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Unformatted text preview: Problem 12—107 The car travels along the curve having a
radius of R. If its speed is uniformly
increased from v, to v2 in time t, determine the magnitude of its acceleration at the
instant its speed is v3. Given: v1=15E t=3s
S V2 27 R=300m m
4.22 — N Problem 1211 1 At a given instant the train engine at E has speed v and acceleration a acting in the direction shown.
Determine the rate of increase in the train's speed and the radius of curvature p of the path. Given: m
v = 20 —
s
m
a = 14 —
2
s
(9 = 75 deg
Solution: a, = (a)cos(6) an = (a)sin( 6) m
a, = 3.62 —
2
S
1’11
an = 13.523 —
2
S
,0 = 29.579 m Problem 12114 The automobile is originally at rest at s = 0. If it then starts to increase its speed at dv/dt = btz,
determine the magnitudes of its velocity and acceleration at s = 5,. Given:
d = 300 ft ‘ I
p 2 240 ft o 1
ft _ A} p i
b = 0.05 — ' t 4 V; \x
S “\E
_ X
s] = 550 ft ‘
Solution: 1
I
b b l2s1
(1,:th v: —z3 s: —t4 21: t1=19.06ls
3 12 b
b ft
v1 = (—jtﬁ v1 2115.4—
3 s If S] 2 550 ft > d = 300ft the car is on the curved path 2
2 b 3 v
: = _ = _ ft
at M v (3)11 an p a 2 laf + an2 a = 58.4043 5
If S] = 550ft < d = 300ft the car is on the straight path ft ft
a, = btlz an = 0—2 a = ,laf +an2 218.166—2 S S Problem 12—139 The slotted fork is rotating about 0 at the rate 6 ’ which is increasing at 6 "when 6?: 6,. Determine the radial and transverse components of the velocity and acceleration of the pin A
at this instant. The path is deﬁned by the spiral groove r = (5 + 49 / 71') in, where 6 is in radians. Given:
9:33
s
gl=2ﬂ
2
s
b=5in
1.
c=—1n
ﬂ'
61=2ﬂrad r=b+c¢9 r'=c€ r"=ct9" Problem 12—139 The slotted fork is rotating about 0 at the rate 19' which is increasing at 6 ” when 6: 6,. Determine the radial and transverse components of the velocity and acceleration of the pin A
at this instant. The path is deﬁned by the spiral groove r = (5 + 6/7!) in., where 0 is in radians. Given:
(9:3ﬂ
5
0.2292
2
s
b=5in
1.
c=—1n
7r
61:2/rrad Solution: (9 = 61
r=b+c¢9 r'=c€ r"=c€" H vr=r vg=r67 ar = r" — r19 ag = r49" + 2r'0’ ‘ in ' in
V, = 0.955 — ya = 21 — a, = —62.363 — *Problem 12—152 At the instant shown, the watersprinkler is rotating with an angular speed (9' and an angular acceleration 0”. If the nozzle lies in the vertical plane and water is ﬂowing through it at a
constant rate r', determine the magnitudes of the velocity and acceleration of a water particle as
it exits the open end, r. Given: 1 I *LWQMWV _
49’ = 2 .m_d ,9" z 3 52
s 2
s
m
r’ = 3 — r = 0.2 m
S 'a wmﬂme—waM‘. , ,W
Solution: 2 i it
,2 2 m
v = r + (r67) v = 3.027 —
s
2
a = (402) + (r67' + 2r'6’)2 a = 12,625 312. S Problem 12155 For a short distance the train travels along a track having the shape of a spiral, r = 0/49. If it
maintains a constant speed v, determine the radial and transverse components of its velocity
when 6: :91. Given: a = 1000 m v = 20 2 61 = 9 % rad
3 Solution: 0 = 01 r: 79 92 6462 5 II
N‘
5 II I r .N m ,
O
N Is Problem 12173 If the end of the cable at A is pulled down with speed v, determine the speed at which block B
rises. Given: Solution: vA=v
L1=SA+2SC _VA
0=vA+2vC VC:T L2=(sB—sc)+sB 0=2vB——vC VC 7 m
= — = —0.5 —
VB 2 VB S Problem 12—179 The hoist is used to lift the load at D. If the end A of the chain is travelling downward at vA and
the end B is travelling upward at v3, determine the velocity of the load at D. Given: T
E W
W w w aw Solution: L=sB+sA+2SD 0=—vB+vA+2vD VB — VA ft Positive means down,
VD = — m z —1.5,— .
2 S Negatlve means up Problem 12199 At the instant shown, cars A and B are traveling at speeds VA and v3 respectively. If A is
increasing its speed at v'A whereas the speed of B is decreasing at v'B, determine the velocity
and acceleration of B with respect to A. Given:
30 mi
v = —
A hr
20 mi
v = —
B hr
mi
v'A = 400 7
hr
mi
v’B = —800 —2
hr
0 = 30 deg
r : 0.3 mi
Solution: 20 )3 vBA='26.458Ei _VIA
aAv = aAv =
0 am _ v’3[_sm(6)] + Efﬁe) 1.555 x 103 mi
an = 7
—26.154 hr ——' laBAl = 19553; aBA = an — aAv aBA =
' hr v hr *Problem 12200 Two boats leave the shore at the same time and travel in the directions shown with the given
speeds. Determine the speed of boat A with respect to boat B. How long after leaving the
shore will the boats be at a distance d apart? Given:
ft
VA =20— t9] =30deg
8
ft
vB=15— 02=45deg
s
d = 800 ft
Solution: —sin(61)
VAV _ VA 003(01)
vAB = vAv — vBv ivAB = 21.673fE t = 36.913 3
l l s ...
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 Spring '08
 Priezjev
 Velocity

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