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 ma.s.s of unit volume of the substance._ In the metric system, for example, the density of a substance is the ma.s.s 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:

Density (lbs. per cu. ft.) = (numerically) 62.4 sp. gr.

=50. Methods for Finding Density and Specific Gravity=

=(a) Regular Solids.=--Solids of regular shapes such as cubes, spheres, etc., whose volumes may be readily found by measurement, may be weighed.

The ma.s.s divided by the volume gives the density, or _D = M/v_.

=(b) Irregular Solids.=--with these the volume cannot be found by measurement but may be obtained by Archimedes' Principle. Weigh the solid first in the air and then in water. The apparent loss of weight equals the weight of the equal volume of water displaced. From this the volume may be found. And then the

density equals ma.s.s/volume; the specific gravity =

wt. in air / wt. of equal volume of water = wt. in air / ((wt. in air) - (wt. in water))

ma.s.s density equals ------; the specific gravity = volume

wt. in air wt. in air ---------------------------- = ----------------------------- wt. of equal volume of water ((wt. in air) - (wt. in water))

=(c) Solids Lighter than Water.=--This will require a sinker to hold the body under water. Weigh the solid in air (_w_). Weigh the sinker in water (_s_). Attach the sinker to the solid and weigh both in water (w'). The specific gravity equals

(wt. of solid in air)/(loss in wt. of solid in water) or _w/((w + s) - w')_

wt. of solid in air _w_ --------------------------- or ------------ loss of wt. of solid in water (_w + s_) - _w'_

The apparent loss of weight of the solid is equal to the sum of its weight in air plus the weight of the sinker in water, less the combined weight of both in water.

=(d) The Density of a Liquid by a Hydrometer.=--One may also easily find the density of any liquid by Archimedes' Principle. If one takes the rod described in Art. 46, and places it in water, the number of cubic centimeters of water it displaces indicates its weight in grams. On placing the rod in another liquid in which it floats, it will of course displace its own weight and the height to which the liquid rises on the scale gives the volume. By dividing the _weight_ of the rod as shown by its position in _water_ by the _volume_ of the _liquid_ displaced we obtain the density of the liquid. Commercial hydrometers for testing the density of milk, alcohol and other liquids are made of gla.s.s of the form shown in Fig. 28. The long narrow stem permits small differences in volume to be noticed, hence they are more accurate than the rod described in the preceding paragraph. For convenience this rod contains a paper scale, so that when the height of the liquid on the stem is noted, the density is read at once.

[Ill.u.s.tration: FIG. 28.--A hydrometer used to find the density of a liquid.]

=Density of Liquids by Loss of Weight.= Weigh a piece of gla.s.s in air (_W_{a}_), in water (_W_{w}_), and in the liquid to be tested (_W_{l}_).

Then (_W_{a}_ - _W_{w}_)gives the weight of the water displaced.

And (_W_{a}_ - _W_{l}_) gives the weight of the liquid displaced.

Hence, (_W_{a}_ - _W_{l}_)/(_W_{a}_ - _W_{w}_) equals the specific gravity of the liquid.

Important Topics

1. Definitions of density and specific gravity.

2. Methods of finding density: (a) regular solids; (b) irregular solids; (c) solids lighter than water; (d) liquids by hydrometer; (e) liquids by loss of weight.

Exercises

_Note._--Consider that 1 cu. ft. of water weighs 62.4 lbs. Consider that 1 ccm. of water weighs 1 g.

1. What is meant by the statement that a block of wood has a specific gravity of 0.6?

2. Considering that the density of the human body is the same as that of water, what is the volume of a 125-lb. boy? Of a 250-lb. man? Of a 62.4-lb. boy? What is the volume of your body?

3. How is the weight of large ships found? Give an example.

4. Mention three cases where determinations of density are important.

5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find (a) the density of the body; (b) its volume; (c) density of the acid.

6. If the specific gravity of a horse is 1, what is the volume of a horse weighing 500 kg.? Of one weighing 1248 lbs.?

7. A weighted wooden box sinks to a depth of 20 cm. in water and 24 cm.