. A text book of elementary mechanics, for the use of colleges and schools. le the point of application of the power makes a revo-lution of 3 feet, the screw advances i of an inch; the power is 50lbs.: What is the weight raised? 5. The angle of the screw is 10°, and the length of the power-arm is twenty times the radius of the cylinder: WThat is the me-chanical advantage? 6. The circumference described by the power-arm is 20 feet, andthe mechanical advantage 480: How many threads in the screware there to the inch ? 7. The circumference described by the power-arm is 14 feet, thepower is 60 lbs.
. A text book of elementary mechanics, for the use of colleges and schools. le the point of application of the power makes a revo-lution of 3 feet, the screw advances i of an inch; the power is 50lbs.: What is the weight raised? 5. The angle of the screw is 10°, and the length of the power-arm is twenty times the radius of the cylinder: WThat is the me-chanical advantage? 6. The circumference described by the power-arm is 20 feet, andthe mechanical advantage 480: How many threads in the screware there to the inch ? 7. The circumference described by the power-arm is 14 feet, thepower is 60 lbs., and the weight 6 tons (6 X 2240 lbs.): What isthe distance between the threads of the screw? 8. The power-arm of a differential screw is 18 inches; there are6 threads to the inch in the larger screw, and 8 threads in thesmaller; the power is 30 lbs.: What weight can be supported? CHAPTER IX.—PENDULUM. 244. Motion in a Vertical Circle. Let ABC (Fig. 188)represent a vertical circle, regarded as perfectly a particle to start from rest at A and slide down. toward B; its velocity (v) at any point M will be thesame (40) as if it had fallen through the vertical heightFF; that is, v* = (1) Since DMB and DAB are right angles, by geometry,MB* = , (2) AB2 = Di?.^. (3) Let ^45 = a, and MB == 2; also, D5 = 2r; substitut-ing these values and subtracting (2) from (3), a9 - z* = 2r (jE« - J7^) = % (4) 245.] SIMPLE PENDULUM. 253 Introducing the value of EFfvom (4) in (1), we obtain v» - I (a* _ z*)} v = ±yl (r^ _ *2). (5) For the point A (or A), z = a, and therefore # = 0;for B, z = 0 and v = ± a y —%, the double sign indicat-ing that the motion may be from A toward Af (+), or thereverse (—). For two points M and M9, equally dis-tant from B, BM = + ,*, and BM = - z; for boththese the value of # is the same, and for each there is a-f- value and a — value, according to the direction ofthe motion. It is evident that if the particle were pro-jected fro
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectmechanics, bookyear18
