A First Course in Physics · Ch. I, §§ 12–19 · Chapter 1: Measurement
2. Weighing, and the meaning of density
Goal: Your student can define density as mass per cubic centimeter, use M = V × D, and find the density of a real object at home.
You'll need
- The book, open to these pages
- A kitchen scale that reads grams
- A measuring cup marked in milliliters (1 mL = 1 cc)
- A few small solid objects: a stone, a potato, a block of wood, a bar of soap
- A ruler
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
How meter sticks and sets of weights are copied from the standards, weighing by substitution, then density: tables of densities of liquids and solids, the formula M = V × D, and the difference between density and specific gravity. Twelve problems follow.
The lesson, step by step
Hook question
SayWhich is heavier, a pound of feathers or a pound of lead?
Both weigh a pound, of course. But a cup of lead is far heavier than a cup of feathers. That difference is what this lesson names.
Read together
Read §§ 12–19. In § 16 notice the careful "method of substitution" for weighing. The key definition:
The term "density" is therefore introduced to denote the mass of unit volume of a substance.
Explain the idea
Density is how many grams one cubic centimeter of a substance has. Water: 1 g per cc. Iron: about 7.4. The book's equation is M = V × D, or D = M ÷ V.
Work the book's example together: a cast-iron block 3 cm × 8 cm × 1 cm has 24 cc and weighs 177.6 g, so its density is 177.6 ÷ 24 = 7.4.
Specific gravity is how many times heavier a thing is than the same volume of water. In grams and cubic centimeters it is the same number as the density.
Try it: find a density
Pick a stone or potato. Weigh it in grams. To find its volume, fill the measuring cup partway with water, read the level, drop the object in (push a floater under with a toothpick) and read again. The rise in milliliters is its volume in cc.
Divide grams by cc. Does it sink? Then its density should be more than 1. A block of wood measured with a ruler (length × width × height) works too.
Look at the table
Find gold, lead, cork and mercury in the table on book page 9–10. Ask: How many times heavier than water is gold? Why would cork float?
Say it back
Your student explains in their own words what density means, and how they measured it today.
Problems
Work several of the twelve problems on book page 11. Problems 10–12 need the area of a circle (πr²) and are good algebra practice. Use the table values printed in the book.
Afterwards
Find the density of two more objects this week and add them to a little table in the notebook.
Tip
Milliliters and cubic centimeters are the same volume. Most kitchen measuring cups are marked in mL, which makes this lab easy.
Answers to the book's problems
Using the book's table (zinc 7.15, gold 19.3, pine .5, lead 11.3, platinum 21.5, alcohol .79, mercury 13.6): 1. 336 g. 2. 0.5 g per cc. 3. 13,600 g = 13.6 kg. 4. About 5.6 cc. 5. No: 8000 cc of gold weighs 154,400 g, about 154 kg (roughly 340 lb). 6. 160 cc. 7. About 5.9 metric tons (volume 4/3 π × 50³ ≈ 523,600 cc). 8. About 2.12 liters. 9. About 7.8 g per cc. 10. About 14.2 cm (1266 cc of alcohol ÷ 8 cm = 158.2 sq. cm). 11. About 0.061 cm (0.4 g of mercury fills 0.0294 cc). 12. About 113 cm.
Worked out for this site from the scan. If a number in your copy differs, trust the book.