79
Section 3.1The Motion of Falling Objects
Example: converting g to different units
Question: What is g in units of cm/s
2
.
Solution: The answer is going to be how many cm/s of speed a
falling object gains in one second. If it gains 9.8 m/s in one
second, then it gains 980 cm/s in one second, so g=980 cm/s
2
.
Alternatively, we can use the method of fractions that equal one:
9.8m
/
s
2
×
100cm
1m
/
=980cm
s
2
Question: What is g in units of miles/hour
2
.
Solution:
9.8m
s
2
×
1mile
1600m
×
3600s
1hour
2
=7.9
×
10
4
mile/hour
2
This large number can be interpreted as the speed, in miles per
hour, you would gain by falling for one hour. Note that we had to
square the conversion factor of 3600 s/hour in order to cancel
out the units of seconds squared in the denominator.
Question: What is g in units of miles/hour/s.
Solution:
9.8m
s
2
×
1mile
1600m
×
3600s
1hour
=22mile/hour/s
This is a figure that Americans will have an intuitive feel for. If
your car has a forward acceleration equal to the acceleration of a
falling object, then you will gain 22 miles per hour of speed every
second. However, using mixed time units of hours and seconds
like this is usually inconvenient for problem-solving. It would be
like using units of foot-inches for area instead of ft
2
or in
2
.
The acceleration of gravity is different in different locations.
Everyone knows that gravity is weaker on the moon, but actually it is
not even the same everywhere on Earth, as shown by the sampling of
numerical data in the following table.
locationlatitude
elevation
(m)
g
(m/s
2
)
north pole90
°
N09.8322
Reykjavik, Iceland64
°
N09.8225
Fullerton, California34
°
N09.7957
Guayaquil, Ecuador2
°
S09.7806
Mt. Cotopaxi, Ecuador1
°
S58969.7624
Mt. Everest28
°
N88489.7643
The main variables that relate to the value of g on Earth are latitude and
elevation. Although you have not yet learned how g would be calculated
based on any deeper theory of gravity, it is not too hard to guess why g
depends on elevation. Gravity is an attraction between things that have