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Conversion Factors
Alice and Bob are two cosmic physicists who grew up on different planets. They meet at an interplanetary symposium
on weights and measures to discuss the establishment of a universal system of units. Alice proudly describes the merits
of the metric system used on Earth (kg, m, s). Bob describes the merits of the planetary system used everywhere else
in the solar system with equal pride. Bob's system uses planetary mass units (pmu), planetary length units (plu), and
planetary time units (ptu).
The constant factors relating the basic mass, length, and time standards of the two systems are µ, 2, and r:
1 kg
=
1 pmu
1m
=
1 plu
1s
1 ptu
(For example, if the plu were an inch, we would have 1 =
1 inch
1m
* 39.37.)
What are the conversion factors needed to convert the following from metric to planetary units?
(a) Acceleration
(b) Force
(c) Energy
(d) Frequency
(e) Density
Express your results as products of u, a, and r.
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