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moved with 5 times the celerity of the second; what is the ratio of the times they have been in describing those spaces? Ans. as 2 to 1.
QUEST. 15. If a lever, 40 effective inches long, will, by a certain power thrown successively on it, in 13 hours, raise a weight 104 feet; in what time will two other levers, each 18 effective inches long, raise an equal weight 73 feet?
Ans. 10 hours 8 minutes. QUEST. 16. What weight will a man be able to raise, who presses with the force of a hundred and a half, on the end of an equipoised handspike, 100 inches long, meeting with a convenient prop exactly 71 inches from the lower end of the machine ? Ans. 2072lb.
Quest 17. A weight of 14 lb, laid on the shoulder of a man, is no greater burden to him than its absolute weight, or 24 ounces: what difference will he feel between the said weight applied near his elbow, at 12 inches from the shoulder, and in the palm of his hand, 28 inches from the same; and how much more must his muscles then draw to support it at right angles, that is, having his arm stretched right out?
Ans. 24lb avoirdupois.
QUEST. 18. What weight hung on at 70 inches from the centre of motion of a steel-yard will balance a small gun of 94 cwt, freely suspended at 2 inches distance from the said centre on the contrary side? Ans. 30 lb.
QUEST. 19. It is proposed to divide the beam of a steelyard, or to find the points of division where the weights of 1, 2, 3, 4, &c. lb, on the one side, will just balance a constant weight of 95lb at the distance of 2 inches on the other side of the fulcrum; the weight of the beam being 10lb, and its whole length 32 inches?
Ans. 30, 15, 10, 71, 6, 5, 42, 33, 31, 3, 2, 21, &c. QUEST. 20. Two men carrying a burden of 200lb weight between them, hung on a pole, the ends of which rest on their shoulders; how much of this load is borne by each man, the weight hanging 6 inches from the middle, and the whole length of the pole being 4 feet? Ans. 125lb and 75lb.
QUEST. 21. If, in a pair of scales, a body weigh 90lb in one scale, and only 40lb in the other; required its true weight, and the proportion of the lengths of the two arms of the balance beam, on each side of the point of suspension ?
Ans. the weight 60lb. and the proportion 3 to 2. QUEST. 22. To find the weight of a beam of timber, or other body, by means of man's own weight, or any other weight. For instance, a piece of tapering timber, 24 feet long, being laid over a prop, or the edge of another beam,
is found to balance itself when the prop is 13 feet from the less end; but removing the prop a foot nearer to the said end, it takes a man's weight of 210lb, standing on the less 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 so 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 2lb weight on the other side is moved to G, within 8 inches of p, before the cane will rest in equilibrio. Required the weight of the body? Ans. 24lb.
QUEST. 24. If AB, BC be two inclined planes, of the lengths of 30 and 40 inches, and moveable about the joint at в : what will be the ratio of two weights P, Q, in equilibrio on the planes, in all positions of them and what will be the altitude BD of the angle B above the horizontal plane Ac, when this is 50 inches long?
Ans. BD24; and P to Q 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 1 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. 22619 lb.
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, or 4·29325 feet.
having its upright section a triangle, tapering to a point at
Ans. the breadth of the rectangle 12, or 5.36656,
but the base of the triangular bank 12, 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 471 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 nearly of the earth's light and heat.
QUEST. 37. A certain body on the surface of the earth weighs a cwt. or 112lb; the question is whither this body must be carried, that it may weigh only 101b?
Ans. either at 3.3466 semi-diameters, or 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 7920 miles ?
Ans. 15oz. 95dr. nearly.
QUEST. 39. Whereabouts, in the line between the earth and moon, is their common centre of gravity; supposing the earth's diameter to be 7920 miles, and the moon's 2160; also.
the density of the former to that of the latter, as 99 to 68, or
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 26·8 of the earth's
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
QUEST. 43. If a stone be 19 seconds in descending from
QUEST. 44. In what time will a musket ball, dropped from
observed to fall through
QUEST. 45. If a heavy body be
Ans. time 3235 sec. and height 2094273 feet.
QUEST. 46. A stone being let fall into a well, it was observ-
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 391 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 pendulum 1561
the second pendulum
the second pendulum 257 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. 26921,
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?
Ans. the veloc. 25-364 feet per sec. and time 7·8352 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 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. 3.9054 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.