Sol

uti
onofchapt
er-
9
For
cesandl
awsofmot
ion
I
ntextQuest
ions–1 Page:
118

1.Whichofthef
oll
owi
nghasmorei
nerti
a:(a)arubberball
andast
oneof
thesamesize?(
b)abi
cycl
eandatr
ain?(c)afi
ve-rupeecoi
nandaone-
rupeecoi
n?
Sol
uti
on
Si
nceiner
tiai
sdependentonthemassoftheobj
ect
,theobjectwit
hthe
gr
eatermasswill
holdgreat
eriner
ti
a.Thef
oll
owi
ngobject
shol dgr
eater
i
nert
iabecauseofthei
rmass.
St
one
Tr
ain
Fi
ve-
Rupeecoi
n
2.Inthefoll
owingexample, tr
ytoidenti
fyt henumberoft i
mest hevel
ocit
y
oftheballchanges: “
Afootballpl
ayerkicksaf ootbal
ltoanotherpl
ayerof
histeam whoki cksthef
ootballtowardsthegoal .Thegoalkeeperoft
he
opposit
et eam coll
ectst
hef ootbal
landki cksittowardsaplayerofhi
sown
team”.Alsoidentif
ytheagentsupplyingthef orceineachcase.
Sol
uti
on
Lett hetwof ootball
teamsbet eam Aandt eam Brespecti
vely.Ini
ti
all
y,t
he
footballisatrest.Now,thefootballi
skickedbyapl ayerofteam At o
anot herplay
eroft eam A.(Thevelocit
yoftheballhaschanged1t i
meso
far).Thischangei sbroughtonbyt heforceappli
edbyt heplay erwho
kickedt heball
.
Thefootbal
l i
snowkickedbytheothert
eam Aplayertowardsthegoal.
(Theveloci
tyoft
heballhaschanged2timessofar).Thischangeisal
so
broughtonduetotheforceappl
iedbytheteam Aplayerwhokickedthe
bal
l
.
Thegoalkeeperofteam Bstopstheball
,br
ingi
ngittorest
.(t
hevel
ocit
yof
thebal
lhaschanged3t imessof ar
).Thi
schangeisbroughtonbythefor
ce
appl
iedbythegoalkeeperofteam Btostoptheball
.
Final
l
y,thegoalkeeperofteam Bkicksthebal
ltowardsanot herplay
erof
team B.thevel
ocityoftheballchangesforaf
inalt
ime, br
ingingthetot
al
countto4.Thischangei salsobroughtonbythegoalkeeperofteam B,
whoappl i
estheforcetokicktheballfor
ward.
Ther
efor
e,t
hev
eloci
tyoft
hebal
lchanges4t
imesi
nthi
sexampl
e.

3.Expl
ainwhysomeofthel
eav
esmaygetdet
achedf
rom at
reei
fwe
vi
gorousl
yshakei
tsbr
anch.
Sol
uti
on
Whenthebranchoft hetreeisshaken,thebranchmov esinato-and-
fro
moti
on.Howev er
,theinerti
aoftheleavesi natt
achedtothebranchresist
s
t
hemot i
onofthebr anch.Theref
ore,theleavesthatar
eweaklyat t
achedto
t
hebranchfal
loffduet oinert
iawhereast heleavest
hatarefi
rmlyattached
t
othebranchremai natt
ached.
4.Whydoyoufal
lint
hef
orwar
ddirecti
onwhenamovingbusbr
akest
oa
stopandf
all
backwar
dswheni
taccelerat
esf
rom r
est
?
Sol
uti
on
I
niti
all
y,whenthebusacceler
atesinaforwar
ddirect
ionfr
om ast
ateofr
est
,
thepassenger
sexperienceaforceexer
tedonthem i
nthebackwar
d
dir
ecti
onduetot hei
riner
ti
aopposingthefor
wardmot i
on.
Oncet
hebusstar
tsmovi
ng,
thepassenger
sareinast
ateofmotioni
nthe
for
war
ddir
ect
ion.Whent
hebrakesar
eappli
ed,t
hebusmov est
owardsa
posit
ionofrest.Now,afor
ceint hefor
war ddi
rect
ionisappli
edonthe
passengersbecausethei
riner
ti
ar esi
ststhechangeinthemot i
onoft
he
bus.Thiscausesthepassengerstofallf
orwardswhent hebr
akesare
appl
i
ed.

Page126-
127
Quest
ion1.I
fact
ioni
sal
way
sequal
tot
her
eact
ion,
expl
ainhowahor
se
canpull
acart
?
Answer:Thethi
rdl
awofmot
ionstat
esthatacti
oni
sal
way
sequal
tot
he
react
ionbutt
heyactont
wodif
fer
entbodies.
I
nt hi
scaset hehor
seexert
saf orceonthegroundwit
hit
sfeetwhil
e
walking,thegroundexer
tsanequal andopposi
tefor
ceonthefeetoft
he
horse,whi chenabl
esthehorsetomov efor
wardandthecarti
spull
edby
thehor se.

Questi
on2.Expl
ain,
whyi
sitdif
fi
cul
tforaf
ir
emantohol
dahose,
whi
ch
ej
ectsalar
geamountofwateratahi
ghvel
ocit
y.
Answer:Thewaterthati
sejectedoutfr
om thehoseinthef or
war
d
dir
ecti
oncomesoutwi thalargemoment um andequalamountof
moment um i
sdevelopedi
nt hehoseintheopposit
edirecti
onandhence
thehoseispushedbackward.Itbecomesdiff
icul
tforafir
emantoholda
hosewhichexperi
encesthi
sl ar
gemoment um.

quest
ion3.From ar
if
leofmass4kg,abul
letofmass50gi sf
ir
edwit
han
i
nit
ial
v el
oci
tyof35m/s.Cal
cul
atet
heini
ti
alrecoi
lvel
oci
tyoft
heri
fl
e.
Quest
ion4.Twoobjectsofmasses100gand200gar
emovingal
ongt he
samelineanddi
rect
ionwithv
eloci
ti
esof2m/sand1m/sr
espect
ivel
y.
Theycol
li
deandaf
tert
hecoll
i
siont
hef i
rstobj
ectmovesatav
eloci
tyof
1.
67m. /
s.Det
ermi
nethevel
ocit
yofthesecondobject
.
pageNo128:
Quest
ion1:
Anobj ectexperi
encesanetz er
oexter
nalunbalancedforce.Isitpossi
ble
fortheobjecttobet r
avel
li
ngwithanon-zer
ov eloci
ty?I
fy es,st
atethe
condit
ionst hatmustbeplacedonthemagnitudeanddi r
ect i
onoft he
veloci
ty.I
fno, pr
ovideareason.
ANSWER:
Yes.Ev enwhenanobj ectexperiencesanetzer oexternalunbal ancedforce,
i
tispossi bl
ethattheobj ectistravel
lingwithanon- zerov elocit
y.Thisis
possibleonlywhent heobj ecthasbeenmov i
ngwi t
haconst antveloci
tyin
aparticul
ardirecti
on.Then, ther
ei snonetunbal ancedf or
ceappl iedont he
body.Theobj ectwillkeepmov i
ngwi thanon- zerovelocity.Tochanget he
stat
eofmot i
on, anetnon- zeroexternalunbalancedf orcemustbeappl ied
ont
heobj
ect
.

Quest
ion2:
Whenacar
peti
sbeat
enwi
thast
ick,
dustcomesoutofi
t.Expl
ain.

ANSWER:
I
nert
iaofanobj ectt
endstor esi
stanychangei ni
tsstat
eofr estorstat
eof
moti
on.Whenacar peti
sbeat enwit
hast ick, t
henthecarpetcomest o
moti
on.But
, t
hedustpar t
iclestryt
oresistt hei
rstat
eofrest.Accordi
ngto
Newton’
sfi
rstlawofmot ion,thedustparticlesst
ayinast at
eofr est
,whil
e
t
hecarpetmov es.Hence,thedustparti
clescomeoutoft hecarpet.

Quest
ion3:
Whyi
sitadv
isedt
oti
eanyl
uggagekeptont
her
oofofabuswi
thar
ope?

ANSWER:
Whenthebusaccel erat
esandmov esf or
war d,i
tacquiresast ateofmoti
on.
However,
theluggagekeptont heroof ,owingtoitsinerti
a,tendstoremain
i
nit
sstateofrest.Hence,wit
ht hef or
wardmov ementoft hebus, the
l
uggagetendstoremai nati
tsor i
ginalpositi
onandul ti
mat elyfal
lsfr
om t
he
r
oofofthebus.Toav oi
dthi
s,i
tisadv isedtot i
eanyl uggagekeptont he
r
oofofabuswi thar ope
Quest
ion4:
Abatsmanhitsacri
cketball
whichthenr
oll
sonalevel
ground.Aft
er
coveri
ngashortdi
stance,
theball
comestorest
.Theball
slowstoastop
because

(
a)t
hebat
smandi
dnothi
tthebal
lhar
denough.
(
b)v
eloci
tyi
spr
opor
ti
onal
tot
hef
orceexer
tedont
hebal
l
.
(
c)t
her
eisaf
orceont
hebal
lopposi
ngt
hemot
ion.
(
d)ther
eisnounbal
ancedf
orceont
hebal
l
,sot
hebal
lwoul
dwantt
ocome
t
orest.

ANSWER:
(c)Abat smanhit
sacr i
cketbal
l
,whi cht
henr
oll
sonal evelgr
ound.Aft
er
cov er
ingashortdi
stance,t
heball
comest or
estbecausetherei
sfri
cti
onal
forceont hebal
lopposingi
tsmotion.

Fr
ict
ional
for
cealwaysact
sinthedir
ecti
onopposi
tet
othedi
recti
onof
moti
on.Hence,
thi
sforcei
sresponsi
bleforst
oppi
ngt
hecri
cketball
..
5.Atruckst
art
sfrom r
estandrol
l
sdownahi l
lwi
thaconstantaccel
erat
ion.
Itt
ravel
sadist
anceof400m in20s.Fi
ndit
saccel
erat
ion.Fi
ndtheforce
acti
ngoniti
fit
’smassis7tonnes(Hi
nt:
1tonne=1000kg.)

Sol
uti
on
Gi
ven,
dist
ancecov
eredbyt
het
ruck(
s)=400met
ers
Ti
met
akent
ocov
ert
hedi
stance(
t)=20seconds
I
nit
ial
vel
oci
tyoft
het
ruck(
u)=0(
sincei
tst
art
sfr
om ast
ateofr
est
)
6.Astoneof1kgisthrownwit
hav el
ocit
yof20ms- 1acr osst
hefrozen
sur
faceofalakeandcomestorestaft
ertravel
l
ingadistanceof50m.
Whatisthef
orceoffri
cti
onbet
weenthest oneandtheice?

Sol
uti
on
Gi
ven,
Massoft
hest
one(
m)=1kg
I
nit
ial
vel
oci
ty(
u)=20m/
s
Fi
nal
vel
oci
ty(
v)=0m/
s(t
hest
oner
eachesaposi
ti
onofr
est
)
Di
stancet
rav
eledbyt
hest
one(
s)=50m
7.An8000kgengi nepull
sat r
ainof5wagons,eachof2000kg,alonga
hori
zontal
track.I
ftheengi
neexertsafor
ceof40000Nandt hetrackoff
ers
afri
cti
onforceof5000N, thencal
cul
ate:
(a)t
henetacceler
ati
ngforceand
(b)t
heaccelerati
onofthetrai
n

Sol
uti
on

(
a)Gi
ven,
for
ceexer
tedbyt
het
rai
n(F)=40,
000N
(
b)For
ceoffr
ict
ion=-
5000N(thenegati
vesi
gni
ndi
cat
est
hatt
hef
orce
i
sappl
iedi
ntheopposi
tedi
rect
ion)

Ther
efor
e,t
henetaccel
erat
ingf
orce=sum ofal
lfor
ces=40,
000N+(
-
5000N)=35,000N
(b)Tot
almassoft
hetr
ain=massofengi
ne+massofeachwagon=
8000kg+5×2000kg
Thet
otal
massoft
het
rai
nis18000kg.

Aspert
hesecondl
awofmot
ion,
F=ma(
or:
a=F/
m)
Theref
ore,accel
erat
ionoft
het
rai
n=(
netaccel
erat
ingf
orce)/(
tot
almass
ofthetr
ain)
=35,
000/
18,
000=1.
94ms-
2
Theaccel
erat
ionoft
het
rai
nis1.
94m.
s-2.

8.Anautomobilevehi
clehasamassof1500kg.Whatmustbethef
orce
betweenthevehicl
eandroadift
hevehi
clei
stobest
oppedwit
hanegati
ve
accel
erat
ionof1.7ms-2?
Sol
uti
on
Gi
ven,
massoft
hev
ehi
cle(
m)=1500kg
Accel
erat
ion(
a)=-
1.7ms-
2
Aspert
hesecondl
awofmot
ion,
F=ma

F=1500kg×(
-1.
7ms-
2)=-
2550N
Therefor
e,afor
ceof2550Nmustactont
hev
ehi
clei
nadi
rect
ionopposi
te
tothatofit
smotion.

9.Whati
sthemoment
um ofanobj
ectofmassm,
mov
ingwi
thav
eloci
tyv
?

(
a)(
mv)
2(b)mv
2(c)½mv
2(d)mv
Sol
uti
on
Sincemoment um i
sdefi
nedast
hepr
oductofmassandv
eloci
ty,
the
correctansweri
s(d),
mv.

10.Usingahori
zontal
forceof200N,weint
endtomoveawoodencabinet
acrossafl
oorataconstantvel
oci
ty.Whati
sthef
ri
cti
onf
orcet
hatwil
lbe
exert
edonthecabinet
?

Soluti
onSi ncethevel
oci
tyofthecabineti
sconstant
,itsaccel
erati
onmust
bezer o.Theref
ore,t
heeffect
ivef
orceacti
ngonitisalsozero.Thisimpl
i
es
thatthemagni t
udeofopposingfri
cti
onalfor
ceisequal t
otheforceexer
ted
ont hecabinet,
whichis200N.Therefore,
thetot
alfr
icti
onforceis-200N.
11.Twoobjects,
eachofmass1. 5kg,aremov i
ngi
nthesamestrai
ghtl
ine
butinopposi
tedirect
ions.Thevel
ocit
yofeachobjecti
s2.5ms-1befor
e
thecol
li
sionduri
ngwhi chtheysti
cktogether
.Whatwil
lbethev
eloci
tyof
thecombinedobjectaftercol
l
isi
on?

Sol
uti
on
Gi
ven,
massoft
heobj
ect
s(m1andm2)=1.
5kg
I
nit
ial
vel
oci
tyoft
hef
ir
stobj
ect(
u1)=2.
5m/
s
I
nit
ial
v el
oci
tyofthesecondobj
ectwhi
chi
smov
ingi
ntheopposi
te
di
rect
ion(u2)=-2.5m/s
Whent
het
womassesst
ickt
oget
her
,ther
esul
ti
ngobj
ecthasamassof3
kg(
m1+m2)
Vel
oci
tyoft
her
esul
ti
ngobj
ect(
v)=?
Asperthelawofconser
vat
ionofmomentum,thet
otal
moment um bef
ore
thecol
l
isi
onisequaltot
hetotal
momentum af
tert
hecoll
i
sion.
Tot
almoment
um bef
oret
hecol
l
isi
on=m1u1+m2u2
=(
1.5kg)(
2.5m/
s)+(
1.5kg)(
-2.
5m/
s)=0
Ther
efor
e,t
otal
moment
um af
tercol
l
isi
on=(
m1+m2)v=(
3kg)v=0
Ther
efor
ev=0
Thi
simpl
iesthatt
heobj
ectf
ormedaf
tert
hecol
l
isi
onhasav
eloci
tyof0
meter
spersecond.

12.Accor di
ngt ot
het hi
rdlawofmot i
onwhenwepushonanobj ect,t
he
objectpushesbackonuswi thanequalandopposi
tef or
ce.Ift
heobj ecti
s
amassi vetruckparkedalongtheroadsi
de,i
twil
lprobabl
ynotmov e.A
studentjust
ifi
esthi
sbyanswer ingthatt
hetwooppositeandequal forces
canceleachot her
.Commentont hi
slogi
candexplainwhyt hetr
uckdoes
notmov e.
Sol
uti
on
Sincet hetruckhasav eryhighmass, thestati
cfri
ctionbetweentheroad
andt hetrucki shigh.Whenpushi ngthet r
uckwi t
hasmal lfor
ce,
the
fr
ictionalforcecancel souttheappli
edf orceandthet ruckdoesnotmove.
Thisi mpli
est hatthetwof orcesareequal inmagnitudebutopposit
ein
di
r ecti
on(sincet heper sonpushi
ngt hetruckisnotdi spl
acedwhenthe
tr
uckdoesn’ tmov e).Theref
ore,t
hest udent’sl
ogiciscor r
ect.

13.Ahockeyballofmass200gt ravel
l
ingat10ms–1i sstr
uckbyahockey
sti
cksoast oret
urnitalongit
sorigi
nalpat
hwithav el
oci
tyat5ms–1.
Calcul
atet
hemagni tudeofchangeofmoment um occurr
edinthemot
ion
ofthehockeyballbytheforceappli
edbythehockeysti
ck.

Sol
uti
on
Gi
ven,
massoft
hebal
l(m)=200g
I
nit
ial
vel
oci
tyoft
hebal
l(u)=10m/
s
Fi
nal
vel
oci
tyoft
hebal
l(v
)=–5m/
s
I
nit
ial
moment
um oft
hebal
l=mu=200g×10ms-
1=2000g.
m.s-
1
Fi
nal
moment
um oft
hebal
l=mv=200g×–5ms-
1=–1000g.
m.s-
1
Ther
efor
e,t
hechangei
nmoment
um (
mv–mu)=–1000g.
m.s-
1–2000
g.
m.s-1=–3000g.m.
s-1
Thi
simpl
iest
hatt
hemomentum oft
hebal
lreducesby1000g.
m.s-
1af
ter
bei
ngst
ruckbyt
hehockeyst
ick.

14.Abul l
etofmass10gt ravel
l
inghori
zontal
lywit
hav eloci
tyof150m
s–1stri
kesast at
ionarywoodenblockandcomest orestin0.03s.
Calcul
atethedist
anceofpenetrat
ionofthebull
eti
ntotheblock.Al
so
cal
culatethemagnitudeofthefor
ceexertedbythewoodenbl ockont
he
bul
let.
Sol
uti
on
Gi
ven,
massoft
hebul
l
et(
m)=10g(
or0.
01kg)
I
nit
ial
vel
oci
tyoft
hebul
l
et(
u)=150m/
s
f
inal
vel
oci
tyoft
hebul
l
et(
v)=0m/
s
Ti
meper
iod(
t)=0.
03s
Tofi
ndthedist
anceofpenet
rat
ion,
theaccel
erat
ionoft
hebul
l
etmustbe
cal
cul
ated.

Ther
efor
e,f
orceexer
tedbyt
hewoodenbl
ockont
hebul
l
et(
F)=0.
01kg×(
-
5000ms-2)

=-
50N

Thi
simpl
iest
hatt
hewoodenbl
ockexer
tsaf
orceofmagni
tude50Nont
he
bul
l
etint
hedir
ect
iont
hati
sopposi
tet
othet
raj
ect
oryoft
hebull
et.

15.Anobjectofmass1kgtravel
l
ingi
nast raightli
newit
haveloci
tyof10
ms–1colli
deswith,
andsti
cksto,astat
ionarywoodenblockofmass5kg.
Thentheybothmoveofft
ogetherint
hesamest rai
ghtl
i
ne.Cal
culat
ethe
tot
almoment
um j
ustbef
oret
hei
mpactandj
ustaf
tert
hei
mpact
.Al
so,
cal
cul
atet
hevel
oci
tyoft
hecombi
nedobj
ect
.

Sol
uti
on
Gi
ven,
massoft
heobj
ect(
m1)=1kg
Massoft
hebl
ock(
m2)=5kg
I
nit
ial
vel
oci
tyoft
heobj
ect(
u1)=10m/
s
I
nit
ial
vel
oci
tyoft
hebl
ock(
u2)=0
Massoft
her
esul
ti
ngobj
ect=m1+m2=6kg
Vel
oci
tyoft
her
esul
ti
ngobj
ect(
v)=?
Tot
almomentum bef
oret
hecol
l
isi
on=m1u1+m2u2=(
1kg)×(
10m/
s)+0
=10kg.
m.s-
1

Asperthelawofconservat
ionofmomentum,thetot
al momentum before
thecol
li
sioni
sequaltothetotal
momentum postt
hecol l
isi
on.Ther
efore,
thetot
almomentum postthecoll
isi
oni
salso10kg.m.s-1

Now,
(m1+m2)×v=10kg.
m.s-
1

Ther
esul
ti
ngobj
ectmov
eswi
thav
eloci
tyof1.
66met
erspersecond.

16.Anobj
ectofmass100kgi
saccel
erat
edunif
ormlyf
rom avel
ocit
yof5
ms–1to8ms–1i n6s.Cal
cul
atet
heini
ti
alandfi
nal
moment um oft
he
obj
ect
.Al
so,
findt
hemagni
tudeoft
hef
orceexer
tedont
heobj
ect
.

Sol
uti
on

Gi
ven,
massoft
heobj
ect(
m)=100kg
I
nit
ial
vel
oci
ty(
u)=5m/
s
f
inal
vel
oci
ty(
v)=8m/
s
Ti
meper
iod(
t)=6s
Now,
ini
ti
almomentum (
m ×u)=100kg×5m/s=500kg.
m.s-
1Fi
nal
moment
um (m ×v
)=100kg×8m/ s=800kg.
m.s-
1

Theref
ore,t
heobject
accel
erat
esat0.5ms-
2.Thi
simpl
i
est
hatt
hefor
ceactingontheobject(
F
=ma)isequalto:
F=(
100kg)×(
0.5ms-
2)=50N
Ther
efor
e,afor
ceof50Ni
sappl
i
edont
he100kgobj
ect
,whi
chaccel
erat
es
i
tby0.5ms-2.

17.Akhtar , Kiran,andRahul wereridinginamot orcart hatwasmov i

ngwi t
h
ahighv eloci tyonanexpr esswaywhenani nsecthitthewi ndshiel
dandgot
stuckont hewi ndscreen.Akht arandKi r
anst art
edponder i
ngov ert
he
sit
uati
on.Ki ransuggest edt hatthei nsectsuffer
edagr eaterchangein
moment um ascompar edt ot hechangei nmoment um oft hemot orcar
(becauset hechangei nt hev elocit
yoft heinsectwasmuchmor ethanthat
ofthemot orcar).Akhtarsai dt hatsincethemot orcarwasmov i
ngwi tha
l
argervel oci t
y, i
texertedal argerforceont heinsect.Andasar esultthe
i
nsectdi ed.Rahul whil
eput ti
nganent i
rel
ynewexpl anat ionsaidthatboth
themot or carandt heinsectexper i
encedt hesamef orceandachangei n
t
hei
rmoment
um.Commentont
hesesuggest
ions.

Sol
uti
on
Aspert helawofconser v
ationofmoment um,thetot
almoment um befor
e
thecoll
isi
onbet weentheinsectandthecarisequalt
othetotalmoment um
aftert
hecol l
i
sion.Theref
ore,thechangei
nthemoment um oftheinsectis
muchgr eaterthanthechangei nmomentum ofthecar(
sinceforceis
proport
ionaltomass) .
Akht
ar’
sassumpti
oni
spart
ial
l
yright
.Sincet
hemassofthecari
sveryhi
gh,
thef
orceexer
tedont
hei
nsectduri
ngthecol
li
sioni
sal
soveryhi
gh.
Kir
an’sstatementisfalse.Thechangeinmoment um oftheinsectandthe
motorcarisequalbyconser vati
onofmoment um.Thev el
ocityofi
nsect
changesaccordinglyduet oit
smassasi tisver
ysmallcompar edtothe
motorcar.Simi
larl
y,theveloci
tyofmotorcari
sveryi
nsignif
icantbecause
i
tsmassi sv er
ylargecompar edtotheinsect
.
Rahul’
sstatementiscompletel
yri
ght.Asperthethi
rdlawofmot i
on,the
for
ceexertedbytheinsectonthecarisequalandopposit
etotheforce
exert
edbyt hecarontheinsect
.Howev er
,Rahul’
ssuggest
ionthatthe
changeinthemoment um isthesamecont r
adict
sthelawofconservati
on
ofmoment um.

18.Howmuchmoment um wi
lladumb-
bel
lofmass10kgtransfertothe
fl
oori
fitf
all
sfr
om ahei
ghtof80cm?Takeit
sdownwardaccelerat
ionto
be10ms–2.

Sol
uti
on
Gi
ven,
massoft
hedumb-
bel
l(m)=10kg
Di
stancecov
ered(
s)=80cm =0.
8m
I
nit
ial
vel
oci
ty(
u)=0(
iti
sdr
oppedf
rom aposi
ti
onofr
est
)
Accel
erat
ion(
a)=10ms-
2
f
inal
vel
oci
ty(
v)=?
Moment
um oft
hedumb-
bel
lwheni
thi
tst
hegr
ound=mv
Addi
ti
onalexer
cise
Quest
ion1:
Thef
oll
owi
ngi
sthedi
stance-
ti
met
abl
eofanobj
ecti
nmot
ion:
(
seet
abl
efr
om ncer
t)
a)Whatconcl
usioncanyoudrawaboutt
heaccel
erat
ion?I
sitconst
ant
,
i
ncreasi
ng,
decreasi
ng,orzer
o?

(
b)Whatdoy
oui
nferaboutt
hef
orcesact
ingont
heobj
ect
?

ANSWER:
(
a)Ther
eisanunequal
changeofdi
stancei
nanequal
int
erv
aloft
ime.

Thus,t
hegivenobjecti
shavi
nganon−uniform mot
ion.Sincethev
eloci
ty
oftheobj
ectincr
easeswit
htime,
theaccel
erat
ioni
sincreasing.

(b)Accordi
ngtoNewt on’ssecondlawofmot i
on,t
heforceacti
ngonan
objectisdi
rectl
yproport
ionaltotheaccel
erat
ionpr
oducedintheobj
ect.I
n
thegivencase,theincr
easingacceler
ati
onofthegiv
enobjecti
ndi
cates
thattheforceacti
ngont heobjecti
salsoincr
easi
ng.

Quest
ion2:
Twopersonsmanagetopushamotor
carofmass1200kgataunif
orm
vel
oci
tyalongal
evel
road.Thesamemotor
carcanbepushedbyt
hree
personstoproduceanaccel
erati
onof0.2m s−2.Wit
hwhatfor
cedoes
eachpersonpusht hemotor
car?(Assumethatal
lper
sonspushthe
mot or
carwit
ht hesamemusculareffor
t)

ANSWER:
Massoft
hemot
orcar=1200kg

Onlyt
wopersonsmanagetopusht
hecar.Hence,theaccel
erat
ion
acqui
redbyt
hecari
sgivenbythet
hir
dpersonalone.

Accel
erat
ionpr
oducedbyt
hecar
,wheni
tispushedbyt
het
hir
dper
son,

a=0.
2m/
s2

Lett
hef
orceappl
i
edbyt
het
hir
dper
sonbeF.

Fr
om Newt
on’
ssecondl
awofmot
ion:

For
ce=Mass×Accel
erat
ion

F=1200×0.
2=240N

Thus,
thet
hir
dper
sonappl
i
esaf
orceofmagni
tude240N.

Hence,
eachper
sonappl
i
esaf
orceof240Nt
opusht
hemot
orcar
.
Quest
ion3:
Ahammerofmass500g,movi
ngat50m s−1,
stri
kesanai
l
.Thenail
stops
t
hehammerinaver
yshor
tti
meof0.01s.Whatist
hefor
ceofthenai
lon
t
hehammer?

ANSWER:
Massoft
hehammer
,m =500g=0.
5kg

I
nit
ial
vel
oci
tyoft
hehammer
,u=50m/
s

Ti
met
akenbyt
henai
ltot
hest
opt
hehammer
,t=0.
01s

Vel
oci
tyoft
hehammer
,v=0(
sincet
hehammerf
inal
l
ycomest
orest
)

Fr
om Newt
on’
ssecondl
awofmot
ion:

Thehammerst r
ikesthenail
withaforceof−2500N.Hence,
from Newt
on’
s
thi
rdl
awofmot i
on, t
heforceofthenail
onthehammerisequaland
opposi
te,
i.
e.,
+2500N.
Quest
ion4:
Amotorcarofmass1200kgi smov ingal
ongast r
aightli
newithauni
for
m
vel
oci
tyof90km/ h.I
tsvel
ocit
yi ssloweddownt o18km/ hi
n4sbyan
unbal
ancedext
ernalfor
ce.Calculat
et heaccel
erat
ionandchangein
momentum.Alsocalcul
atethemagni t
udeoftheforcerequi
red.
ANSWER:
Massoft
hemot
orcar
,m =1200kg

I
nit
ial
vel
oci
tyoft
hemot
orcar
,u=90km/
h=25m/
s

Fi
nal
vel
oci
tyoft
hemot
orcar
,v=18km/
h=5m/
s

Ti
met
aken,
t=4s

Accor
dingt
othef
ir
stequat
ionofmot
ion:

v=u+at

5=25+a(
4)

a=-
5m/
s2

Changei
nmoment
um =mv−mu=m (
v−u)

=1200(
5−25)=-
24000kgm s−1

For
ce=Mass×Accel
erat
ion

=1200×(
-5)=-
6000N
Accel
erat
ionoft
hemot
orcar=-
5m/
s2

Changei
nmoment
um oft
hemot
orcar=-
24000kgm s−1

Hence,
thef
orcer
equi
redt
odecr
easet
hev
eloci
tyi
s-6000N.
(
Negativ
esigni
ndicatestheret
ardat
ion,
decr
easei
nmoment
um and
r
etar
dingfor
cerespecti
vely
)
By
-NI
SHASHARMA