Core Unit I: The Physics of Everyday Things

C. Measurement and Data Analysis

Key Concepts

An internationally agreed upon standard system of units is needed to measure and represent a wide variety of physical quantities. Scientists have accepted the SI system for this purpose.

The fundamental units of measurement are: length (metre), time (second), mass (kilogram), electric current (ampere), temperature (degree kelvin), luminous intensity (candela), and the amount of substance (mole). (You may find that some resources also refer to fundamental units as "basic" units or "base" units. Adopt one usage and apply it consistently in Physics 20 and 30.)

Derived units are combinations of the fundamental units.

Many of the units in the SI system are based on powers of ten for simplicity in conversion .

The order of magnitude of a number is the value of the number when rounded to the nearest power of ten.

The order of magnitude of a number in scientific notation should be rounded up if the mantissa is larger than 3.16. (10^0.5 = 3.16)

Prefixes are used in the SI system to serve as multipliers of fundamental and derived units.

All measurements include a value and a unit. Some also require a direction.

Scientific notation enables very large and very small numbers to be expressed conveniently.

Every measured quantity contains uncertainty.

Uncertainty is usually expressed either in absolute terms or as a percentage.

Measured quantities should be expressed to the number of significant figures which best represent the accuracy of the measurement.

When arithmetic operations are performed on measured quantities, the resulting answers should be expressed to an appropriate number of significant figures.

In many experiments, measurements are taken of two or more variables to search for patterns or relationships which govern the way things behave.

Various techniques are used in physics to gather and interpret data.

Data which are arranged in tables and then plotted on graphs can assist in the interpretation of those data.

Computers are useful tools in manipulating and analyzing data.

The shape of a curve on a graph may help to suggest a relationship between variables.

Reading data from graphs is essential in interpreting numeric information.

Interpolation and extrapolation are useful in interpreting graphical information.

Learning Outcomes

Students will increase their abilities to:

1. Express physical quantities using a value, appropriate SI units, and (if necessary) direction.

2. Recognize the advantages of the SI system of measurement.

3. Distinguish between fundamental units and derived units.

4. Demonstrate the correct use of the SI system of measurement.

5. Recognize the limited accuracy of measured quantities.

6. Express numbers in scientific notation.

7. Express numerical information to the correct number significant figures.

8. Determine the order of magnitude of physical quantities .

9. Collect experimental data.

10. Graph numeric information.

11. Interpret information from a graph.

12. Extrapolate and interpolate graphical information.

Teaching Suggestions, Activities and Demonstrations

1. It is important to teach this topic in the context of experimental activities. There is no universal agreement on this, but many experienced physics teachers find doing so to be more effective than trying to teach this topic in an isolated manner. Emphasize key concepts relating to measurement and data analysis during those timely moments when they are most relevant to the learners.

2. Arrive at some agreement with other science teachers in your school about the use of significant figures and uncertainties of measurement. Students are often confused by the lack of consistency in the way these topics are handled. Different resources may have a different set of rules for expressing the uncertainty of measurement. Sometimes resource materials are not even consistent with the way significant figures are handled. Answers to problems may not be stated to the correct number of significant figures. Differences also appear in the way these topics are handled in physics and chemistry. See the following suggestion as well.

3. Students often have difficulty determining the correct number of significant digits resulting from an addition or subtraction operation. Stress that the result is given to the least number of significant decimal places, not to the least number of significant figures, as it is in multiplication and division.

   For instance:

     1.234   (4 significant figures)
   +0.013   (2 significant figures)
     1.247   The sum has 4 significant figures.

4. It is not necessary to stress the conversion to and from non-SI units. Occasionally though, it may be useful, and even desirable, to show students how this is done. There are may practical instances when this has to be done. Students should not be expected to have to memorize conversion figures. Instead, they should be able to look them up as they are needed.

5. Derived units can be checked for their feasibility with other derived units by comparing their dimensions. For example, the unit km/h for speed combines the dimensions of length [L] and time [T] as [L]/[T]. Other derived units that combine the dimensions of length and time in the same way, such as m/s or cm/min, could also be units of speed. Also, for equations to balance properly, they must be able to be shown using the same dimensions on both the left and the right sides.

6. Consider the students' mathematical abilities and background. Limit experimental activity in data collection and analysis to what their mathematical skills will allow. Consider that in semestered programs some students may not yet have taken the math courses which might be necessary. If that is the case, students may need to be taught certain mathematical skills and concepts in physics class. Doing so will be a good investment of time Ä not a waste of time.

7. Using computers to gather and interpret data should assist students, but it should not replace their ability to do so manually.