A First Course in Physics · Ch. III, §§ 73–80 · Chapter 3: Pressure in Liquids
9. Archimedes' principle: floating and sinking
Goal: Your student can state Archimedes' principle, explain why things float, and use loss of weight in water to find volume and density.
You'll need
- The book, open to these pages
- A kitchen scale or luggage scale and a string
- A bucket or deep bowl of water
- A stone or heavy object you can tie a string to
- Modeling clay (for a sinking ball and a floating boat)
- An egg, a glass of water and salt
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Loss of weight in a liquid and the story of Archimedes and the crown; a proof that the upward force equals the weight of the displaced liquid; floating bodies; finding the density of heavy and light solids and of liquids; hydrometers. Nineteen problems follow, with a portrait and short life of Archimedes.
The lesson, step by step
Hook question
SayA steel battleship weighs thousands of tons. A steel nail sinks. Why does the ship float?
Read together
Read §§ 73–80, including the crown story. The rule, in the book's words:
any body immersed in a liquid must lose a weight equal to the weight of the displaced liquid.
The book says Archimedes "is said to" have run through the streets shouting "Eureka"; it is a famous old story, told by a Roman writer long after.
Try it: weigh a stone in water
Hang the stone from the scale by a string and weigh it in air. Then lower it into the water (not touching the bottom) and weigh it again. The loss of weight in grams equals its volume in cubic centimeters (§ 76). Density = weight in air ÷ loss of weight.
Try it: clay boat
Roll a ball of clay and drop it in: it sinks. Shape the same clay into a wide boat: it floats, because it now pushes aside more water than its own weight. Add coins one at a time to see how much it can carry.
Try it: the floating egg
Put an egg in a glass of fresh water: it sinks. Stir in salt, a spoonful at a time, until it floats. Salt water is denser, so the egg displaces its weight with less of itself under water (question 3).
Explain the hydrometer
A floating stick sinks deeper in a light liquid and less deep in a dense one (§ 78). That is a hydrometer. Your student can make one from a pencil with a thumbtack in the end, floated in fresh water and then in salt water.
Say it back
Your student tells the crown story and explains how Archimedes' idea could test the crown without harming it.
Problems
Choose about ten of the nineteen problems on book pages 56–57. Problems 2, 4, 6–10, 13, 15 and 17 are good choices.
Afterwards
Next bath or swim, notice how light your body feels, and how much easier it is to lift a friend in the water.
Tip
A luggage scale or a kitchen scale with a hook is enough for the weigh-in-water experiment; weigh the stone in a bag hung below it.
Answers to the book's problems
1. The hollow hull pushes aside a weight of water greater than its own weight. 2. 150 cu. ft. of water, about 9345 lb. 3. It rises (the boat floats higher in denser salt water). 4. About 941 ft. in all; about one ninth (0.106) of an iceberg shows above water. 5. In fresh water about 0.43 ft. (about 5 in.), taking 100 tons = 200,000 lb. 6. 0.6. 7. About 0.86. 8. About 6.9 in. 9. About 1.14 (35 cc displaced). 10. 6680 g. 12. 200 lb. (the stone loses 1/2.5 of its weight in water). 13. About 0.17 (the cork displaces 360 cc). 14. About 113.7 liters (the lead takes up 1.33 liters). 15. Oil 0.92, alcohol 0.80. 16. About 0.57. 17. Volume 15 cc; platinum density 22; acid density 1.8. 18. So the bubble always rests at the highest point of the curve, the middle, when the level is true. 19. One fourth.
Worked out for this site from the scan. If a number in your copy differs, trust the book.