11. An object weighing 500 g. just floats in water. What is its volume? How much water does a floating block of wood displace if it weighs 125 lbs.? 125 g.? 2 kg.? 2000 kg.? 12. A flat boat 10 × 40 ft. in size will sink how much in the water when 10 horses each weighing 1250 lbs. are placed on board? 13. A ship 900 ft. long and 80 ft. average width sinks to an average depth of 25 ft. when empty and 40 ft. when loaded. What is the weight of the ship and of its load? 14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? If it weighs 1200 g.? Explain. 15. If a 1000 cc. block of metal weighing 1200 g. is placed in the water in mid ocean what will become of it? 16. Prove Archimedes' Principle by use of the principles of liquid pressure. 17. An irregular stone, density 2.5 g. per ccm. displaces 2 cu. ft. of water. What is its weight? Its apparent weight in water? 18. Will the depth to which a vessel sinks in water change as she sails from Lake Ontario into the Atlantic Ocean? Why? 19. If the density of sea water is 1.0269 g. per cubic centimeter and that of ice 0.918 g. per ccm., what portion of an iceberg is above water? 20. In drawing water from a well by means of a bucket, why is less force used when it is under water than when entirely above? 21. A stone which weighs 300 lbs. can be lifted under water with a force of 150 lbs. What is the volume of the stone? 22. The average density of the human body is 1.07 grams per c.c. How much water will a man who weighs 150 lbs. displace when diving? How much when floating? (4) DENSITY AND SPECIFIC GRAVITY =48. Density.=--The density of a substance is often used as a test of its purity. Archimedes in testing King Hiero's crown to find out if it were made of pure gold determined first its density. It is by such tests that the purity of milk, of alcohol, of gold, and a great variety of substances is often determined. Knowledge of methods of finding density is of value to everyone and should be included in the education of every student. _The density of a substance is the mass of unit volume of the substance._ In the metric system, for example, the density of a substance is the mass in grams per 1 ccm. Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1 g. to the cubic centimeter. A cubic centimeter of aluminium weighs 2.7 g. Its density therefore is 2.7 g. per ccm. =49. Specific Gravity.=--_Specific gravity is the ratio of the weight of any volume of a substance to the weight of an equal volume of water._ Its meaning is not quite the same as that of density, since specific gravity is always a _ratio_, _i.e._, an _abstract_ number, as 2.7. Density of a substance is a _concrete_ number, as 2.7 grams per ccm. In the metric system the density of water is one gram per cubic centimeter, therefore we have: Density (g. per ccm.) = (numerically) specific gravity. In the English system, the density of water is 62.4 pounds per cubic foot, therefore in this system we have: