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

91962_05_R1_p0479-0512 6/5/09 3:54 PM Page 499
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R1–29. The motor pulls on the cable at A with a force
F = (30 + t 2 ) lb, where t is in seconds. If the 34-lb crate is
originally at rest on the ground when t = 0, determine its
speed when t = 4 s. Neglect the mass of the cable and
pulleys. Hint: First find the time needed to begin lifting
the crate.
A
t = 2 s for crate to start moving
30 + t 2 = 34
( + c) mv 1 +©
L
Fdt = mv 2
0 +
L
4
2
(30 + t 2 )dt - 34(4 - 2) = 34
32.2 v 2
[30 t + 1 3 t3 ] 4 2 - 68 = 34
32.2 v 2
v 2 = 10.1 ft>s
Ans.
R1–30. The motor pulls on the cable at A with a force
F = (e 2t ) lb, where t is in seconds. If the 34-lb crate is
originally at rest on the ground when t = 0, determine the
crate’s velocity when t = 2 s. Neglect the mass of the cable
and pulleys. Hint: First find the time needed to begin lifting
the crate.
A
F = e 2t = 34
t = 1.7632 s for crate to start moving
( + c) mv 1 +©
L
F dt = mv 2
0 +
L
2
1.7632
e 2 t dt - 34(2 - 1.7632) = 34
32.2 v 2
1
2 e 2 t 2
2
1.7632
- 8.0519 = 1.0559 v 2
v 2 = 2.13 ft>s
Ans.
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