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Unformatted text preview: PROBLEM 13.182 A 31b biock B is attached to an undcfornted spring of constant * “"1””1 it = ﬁt] 1th and is resting on a horizontal frictionless surface when it is
struck by an identical block A moving at a speed of 16 Ws. Considering
"$1.1ccessive13rr the cases when the coefﬁcient of restitution between the two blocks ta {1} e — 1 {2} e: D, determine L”) the maximum deﬂection of
the spring, [33} the ﬁnal veioeity of blockA SDLU TIDN Phase I impact
Conservation of total molnent'tnn
.+ vaA + new}, = mﬂiﬂ + Mair}: lﬁ = v_'_, + v}:
Relative velocities
[v.1 ‘ vﬁ}€ = (”is — “iii 3 “is — “it =16“:
Solvingtl] and [2}; u}, = s[1+ e], iii = s{1— e]
e: I: thiﬁW$.1r‘:r= [l
e = I]: v'Er =3f‘b’3. vi, = 8W5 {a} Conservation of energy phase II k=oﬂlwﬂ
v}; =isﬁo, if, =0 l l “was Elb 2 32.2 on?
{isaa}2 =11.sas; V, = o l _ n
I = xmax' T2 = 0; V2 = E'Ii'F{'I‘.1nnnJ”.I = EHI‘ nus PROBLEM 14.5 A. system consists of three particles... A, B. and C. We know that
mr1 = m3 = 2 kg and m5 = 14 kg and that the 1ia'elomties of the particles, expressed in mfs are, respectively, V; = Mi + 21j, VB =—14i+21j,end
”r: = —3j — 2k. Determine the angular momentum IlU of the system about 0. SDLUHON Position vectors expressed in meters. rA = [LSIi +1.3j. r5 = LSj + ﬂﬂk, rc = 0.9i + 119k Momentum of each particle expressed in kg m3! . “NA = 231 +421. mews = —23i + 42j, matIt. = .42j _ 23k
Angular momentum of the system about 0 expressed in kg  mitts. Ho = rA x {min} + 13 x {mtpug] + r: x [mcvd
i j k i j. k i j k
= '33 LE {1 + [I 1.3 [1.9 + 0.9 [1' 13.9
23 42 U —23 42 U '0 411 —23 = [—12.6k} + [—313i — 2521' + 50.41:} + {318i + 25.2j — 31.31;}
= m + :3] + cs PROBLEM 14.13 A system consists of three particles A, B, and C. We know that
ms = 3 kg, m3 = 2 kg, and mt. = 4 kg and that the velocities of the
particles expressed in rru’s are, respectively, 1;, = 4i + 2j + 2k,
v3 = 41 + 3j, and vc = —2i + 4j + 2k. Determine the angular
momentum H0 of the system about 0. SOLUTION
Linear momentum of each particle expressed in kg  mfs.
”2/va =12i+ 13] + 6k NibV5 = 8i 'l' ﬁj
mcvt. = —Ei + 16] + 8k Position vectors, {meters}: r .4. = 3j. r3 = 1.2i + 2.4] + 3k.
Angular momentum about 0, [kg mifs}. H0 = rA x{mdv‘4}+rﬁ xlmgvﬁ} +1} Klimtv5]
i jk i j I: i j k
ﬂ30+12143+160ﬂ
12 IS ti 8 6 {1 —3 If} E
={1si— 36k] + [—131 + 24j—12k}+{_2s.sj+ 516k}
=ﬂi—4.Ej+9.ﬁk Ha = —(4.so kgmge‘sh + {9.45s kgnﬂs] Ir «1  _. —.._._...___ ::.. H... " 1"1‘I'u I PROBLEM 14.21 In a game of pool, ball A is traveling With a velocity vn when it strikes
balls 3 and C which are at rest and aligned as shown. Knowing that after
the collision the three halls move in the directions indicated and that
v” = 4 mfs and vt. = 2.1 mts. determine the magtitude of the velocityr of to} ball A, [in] ball 3. EDLUTIUN
Velocity vectors: v“ = v.3.[cos 30"i + sitﬂﬂ‘ﬁ} V v_,, {sin T.4°i + cos 14“ j]
v13: Va sin 49.3% — cos 49.3%]
i “o = vi. cos45°i + sitt45°j}
Conservation ofmomentum:
mm = Fiﬁ"A + mHvH + chC
Divide by iii4 = m3 = int. and substitute data.
attcosIitPi + sin30°j} = main 14% + cos Maj} + v3[si1149.3"i — cos 49m}
+ 2.1{cos45°i + sin 45°j} Resolve into components and rearrange. i: {sinistﬁvA + {sin49.3°]vﬁ. = 4oos3ﬂ — 2.1cos45" j: [cos 14°}er — [cos 49.3”]v3 = 4stn3t] — 2_lsin45°
Solving simultaneously, {‘1} VJ = 2.01MB ‘ {bi v3 = 2.2? nv‘si PROBLEM 14.24 Two spheres, each ofmass m, can slide freel}.r on a frictionless. horizontal
surface. Sphere A is moving at a speed v” = Id ft“s 1tvhen it strikes sphere
B which is at rest and the impact causes sphere B to break into two
pieces, each oi" mass mil Knowing that 1].? s after the collision one piece
reaches point C and {1.9 s after the collision the other piece reaches point
D, determine in] the velocityr of sphere A alter the collision, {Err} the angle
I9 Emd the speeds of the two pieces after the collision. EDLUTIDN
Velocities of pieces C and D aﬁer impact and fracture. 9 ﬁts, {VB L = 9tanﬂﬂ° fb’s Tﬁi‘s, {v13}? = TtanHﬁ“s Assume that during the impact the impulse between spheres A and B is directed along the x axis. Then. the
3/ component of momentum of sphere A is conserved. t} = miiviij
Conservation of momentum cl" system:
L' mgl’u +31”sz = mell'lll + me {ill}: + "townh I?! sine} + ti = mg + Em} + 3U}
v} = set: it"s—e 4 +1: inﬁll} + mBlIt'JI} = "7.“:th + ”Tclvl‘ll + millviih. [i + t} = t} + gEQtaniﬂﬁ] — l—g—{Ttane‘l} tam;l = EtanEil‘j = [IN23 t9 = 36.6‘7‘1 T
up. = I'M]: + {up}: = Jigs}: + (steamer)1 1;: =1c.3s tits1
v” = div'2‘]: + (Vol: =1I[:?]1 + (TianE'ttthi')2 VD = 3.?2 ﬁts *1 ...
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 Summer '06
 

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