Unit Conversion
AKA Dimensional
analysis (factor-label method)
Ideally, this will be a stroll down memory lane – converting
from one unit to another. Let us look at
an conversion example:
m mile
sec hour
We are trying to change meters to miles and seconds to hours. We could reason through each, multiplying or dividing
as necessary. However, if this is
approached carelessly, it is easy to make mistakes. Look at this methodical approach, wherein we
multiply by conversion factors. Note how
the numerators cancel with denominators, leaving us with the desired units (and
multiplication factor). Also note – and
this is the beauty of the endeavor – you’re really just multiplying by 1 with
each factor.
m km mile 60 sec 60
min = 2.24 mile
sec 1000m 1.609 km 1 min 1
hour hour
Use this technique to make the following conversion factors:
m/s à
furlong/fortnight
mile/gallon à
km/liter
gallon/minute à
cubic meter / day
parsec/century à
ft/sec
cm/minute à
Park/Kardashian
·
Park is an unofficial unit equal to the
approximate length of our campus (2750 feet), and Kardashian is equivalent to
72 days (or marriage).
Related problems, some of which may require orders of
magnitude estimations:
1. How many times
will you blink in your lifetime?
2. How many rotations
does the average tire make in its lifetime
3. How long does it
take a photon of light to orbit the Earth once?
4. How many hairs are
on your head?
5. If all people in
the world were gathered at once, how great an area is needed?
6. How many gallons
of paint do you need to paint the roof of the athletic center?
7. How long should it
take a spaceship to reach Mars? Alpha
Centauri?
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