HOMEWORK
(Chapter 1
‐
Solution)
Prob 7)
Hydraulic engineers in the United States often use, as a unit of volume of water, the
acre
‐
foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A
severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area 26 km
2
. What volume
of water, in acre
‐
feet, fell on the town?
Solution:
23
1 acre ft = (43,560 ft ) ft = 43,560 ft
⋅⋅
Since 2 in. = (1/6) ft, the volume of water that fell during the storm is
22
2
7
3
(26 km )(1/6 ft)
(26 km )(3281ft/km) (1/6 ft)
4.66 10 ft .
V
==
=
×
Thus,
V
=
×
×⋅
=×
⋅
466
10
4 3560
10
11
10
7
4
3
.
.
.
ft
ft
acre ft
acre ft.
3
3
Prob 8)
Harvard Bridge, which connects MIT with its fraternities across the Charles River, has
a length of 364.4 Smoots plus one ear. The unit of one Smoot is based on the length of Oliver
Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge
so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint)
1
‐
Smoot lengths along the bridge. The marks have been repainted biannually by fraternity
pledges since the initial measurement, usually during times of traffic congestion so that the
police cannot easily interfere. (Presumably, the police were originally upset because the Smoot
is not an SI base unit, but these days they seem to have accepted the unit.) Figure
1
‐
4
shows
three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of
50.0 Smoots in (a) Willies and (b) Zeldas?
Figure 1
‐
4
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View Full DocumentSolution:
From Fig. 1
‐
4, we see that 212 S is equivalent to 258 W and 212 – 32 = 180 S is equivalent to
216 – 60 = 156 Z. The information allows us to convert S to W or Z.
(a) In units of W, we have
()
258 W
50.0 S
50.0 S
60.8 W
212 S
⎛⎞
==
⎜⎟
⎝⎠
(b) In units of Z, we have
156 Z
50.0 S
50.0 S
43.3 Z
180 S
Prob 13)
Three digital clocks
A, B
, and
C
run at different rates and do not have simultaneous
readings of zero. Figure
1
‐
6
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 Fall '11
 PAN
 Astronomical unit, real house, PROB, Reed Smoot, Jr.

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