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7. A floating dock is shown in Fig. 478. When the chambers c are filled with water, the dock sinks until the water line is at A. The vessel is then floated into the dock. As soon as it is in place, the water is pumped from the chambers until the
water line is as low as B. Workmen can then get at all parts of the bottom. If each of the chambers is 10 ft. high and 10 ft. wide, what must be the length of the dock if it is to be available for the Berengaria (Cunard Line), of 50,000 tons' weight?
с с с C с с с
FIG. 478. Floating dock
8. If each boat of a pontoon bridge is 100 ft. long and 75 ft. wide at the water line, how much will it sink when a locomotive weighing 100 tons passes over it?
9. What must be the specific gravity of a liquid in which a body having a specific gravity of 6.8 will float with half its volume submerged? 10. A block of wood 10 in. high sinks 6 in. in water. Find the density of the wood.
11. If this block sank 7 in. in oil, what would be the density of the oil? 12. A graduated glass cylinder contains 190 cc. of water. An egg weighing 40 g. is dropped into the glass; it sinks to the bottom and raises the water to the 225-cc. mark. Find the density of the egg.
CHAPTER III. 1. Explain the process of making air enter the lungs; of making lemonade rise in a straw.
2. If a circular piece of wet leather having a string attached to the middle is pressed down on a flat, smooth stone, as in Fig. 479, the latter may often be lifted by pulling on the string. Is it pulled up or pushed up? Explain.
3. Make a labeled drawing of a simple Torricellian barometer, naming all the parts in the diagram.
4. The body of the average man has 15 sq. ft. of surface. What is the total force of the atmosphere upon him? Why is he unconscious of this crushing force?
5. If the variation of the height of a mercury barometer is 2 in., how far did the image rise and fall in Otto von Guericke's water barometer? (See § 42.)
6. What is Boyle's law? A mass of air 3 cc. in volume is introduced into the space above a barometer column which originally stands at 760 mm. The column sinks until it is only 570 mm. high. Find the volume now occupied by the air.
7. There is a pressure of 80 cm. of mercury on 1000 cc. of gas. What pressure must be applied to reduce the volume to 600 cc. if the temperature is kept constant?
8. Pressure tests for boilers or steel tanks of any kind are always made by filling them with water rather than with air. Why?
9. If the water within a diving bell is at a depth of 1033 cm. beneath the surface of a lake, what is the density of the air inside if at the surface the density of air is .0013 and its pressure 76 cm.? What would be the reading of a barometer within the bell?
10. If a diver descends to a depth of 100 ft., what is the pressure to which he is subjected? What is the density of the air in his suit, the density at the surface where the pressure is 75 cm. being .0012? (Assume the temperature to remain unchanged.)
11. How many of the laws of liquids and gases do you I find illustrated in the experiment of the Cartesian diver?
12. Pascal proved by an experiment that a siphon would not run if the bend in the arm were more than 34 ft. above the upper water level. He made it run, however, by inclining it sidewise until the bend was less than 34 ft. above this level. Explain.
13. How high will a lift pump raise water if it is located upon the side of a mountain where the barometer reading is 71 cm.?
14. Find the lifting power of a kite balloon whose capacity is 37,000 cu. ft., the lifting power of the gas being 64.4 lb. per 1000 cu. ft. and the weight of the balloon, cordage, car, and observer being 1300 lb.
CHAPTER IV. 1. Why does a confined body of gas exert pressure inversely proportional to its volume?
2. A lump of copper sulphate placed at the bottom of a graduate filled with water will dissolve and very slowly pass upward, although a copper-sulphate molecule is many times heavier than a water molecule. Explain.
CHAPTER V. 1. An airplane which flies in still air with a velocity of 120 mi. per hour is flying in a wind whose velocity is 60 mi. per hour toward the east. Find the actual velocity of the airplane and the direction of its motion when headed north; east; south; west.
2. Represent graphically a force of 30 lb. acting southeast and a force of 40 lb. acting southwest at the same point. What will be the magnitude of the resultant, and what will be its approximate direction?
3. Two concurrent forces, each of 50 lb., act at an angle of 60° with each other. Find the resultant graphically.
4. A child weighing 100 lb. sits in a swing. The swing is drawn aside and held in equilibrium by a horizontal force of 40 lb. Find the tension in each of the two ropes of the swing.
5. Four clothes posts were arranged to form a square. A clothesline was drawn around the outside of the posts with a force of 60 lb. With what force is each post drawn toward the center of the square?
6. A man weighing 150 lb. stood at the middle of a tight-rope whose two parts were each 50 ft. long. What was the tension on the parts of the rope, the weight of the man depressing the center of the rope 1 ft.?
7. A boy pulls a loaded sled weighing 200 lb. up a hill which rises 1 ft. in 5 measured along the slope. Neglecting friction, how much force must he exert?
8. A cask weighing 100 lb. is held at rest upon an inclined plank 8 ft. long and 3 ft. high. By the resolution-and-proportion method find the component of its weight that tends to break the plank.
9. What force will be required to support a 50-lb. ball on an inclined plane of which the length is 10 times the height?
10. A boy is able to exert a force of 75 lb. Neglecting friction, how long an inclined plane must he have in order to push a truck weighing 350 lb. up to a doorway 3 ft. above the ground?
11. Could a kite be flown from an automobile when there is no wind? Explain.
12. Why is it unsafe to stand up in a canoe ?
13. If a lead pencil is balanced on its point on the finger, it will be in unstable equilibrium, but if two knives are stuck into it, as in Fig. 480, it will be in stable equilibrium. Why?
14. Why does a man lean forward when he climbs a hill?
15. A boy dropped a stone from a bridge and noticed that it struck the water in just 3 sec. How fast was it going when it struck? How high was the bridge above the water?
16. If a body sliding without friction down an inclined plane moves 40 cm. during the first second of its descent, and if the plane is 500 cm. long and 40.8 cm. high, what is the value of g? (Remember that the acceleration down the incline is simply the component (§ 80) of g parallel to the incline.)
17. A ball shot straight upward near a pond was seen to strike the water in 10 sec. How high did it rise? What was its initial speed?
18. A trolley car moving from rest with uniform acceleration acquired a velocity of 10 mi. per hour in 15 sec. What was the acceleration and the distance traversed?
19. A bombing airplane is flying 60 mi. per hour in still air at a height of 1600 ft. In order to score a "bull's-eye,” at what distance in advance of the target must the bomb be let go?
20. A rifle weighing 5 lb. discharges a 1-oz. bullet with a velocity of 1000 ft. per second. What will be the velocity of the rifle in the opposite direction?
21. A steamboat weighing 20,000 metric tons is being pulled by a tug which exerts a pull of 2 metric tons. (A metric ton is equal to 1000 kg.) If the friction of the water were negligible, what velocity would the boat acquire in 4 min.? (Reduce mass to grams, force to dynes, and remember that F = mv/t.)
22. If a train of cars weighs 200 metric tons, and the engine in pulling 5 sec. imparts to it a velocity of 2 m. per second, what is the pull of the engine in metric tons?
CHAPTER VI. 1. What must be the cross section of a wire of copper if it is to have the same tensile strength (that is, break with the same weight) as a wire of iron 1 sq. mm. in cross section? (See §107.)
2. How many times greater must the diameter of one wire be than that of another of the same material if it is to have five times the tensile strength?
3. If the position of the pointer on a spring balance is marked when no load is on the spring, and again when the spring is stretched with a load of 10 g., and if the space between the two marks is then divided into ten equal parts, will each of these parts represent a gram? Why?
4. A wire which is twice as thick as another of similar material will support how many times as much weight?
5. A force of 3 lb. stretches 1 mm. a wire that is 1 m. long and .1 mm. in diameter. How much force will it take to stretch 5 mm. a wire of the same material 4 m. long and .2 mm. in diameter?
6. Why does a small stream of water break up into drops instead
of falling as a continuous thread?
7. Give four common illustrations of capillary attraction.
8. Explain the watering of flowers by setting the pot in a shallow
basin of water.
9. Why does a new and oily steel pen not write well? Why is it difficult to write on oiled paper?
10. Would mercury ascend a lamp wick as oil and water do?
11. Why do some liquids rise while others are depressed in capillary tubes?
12. If water will rise 32 cm. in a tube .1 mm. in diameter, how high will it rise in a tube .01 mm. in diameter?
13. How can you tell whether bubbles which rise from the bottom of a vessel which is being heated are bubbles of air or bubbles of steam?
CHAPTER VII. 1. A woman in sweeping a rug moved the nozzle of a vacuum sweeper a total distance of 130 ft., using an average force of one-half pound. How much work did she do?
2. Analyze several types of manual labor and see if the definition (WFs) holds for each. Is not Fx s the thing paid for in every case? 3. Explain the use of the rider in weighing (see Fig. 22).
4. Two boys are carrying a bag of walnuts at the middle of a long stick. Will it make any difference whether they walk close to the bag or farther away, so long as each is at the same distance?
5. If 3 horses are to pull equally on a load, how should the whippletree be designed?
FIG. 481. The automatic float valve
6. Why is it that a couple cannot be balanced by a single force? 7. If the ball of the float valve (Fig. 481) has a diameter of 10 cm., and if the distance from the center of the ball to the pivot S is 20 times the distance from S to the pin P, with what force is the valve R held shut when the ball is half immersed? Neglect weight of ball.
8. In the Yale lock (Fig. 482) the cylinder G rotates inside the fixed cylinder F and works the bolt through the arm H. The right key raises the pins a, b, c, d', e' until their tops are just even with the top of G. What mechanical principles do you find involved in this device?