. Natural philosophy. including statics, hydrostatics, pneumatics, dynamics, hydrodynamics, the general theory of undulations, the science of sound, the mechanical theory of music, etc. : designed for the use of normal and grammar schools, and the higher classes in common schools . t consists of two screws of dif- Fig. 14. ferent pitch, working one withinthe other (Fig. 14), so that at eachrevolution of the power lever theweight is raised through a spaceonly equal to the difference be-tween the pitch of the exteriorscrew and the pitch of the innerscrew. It follows that the mechan-ical effect o
. Natural philosophy. including statics, hydrostatics, pneumatics, dynamics, hydrodynamics, the general theory of undulations, the science of sound, the mechanical theory of music, etc. : designed for the use of normal and grammar schools, and the higher classes in common schools . t consists of two screws of dif- Fig. 14. ferent pitch, working one withinthe other (Fig. 14), so that at eachrevolution of the power lever theweight is raised through a spaceonly equal to the difference be-tween the pitch of the exteriorscrew and the pitch of the innerscrew. It follows that the mechan-ical effect of the differential screwis equal to that of a single sere >having a pitch equal to the differ-ence of pitch of the two screws. For instance, in Fig. 14, the part B works within the part A. Xow, if Bhave a pitch of ^gigth of an inch and A a pitch of -,i-, then at each revolu-tion of the handle the weight will be raised through .1^ — _^i^- = -i - of aninch, and the whole instrument has the same mechanical effect as a singlescrew having a pitch of Tjsoth of an inch. 130. For the differential screw, let P = power, W = weight,1 =r length of lever, and d = difference of pitch of the tico screws. ThenP: W :: d : /x2x3-1416. W X d PX/X2X3-1416 Hence P = /x 2 X 3-i41G ^ ^^ = rf. Art. 131] THE ENDLESS SCREW. 45 Example 101.—What power will exert a pressure of 20000 means of a flifFerential screw having a power lever 50 inchesin length, the exterior screw a pitch of y( of aa inch, and theinner screw a pitch of-/,ith of an inch? SOLVTlOy. HprpTr=20000,/ = 50in., and(Z= rr — ifo =an incti. Tbp„p E^l _ 20000 xi/o-^5^i^ /X2x31416~ 50x2x314:16 31416= 7-81 lbs. Ans. ExAyrpLB 102.—What pressure will be exerted by a power of1000 lbs. acting on a differential screw in whioh the power leveris inches long, the pitch of the exterior screw -^f of an inch,and that of the interior screw -J^j of an inch ? SOLUTION. Hpre P = 1000 lbs., := /75 , and d = -if—^o = If o —iu5
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Keywords: ., bookcentury1800, bookdecade1860, booksubjectphysics, bookyear1867
