2""

34


35/40

*. 9a: 3=% m s −%

9b: %$=% m s −%

'(ua!ions o) mo!ion

%. 2,; m

2. 3%=2 m

". 2, m s −%

$. %*=/ s

3. "=; s

*. 9a: /3; m s −2

9b: ;=;$ s

/. =3 m s −2 or A g−%

,. 9a: ;=2% m s −2

9b: %=$ s

. 2"$ m

%;. 9a: 9i: 2%=$ m

9ii: %3=* m s −% downwards

9b: "$=* m

Mo!ion+!ime graphs

%. 9a: 2 m s −%

due nor!h9b: ; m s −%

9d: ;=/3 m s −%

2. 9a: $ m s −% due nor!h

9b: %=; m s −% due sou!h

9d: %=* m s −%

9): displacemen! 2 m due nor!h veloci!y $ m s −% due nor!h

9g: displacemen! 2 m due nor!h veloci!y % m s −% due sou!h

35


36/40

". 9a: % m s −% due nor!h

9b: 2 m s −% due sou!h

9d: % m s −%

9): displacemen! ;=3 m due nor!h veloci!y % m s −% due nor!h

9g: displacemen! ; veloci!y 2 m s −% due sou!h

$. 9a: 2 m s −2 due nor!h

9b: ; m s −2

9c: $ m due nor!h

9d: "2 m due nor!h

3. 9a: % m s −2 due nor!h

9b: 2 m s −2 due sou!h

9d: displacemen! " m due nor!h veloci!y ; m s

−%

9e: displacemen! 2 m due nor!h veloci!y 2 m s −% due sou!h

*. 9a: 9i: %/=3 m due nor!h

9ii: 22=3 m due nor!h

9iii: %/=3 m due nor!h

. D. Ao!e !ha! in !his (ues!ion downwards is !aen !o be !he

posi!ive direc!ion )or vec!ors.

%;. . Ao!e !ha! in !his (ues!ion upwards is !aen !o be !he posi!ive

direc!ion )or vec!ors.

0alanced and unbalanced )orces

2. $;; A

". 9a: 9i: %=5 @ %;−2 m s −2

9ii: "=; @ %;* A

9b: +2=/ @ %;−" m s −2

3. ;=;2 m s −2

*. %3; A

/. 9a: %2; A

9b: 2; A

36


37/40

,. 9a: %2;; A

9b: %;, m

9c: 232 A

. 9a: 9ii: /=/ m s −2

%;. 9a: %=/, @ %;" g

9b: *=2$ @ %;$ A

%%. 2=,* @ %;$ A

%2. 9a: %=* @ %;" A

9b: 2.2* @ %;" A

9c: %.* @ %;" A

9d: %.** @ %;

"

A

%". 9a: 9i: 2=$3 @ %;" A

9ii: 2=$3 @ %;" A

9iii: 2=3 @ %;" A

9iv: %=3 @ %;" A

9b: $=2 m s −2

%$. 3%=2 A

%3. 9b: ;=$ s reading "/=2 A

$ s !o %; s reading "=2 A

%; s !o %2 s reading $"=2 A

%*. 9a: , m s −2

9b: %* A

%/. 9a: 3=% @ %;" A

9b: 2=3 @ %;" A

9c: 9i: /;; A

9ii: 3;; A

9d: %=;" @ %;$ A

%,. 2$ m

%. 9a: 9i: 2 m s −2

9ii: $; A

9iii: 2; A

9b: 9i: %2 A

37


38/40

2;. 9a: "=2/ m s −2

9b: *=3$ A

Resolu!ion o) )orces

%. 9a: $"=" A

2. "3"=* A

". 9a: ,=/ A

9b: $"=3 m s −2

$. ;=3%" m s −2

3. 9a: 22* A9b: ;="/% m s −2

*. =, A up !he slope

/. ;=/"3 A

,. 9a: 22," A

9b: 2=2 m s −2

9c: %$=, m s −%

. 9a: 9ii: %, A down !he slope

9iii: m s −2 down !he slope

9b: 9i: %* A down !he slope

9ii: , m s −2 down !he slope

1or done ine!ic and po!en!ial energy

%. 9a: "=2

9b: ,= m s −

% 9c: *=" m s −%

2. 9a: %;,;

9b: %2;

". 9a: =,

9b: 9i: "=% m s −%

$. 9a: $; A9b: =, @ %;"

38


39/40

9c: "= s

3. "=; @ %;3 1

*. 9a: ""; A

9b: 2=; @ %;−"

s

4ollisions and e5plosions

%. 9a: 2; g m s −% !o !he righ!

9b: 3;; g m s −% downwards

9c: g m s −% !o !he le)!

2. 9a: ;=/3 m s −% in !he direc!ion in which !he 7rs! !rolley was

moving

". 2=$ m s −%

$. "=; g

3. 9a: 2=/ m s −%

9b: ;=%

*. ,=* m s −% in !he original direc!ion o) !ravel

/. 9a: 2" m s −%

,. ,=/ m s −%

. ;=* m s −% in !he original direc!ion o) !ravel o) !he %=2 g !rolley

%;. %*=/ m s −% in !he opposi!e direc!ion !o !he 7rs! piece

%%. $ g

%2. ;=, m s −% in !he opposi!e direc!ion !o !he veloci!y o) !he man

%". %=" m s −% in !he opposi!e direc!ion !o !he veloci!y o) !he 7rs!

!rolley

%$. %=3, m s −%

%3. %;; A

39


40/40

%*. "=; @ %;−2 s

%/. 2=*/ m s −%

%, 9a: Q ;=" g m s −

% i) you have chosen upwards direc!ions !o beposi!ive +;=" g m s −% i) you have chosen downwards

direc!ions !o be posi!ive

9b: Q ;=" A s i) you have chosen upwards direc!ions !o be

posi!ive

9c: %3=* A downwards

9d: %3=* A upwards

9e: %*=* A upwards

%. 9a: v be)ore ? "=* m s −

% downwards v a)!er ? 2=/ m s −

% upwards

9b: = @ %;−2 s

2;. 9b: ;=2 s

9c: 2; A upwards 9or +2; A )or !he sign conven!ion used in !he

graph:

9d: $=;

2%. %=23 @ %;"

A !owards !he wall

22. =; @ %;$ A

2$. 9a: 9i: $=; m s −% in !he direc!ion !he 2=; g !rolley was !ravelling

9ii: $=; g m s −% in !he direc!ion !he 2=; g !rolley was

!ravelling

9iii: $=; g m s −% in !he opposi!e direc!ion !he 2=; g !rolley

was !ravelling

9b: ,=; A

odu mechanics questions o level a level physics

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