also the density of the former to that of the latter, as 99 to 68, or as 10 to 7 nearly, and their mean distance 30 of the earth's diameters ? Ans. at 105 2 parts of a diameter from the earth's centre, or 50 parts of a diameter, or 648 miles below the 4 I surface. QUEST. 40. Whereabouts, between the earth and moon, are their attractions equal to each other? Or where must another body be placed, so as to remain suspended in equilibrio, not being more attracted to the one than to the other, or having no tendency to fall either way? Their dimensions being as in the last question. Ans. From the earth's centre 26 of the earth's di- ameters. QUEST. 41. Suppose a stone dropt into an abyss, should be stopped at the end of the 11th second after its delivery; what space would it have gone through? Ans. 1946 feet. QUEST. 42. What is the difference between the depths of two wells, into each of which should a stone be dropped at the same instant, the one will strike the bottom at 6 seconds, the other at 10? Ans. 1029 feet. QUEST. 43. If a stone be 19 seconds in descending from the top of a precipice to the bottom, what is its height? Ans. 6115 feet. QUEST. 44. In what time will a musket ball, dropped from the top of Salisbury steeple, said to be 400 feet high, reach the bottom? Ans. 5 seconds nearly. Quest. 45. If a heavy body be observed to fall through 100 feet in the last second of time, from what height did it fall, and how long was it in motion? Ans. time 333 sec. and height 2094273 feet. 86 QUEST. 46. A stone being let fall into a well, it was observed that, after being dropped, it was 10 seconds before the sound of the fall at the bottom reached the ear. What is the depth of the well? Ans. 1270 feet nearly. QUEST. 47. It is proposed to determine the length of a pendulum vibrating seconds, in the latitude of London, where a heavy body falls through 16 feet in the first second of time? Ans. 39-11 inches. By experiment this length is found to be 394 inches. QUEST. 48. What is the length of a pendulum vibrating in 2 seconds; also in half a second, and in a quarter second? Ans.. the 2 second peudulum 156 the second pendulum 2 935 second pendulum 2,5 inches. 129 QUEST. 49. What difference will there be in the number of vibrations, made, by a pendulum of 6 inches long, and another of 12 inches long, in an hour's time? Ans. 2692. QUEST. 50. Observed that while a stone was descending, to measure the depth of a well, a string and plummet, that from the point of suspension, or the place where it was held, to the centre of oscillation, measured just 18 inches, had made 8 vibrations, when the sound from the bottom returned. What was the depth of the well? Ans. 412-61 feet. QUEST. 51. If a ball vibrate in the arch of a circle, 10 degrees on each side of the perpendicular; or a ball roll down the lowest 10 degrees of the arch; required the velocity at the lowest point? the radius of the circle, or length of the pendulum, being 20 feet. Ans. 4.4213 feet per second. QUEST. 52. If a ball descend down a smooth inclined plane, whose length is 100 feet, and altitude 10 feet; how long will it be in descending, and what will be the last velocity 80 Ans. the veloc. 25.364 feet per sec. and time 7.8852 sec. !་ QUEST. 53. If a cannon ball, of 1lb weight, be fired against a pendulous block of wood, and, striking the centre of oscillation, cause it to vibrate an arc whose chord is 30 inches; the radius of that are, or distance from the axis to the lowest point of the pendulum, being 118 inches, and the pendulum vibrating in small arcs 40 oscillations per minute. Required the velocity of the ball, and the velocity of the centre of oscillation of the pendulum, at the lowest point of the arc; the whole weight of the pendulum being 500lb ? Ans. veloc. ball 1956 6054 feet per sec. and veloc. cent. oscil. 3.9054 feet per sec. QUEST. 54. How deep will a cube of oak sink in common water; each side of the cube being 1 foot? QUEST. 55. How deep will a globe of oak sink in water; the diameter being 1 foot ? Ans. 9.9867 inches. QUEST. 56. QUEST. 56. If a cube of wood, floating in common water, have 3 inches of its height dry above the water, and 4+ inches dry when in sea-water; it is proposed to determine the magnitude of the cube, and what sort of wood it is made of? Ans. the wood is oak, and each side 40 inches. QUEST. 57. An irregular piece of lead ore weighs, in air 12 ounces, but in water only 7; and another fragment weighs in air 14 ounces, but in water only 9; required their comparative densities, or specific gravities? Ans. as 145 to 132. QUEST. 58. An irregular fragment of glass, in the scale, weighs 171 grains, and another of magnet 102 grains; but in water the first fetches up no more than 120 grains, and the other 79: what then will their specific gravities turn out to be? Ans. glass to magnet as 3933 to 5202 or nearly as 10 to 13. QUEST. 59. Hiero, king of Sicily, ordered his jeweller to make him a crown, containing 63 ounces of gold. The workmen thought that substituting part silver was only a proper perquisite; which taking air, Archimedes was appointed to examine it; who, on putting it into a vessel of water, found it raised the fluid 8.2245 cubic inches: and having discovered that the inch of gold more critically weighed 10.36 ounces, and that of silver but 5.85 ounces, he found by calculation what part of the king's gold had been changed. And you are desired to repeat the process. Ans. 28.8 ounces. QUEST. 60. Supposing the cubic inch of common glass weigh 14921 ounces troy, the same of sea-water 59542, and of brandy 5368; then a seaman having a gallon of this liquor in a glass bottle, which weighs 3.84lb out of water, and, to conceal it from the officers of the customs, throws it overboard. It is proposed to determine, if it will sink, how much force will just buoy it up? Ans. 14 1496 ounces, QUEST. 61. Another person has half an anker of brandy, of the same specific gravity as in the last question; the wood of the cask suppose measures of a cubic foot; it is proposed to assign what quantity of lead is just requisite to keep the cask and liquor under water? Ans. 89.743 ounces. QUEST. 62. Suppose, by measurement, it be found that a man-of-war, with its ordnance, rigging, and appointments, sinks so deep as to display 50000 cubic feet of fresh water; what is the whole weight of the vessel? QUEST. 63. It is required to determine what would be the height of the atmosphere, if it were every where of the same density as at the surface of the earth, when the quicksilver in the barometer stands at 30 inches; and also, what would be the height of a water barometer at the same time? Ans. height of the air 291663 feet, or 5.5240 miles, height of water 35 feet. QUEST. 64. With what velocity would each of those three fluids, viz. quicksilver, water, and air, issue through a small orifice in the bottom of vessels, of the respective heights of 30 inches, 35 feet, and 5.5240 miles, estimating the pressure by the whole altitudes, and the air rushing into a vacuum? Ans. the veloc. of quicksilver 12.681 feet. the veloc. of water the veloc. of air 47.447 QUEST. 65. A very large vessel of 10 feet high (no matter what shape) being kept constantly full of water, by a large supplying cock at the top; if 9 small circular holes, each of an inch diameter, be opened in its perpendicular side at every foot of the depth: it is required to determine the several distances to which they will spout on the horizontal plane of the base, and the quantity of water discharged by all of them in 10 minutes? √36 6.00000 and the quantity discharged in 10 min. 123-8849 gallons. Note. In this solution, the velocity of the water is supposed to be equal to that which is acquired by a heavy body in falling through the whole height of the water above the orifice, and that it is the same in every part of the holes. VOL. II. Τ QUEST. QUEST. 66. If the inner axis of a hollow globe of copper, exhausted of air, be 100 feet; what thickness must it be of, that it may just float in air? of Ans. 02688 of an inch thick. QUEST. 67. If a spherical balloon of copper, of an inch thick, have its cavity of 100 feet diameter, and be filled with inflammable air, of of the gravity of common air, what weight will just balance it, and prevent it from rising up into the atmosphere? Ans. 21273 lb. QUEST. 68. If a glass tube, 36 inches long, close at top, be sunk perpendicularly into water, till its lower or open end be 30 inches below the surface of the water; how high will the water rise within the tube, the quicksilver in the common barometer at the same time standing at 29 inches? Ans. 2.26545 inches. QUEST. 69. If a diving bell, of the form of a parabolic conoid, be let down into the sea to the several depths of 5, 10, 15, and 20 fathoms; it is required to assign the respective heights to which the water will rise within it : its axis and the diameter of its base being each 8 feet, and the quicksilver in the barometer standing at 30-9 inches? Ans. at 5 fathoms deep the water rises 2·03546 feet. at 10 at 15 at 20 3.06393 3.70267 4.14658 |