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31. Specific gravity of a solid lighter than water. If the body is too light to sink of itself, we may still obtain the weight of the equal volume
of water by forcing it beneath the surface with a sinker. Thus, suppose w, represents the weight on the right pan of the balance when the body is in air and the sinker in water, as in Fig. 19, while w is the weight on the right pan when both body and sinker are under water. Then w1
is obviously the buoyant effect FIG. 19. Method of finding specific of the water on the body alone gravity of a light solid
and is therefore equal to the weight of the displaced water.
32. Specific gravity of liquids by the hydrometer method. The commercial hydrometer such as is now in common use for testing the specific gravity of alcohol, milk, acids, sugar solutions, etc. is of the form shown in Fig. 20. The stem is calibrated by trial so that the specific gravity of any liquid may be read upon it directly. The principle involved is that a floating body sinks until it displaces its own weight. By making the stem very slender the sensitiveness of the instrument may be made very great. Why?
FIG. 20. Con
33. Specific gravity of liquids by "loss of weight" method. If any suitable solid be weighed, first in air, then in water, and then in a liquid of unknown specific gravity, by the stant-weight principle of Archimedes the loss of weight in the liquid is equal to the weight of the liquid displaced, and the loss in water is equal to the weight of the water
displaced. If we divide the loss of weight in the liquid by the loss of weight in water, we are dividing the weight of a given volume of liquid by the weight of an equal volume of water. Therefore,
To find the specific gravity of a liquid, divide the loss of weight of some solid in it by the loss of weight of the same body in water.*
QUESTIONS AND PROBLEMS
1. Let a vessel of water, together with an object heavier than water, be counterpoised as in Fig. 21 (position a). Now if the object be placed inside the vessel of water (position b), will the scales remain balanced? Predict the result and then
try the experiment.
2. Does the weight apparently lost by a submerged body depend upon its volume or its weight? Explain.
3. A brick lost 1 lb. when submerged 1 ft. deep; how much would it lose if suspended 3 ft. deep?
4. Will a boat rise or sink deeper in the water as it passes from a river to the ocean?
5. A fish lies perfectly
motionless near the center
of an aquarium. What is the average density of the fish? Explain. 6. Where do the larger numbers appear on hydrometers, toward
the bottom or toward the top of the stem? Explain.
7. A 150-lb. man can just float. What is his volume?
8. Describe fully how you would proceed to find the specific gravity of an irregular solid heavier than water, showing in every case why you proceed as you do.
9. A body loses 25 g. in water, 23 g. in oil, and 20 g. in alcohol. Find the specific gravity of the oil and of the alcohol.
*Laboratory experiments on the determination of the densities of solids and liquids should follow or accompany the discussion of this chapter. See, for example, Experiments 7 and 8 of the authors' Manual.
10. A platinum ball weighs 330 g. in air, 315 g. in water, and 303 g. in sulphuric acid. Find the volume of the ball and the specific gravity of the platinum and of the acid.
11. A piece of paraffin weighed 178 g. in air, and a sinker weighed 30 g. in water. Both together weighed 8 g. in water. Find the specific gravity of the paraffin.
12. A cube of iron 10 cm. on a side weighs 7500 g. What will it weigh in alcohol of density .82?
13. What fraction of the volume of a block of wood will float above water if its density is .5? if its density is .6? if its density is .9? State in general what fraction of the volume of a floating body is under water.
14. If a rectangular iceberg rises 100 ft. above water, how far does it extend below water? (Assume the density of the ice to be .9 that of sea water.)
15. A barge 30 ft. by 15 ft. sank 4 in. when an elephant was taken aboard. What was the elephant's weight?
16. A cubic foot of stone weighed 110 lb. in water. Find its specific gravity.
17. Steel is three times as heavy as aluminum. When equal volumes of each are submerged in water, how do their apparent losses of weight compare?
18. The density of cork is .25 g. per cubic centimeter. What force is required to push a cubic centimeter of cork beneath the surface of water?
19. A block of wood 15 cm. by 10 cm. by 4 cm. floats in water with 1 cm. in the air. Find the weight of the wood and its specific gravity. 20. The specific gravity of milk is 1.032. How is its specific gravity affected by removing part of the cream? by adding water? May these two changes be made so as not to alter its specific gravity at all?
21. A piece of sandstone having a specific gravity of 2.6 weighs 480 g. in water. Find its weight in air.
22. The density of stone is about 2.5. If a boy can lift 120 lb., how heavy a stone can he lift to the surface of a pond?
23. The hull of a modern battleship is made almost entirely of steel, its walls being of steel plates from 6 to 18 in. thick. Explain how it can float.
PRESSURE IN AIR
34. The weight of air. To ordinary observation air is scarcely perceptible. It appears to have no weight and to offer no resistance to bodies passing through it. But if a bulb is balanced as in Fig. 22, and then removed and filled with air under pressure by a few strokes of a bicycle pump, it will be found, when placed on the balance again, to be heavier than it was before. On the other hand, if the bulb is connected with an air pump and exhausted, it will be found to have lost weight.* Evidently, then, air can be put into and taken out of a vessel, weighed, and handled, just like a liquid or a solid.
FIG. 22. Proof that air has weight
We are accustomed to say that bodies are "as light as air"; yet careful measurement shows that it takes but 12 cubic feet of air to weigh a pound, so that a single large room contains more air than an ordinary man can lift. Thus, the air in a room 60 feet by 30 feet by 15 feet weighs more than a ton. The exact weight of air at the freezing temperature and under normal atmospheric conditions is .001293 gram per cubic centimeter, that is, 1.293 grams per liter. A given volume of air therefore weighs as much as an equal volume of water.
* Another experiment is to weigh an electric-light bulb, then puncture it with a blowpipe and weigh again.
35. Proof that air exerts pressure. Since air has weight, it is to be inferred that air, like a liquid, exerts force against any surface immersed in it. The following experiments prove this.
Let a rubber membrane be stretched over a glass vessel, as in Fig. 23. As the air is exhausted from beneath the membrane the latter will be observed to be more and more depressed until it will finally burst under the pressure of the air above.
Again, let a tin can be partly filled with water and the water boiled. The air will be expelled by the escaping steam. While the boiling is
still going on, let the can be tightly corked, then placed in a sink or tray and cold water poured over it. The steam will be condensed and the weight of the air outside will crush the can (see Fig. 24).
36. Cause of the rise of liquids in exhausted tubes. If the lower end of a long tube be dipped into water and the air exhausted from the upper end, water will rise in the tube. We prove the truth of this statement every time we draw lemonade through a straw. The old Greeks and Romans explained such phenomena by saying that "nature abhors a vacuum," and this explanation was still in vogue in Galileo's time. But in 1640 the Duke of Tuscany had a deep well dug near Florence, and found to his surprise that no water pump which could be obtained would raise the water higher than about 32 feet above the level in the well. When he applied to the aged