Aristotle is acknowledged to be the founding father of natural science in Western culture. Aristotle introduced the idea of doing experiments in order to understand the natural world. For Aristotle, natural science was the same as natural philosophy. Science was a branch of philosophy.
Peripatetic: To walk around (peri) the patio garden (patetic).
Steps and beats: an introduction to thinking about space, time, and measurement.
To walk requires making steps. Steps move one through space. Steps also take time. One cannot move from one place in space to another in zero time. Movement requires changing one's location in space and time. Space and time are intertwined. Time itself is often measured as a movement through a distance on older dial-style clocks with moving hands. Today's digital watches and timers no longer show us the movement, but time is still deeply connected to space.
We can speak of the number of steps covered per beat. Per refers to division. Steps ÷ beats is a measure of space per unit time. Steps per beat can also be called a speed. In this class speed and velocity are treated as being the same.
There is a difficulty with steps and beats. Each person will measure a different number of steps for a given distance in space. Each person will also measure a different number of beats.
Space consists of three dimensions. Three dimensions means three directions. Think of the directions as forward-backward, right-left, up-down. Backward, left, and down are not three new directions. Backward, left, and down are simply the opposite of forward, right, and up. If forward, right, and up are positive directions, then backward, left, and down are negative directions.
Time has only one direction, forward. Time, as we experience time, cannot be stopped or reversed, not with current knowledge and technology.
Matter is the amount of stuff in an object. Matter has no direction. Only when matter moves through space can one speak about a direction. The direction is the result of movement, not a property of the matter.
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 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?
Note that density was matter divided by space. In that formula space was cubed. Full three-dimensional space. In the world of physical science the degree is the number of dimensions.
This week we explore motion. Motion was first introduced in the day one lab. Space divided by time. In motion, space is not squared nor cubed. Space is to the first degree. Linear. One dimensional. Motion has a single direction.
Measuring motion requires measuring both space and time. Space is measured using meters or centimeters. Time is measured using seconds. Motion in a direction is called velocity in physical science. Motion without reference to a direction is called speed. Working with motion in a direction usually requires working with vectors and trigonometry. In this section we will restrict ourselves to straight line motion. In straight line motion velocity and speed are the same thing.
If the distance is measured between two points in space, and the time is measured between two points in time, then the above formula is sometimes expressed as "the change in distance" divided by the "the change in time." The Greek letter delta (Δ) is used for the words "the change in."
The above formula is mathematically the same structure as the formula for the slope of a line between two points.
In physical science the relationship between distance, velocity, and time is often algebraically rearranged and written:
A rolling marble passes 0 centimeters (cm) at a time of 1.5 seconds (s). The marble passes 100 centimeters at a time of 3.5 seconds. Calculate the velocity of the marble.
A graph of duration versus distance is a graph of time versus space. The linear relationship distance = velocity × duration is a relationship between time and space.
On a graph of duration versus distance one gets a straight line if the speed is constant. The actual path over the ground might be straight or curved.
In the graph on the left above, time is plotted against space in the form of duration in seconds against distance in centimeters. The object, for example a rolling ball, is moving at a constant speed. The graph on the right is a "bird's eye view" of a ball rolling in a parking lot. The ball may roll straight, left, or right. The speed of the ball on any of the three paths shown can be the same speed.
Note that in vector physics velocity is always a speed in a particular direction. Change the speed, and the velocity changes. Change the direction, and the velocity also is said to change. A ball moving at a constant speed on a curved path is changing directions. The speed is staying the same but the velocity is changing. This is the difference between speed and velocity. Speed has no specified direction, velocity has to take into account the direction.
Graphs of time versus space, duration versus distance, do not tell us the direction of motion. Time versus distance depicts only the speed as the slope of the line. If the slope is changing, then the speed is also changing.
The graph shows a ball rolling with the speed of the ball changing.
Note that the above graph says nothing about the direction that the ball is rolling. The information is only about how far a distance the ball has moved from zero centimeters in how long a duration of time in seconds.
Using instruments that measure time and distance, determine your speed.