Questions and Example Problems from Chapter 6
Question1
If youpressanapplecrateagainsta wall sohardthatthecratecannotslidedownthewall, what
is thedirectionof (a)thestaticfrictionalforcefronthecratefromthewall andft) thenomral
forceFNonthecratefromthewall. Ifyou increase
yourpush,whathappens
to (c)f,, (d) Fn,and
(e)"6.'*?
-4|II
n
r-Jl
"---vl II
(")
"r\
+lavrd
1
| L.-B\o
-1-=:_-_
Dr<!9
C =.g
,*,ffi)i'-A^,*G)
-.':
'
z t\
td
))ry4
t-l
Problem 1
/ t-)
l=
'
te) ryw
A personpusheshorizontallywith a force of220 N on a 55 kg crateto moveit acrossa level
floor. The coefficientof kinetic friction is 0.35.What is the magnitudeof (a) the frictional force
and (b) the crate'sacceleration? d\
f- +
1
Xr'=rr)Q' =6
F='rroN
J
yrr?
\ - ng =o ---rrT\--rc,s
l=(ssrc516q,so,,/s)=
_g
O.56nftt
rq
problem 2
55 Fg
A 2.5 kg block is initially at rest on a horizontalsurface.A 6.0N horizontalforce anda vertical
force .P areappliedto the block asshownin the figure below The coefficientsof friction for the
block and surfacearep6= 0.40 and |rr = 0.25.Determinethe magnitudeanddiregtionofthe
frictional force actingon the block if the magnitudeof F is 1a;S.0N, O) 10N, and(c) 12N.
C"oru
e:
/,1
t
XFr= fQav=o
W
.fu
$ f',*,* 2 6.on.r)
: c-o.
;'4
blt\n'-\*4
(
€,,,."o t.oror
*,,J +tDf'^' A
J'*;rL +"^h,a ( fo={n,y1)
,i\* P- -?=o --+ n[1= rrrg- P = (r.soFs)
(t.to*fr,) - | ---+ = ll"SN _p
"f\
(")
\=
(.b) \=
aa.SAr -l.oru = l{o.b.D frr*rry=u,I
"
- (,,oo b.btr
= (o.ro)(ro.s.;= 6.6r\)
= /?.snl f,,*^a.f.Sn)-ion-r
=l, tf\ = (0"+'7
irv-st; = 5.r A)
f,,*^*=l,rf1=10"+
= 3.r,ro __+ f" = S.6n'lF"&-0"+f
f,<=rroq)= (D.rc)(11-5ru)
Problen 3
A loadedpenguinsledweighing 80 N restson a planeinclined at 20" to the horizontal(seethe
figure belovr).Betweenthe sledandthe plane,the coefficientof staticfriction is 0.25,andthe
coefficientof kinetic friction is 0.15.(a) What is the minimum magnitudeof the force F,
parallelto the plane,that wiil preventthe sledfrom slippingdown the plane?@) What is the
minimum magnitudeF that will startthe sledmoving up the plane?(c) What valueof F is
requiredto movethe sledup the planeat constantvelocity?
-)
W4/
VZa
)>'
V;*&
I'n
-....
r
P'"J uAlA
/+.^-{-,{ tr.ra'.^1l9u *l-^ \r^N'Yh +"'^t
/Arq
,: .,i
-rA
fr,.*
--':-=:-
lt
\lrF
Y/
=A'Y\
I-
/
\
\/'_x
4a\
Xf,/=foqy=o
ol) * rg c.64O
=o
=
tF-=frra^=9
trn f.-hga,rrDO=o
*m3a41e
^ i"
\r\3''d4o
(")
'\
-
-t""'o/
\,,'
,.x
|\\r.xa rv
ztr
\\,
fqt coag
1xl
a,;::-l-"'
if)
:
ts=6"n)i*ao- (o,as)(rs,rt)
W
,n,o*tu"A.,e f.,ror=/-{r4)
:Fy=rro,=o --) T'l =ter-oa$= ?s.AN
=c)
tF*-Ntax ---r F- fr-mr1a,v.'",O
F = mga,arog+1rff1 = (SbN).iJr"oAo.+
1o.ts)(f s ,N) =@
4,u, aut ra ruraw;v.6
4t7}u p!p,"a) < ,n-'n*
,,'a^),/.,.;^t;'&W"
.l(
p-- m3^'he- fs'= mgi't"9-lf
H\e,\ ft +iv"n dtd"\ Iat pl,^^At\,.,*b
"
frl
\-"F
e6t/\
rrt' &vntt"n
.
,c
LO= r",?
21,\^ b' PIA^I)
-r
' A"+W
'r
Nf-',
u
n
/.t't, 19, 4AAn'J d'") }'^4 fii
fs f*"b
N-h)t
0ll
tu ))d
a"J p"..,',bA,'',qfiu
r"a;Lg)
P*\ 4^;'h^
b
pU'r,,a
nl = roX@O. ?5"3N
:tr) = reoy=o -----1
fn=rlonl
Xf-= N\o,r=o----+ ,E- r.rgl,,r.,&-f,.=O
f = mguno+r rO = ( tors)-"r0".r (o./s)(?6.3N)
,E= 39N
Problem4 (Problemfrom Exam I - Spring2002)
In the figure below, two blocks areconnectedover a frictionless,masslesspuiley. The weight of
block A is 50 N andthe coefficientof staticfiiction betweenblock A andthe incline is 0.20.The
angled of the incline is 30.0o.What is the maximumandminimum massthat block B canhave
suchthat both blocksremainstationary?
frui ly.rl, A /.4-'1 W ro<^a"6 /J.i+^*A /4\t"
N"il-re A. +r=f,,.\^,, ft""J{rre &
V" )^,.g^\,
't-Qruar g
',7
T-Do=6
I
-1-=
I,B
)
ure ( r )
1- V-"*
p+l},,A:
\-,
f-
a) =o
)_,Fy=h
l5
u)p9 taO
)j F* - tf)A* =D -;
we'ote
ol : tDq ceoQ
-,
l--
r-D,\,5.r^lO-f, = O
o
c4ao = ( sor.l).a;q:o. o"1
1o.ao)(sa6)oa\l"
tDF = 33-ZN
-/
P.
---.--\
1.f\
- 33.?Nl
/ 1'x",/r'
^{rYur.n M(qh^'aA1 -b!4wA\ B
",rr\ }rArv" /h-{l',.ru #,^j
rnB=. - 3-t) Ys
ll.r\
A p
,a, b*
hl,<^*".
XR=
T
a
tclo.r=5
-f*
T= wo-A,tnO-f, +
l^)B= trAi)^t0
LDqg'.r o
Wa rzaD
f,-dAar.rb
:o
T= uon,a;;'..'O-l,lr1)
-1.t. (w*r.cO)
\___,
Lds = (56N) o,.3o.o"- ( o.ro)[so N) ta:]o.o- _) 1 " . 3N
t\o= 0"/o
t
<t'
I L'3^/r."on1r'--,
=
i Fru l.?l1s
Problem5
Block B in the figure below weighs71I N. The coefficientof staticfriction betweenblock and
tableis 0.25; assumethat the cord betweenB andthe knot is horizontal.Find the maximum
weight of block A for which the systemwill be stationary.
uo^qht Xp bA&\ A ^."r,a^a
)
F;
ltW. B},l ^r b* rv+r'4totruM,
*o
ft= fr,"^* = /l"ff)
$.,.ra nIAt\
)n"4"f\"j"
$Z
€
tF, =nay=o
r^A
'
^n
nn
'1\
-tl" =O
----r'Y')'r.rD
------'))
= ?ll N
+===-
!F-=fo^* =6
-[G :" -r
\= f, = !"1)
--r
JD., 3".-" o1,& g.,l :
-Wy
=
\= (o.ts)(r,rr.r) t? rN
Tq
Ta-0)qo
l*<aae
(=lDo*=o
luLo" O -T, = o
Jr = f,/r-n
l?rN
<&30 ..
----J
T1 = Ao551
Xtrr-Mar=6
7"
-Al^q O
-@A=o
Ua= lo3N
-+
_.F.
trft-- I aA/Vn fJ = (xosN)
-axn36"
Problem6
Supposetlle coefEcientof staticfriction betweenthe roadandthe tires on a car is 0.60 andthe
car hasno negativelift. What speedwill put the car on the vergeof sliding asit roundsa level
curveof 30.5m radius?
/ +{ /
I I ln
/ p[+!
l'.J[
I
\
{+
\ \v
\
L
XF-=Ir)Ax
(
|
Ts
l.D=f,)g
Fr = ftt ov -o
)
o-'"h" ') N'\u.tti
-l.n
-
= mz
4
f.--. (,7,)
1 -a,Yvtl c-Dl '14o-'"Je,w
4 W^u
f"
-
|s,,n*x
,
= f-\, dI\
v='l )^srz
,u/.?
V: 'l (o.t".1Qo,v-)(7.2o.1r1
=
Problem7
t{9
As shownin the figure below, a I .34 kg ball is connectedby meansof two masslessstringsto a
vertical,rotatingrod. The stringsaretied to the rod andaretaut. The tensionin the upperstring
is 35 N. (a) Draw the free-bodydiagramfor the ba1l.What are(b) the tensionin the lower string,
(c) the net force on the ball, and(d) the speedof the ball?
lra.rt
D.t5rn
-[ =
35nl
t-| -
-:- ..
lrr'L4frti
| uh
l.lrr.t
,J
Ia4
I
f
DJ
I t)'vt
I
=ma)'o
--T.
l^
O -
ll.d-t"n 6)
= (35n:)-Urn3o-o'JL^\
(.)
Ma=6
=
-i-l
v
f'\ t7
-& O--1
*4,,\le
?,zoof 5')
J^ = 9.?N
JO"
)r;^, Xtrv=o.,;l. ^A+e1*";"Jr^^*yl=- -J,.-o-oDtTico.O
(:.tN) .or3o'-----+Xtrr=3?.tN=Fq
ttr^ = (:sN)tr,:3o"+
v =6,4 nf5