PHY 341 Quiz 1
Answer Key
1
I) Three Quickies
1.)
Evaluate
g
, the acceleration due to gravity at the earth’s surface,
in “Star Trek” units where time is measured in years and distance in
lightyears.
Let
T
be the number of seconds per year.
T
≈
π
×
10
7
s
/
yr.
g
≈
10 m
/
s
2
×
T
2
/
(
c
×
T
) =
gT/c
.
Therefore,
g
≈
1 lt
·
yr
/
yr
2
!
Socalled “natural units” of measure can be derived from various physical quantities
by combining the quantity with powers of the speed of light
c
(SI units:
m
/
s) and
Planck’s constant
h
(SI units: J
·
s) to achieve the desired unit of measure. Suppose
we choose the mass
m
of some particle as the standard of a system of natural units.
Then, for example, the unit of energy is
mc
2
.
2.) What will be the unit of length in such a system of natural units?
mc
2
/h
will have units of [ energy]
/
[ energy
·
t]
=
[ t
−
1
].
This
collection
needs
to
be
divided
by
c
to
have
units
of
[ L
−
1
].
Hence, the combination
h/mc
will have units of length.
3.) Estimate the number of barber shops in Austin, giving your reason
ing. Take the population of Austin to be 1 million.
There are approximately 10
6
people needing a haircut every four
weeks.
A given shop has about 4 or 5 people giving a hair
cut in about 1/2 to 1 hour.
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 Fall '08
 RITCHIE/LANG
 Physics, Acceleration, Gravity, Light, Speed of light, Star Trek, Natural units, different hash marks

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