Physical Science
Measurement
Slides subject to change
1
What to Measure?

Fundamental Units such as
 Length (meter, abbr. m)
 Mass (kilogram, abbr. kg)
 Time (second, abbr. s)

Derived Units such as
 Velocity: kilometers/hour, miles/hour
 Area: square meters (abbr. m2 )
 Volume: cubic meters (abbr. m3)
2
Vitruvian Man (Leonardo da Vinci)
3
Metric System


The international “decimalised” system of
measurement was first adopted by France in
1791. Common system of measuring units
used by most of the world.
In the United States, metric units are widely
used in science, military, and industry.
Some names for metric system
“mks” = m − kg − s
or SI (“Le Système international d'unités”)
or simply, the “metric system”
4
Length
Historically, in 1790, French must make a
decision:
 1 meter = length of a pendulum with
a “half-period” of one second.
 OR


1 meter = one ten-millionth of the
distance from the equator to the
north pole.
1
10
,000
,000
5
Dunkirk
Barcelona
Meter
So ... distance was chosen.
 One meter defined in 1793 as the distance
between two scratches on a metal bar in
Paris, pending completion of the survey.
 Became official in 1795, lasted to 1960.


Today one meter equals the distance
travelled by light in vacuum during a time
interval of 1/299,792,458 of a second.
7
Lengths in Metric System
Common multiples, submultiples:

kilometer (103 meter)
centimeter (0.01 or 10-2 meter)
 millimeter (0.001 or 10−3 meter)
 micrometer (10−6 meter)
 nanometer (10−9 meter)

larger >

8
Compare to English
1 inch = 2.54 cm (approx. width of your
thumb)
 1 meter = 1.09 yard
 Slightly more than three feet.
 100 meter race is longer or shorter
than 100 yard race?
 1 kilometer = 0.6 mile
 10 km (10K) race is what distance in
miles?

International 1-kg Standard
1 gram (mass of 1.0 cm3 H2O).
 1,000 grams is a kilogram.

Exact mass kept in France.
 Accurate copy sent to U.S. in 1899.
 Platinum-iridium cylinder.


1 kg = 2.2 lbs.
10
More About Grams
1 gram = tiny cube of water.
 1.0 cm X 1.0 cm X 1.0 cm. = 1.0 cm3
 In medicine this volume is called a “cc”–—
“cubic centimeter.”
 In drinking water, it is called a milliliter (ml).


Common bottle of water is 500 ml or 500 cc.
Mass is 500 g or 0.500 kg.
Time
Egyptians subdivided daytime into twelve
hours since at least 2000 BC.
 Greeks divided a full day into 24 equal
hours around 150 BC.
 Hour subdivided into 60 units to
what we call “minutes,”
 to 60ths of that − to what we call “seconds”
− by the Babylonians after 300 BC.

hour: Latin hora, hour, time, season..
minute: Latin pars minuta prima, first small part.
second: Latin pars secunda minuta, second small part.
12
One Second

Today ...

Officially one second is related to the
frequency of the radiation from cesium133–the time to perform 9,192,631,770
oscillations.
Time in Metric

Common multiples, submultiples:
 millisecond or “ms” (10-3 s)
 microsecond or “μs” (10-6 s)
 Minute (60 s) ... hmmm, this isn’t
metric.
 Hour (60 minutes) ... hmmm, this isn’t
metric either.
14
Metric 10-Hour Watch
What time is it?
 Decimal time introduced
during the French
Revolution in the decree of
October 5, 1793.
 Midnight is 10 o’clock.
 Noon is 5 o’clock.


7:45:07 pm
15
Major Submultiples, Multiples
Submultiples
Multiples
centimilli-
10-2
10-3
kilo-
103
mega-
106
micronano-
10-6
10-9
gigatera-
109
1012
16
Convert Units

The power of “One”

Conversion factor: 2.54 cm = 1 inch
2.54 cm
1 in

=
1
=
1
And so does ...
1 in
2.54 cm
17
Convert Units

Convert 5 inches to centimeters

5 in. = 5 in. x 1
= 5 in. x
2.54 cm
1 in
= 12.7 cm
 Use
dimensional analysis to get the units
straight. “Inches” cancel, leaving
centimeters (cm).
18
Convert Speed

Conversion factors:





1 m = 3.28 ft
1 mile = 5280 ft
What is 60 mi/hr in km/hr?
60 mi
hr
x 5280 ft
1 mi
x 1m
3.28 ft
x 1 km
103 m
= 97 km/hr
19
Another Example
 Given
1 mile = 5,280 feet
 What is 60 mi/hr in ft/s ?


60 mi
hr
x
5280 ft
1 mi
x
1 hr
60 min
x
1 min
60 s
= 88 ft/s
20
Rounding

Round 387 to “two places”
 Locate the digit in that place (the “8”).
 Consider the digit to its right (the “7”).
 If the digit to the right (the “7”) is 5 or
higher, round up; if the digit to the
right is less than 5 round down.
 Answer is 390.
21
Rounding Exercise

Round 3872.2459 to the nearest:








a. thousandth
b. hundredth
c. tenth
d. one
e. ten
f. hundred
g. thousand
View π (pi) on your calculator. Round to
four significant figures.
22
More about Sig Figs
0.00052 has two sig figs, 1.00052 has six,
1.230 has four.
 When we say one foot has 12 inches, the
12 is exact, don’t consider it when figuring
the number of significant figures.
 Assume values in text problems are exact,
thus the text’s “100 miles” has three sig
figs.)
 Scientific notation is relatively easy for
significant figures: 5.66x108 has 3 sig figs.

23
Even More on Sig Figs

In multiplication or division, your answer
will have lowest sig. figs. of the terms you
are calculating.
4.2 x 3.4159 - least significant figure term
has 2 sig figs (14).
 Answer is 14. (not 14.34678).


If you do the entire problem on your
calculator, adjust the answer for significant
figures at the end.
24
An Equation: Density
Density is the mass per unit volume of an
object.
 In Words: Density = Mass / Volume

Symbols
Greek letter “rho”
 mass = m
 density = ρ
 volume = V
 Equation ρ = m/V
 Example: Water density is 1.00 gram/cm3.

25
Density

A certain bar of gold has a mass of 9,650 g
and volume of 500 cm3. What is its density
(in g/cm3)?
1. Understand the problem.
2. Givens
3. Potential Formula
m = 9,650 g (√ right units)
ρ = m/V
V = 500 cm3 (√ right units)
4. Solve
ρ = 9,650 g / 500 cm3
= 19.3 g/cm3
26