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Unformatted text preview: 135. A block having a mass of 2 kg is placed on a spring
scale located in an elevator that is moving downward. If
the scale re ding, which measures the force in the spring,
is 20 N, dltermine the acceleration of the elevator. Neglect the mass of the scale. 20 I0 Equation of Motion : +T25l=ma,; 20—l9.62=2a a=0.l90m/szT Ans 2148!) =/ 5761/ *136. As a point of historical interest, the acceleration
of gravity g used to be determined using an “Atwood
Machine,” which is simply the arrangement of the blocks
and smooth pulley shown. ln an experiment of this type,
consider block A to have a mass of 2 kg and block 3 a
mass of 2.6 kg. If it is observed that B descends 3 "l in
2.2 5 starting from rest, determine the value of g. Di rcuss
what effects must be considered in order to increas the
accuracy of this experiment. 1
Kinematics : Applying equation s = so + on t+ 54,12, we have (+t) ‘3=o+o+—;a,(2.2‘) a,,=1.240m/s2 Equation of Motion : Here. «A = a, = 1.240 m/sz. Site: .56 cord passes over
a smooth pulley, the tension developed in the cord is the 5:5" zhroughout the
entire cord. Applying Eq.13—7 to FBD(a) , we have +TZI';=ma,: r—2g=2(1.2403 [ll Applying [5413—7 to FBD(a) . we have
+1Tzr. =ma,; T—2.6g= 2.5(— vJ)‘ [2] Solving Eqs.[l] a‘tid t? . yields ‘ g = 9.50 m/s2 Ans
T= 21.49 N ‘ The following effects list be considered in order : use the accuracy of the
experiment: ‘
Reduce the dis or fall and thus the ﬁnal spea % the blocks so that air
resistance can It: .zeed. '
kednee the Ms of pulley and cord or account for these mass in the
alculation (as in ct. m 17).
~eduoe friction“ the , allcy's axle. 128 a. l ##240/0/5” (a) ”i
(b) de‘r'i'wm/S ll 1318. The man pushes on the 60lb crate with a force
F. Thelforjrce is always directed down at 30° from the
horizo taléas shown, and its magnitude is increased until
the cr te begins to slide. Determine the crate‘s initial
acceler tion if the static coefﬁcient of friction is m. = 0.6 '5 g and m kinetic coefﬁcient of friction is ”=03. Force to produce motion : .3}; =b; Fcos30°0.6N=0
+T2ﬁ=l0; N60Fsin30"=0
N=9l.801b F=63,601b smoc~=91.al)ib. Jam". ‘ so
= ,; 53. so°o. 91. —
ma 6060: 3( 80)=(32'2)a , l
1 i
l
l a = 14.8 ml Am 1322.; The 1le block 'A is traveling to the right at
21,1 = Zlft/s at the instant shown. lf the coefﬁcient of kinetic frictiorLis pk == 0.2 between the surface and A, determine
the veil city of A when it has moved 4 ft. Block B has a weight lot 20 ll). BlockAj: 94 Io/L
l . l ; 10 (—zE‘Fmbx. T+2=(m)a4 (I) T.
; ‘ egg/apes Weights: N=/0/£
‘ i r 7' +~L2F,¢=nta,: 2047:6293)“ (2) g Kinematicss ‘ J“!
= 34+2.r.i=l?
aA='2d‘l (3} 20/6 Solving slur(3): 54
a4él7‘l73ﬁ/sz a.=l3.5237n/s2 T=7.331b I
V=Vé+ ctsSo)
v1 = (2)’+2(l7.173)(4—0)
v=ll.9fL/s Am _——"?—"’— —>a &.
V .——__w l_.. .—_~._.—__.. 13in. The IOlb block A and the 20lb block B are
initially at rest. If a force of P = 20 lb is applied to B as
sh wh, determine the acceleration of each block. The
coifﬁbient of kinetic friction between any two surfaces is
pk‘= 0.2, and the coefﬁcient of static friction is u, = 0.3. NaﬁmA slips on B as B slips. Blodt A: 2 Q 10
—9 EF, l= 1pm,; 2=(§TZ)“‘ 04 = 6.441’t/s2
Bl B : . 20
—) ‘5} =ma,; 206—2=(ﬁ)a, T a. = 19.323131
NotetlmtforA. F", = 0.3M = 3 lbmd ifA was none slip onB then. fotB. c ‘ 2° —
all}; =ma,; 206—3=(§Z§)a, a, = 17.71 ﬁls’
Thus. ForA.
a,‘ = 6.44 ft/s2 .+Zlv‘,=ma,; 3=(‘° )a. =9.cs:sn/s’<17.7m/s2 OK AllipaonB. m a, = 19.3 ft/sz Also. 1“ the ground. F... = 01300) = 9 lb < 20 lb. so indeed motion occurs. 143 \
i
i
i
i
\ 1334. If 5 Horizontal force of P = 10 lb is applied to
block/1, etermine the acceleration of block B. Neglect
friction. int: Show that a” = a,‘ tan 15°. Equation of Motion : Applying Eq. 13~7 to FBD(I) , we have ¢ 8
= ; lO—N ' ° ——
—) Elf, ma, ”sin 15 = (32.2)aA l3r7 to FBD(b), we have 15
FiTEF;==ma,; N.COS 150—15=(3—23)ﬂ. K incmatic: : me the geometry of Fig. (c).
.r, = a" tan 15°
Taking time derivative twice to the above expression yids a, =aAlan 15° (Q.E.D.) [1]. 1212mm yidds a, = 5.68 ids’
«A = 2122 {115’ N, = 13.27 lb ...
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 Fall '08
 Hudyma
 Dynamics

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