A First Course in Physics · Ch. I, §§ 1–11 · Chapter 1: Measurement
1. Why the metric system? Length, mass and time
Goal: Your student can explain why the metric system was invented, name the meter, liter, gram and second, and convert between inches, centimeters, pounds and kilograms.
You'll need
- The book, open to these pages
- A ruler or tape measure marked in both inches and centimeters
- A kitchen scale (grams if possible)
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The opening of the book: old units of length taken from the human foot and arm, the French Revolution and the metric system, the standard meter and kilogram kept in Paris, prefixes, a conversion table, and the three fundamental units (centimeter, gram, second). Seven problems follow.
The lesson, step by step
Hook question
SayIf everyone's foot is a different size, how could "a foot" ever be a fair measure?
Let your student guess. Then measure both of your feet in inches and compare.
Read together
Read §§ 1–11 aloud, taking turns by paragraph. Stop at the list of old feet in § 1 (Greek, Macedonian, Roman) and enjoy how different they were.
The book's own reason for the metric system:
every unit of length, area, volume, or mass is connected with the unit of next higher denomination by an invariable multiplier, and that the simplest possible multiplier, — namely, ten.
Explain the idea
In the old English system, 12 inches make a foot, 3 feet a yard and 5½ yards a rod: no pattern. In the metric system, every step is a factor of ten. The book says three relations should be memorized: 1 in. = 2.54 cm, 1 m = 39.37 in., and 1 kg = 2.2 lb.
Scientists reduce every measurement to just three kinds: length, mass and time. The book calls this the C.G.S. system (centimeter, gram, second).
Try it: measure in two systems
Measure a book, a table and your student's height in both inches and centimeters. Check: does inches × 2.54 give the centimeters?
Weigh a few things on the kitchen scale (a bag of flour, an apple). If the scale shows grams, change to kilograms (divide by 1000) and then to pounds (multiply by 2.2).
What we know now
Today's system is called SI. It uses the meter, kilogram and second (not the centimeter and gram), and the units are no longer defined by metal bars in Paris. Since 1983 the meter has been defined by the speed of light, and since 2019 the kilogram by a fixed constant of nature (Planck's constant). The second is now defined by the vibrations of cesium atoms, not by the length of a day.
Say it back
Your student closes the book and explains: Why was the metric system invented? What are the three fundamental units? Why is ten the best multiplier?
Problems
Work the problems at the end of § 11 (book page 6–7) in the notebook, showing the conversion used. Problem 7 is a good challenge: change the gallons to cubic inches first.
Afterwards
Find three packages in the kitchen that show both metric and English units. Check one conversion with the book's table.
Tip
Write 1 in. = 2.54 cm, 1 m = 39.37 in. and 1 kg = 2.2 lb on a card and keep it in the book. The problems use them all year.
Answers to the book's problems
1. About 1099 ft. 2. About 16.08 ft. 3. About 72.7 kg (160 ÷ 2.2). 4. 3⅓ lb, about 1.51 kg. 5. 5,000,000 mm; 3 mi = 190,080 in. 6. About 146.9 square rods (40,000 sq. ft ÷ 272¼); 90,000 square meters. 7. About 50.1 in. deep (346,500 cu. in. ÷ 6912 sq. in.); 1 m deep (6 cu. m ÷ 6 sq. m).
Worked out for this site from the scan. If a number in your copy differs, trust the book.