479 Horizontal Motion: The horizontal component of velocity ... - Wuala

91962_05_R1_p0479-0512 6/5/09 3:55 PM Page 504
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*R1–36. The rocket sled has a mass of 4 Mg and travels
v
along the smooth horizontal track such that it maintains a
T
constant power output of 450 kW. Neglect the loss of fuel
mass and air resistance, and determine how far the sled must
travel to reach a speed of v = 60 m>s starting from rest.
: + ©F x = m a x ; F = m a = ma v dv
ds b
P = F v = ma v2 dv
ds
b
L P ds = m L v2 dv
s
v
P ds = m v 2 dv
L L
0
Ps = m v3
3
s = m v3
3 P
0
s = 4(103 )(60) 3
3(450)(10 3 ) = 640 m
Ans.
R1–37. The collar has a mass of 20 kg and can slide freely on
the smooth rod. The attached springs are undeformed when
d = 0.5 m. Determine the speed of the collar after the
applied force F = 100 N causes it to be displaced so that
d = 0.3 m. When d = 0.5 m the collar is at rest.
k¿ 15 N/m
F 100 N
60
d
k 25 N/m
T 1 +©U 1 - 2 = T 2
0 + 100 sin 60°(0.5 - 0.3) + 20(9.81)(0.5 - 0.3) - 1 2 (15)(0.5 - 0.3)2 - 1 2 (25)(0.5 - 0.3)2 = 1 2 (20)v2 C
v C = 2.36 m>s
Ans.
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