23.
The work to raise a thin disk is
p
r
2
(56)
h
5
p
(
ˇ
1
w
0
w
2
w
2
w
y
w
2
w
)
2
(56)(10
1
2
2
y
)
D
y
5
56
p
(12
2
y
)(100
2
y
2
)
D
y
. The total work is
E
10
0
56
p
(12
2
y
)(100
2
y
2
)
dy
, which evaluates using NINT
to
<
967,611 ftlb. This will come to
(967,611)($0.005)
<
$4838, so yes, there’s enough money
to hire the firm.
24.
Pipe radius
5 }
1
6
}
ft;
Work to fill pipe
5
E
360
0
p
1
}
1
6
}
2
2
(62.4)
y dy
5
112,320
p
ftlb.
Work to fill tank
5
E
385
360
p
(10)
2
(62.4)
y dy
5
58,110,000
p
ftlb.
Total work
5
58,222,320
p
ftlb, which will take
58,222,320
p
4
1650
<
110,855 sec
<
31 hr.
25. (a)
The pressure at depth
y
is 62.4
y
, and the area of a thin
horizontal strip is 2
D
y
. The depth of water is
}
1
6
1
}
ft, so
the total force on an end is
E
11/6
0
(62.4
y
)(2
dy
)
<
209.73 lb.
(b)
On the sides, which are twice as long as the ends, the
initial total force is doubled to
<
419.47 lb. When the
tank is upended, the depth is doubled to
}
1
3
1
}
ft, and the
force on a side becomes
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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