Page images
PDF
EPUB

end, to hold it in equilibrium. Required the weight of the tree?

Ans. 2520lb. QUEST. 23. If AB be a cane or walking-stick, 40 inches long, suspended by a string sp fastened to the middle point D: now a body being hung on at E, 6 inches distance from D, is balanced by a weight of 2lb, hung on at the larger end A; but removing the body to F, one inch nearer to D, the 21b weight on the other side is moved to G, within 8 inches of , before the cane will rest in equilibrio. Required the weight of the body?

Ans. 241b. QUEST. 24. If AB, Bc be two inclined planes, of the lengths of 30 and 40 inches, and moveable about the joint at B: what will be the ratio of two weights P, Q, in equi. librio on the planes, in all positions of them: and what will be the altitude of the angle B above the horizon:al plane AC, when this is 50 inches long?

Ans. ED = 24; and p to g as AB to BC, or as 3 to 4. QUEST. 25. A lever, of 6 feet long, is fixed at right angles in a screw, whose threads are one inch asunder, so that the lever turns just once round in raising or depressing the screw one inch. If then this lever be urged by a weight or force of 50lb, with what force will the screw press ?

Ans. 2261921b. Quest. 26. If a man can draw a weight of 150lb up the side of a perpendicular wall, of 20 feet high ; what weight will he be able to raise along a smooth plank of 30 feet long, laid aslope from the top of the wall?

Ans. 225lb. QUEST. 27. If a force of 150lb be applied on the head of a rectangular wedge, its thickness being 2 inches, and the length of its side 12 inches; what weight will it raise or balance perpendicular to its side?

Ans. 900lb. Quest. 28. If a round pillar of 30 feet diameter be raised on a plane, inclined to the horizon in an angle of 75°, or the shaft inclining 15 degrees out of the perpendicular; what length will it bear before it overset ?

Ans. 30 (2 + 3) or 111.9615 feet. QUEST. 29. If the greatest angle at which a bank of natural earth will stand, be 45°; it is proposed to determine what thickness an upright wall of stone must be made throughout, just to support a bank of 12 feet high; the specific gravity of the stone being to that of earth, as 5 to 4.

Ans. 4. V š, or 4.29325 feet. QUEST. 30. If the stone wall be made like a wedge, or having its upright section a triangle, tapering to a point af

tors

top, but its side next the bank of earth perpendicular to the horizon; what is its thickness at the bottom, so as to support the same bank ?

Ans. 12V }, or 5.36656 feet. QUEST. 31. But if the earth will only stand at an angle of 30 degrees to the horizontal line; it is required to determine the thickness of wall in both the preceding cases ? Ans. the breadth of the rectangle 12V, or 5.36656,

but the base of the triangular bank 12V to, or 6.53667. QUEST.32. To find the thickness of an upright rectangular wall, necessary to support a body of water; the water being 10 feet deep, and the wall 12 feet high; also the specific gravity of the wall to that of the water, as 11 to 7.

Ans. 4•204374 feet. QUEST. 33. To determine the thickness of the wall at the bottom, when the section of it is triangular, and the altitudes as before.

Ans. 5.1492866 feet. Quest. 34. Supposing the distance of the earth from the sun to be 95 millions of miles; I would know at what distance from him another body must be placed, so as to receive light and heat quadruple to that of the earth.

Ans. at half the distance, or 474 millions. Quest. 35. If the mean distance of the sun from us be 106 of his diameters; how much hotter is it at the surface of the sun, than under our equator?

Ans. 11236 times hotter. QUEST. 36. The distance between the earth and the sun being accounted 95 millions of miles, and between Jupiter and the sun 495 millions; the degree of light and heat received by Jupiter, compared with that of the earth, is required?

Ans. Or, or nearly a', of the earth's light and heat.

090T, QUEST. 37. A certain body on the surface of the earth weighs a cit, or 1121b; the question is whither this body must be carried, that it may weigh only 10lb ? Ans. either at 3.3466 semi-diameters, or is of a semi

diameter, from the centre. Quest. 38. If a body weigh 1 pound, or 16 ounces, on the surface of the earth; what will its weight be at 50 miles above it, taking the earth's diameter at 7930 miles ?

Ans. 1502. 9 dr. nearly. QUEST. 39. Whereabouts, in the line between the earth and moon, is their common centre of gravity; supposing the carth's diameter to be 7930 miles, and the mioon's 2160; also

the

361

a

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 1 { parts of a diameter from the earth's centre,

or 42 parts of a diameter, or 648 miles below the

surface. QUEST. 40. Whereabouts, between the earth and moon, àre 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 dihenartha's

TT

moon's

. QUE67. 41. Suppose a stone dropt into an abyss, should be stopped at the end of the 1lth second after its delivery; what space would it have gone through?

Ans. 1946 4 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 194 seconds in descending from the top of a precipice to the bottom, what is its height?

Ans. 611515 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 2094272 feet. 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 161, feet in the first second of time?

Ans. 39:11 inches. By experiment this length is found to be 394 inches.

2 5

3

QUEST. 48.

I

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 pendulum 1564

the second pendulum 931

the second pendulum 2117 inches. 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. 26927.

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 dc. grees 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 wliat will be the last velocity?

Ans. the veloc. 25°364 feet per sec. and time 7.8852 sec. QUEST. 53. If a cannon ball, of llbweight, 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 arc, 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, 3.90.54 feet per sec. QUEST. 54. How deep will a cube of oak sink in common water; each side of the cube being 1 foot ?

Ans. Il' inches. Quest. 55. How deep will a globe of oak sink in water; the diameter being 1 foot ?

Ans: 9.9867 inches.

a

TO

QUEST

QUEST. 56. If a cube of wood, floating in common water, have three inches of it dry above the water, and 416 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 141 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 glasg weigh 1.4921 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 ouncesi 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,

a

« PreviousContinue »