2-1
LAB 2:
Measurement of Mass, Length, and Time
Consider the following statement: “Beer costs ten.”
Ten what?
If we’re talking about a beer for ten dollars, it’s a little steep.
Ten Euros, it’s a
lot
steep.
Ten
pesos?
Pass.
The problem is compounded when we realize the amount of beer is also unknown.
If we
settle on $10, questions remain about this deal if
it’s
for a single draw, a can, a case or a keg.
Anything that can be counted has a
unit
.
“1
six-pack
costs ten
dollars
.”
Without a unit, measured
values are meaningless.
After all, the point of a measurement is to tell us how much
of something
we
have.
Different
systems of units
exist around the world.
You are probably most familiar with the
English System
of feet for distance and pounds for force.
The
metric system
or
MKS (meter, kilogram,
seconds)
is another system used globally for science and is part of the
International System (SI)
of units.
Four fundamental units
—
length, time, mass and charge
—
are not the only physical quantities, but they
are the most basic.
Velocity (m/s), Acceleration (m/s
2
), Force (N or kg m/s
2
), Energy (J or kg m
2
/s
2
) are
real physical quantities
, but they are made (derived) from relationships between the most basic units.
Because the units for these
derived quantities
can sometimes get to be large and cumbersome, we give
them special names like Newtons (N) or Joules (J).
Anytime you must perform a calculation,
*always*
include the units in your work and break them down to their most basic forms if necessary to cancel any
out.
Units in calculations can always signal when something might be wrong, such as a velocity that
comes out in
hours per miles
because we performed the calculation upside down!
Most of the time when reporting measurements we will do so in standard units (m, kg, s).
If
measurements are small, they will often be recorded in smaller units (cm, mm, g, etc.).
It is important to
know how the metric prefixes modify the base units, and to be able to convert them accordingly.
Prefix
Modification to Base Unit
Example
pico- (p)
× 10
-12
or ÷ 1 trillion
0.3pF = 3 × 10
-13
F
nano- (n)
× 10
-9
or ÷ 1 billion
532nm = 5.32 × 10
-7
m
micro-
(μ
or
“mu”)
× 10
-6
or ÷ 1 million
3.6
μ
m = 3.6 × 10
-6
m
milli- (m)
× 10
-3
or ÷ 1,000
256ms = 0.256s
centi- (c)
× 10
-2
or ÷ 100
2.5cm = 0.025m
kilo- (k)
× 10
3
or × 1,000
78.5g = 0.0785kg
mega- (M)
× 10
6
or × 1 million
500MJ = 5 × 10
8
J
giga- (G)
× 10
9
or × 1 billion
8.21GW = 8.21 × 10
9
W
tera- (T)
× 10
12
or × 1 trillion
2TB = 2 × 10
12
B
Special Note: Even though kg are not the base unit, in SI
the “kg” is the standard unit.
It is a mystery.

2-2
Unit Conversions
All systems have something in common: they measure the same physical quantities, but the standard
“amount” may vary from system to system.
Because different units of distance still measure
distance
,
you can easily convert from one system to another if you know the
conversion factor
(an “exchange
rate”) between systems.
Consider a conversion of 1 ft to cm knowing 1 in = 2.54 cm
1 ft
12 in
2.54 cm
=
30.48 cm
ft
in
In the conversion above, begin with the amount needing conversion.
Because we don’t know the
conversion factor from cm to ft, we will need to use a
second