Questions and Example problems from Chapter 4
QuestionI
why do you lung forward whenyour car suddenry
comesto a halt? why areyou pressed
backwardagainstthe seatwhenyorr car rapidly accelerates?
J\
\
4 9i
)
-U-o-t:LrA-.w-a)
*r]4
ED-./r.l),^-l
^t -)A lb,e-lddtuA! 4 ^*^n
(nu^r*r",r,z
..i
\
,.-, .
""'r,/F'A,l
/ "V^)a )4,cc",}rNr,
L nn rn * q
:-*
W
cd\Mn
4+4-{ (+ th**V*
h^,) il}+Jh bro cz"y An-ttz o2
uestion2
Question
qfn -1,bbz
f\,b+AJU
"
is ona_ftictiontesl,*f#,^ shown
below.
Rank
|
rhese
ly.:j::.::g
1l
"!j".that
situations'u't
fiom greatest
acceleration
Ers4reslauugrerauon
to leurt
teastu"c"le.utiorr.
acceleration.fNote: All vectors *"vv!wu
directedto
'v the
urr right
arepositive, and those to the left are negative.
Also, 0 Jsf> _10;rr.i-"
F=8N
I
!=u"
f, =SN
F,.=6N
a--{t
llr=4 kg
(.4 -
o,5 nn/sl
-F, = t t r
-a_-t -
I______*
rr=l
pr:i
E
a*/rrs=
f=
t0t\
I
---------)
-,...
t--l
|
^
C\ --
k-{
-\\t/
ovu/^t(a
'-
=
a
r
/:
Im,/S*
N
I
kg
rr =4 kg
D
1
6=
:-i
i-,
\-.
ln
4-- r-!1 :-
-?+.-*o"5.7ra
1t-'t
Least
Question3
Ifyou pressan applecrateagainsta wall so
hardthat the cratecannotslide down the wall, what
is the direction of (a) the staticfrictional force
f on the cratefrom the *ar *a oIrr" ,,"."r"r
*"" fiom the wall? If you inueaseyour push,what
happensro (c)1, (d) !.p,
3":"3
:1-::"
and(e)f,max?
') I
;
-.4
I rN
l
Jto
l-lrd-Ql
(s,- . g
)
Question4
In the figure beiow, ifthe box is stationaryandthe angle0 of force F is increased,do the
or remainthe same:(a) F*; (b)"6;(c) Fr'r;(d);{,max?(e)
decrease,
followirigquantitiesincrease,
the
If. instead.the box is sliding and0 is increased,doesthe magnitudeofthe frictional force on
or remainthe same?
decrease,
box increase,
a)
(4o,.or f'= F*)
b)
c)
d)
Problem I
o\
(f, =,r.r* )
)IWV'a.A2
_)IY\\cA94A2
when a 58-g tennisball is served,it acceleratesfrom lest to a speedof 45 n/s th: impact with
the racketeivesthe ball a constantaccelerationover a distanceof44 cm. What is the magnitude
ofthe net force acting on the ball?
|fi= tr9o=
)
t r 9 y l n - 3 K' d.
1 /o = O n i s
yl -^ t tS rtls
,r.u* +;f
r''.,-'A }}'-B/"^J Mlc c'-c-
f, "P X9" ,"'f 8"'-*
oo
v^ = ij-
Xo-om
..o
A'. Lx-o")---* q;= )'a x
o = l.3,.lDlVl
ue'219^
';
{-_1o"vl
Y.'o"44m
-.=----
Problem2
only two forcesacton anobject(mass= 3.00.kg), asin the drawingbelow.Find the magnitude
and direction(relativeto the x-axis) of the accelerationof the object'
teo.oN
(too"aru)aro95"D"
/z
,/ 15,o"
a__-_-__7
e1g,oN
({aa.on) baLj6.Du
'4o"DN
2" Fy = Day
(
\ir-
I
l-1 = fr) Q1
-.x -
)-
z'k = (to. o r:r)a.r,',tt5'o" --i
zE=@
(:. oog,
)
ay = l1"l t6.
-=:'
) 0x = J\,51y
':#
( 3.ooKg)
--,
(*) -,taN'(
o - )b,a*ffrJ
.a -(,
n e-) ro
€r-rrl
'"---l
Problem3
A rock of mass45 kg accidentallybreaksloosefiom the edgeof a cliffand falls straightdown.
The magnitrideof the air resistancethat opposesits downwardmotion is 250 N. What is the
magnitudeof the.accelerationoftle rock?
6a =lsot"t
I
g$p"v ola^e,naa a
XFr=rey
I
{
I
N9-Fr-=rqy
t-D=fog
0r=
Q-
tr*/.
---r Q,l = 4,\nf s'
*/s'- *#,
ol = Q"eo
e.= 4.Am/s}ev ettt
Problem4
The helicopterin the drawingis moving horizontallyto the right at a constantvelocity. The
weigltt of the helicopteris 53,800N. The lift force L generatedby the rotatingblademakesan
angleof 21.0'wittr respectto the vertical. (a) What is the magn-itudeof the lift force?
(b) Determinethe magnitudeof the air resistanceR that opposesthe motion.
Lc,6r tl.O"
21.0"
L ,ozr Q.l.o"
v/\ \ )|
\
| t
ZJrr/-
-
tY\
Ltao)\,O"
"b)
- tr) =
XF*=mo,
A
Xtrr=o
^
r.,aY
o
Ax--o
L=
*/**
r.Do= Elt#'
XF"=o
= LA^n at.oo= ( s.?oxtoYN);0l,o. =
l.o?" lo{N
!\."-
--'.-r
Problem5
=
cord ftom a knot' which hangs
itt rft" ftgt* t+ow, block B of massM 15'0 kg hangsby a
is the tension
ty m"^ns of t*o oAo cords.The cordshavenegligible mass.What
n""?ifi"g
cords?
in the"three
Eri15"
'-r
Vf '
Tr
T* ,a,.4
Te r,aatl?"
T, cac11'
13
?'u.*r .'
<.l
r.
= IT)Q" = c'
)-i t-x
Tx..a'J?"--T r@!$'
-T
'A
Tc = l'l? N
-T
- -, c.at\b'
--1
^,.r* rr.'h sa,(D
06)11
-i
qa^"iK'. tfr-cqat=D
T, a,..2st (-r'3f
+---
=
)
=
|1
^,^,ae+
(#,)n"tl
a^= \:glL
anul = Tz
=l;il
/9'l l"l
-----'---------:1
6.11
= (tortru)caalr{l3sNl
I
oa 47
Problen 6
weightwhentheelevator
A 95.0kg personstandson a scalein anelevator'Whatis theapparent
of 1'80rn/J' Q) lwing^unward ata constant
upwardwith anacceleration
i; i;t;;"d."ti"g
of 1'40rn'/s'?
do*o*ard with anacceleration
rpi":aiJicj
";:"lirutiog
i$"* }}\0
F*
)
1
I
t.
,,I
Jf,,
)rt^4tt
it nry-|aa M'g d'rtw"''!4-o-'^j
"4+"-'J
1)-'"h -e,bk^ )e W
d-o+
dr$^^,w
--). fl' - rng = rog
X F., = sqa,
F*= ttg*o)
mq
a)
\ b)
-=
F; = ( 9s.or ,7 (a.ta*/ si'+tisoalst)
q=+l'Eonls'-.'-+
a = aft/3r'*---' lr
C) a : -1,\Dqfe^-a
=li3TNi
= (rs,oq)(9.r0.1s-)
f
Iq Sq
(a'*on1r'l,qo"t/s')=J
= Tns.ovg\
n=d/s!= o4*,,r
= tl.E1 K*
Problem 7
A b]gc]rwlose weightis 45.0N restson ahorizontartable.A
horizontalforceof 36.0N -is
appliedto theblock.Thecoefficientsof sratic*a r.i""ti" *r.tion
areo.os0anJn:;;O,-'
respectively.
will thebiockmoveundertrreinfluenceof theforc",*a, 'rrro,
'v' *rru,
wr<r'r*iri
wru u"
u€ ,r*
block's acceleration? Explain your reasoning.
^&
?
3t -o N ) fs,*-,y, fu
fs = 3b.oN ^a".o\hla'\^a;LAl
r' 11\r-r
.t
FnJ
I
^rrr;"^"1 -*"b;.r^"4
X tr, --Day = o --r F- = r^r--t/ 5.oN
t
f e_t___+F
ls
tt"'i^4 'ut q = (o'aso) (4s'au) 'X?'lrN
w'e6.oN
=),a,lr.we 3t''oN
beo.t\ ^r)-at n*^rt ,, y$*vyzit
-=-
, i,**"
,
> n=t\ex -J ax=E! = F-t' = f:3nF'
Problem8
*
L:t"*-:*':^if
i::L.l*"^1ybl$iltiil??"-0"*itruro.kii66-il?-fr
15oabovethehoizontai.If
pr : 0.35,wttatis trreacceleration
ofthe crate?
5,, ^ F-ar.r15"
E06N
F> sooN
Fy =o
(-.l-
Ay=o
tFt=r4y
\*
F^*tSo-.g
)- l-, = lY)A"
=u
0x=LEr =
fc)
fr.r: [ng-ts-a;&15'
( rrre;1q,76
r7""; C5orN;oin,t.
= 55?N
FUots"
f*
)A
4r
=
F c"a lgo - ,l,l p Frv
ax : C.9,"N),.r,
rS: (o"lg
t.rofnl
Problem 9
A 3.50kg block on a smoothtabletopis attachedby a string to a hangingblock ofmass 2.8 kg,
as shownin the figure below. The blocks arereleasedfrom rest and allowed to move fieely.
(a) Is the tensionin the string greaterthan, lessthan, or equalto the weight of the hangingmass?
(b) Find the acceierationof the blocks and the tensionin the strin$.
(")
T4 ^r-^a9",.Tt
4 fr\, A.xafg l,,ear9-r'^^
IA,''I Jso Fuz'"il6rll"v.' J -!rt "pvty #^^"
"l,ca,t,,ne,,.:.^)a,
#" ,r-.,il*
'V
.iA, -d[ivl^b *il
t!
dd u)
aufuu&ta
'v..'all pt&a1
lr$ In\4/t'r LB10-/-"1/r'\!
u9:
'+'^'n
4 e*/"h ]'pt&-ufiv
2 . z o4 be-O\ -.
3 , 5 o Y 9h 4 , ! \ ' .
F-
X \
I
1p,*,ua*.*
Wx a'lac'v'v"'h'J
'
d..up,-',J.o"^n
a +
- m4y ---) rerqg-l-'rnxo
Nisg- (r.r,a)=
{
T = ,t,,o
(i'*"
()
,lT
X F,= t,^*
T
Nv1^l .
$)fu.r'bt'qiY
L
e =!:j__
m."g
=
lluQ
q:"h)sP:!d
(r, ,*rOx)'
(l.sug ").zoY\-,
Problem 10
A crateis restingon a rampthat is inclinedat anangleofO abovethehorizontal.As 0 is
q= 4.4nls^
increased,the crateremainsin place untii 0 reachesa value of38.0o. Then the cratebeginst6
of themovingcrateis the coefficientofkinetic J
slidedowntheslope.Find the acceleration
frictionbetweenthecrateandtherampsurfaceis 0.600.
'.,1;^ 'ff,r.
?.*
< tO 1Q
1= (3.soq)(e41
-T=
/5 N
Tfrl
mAcas
Ytr= fnar=p
<-..l -
) F" = [0ex
F11-rnq.aao=d
E
/11
= 'tt\ficatb
mg a.vng
log {rr.' } - f* = fO ex'
m3 a,uno - l.tr Fp = ff) 4.1
tnX a,hlO-,r-tp
{rn6cao) = fi4y
Ax = ga.noO--dr ? tnb
4" = l.to rn/s*
- (a,to"1sJ)tt*Zg.t- qo.u'o)(l,ao,ll)c-35.o"
Problem11
A box is sliding up an incline that makesan angleof 15.0" with respectto the horizontal.The
coefficientofkinetic friction betweenthe box andthe surfaceofthe incline is 0.180.The i.nitial
speedofthe box at the bottom ofthe incliire is 1.50mls. How far doesthe box travel along the
incline beforecomins to rest?
--+
N
=)
. U 4,u,tu.ozXF=mP.t4
atzolfu
rc,t-Pz:u!-tt b
a"q^tt\
fr\, )i\.,^).*tu: &\ ,r* )niuot'h:ca
!v;tW
fr cp,luA^X'olr'ota * 4fu
l-
,7
l)
v
m4
Z F, = rctay-- o
c' K
F
,N
fc\gcroe
E
F,gaarn
E
/N
.+ r{\Xu+er
-- O
=
t\
m %O,r'JA
XF*= [Y)Ax
f**-3
a"tp = ff)Ax
fOqx
r"i* f, i mg ^.,,q9:
*
,t^r (fyc,utg) + $gin 9= fl)qx Qx= %(une"Ap *r)
+ q i^g
A1= ./lpg caz:O
- fl,r-om/s)f o
Qx = 4/o\1 ,nls^ ---+ pa
)afut
,5.oo+-(olu) c,o-tt5.o"l
qrxpbuW;
ANt\ m@N
.--._-...-.-..---
a-a+
+ d,tli,t," u+ M/{A/\\z.
'r-t
Vo^* Aa (x-x,)
'.Xo=Dcl
X=?
Vo = l"Soqls
o=vi+ a^x
ln
v ="Dr/s
a = - +,t1^)S
f
= 1
o
( r.so '/s )a
L(tt,tin/s)
f X= O"e.orrn
-J.I
[--
tlre='.
Problen 12
A girl is sleddingdown a slopethat is inclined at 30.00witi respect
to the horizontal.A moderate
wind is aiding the.r.notionby providing a steadyforceof r os r.r'aaiis
par.iier to tn" motion of
the sled' The combinedmassof the girl andstedis 65.0kg, *a
trr"
of kinetic friction
betweenthe runnersof the siedand the snowis 0.150.rroi" -""t
"oirrt"i""t
ti-"
is requirea1brthe sledto
travel down a 175m slope,startingfrom rest?
[\
,d4,v"r oaaa
,/^
A.*,"',
"a $"U,a'a
,.
^'y'
rog oro S
m6uog
\X
* poo.*
X F,
XF,= r)ar=6
A*-*grarb-A
F " , - ^ + T q g a Y q A- $ x ' = N ) Q *
F =.rq.',rD
= (bv.o!g) (9.2u ,,,1g,)
ca j,o"
,{n = 55eN
0x= lo5N *(6F.o
1,Bon1t^a,i.*,
3o o"-
(o, t5o 551N
(as.oP2;
5.Al 'r/sr
o .o/s
2
X-J-
(-
Otn
x=
(,/ : =
xD=
../
r/ -I
YoL?
'/aat i
--+
^
5.1\ n/S\
I
?
t)
Tfl
t = x.t1e
t/aqt^
*, =