Physical science has special terms used to describe measurements.
Primary measurements: A quantity that is directly measured using an measuring device or instrument. Measuring devices might include rulers, stopwatches, mass balances, protractors, and thermometers.
Calculated measurement: A quantity calculated from a mathematical combination of primary measurements.
All measurements are expressed as the combination of a number and the units of measure. Whenever I speak about a measurement in science I must say both the measurement and the units. Thus I say "Five centimeters" or "Three volts." Number and units. Together forever. Leave either one out, and the answer is incomplete and incomprehensible. Wrong.
There are two types of units of measure in science.
Fundamental units: Measurements of length, mass, and time using either the meter-kilogram-second (mks) or centimeter-gram-second (cgs) system. Fundamental units measure space, time, and the amount of matter contained in an object. In this laboratory measurements will be made using centimeters and grams. The first four laboratories will use the "cgs" system of measurement.
Derived units: Measurements expressed using arithmetic combinations of fundamental units. For example, volume is derived from multiplying together three independent measurements of length. To avoid confusion these three measures are usually described as length × width × height. All three are still measures of length. Length is the fundamental measurement. Volume is the derived measurement.
Density is another derived measurement. Density is derived from the mass divided by the volume.
Yet another example of a derived unit is the metric measure of liquid volumes, the liter. A liter is defined to be 1000 cm³. The liter is defined using a fundamental unit of length.
All measurements have limits in terms of their accuracy. There are terms used to describe these limits.
Uncertainty: the limit of our measuring tools for a single measurement, our uncertainty based on the smallest measurement our tools can accurately make. For a ruler marked in millimeters there is always at least a half a millimeter of uncertainty, often more. Some electronic devices tell you the uncertainty. Global positioning satellite (GPS) receivers usually provide an estimated uncertainty.
Precision: the average variation in multiple measurements of an experiment usually expressed using the standard deviation.
Error: the difference between the measured result and the actual value. The actual value is usually unknown, hence the error is never truly known.
To "quantify" means to attach a numeric value to something. Words that are associated with quantifying space are distance, length, width, height, radius, and diameter.
Words that are associated with quantifying time are duration, interval, and frequency.
A word that is associated with quantifying matter is mass.
In this class we will use only the metric system to measure the fundamental qualities. To measure space we will use meters. To measure time we will use seconds. To measure mass we will use kilograms. The meter, kilogram, second system is also called the MKS system.
Sometimes, to make measuring and calculating easier, we will use centimeters, grams, and seconds. A centimeter is one-hundredth of a meter, a gram is one-thousandth of the kilogram. When we use centimeters, grams, and seconds we say we are using the CGS system. MKS and CGS are both metric.
| Quality | Quantity | Fundamental unit of measurement | |
|---|---|---|---|
| MKS | CGS | ||
| Space | Distance, length, width, height, radius, and diameter | meter | centimeter |
| Time | Duration, interval, and frequency | second | second |
| Matter | Mass | kilogram | gram |
In class you will determine your height in meters and your mass in kilograms. For homework you will work on your age in seconds. Include both the number and the units.
Space: height in meters: ______________________ Matter: mass in kilograms: ______________________
A useful use of your height and mass is that these two numbers can be used to calculate your Body-Mass index. If your body mass index is over 26, then you are considered to be "overweight" for your height. This does NOT necessarily mean "too much fat." If one is a weightlifter, one can have a BMI over 26. Note that 26 is a recommended cut-off for Pacific islanders. For non-Pacific islanders the cut-off is 25.
Calculate your BMI by dividing your mass in kilograms by the square of your height in meters.
BMI = (mass in kilograms)/(height in meters)² = __________________________ kg/m²
The units of BMI, kg/m², are called derived units. Derived units are combinations of fundamental units of measurement.
Are you "overweight" as measured by your BMI? _____________
This exercise will be introduced in class. The actual calculation will be left as a homework exercise. Calculating your age in seconds is more complicated than simply stating your age in years. This exercise outlines how to set up a spreadsheet such as OpenOffice.org Calc or Microsoft Excel to calculate your age in seconds. You will also be able to determine the week day on which you were born. The intent of this exercise is to also introduce you to using functions in spreadsheets to make calculations.
The spreadsheet will calculate your age in days. Days are not a metric unit. To convert days to seconds requires multiplying by 24 hours in one day, 60 minutes in hour, and 60 seconds in one minute.
Days × 24 hours/day × 60 minutes/hour × 60 seconds/minutes = seconds
Note that functions and formulas always START with an equals sign in a spreadsheet.
| A | B | |
|---|---|---|
| 1 | 1/31/1990 | =WEEKDAY(A1) |
| 2 | =NOW() | |
| 3 | =A2-A1 | |
| 4 | =A3*24*60*60 |
The value in A4 is your age in seconds at the time you entered your formulas.
I am ____________________________________ seconds old.
At one time I lived in West Africa. Among the Akan your name at birth depends only on your gender and the day of the week. These names are called day names.
| Day | Female | Male |
|---|---|---|
| Sunday | Akosia | Kwasi |
| Monday | Adjoa | Adjoa |
| Tuesday | Abenaa | Kwabenaa |
| Wednesday | Akua | Kwaku |
| Thursday | Yaa | Yaw |
| Friday | Afia | Kofi |
| Saturday | Ama | Kwame |
At present you can use the conversion 365.25 days = one year. The 0.25 is why we have a leap year with a 29 February every four years. Leap years are divisible by four.
The actual conversion is 365.2422 days = one year. The actual conversion would have to be used for dates prior to 1900. In century years not divisible by 400, including 1900, there is no leap day. The year 2000 was divisible by 400, so 2000 was a leap and included 29 February. Thus if you were born after 1900, 365.25 is the correct conversion. At least until 2100 when we skip a leap year again.
Once you know how old you are in seconds, check to see how many seconds you have left to live. Go to the DeathClock. You will need the BMI number you calculated above.
How many seconds do you have left to live? _____________________________
Is the DeathClock real? Is that how long you really have left to live? Why or why not?