.
Questionsand Example Problemsfrom Chapter 5
Question 1
A ball is thrown straight up. Taking the drag force of air into account,doesit take longer for the
ballto favel to thelop of itsmotjonorforit to fall backdownagpin.
I_t-_
xr-tft :
J,ur.ic r 0:
Jta^ur:
,6-g
1D
?l
tt
rrr D
_*.
XF" L A^^arb\^\-fuvr*A
An"*
d,D,A^\) Nt
I
|l
n
u" 6?'Po4X' 'el^^tJta ot "tt'{1/2'\
+ ( "1"-€ ) AwAc^zi'
otn rt ifr,
\--l
,rttpl"^r*-;
ta Z^'-!b"aa
IJ\
U,
Question2
down the wall, what
If you pressan apple crate againsta wall so hdld that tFe-crateTannoTslide
is the direction of (a) the static frictional force .f on the crate from the wal1and (b) the normal
force fr on the crate from the wall? Ifyou increaseyour push,what happensto (c)1, (d) N, aad
(e){,max?
(") ,r+
fu" vrA
-:-
(u)
(.)
(l)
a-tf-*
^*..-;^"
....-=::_
t**
(f',".,.,.=ru"'n)
t ) @
Question3
In the figure below, if the box is stationaryand the angle 0 of force F is inceased, do the
foliowing quantitiesinctease,decrease,or remain the same:(a) F-; (b)I; (c) N; (d)I'"",.? (e) If,
instead,the box is sliding and 0 is increased,doesthe magnitudeof the frictional force on the
box increase,decrease,or remain the same?
aA
6{\
t9
I
F*
I
J
( a ) rJr^N-aaa
<1:-<
(i: a*:o, &
(b) ^W
(.)
lrur,+,ea-Ap
==:
\ b""rtat"^
(d)
N{6Jv44A9
(tj!.,Cdrr'^,
=:-
k\ ,ry
F-)
f':
F, )rrr^a-^na
f[\
/^\4;rAj-r'
*n)
1
€,*^*
(l"t^+'^'"5\
P^*,"au"Afr--'r.0)
=U,tr/ ,,\__,
Problem I
A 2.0 kg 6al1is suspendedby two light strings as shownin the figwe beiow. What is the tension
in eachstrine?
12ir,n 5b"
l-c5b-
I
rr = 2.0kg
T1 r-ao50"
Tl
F^i=o
Ta**,500-q1
=o
F* . {Y)4x.
t
=g
-T, 'o
Txa'b5oo-
na
-4t\ 5D"
T,
Tqtd5D"
f-;
(aa.orD c& 50"
A)/r,50'
-l-, =
l6 tV
Problem 2
ft1[E rcp*ffitne
A 1000kg steelbeamis supportbd
rrgrFu"lorv.ra"n top- can
suppo a maximum sustainedtensionof 5600 N. Do the ropesbreak?
r4. r(t{r"1\
R,,ne
Ronc
:
{rD.*-r,
r.'t-t be"afivt'.
Wr^n-,hC """^tM)
Iur,rtalroqn^ /rf)'4
-l;(aioTt
c,dl"3e.
-->'
= rcrax-D
tE
t\
Axn tT;" - l-^ -rrar^7O"-- D
rng
I,=Ta
XF,-
fqOy = O
-TycaSoo+T
1 ta7€-
-I-,
3., coo30- - rn g .=o
l-r = (lo..r<g)(q xo-/r')
S &d4 3Do
.=.
I+e
nnq
t
= \-/
I
'\
:
mq
---)a-
Jtal
E6 b s N -1 tlto *4-aa $^*^!\
Problem 3
The heliccipterin the drawing is moving horizontally to the dght at a constantvelocity. The
weight ofthe helicopter is 53,800N. The lift force L generatedby the rotating blade makesan
angle of21.0o with respectto the vertical. (a) What is the magnitudeof the lift force?
(b) Determinethe magnitudeof the air resistanceR that opposesthe motion.
L /co. xl"oo
A
I
F"*t ="
X FV: fqay =o
{r)Qx=D
L a,n^xl.oo-{
4 = L*.
L : /,ae,-o"
=
F^*t =o
XF*=
/-cd4f l,o" - u) = o
'-/
L-a;r'rAl.o"
E3,sooN
<
5"?6ylO?JV
=6
al-o"
- at.00
A.lf)
= (tr,?{"xforrNr)
\-/
Ct" 0,|.6"
Problem 4
A rock ofmass 45 kg accidentallybreaksloose from the edgeofa cliff and falls straightdown.
The magnitudeof the air resistancethat opposesits downwardmotion is 250 N. What is the
-)
magnitudeofthe accelerationof tle rock?
.D
,)
| 1
I
r
-gt
oQ /44K'I\ o^9 :
,(4 ("ts)
o' "ta;X"w (Sl
I
?
I
I
l, r"*
J--n
u)
2tr. = NAy
a.t=tYn
I
= (P-tt'g)
I'oi
a) '- D/*- 3 .=
a' = 4.2,af92
(>so N
q.zo*/s'
- 1.9? m/5)= - Ll,a^/x-
Problem 5
A 95.0 kg'personstandson a scalein an elevator.What is tle apparentweight when the elevator
is (a) acceleratingupward with an accelerationof 1.80mis', (b) moving upward at a constant
speed,and (c) acceleratingdownwardwith an accelerationof 1.40m/s'?
tt.
t..
I
F= mqy
): Fy
<---l
I
?
----*
T) - r-,: = rqqy
I
v
{Y, 3 + N\ aV
=
9q) +fY\(11
I
-----*
*a'att'^
"++-r-.)
\ = * (g*or)
t
=
\
Fi
i/." ff a4"^rfi,lg 4 V^, cr"f;A$'^*
tatt++"X
A Pa^A'it\
u)rr.p= m(g+ay)
= l'l0r)o)N
o=+f.8om/sr --) LD*m=(ls,ora)(9'rDm/5a.-l.vam/se)
b) o = O,n,/s]--) to-n* = Cc5.oV\(9,yo,r'/s'+o)= 931 N
-- (n,oY+)(z"zon/5, '1"4onf
o.= - l.46nlse -+ u,J
s7)= ?9sN
+o
:)..
Problem 5
a)
A 1000 kg car is traveling at a speed of40 no/s skicis to b halt on wet concrele Where & = 0.60.
= tn4 ifu'r rr-tr
,dx
X tr, = N\av
-d
4-- ---------)
AX
X tr" : rY)Ar
- fO = [r)4x
_ )^(ry\ _ rrtex /
( V* ).'
=
' " l u t \ /I - <
(v*)r .
O on19
4* = - 5"1o nl5
Ax =
l-o=o
\=*-fr)$
nlea)
1\t \ = /lDoolcql6q.3d
--\
4x- -&!\
ft
- ( o.t"o) (g,ro* to3r..r)
?.YDx\03 N
\
( too- pt;
,
. )
(V*)f
/
,\
= LV.),
,r
l,
- 1z".rr ) t r' / A
e,,
=
AX
AX = l3t.t --
-+
a eqxAx
--
D = (/*),3*larax
y:%.(-s"e-/s)
4.X= l"lxto'y.r
probtem./
LlS"olY
- /w =- -{6^ft^
s1
rrr =0/n
= 4'51(g
A block who'seweight is 45.0N restson a horizontal table. A horizontal force of 36.0 N is
appliedto the block The eoefficientsof static and kinetic friction are 0.650 arrdO.420,
respectively.Will the block move under the influence of the force, and, if so, what will be the
block's acceleration?
Explainyour reasoning.
)
4 3b,o N' t fr,,o, , ll rna.I*n\ u.fu rr^.,c",
fr = ?o.ottt tuAgl,c\;ru
r=3o.
"-;^
a.r^"44)
;,Fr= fhey!o f- 3=u
:fr' n fl, F
4\= -= 4s.oN
J
--5
\t)
-/
A^A0
,,^.*-.,{ttT\=
5 to"o,N. ,2 +, s ) m q x)
+ 7r^rh;" u
"L24,A ryn-""J
\--,
-
/'s
) ' , 1 - = tI ^' 'a- .\ .^ . - 4
4x
( o . 6s _ oC
) t9.aN)=
el"xs)\\
=tn = F-9,
(30-"N)
(0.".r)(qsd
r) - (0..rroj(q5.at9
A* =
Problem 8
A 70.0 kg crate is draggedacrossa floor by puliing on a rope with a force of 500.0N at an angle
of 15.0' abovethe horizoatal. lf pr = 0.35, what is the accelerationofthe crate?
'l- =
SooN
\
T.oi^'t5'o"
ptals.o"
+, l <
X F, = rid', =O
\
+-i-a,n*'ts.oo*
hg-*a
\
= f.ng-Tf/'r l1"o.
\
-r (
to"oyz) L9"ro,1
r,1- ( soo,o1)-al.I 5. o.
I tr- =foAx
4\= ssrN
qv
u > =m 6
t ,l = tcrt
F ,,oart.oo-S* = rn4*
Fc.oaf5.o"-l,t.o|1= roex
rai
" r*,
I ooatSo'-)Ls\
= (E oo, oN) ca t5.o. - (
0,35) (557N)
(lt,otg)
Ll.l' fs"
ll ,= 3'561<?
fra= A,to(g
Problem p
A 3.50 kg block on a frictionless tabletop is attachedby a string to a hanging block of mass2.8
kg, as shownin the figure below. The blocks are releasedftom rest and allowed to move ffeely.
(a) Is the iension in the string greaterthan, lessthan, or equalto tle weight of the hangingmass?
(b) Find the accelerationof the blocks and the tensionin the string.
( 4 ) \8 j$o 1-xo Xs -tl'.r/t ^^ fi "$tps"'L
-f
, ,^rt ,cn-u-aitt ^ra
< ur
p" namwt'r"' p^^h
: W),s^"v"6 i;
"-00
}.,,rn
auslr^
1)d' n^aq^rt^k,4 eail lpe"bt=
fit *-. ( 4,.^'.afu o"'o'cn''v"Ju) )
( b) ^4
I'94<\:
3-5oVt
!r%4>\ |
^,s"tra
XFy=nor
1,'f
I
l
,
l/
(.Da
t pdl'cQ t4A.L
{ r"*
Y
T-
rra -- rqa (-^)
= -f.";l-aa4'L'
II r- *;";
- d
l+-
1 no"/a( m/ , . ' t t )
F ), A - f f a 3 = - i l i " q
<--.---_
a.bora\(q,r}nl),
l Y l, 4 + r n 4 Q = f a a g
A - = (----Tt
, =Wilrrl
Problem10
A 23kg childgoesdowna r*'ei?#at fl;JriL%8'F5#e-tF#ontal. rhe childis actedon
C\=
by his weight, the normal force from the slide, kinetic frictior, and a horizontal rope exerting a
30 N force as shown in the freure below. How larse is the normal force of the slide on the child?
J
tv-
fl
vt
T=3oN
\x
u) : M B
t
XFr=mr a)=o
X#-='
oA
tD ,Aa )S'
\
F
'
/{Lct
ll,o.ri 3!." - ,,.r'coe37D ' A
"
= ,r, ue3g- --'T.,trn3t"
"D = ( A34j(e:Bo^/"r) @3t" - (?on ),,rurZg-
T'l : / 5q N ----) otr\= t' 6* lo' N
Problem 11
A box is siiding up an incline that makesan angle of 15.0"with respectto the horizontal. The
coefficient ofkinetic fiction betweenthe box and the surfaceofthe incline is 0.180. The initial
speedof the box at the bottom of the incline is 1.50 m/s. How far doesthe box havel along the
incline before coming to rest?
--+
l-^'.r*
\
I
^f\
aF, = may --6
I
Ar"
o
= Lo c-,t}3 0
- mqc-bao
\-wur:Q--o
\,rrg to o
w-cdp
X F. = N)Ax
-
frr* wrv.o
= loAx
f< ="tari|.) = 'alt ('m g4xo)
- ^^FmL(.o1O-mg+"ng = N)Q^ --?
4r =
-A,rX@g-
$sr06v
Ay = - ( r" tto) Cl,to */s^) cnls,oo- (l.to*o/5") ( s'n ls'o1
= 1"5o*fs,
\ vx / c'
tvr )+ - O^/s
g = (V.)] * 0,qx A x
-4":.1 ,^n
/s\
AX =
(u")i=(v.);r- Aq*AX
?
-!!t
=
ax
]qt
Ax'=
t--l--t
llr=
I
- ( t"g o ,n1s
)r
f['fil",7";
o.at"5d