150
chaptel 6
triction
PROBTEMS
613 The force P is applied to the 100-lb block when it is at
lntroductory Problems
I
6/l
The force P is applied to the 90-kg crate, which is stationarf before the force is applied. Determine the
magnitude and direction of the friction force F exerted by the horizontal surface on the crate if (@)P :
300 N, (6) P = 400 N, and (c) P = 500 N.
Ans. @) F = 300 N, (b) r : 400 N
(c) F = 353 N (all to the left)
rest. Determine the magnitude and direction of the
friction force exerted by the surface on the block if
(o) P : 0, (b) P = 40 lb, and (c) P = 60 lb. (d) Wltat
value of P is required to initiate motion up the incline? The static and kinetic coefflcients offriction between the block and the incline are p" = 0.25 and
/.ft : 0.20, respectively.
Ans. (a) F = 19.32 lb (up the incline)
(6) F = 11.71 lb (down the incline)
(c) F = 15.21 lb (down the incline)
(d)P=48.8Ib
90 kg
=
_Jr" 0.50
/ luu=ono
Problem5/l
p s -- 0.25
lth = 0.20
6/2 The 50-kg block rests on the horizontal surface, and a
force P = 200 N, whose direction carl be vaded, is applied to the block. (a) If the block begins to slip when
I is reduced to 30', calculate the coefficient of static
friction 7-r,between the block and the surface. (b) IfP
is applied with d : 45', calculate the friction force .F.
FloDlem
b/5
6/4 The designer ofa ski resort wishes to have a portion of
a beginner's slope on which the skier's speed will remain fairly constant. Tests indicate the average coefficients of friction between skis and snow to be rrs = 0. 10
arrd pr = 0.08. What should be the slope angle d ofthe
constant-speed section?
Problem 6l?
j.,i",. ,t
P.oblem 6/4
A r t i c l e6 / t
6/5 Determine the magnitude and direction ofthe friction
force which the vertical wall exerts on the 100-lb
block if (o) d = 15' and (6) I : 30'.
Ans. (a) F :46.4 lb uP, (6) F = 40 lb uP
Problems 551
6/7 Two men are sliding a 100-kg crate up an incline. If
the lower man pushes horizontally with a force of 500
N and if the coefficient of kinetic friction is 0.40, determine the tension ? which the upper man must
exert in the rope to maintain motion ofthe crate.
Azs.?:465N
Problem 6/5
6/6 The light bar is used to support the 50-kg block in its
vertical guides. If the coefficient of static friction is
0.30 at the upper end ofthe bar and 0.40 at the lower
end of the bar, find the friction force acting at each
end for r = ?5 mm. Also find the maximum value ofr
for which the bar will not slip.
Problem6/7
6/8 The force P is applied to the 200-lb block A which
rests atop the 100-lb crate The system is at rest when
P is flrst applied. Determine what happens to each
body if (o) P = 60 lb, (6) P = 80 lb, and (c) P : 120 lb
= 0 . 5 ,1 t n =0 . 3
"
Problem6/8
Prcblem 6/6
= 0 . 2 5 ,P k = o . $
554
C h a p t e r6
Friction
6/17 A 180-lb man pulls the 1001b cart up the incline at
steady speed. Determine the minimum coelfrcient p,"
of static friction for which the man's shoes will not
slip. Also determine the distance s required for equilibrium ofthe man's body.
426. /,r,": 0.409, s : 5.11 in.
6/19 The wheel shown will roll to the ieft when the angle
a of the cord is small. When a is large, the wheel
rolls to the dght. Determine by inspection from the
geometry of the free-body diagram the aagle a for
which the wheel will not roll in either direction. If
the coefncient of static friction is g. and the mass
ofthe wheel is m, determine the value ofP for which
the wheel will slip for the critical value ofa.
r,
u mgr.
-A_n-s,._o -- _
"in fz
,r+
1r",lrij
,"7
Probtem6/I7
6/18 The uniform bar,4B of mass m and length I is leaning against the vertical wall as shown. The coefficient of static friction between the supporting
surfaces and the ends of the pole is pc"= 0.30. Determine the force P which causesimpending stip ifP (o)
acts to the right and (b) acts to the left.
Problem5/19
6/20 The homogeneous rectangular block of mass m rests
on the inclined plane which is hinged about a horizontal axis through O. Ifthe coefficient of static friction between the block and the plane is p, specify the
conditions which determine whether the block tips
before it slips or slips before it tips as the angle d is
gradually increased.
Problem 6/20
Problem6/18
Article 6/f,
6/21 The inverted track ? with freely floating rylinder C
comprisea systemwhich is designedto hold paperor
other thin materials P in place. The coefficient of
static friction is g, for all interfaces. What minimum
value ofp ensures that the device will work no matter how heary the supported material P is?
An* p = 9.263
6/2I
Problems 555
The figure shows a device, called a jam cleat, which
secures a rope under tension by reason of large friction forces developed. For the position shown determine the minimum coefficient g," of static friction
between the rope and the cam surfaces for which the
cleat will be self-locking. Also find the maglitude of
the total reaction -R on each of the cam bearings.
Azs rl. = 0.208,l? = 1471N
Ptoblem5/21
Ploblem5/25
6/22 'T}l'e system of two blocks, cable, and fixed pulley is
. ,,j ]Jlffally at rest. Determine the horizontal force P
'--r'
necessaryto causemotion when (o) P is appliedto
.r / the 5-kgblockand (6)P is appliedto the 10-kgblock.
Determinethe correspondingtension ? in the cable
for each case.
.x = 0.50
:r->P(b)
6124'Determine the range of weights W for which the
's--' 100-lb block is in equilib um. All wheels and pulleys
-''havenegligiblefriction.
p"=o.soI
pk= 0.25
|
P"= 0.60
Problem 5/22
Problem5/24