Science and Measurement

Georgia Perimeter College

Objectives

1. Know the four common parts of any measuring unit.

2. State the difference in cause and effect of random and systematic errors.
3. State two ways to reduce errors in an experiment.

4. Know where the units of time came from.

5. Know how to pick appropriately sized units for measuring something.

6. Know the difference between basic units and secondary units based on them.

7. State an operational definition of speed.
 This section addresses, in whole or in part, the following Georgia GPS standard(s): S8P3. Students will investigate relationship between force, mass, and the motion of objects.   S8CS3. Students will have the computation and estimation skills necessary for analyzing data and following scientific explanations. a. Analyze scientific data by using, interpreting, and comparing numbers in several equivalent forms, such as integers, fractions, decimals, and percents. b. Find the mean, median, and mode and use them to analyze a set of scientific data. c. Apply the metric system to scientific investigations that include metric to metric conversions (i.e., centimeters to meters). d. Decide what degree of precision is adequate, and round off appropriately. e. Address the relationship between accuracy and precision. f. Use ratios and proportions, including constant rates, in appropriate problems.   S8CS4. Students will use tools and instruments for observing, measuring, and manipulating equipment and materials in scientific activities utilizing safe laboratory procedures. a. Use appropriate technology to store and retrieve scientific information in topical, alphabetical, numerical, and keyword files, and create simple files. b. Use appropriate tools and units for measuring objects and/or substances. c. Learn and use standard safety practices when conducting scientific investigations.

 This section addresses, in whole or in part, the following Benchmarks for Scientific Literacy: Almost anything has limits on how big or small it can be. Finding out what the biggest and the smallest possible values of something are is often as revealing as knowing what the usual value is. Things in nature and things people make have very different sizes, weights, ages, and speeds. Estimate distances and travel times from maps and the actual size of objects from scale drawings. Determine what unit (such as seconds, square inches, or dollars per tankful) an answer should be expressed in from the units of the inputs to the calculation, and be able to convert compound units (such as yen per dollar into dollar per yen, or miles per hour into feet per second).

 This section addresses, in whole or in part, the following National Science Education Standards: Tools help scientists make better observations, measurements, and equipment for investigations. They help scientists see, measure, and do things that they could not otherwise see, measure, and do. Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations and communicating results. Scientists rely on technology to enhance the gathering and manipulation of data. New techniques and tools provide new evidence to guide inquiry and new methods to gather data, thereby contributing to the advance of science. The accuracy and precision of the data, and therefore the quality of the exploration, depends on the technology used.

“Are we there yet??” - The need to measure

This ancient wail, whether from the back seat of that aged Chevrolet or the back of an ancient Roman chariot, expresses the primal need that even non-scientists will recognize - the need to measure

The most common measures are those of distance and time.  These two measures are separate, and yet intricately linked.  With these two items, together and apart, we determine our place.  It isn’t called the space-time continuum in Star Trek, or physics, simply because it rolls off the tongue so well.

Vocabulary

Measurement

Origin

Positive Direction

Unit

Random Error

Systematic Error

Units of Time: Eon, Year, Month, Week, Day, Hour, Minute, Second

Units of Distance:  Astronomical Unit, miles, meters, kilometers.

Metric

Speed

The Science of Measurement

Measurement is the second level up from the most basic level of scientific observation.  Anyone can observe a planet, a sunset, the road ahead, the day just past, and give a description of it.  But to know it better, one must determine its extent and limits, and how that connects with other extended and limited its.

These require some quantitative way of assessing it, something other than general appearances (which is qualitative in nature).

Quantitative requires a system of measures.

Science needs measures.  It’s the starting point and sometimes the end point.

Sometimes it is the item that supports a new theory, sometimes theory and measurement don’t agree— and out goes the theory.

The measurement is all but sacred. And yet…

All measurements do have four things in common:

1.  You have to have a starting point or origin

Where’s zero?

It can be quite arbitrary where zero is but you have to have one somewhere.

On the highway, zero can be the southern or western boundary of the county, or the state line. It could start from the northern or eastern side, if we wanted to.

But once we all agree (or somebody stronger than you says so), that’s where the zero is.

Most rulers have zero on the left end.  It doesn’t have to be.  But zero DOES have to BE…somewhere.

2.  You have to have a positive direction.

Which way do we go to get to 1, or a hundred?

Left, right, up, down, along the incline, around the circle clockwise (and what is clockwise anyway, who decided that?), radially away from the center —

Some direction has to be declared to be the way the measurement increases.

In some cases, nature suggests a ‘logical’ way (clockwise for one, it’s the way the shadow moves on a sundial, the first clocks).

Sometimes it’s arbitrary—azimuth increases to the east instead of to the west.

3.  You need a unit of length.

Feet, inches, miles, centimeters, meters, kilometers, parsecs, angstroms, atomic mass (1/12th of a carbon atom), solar masses (Sun = 1).

Again, sometimes these seem to follow a natural path, other times it comes from some quirk of a human.

4.  Finally, no measurement ever made is perfect.

There is no absolutely precise measurement.

You can never get infinitely accurate because no measuring device can do it, and human frailties never go away either.

All measurements are some number X plus or minus some (hopefully very small!) Y.

And if you change your origin or scale or just use a ruler that was made systematically larger than it should, your measurements will change as well.

Use a different reference framework and you can literally go from zero to infinity in no time at all.

You are sitting here at the computer reading; but sitting is saying you have no measurement of speed compared to the computer, which is true.  It is also true that you are moving just under 1000 miles per hour around the Earth’s axis and nearly at the speed of light compared to a galaxy at the far end of the universe.  All it took was to change from where you are referencing your measurements.

Part of the history of science has been the refinement of measurements.

How big exactly is one meter?

Where is the Earth located in reference to the center of the universe?

Where IS the center of the universe (flipped around, where’s the edge of the universe so we can determine the center!)?

(If you don’t think accurate measurements are important  - accurate in origin point, positive direction, most precision, and proper units - just ask the NASA engineers who lost a Mars probe a few years ago because they didn’t convert between feet and meters on a crucial command to the probe!!)

Time and Distance

The two most common measurements are those of time and distance

There are many units for each.

What is the amount of distance for a distance of “one”?  That depends on what units you want.

One meter is the metric standard unit but it’s one ten-millionth of the distance from the equator to the pole through Paris.

One astronomical unit is the measurement used for distances in the solar system; it’s also about 93,000,000 miles or 149,000,000 kilometers.

All distances can be used interchangeably with some mathematical conversion formulae but some are more convenient than others.

Would you tell that "Wailing Willy" in the back of Chevy it is only 23,459 meters to Grandma’s house?  Wouldn’t “about 23 and half kilometers” work better?  Well, probably not unless the child was raised in a house of American scientists or almost any other country in the world that uses metrics!

Wailing Willy is more used to short distances, like feet and inches, rather than miles and kilometers.

But he does have some understanding of time.  Time is pretty standardized.

Seconds, minutes, hours, days, weeks, years.  Notice I left out months.

But there are different definitions of seconds going back to the dim mists of history and forward to atomic oscillations.

On the other end, the Earth is but a "mere" 4.5 billion years old.

Months came about from the time it takes for our moon to change its shape.

That’s different from the ‘month’ it takes to actually orbit the Earth.

Year units actually depend on whether you are measuring the Sun’s actual motion against the stars, or motion taking into account the slightly precessional motion of the Earth’s orbit, or where the closest point to the Sun points to during consecutive years, or….hopefully you get the idea.

And maybe time isn’t so standardized after all.

Bottom line is….pick the units that are most convenient (generally comparable in size to the thing being measured).  And remember to be as precise as you can, but be aware that you can’t be infinitely precise.

Measurements in Science Experiments

When scientists make measurements in experiments or studies, the measurements are made more accurate by one of two similar ways.

The ONE way is making more and more measurements.  The DIFFERENCE is either the scientists makes many measurements over and over again himself, or gets many other people to make measures.  The reason is that if you make many measurements, your final average of them will be much closer to the real answer (whatever that is) than any individual measures.

Remember that each measure has some uncertainty in it due to measuring device inaccuracies and humanity’s imperfect perception abilities.

Any individual measurement can be close or far but there’s no way to tell.  But measure a lot and the answers tend to fall around a mean value, which may still be off but a whole lot closer than the individual measures.

This is called random error and it can be made as small as possible but never eliminated.  This is where the plus and minus part comes in.

There is another form of measurement problem called systematic error

You measure the sun’s diameter, and measure and measure…and your final answer is 10% higher than it should be.  Why?

• Perhaps your measuring device is heat sensitive and the scale expanded 10% so all the lengths are 10% bigger than they should be.

•

• Perhaps the scale is fine but you always, even unconsciously, take your reading a bit to the right of the black marks on the scale.

•

• How do you know if you are ON the scale mark anyway?  That 10 cm line on the meter stick isn’t infinitely thin; is 10 cm on left or right edge or in the middle of the black line?

• Maybe the manufacturer put the scale on 5 mm to far to the right?

• Maybe the zero end of the meter stick has been worn off a little so that the end is now at 2 mm.  All your measures will be 2 mm off.

All these contribute to measures being systematically over- or under-estimated.

Wailing Willy may like it if your time sense is so off that “we’ll be there in five minutes” turns out to be really 20 minutes.

Systematic errors can be eliminated, through calibrations, through changes of measuring origins and directions (measure from the left, measure from the right, average them together, fight fight fight!  Sorry….mathematicians cheer…), using other measuring devices (3 different spectroscopes), and so on.

Speed

There are units of measurements…..and there are new units built on the base units.  There is nothing more basic than time and length, say seconds and meters.  But if you combine them, you get new units.  Measure the distance between two places in meters, start from A and go to B.  Now run back to A and measure how many seconds it takes to get back.  Divide the distance by the time and you get…..speed!  New unit:  meters per second.    This is the unit for speed, a measure of how fast something is going (in this case, you).

Not good enough?  Start at the Sun (ouch!) and follow a light beam to the Earth.  How far?  (1 astronomical unit or 93,000,000 miles, or….) How long did it take? (About 500 seconds).  Speed?  Wellll, you could go 93,000,000 divided by 500 and about 25,000 miles per second, another unit of speed.  But how about 8.3 light-seconds?  That’s how long it takes light to travel from there to here but we’ve turned it into a unit of distance!  See, speed and distance and time are all linked.  You can’t get the first at all unless you have the last two.

As you progress through the sciences you will find many other units of measurements. Some quite basic but most are somewhere, somehow based on more primitive units. The former are called derived units. They are derived as combinations ultimately based upon the seven Basic Units, of which time and length are two.

 Units of Measure   Below is a web page with many units of measures you can check out, including some of historical interest.  It can be perused by system (UK, American, metric, more), what they measure (length, heat, force, etc.), and extra stuff, like those pesky, Greek-sounding prefixes for bigger and smaller amounts of each unit.

Review

1. What are the four common parts of any measuring unit?

2. What is a random error and how is it caused?

3. How does a systematic error differ from a random error?

4. There are at least two ways to reduce the size of random error.  What are they?

5. What is the origin of the week?

6. List what units would be appropriate….and inappropriate for measuring the length of a table top side.  Explain why.

7. What is the difference between basic units and secondary units, and name examples.

8. State an operational definition of speed.

Define

Measurement

Origin

Positive Direction

Metric

Speed

A Problem

A Georgia science teacher wins a free trip to Los Angeles, California.  It takes her 50,756 seconds to make the trip.  Using a ruler and map with a distance scale, determine how far it is to Los Angeles in miles, and then determine:

1. Speed in miles per hour

2. Speed in kilometers per minute

3. Speed in Earth diameters per day

Content provided by Mr. Larry Krumenaker, Georgia Perimeter College and

Some content from NASAExplores.com website http://www.nasaexplores.com/show_912_teacher_st.php?id=040908101213

Icon from http://serc.carleton.edu/usingdata/nasaimages/index4.html

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created December 14, 2006
Modified December 20, 2006
Modified February 3, 2007