. 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 . the wheel ? jins. 151^f inches. 35. By means of a wheel and axle a power of 22 lbs. balances aweight of 870 lbs. If the radius of the wheel be 67 incheswhat will be the radius of the nxle ? Jn$. IJ^ inches. 28 THE WHEEL AND AXLE. [,88. THE DIFFERENTIAL WHEEL AND AXLE. 87. In the differential wheel and axle, t
. Natural philosophy. including statics, hydrostatics, pneumatics, dynamics, hydrodynamics, the general theory of undulations, the science of sound, the mechanical theory of music, etc. : designed for the use of normal and grammar schools, and the higher classes in common schools . the wheel ? jins. 151^f inches. 35. By means of a wheel and axle a power of 22 lbs. balances aweight of 870 lbs. If the radius of the wheel be 67 incheswhat will be the radius of the nxle ? Jn$. IJ^ inches. 28 THE WHEEL AND AXLE. [,88. THE DIFFERENTIAL WHEEL AND AXLE. 87. In the differential wheel and axle, the axle consistsof two parts, one thicker than theother. By each revolution of thewheel the rope rolls once off thethinner portion and once on thethicker portion, and is consequentlyshortened only by the differencesbetween the circumferences of theaxles; and the distance throughwhich the weight is raised is equalto half the shortening of the effect is therefore the sameas if an axle had been used witha radius equal to half the differencebetween the radii of the thicker and thinner parts of thedifferential axle.^ 88, For the differential wheel and axle let d = the differencebetween the radii of the axles, R =i radius of the wheel^ F =z thepower, and W = the ThenP: W: : Id : R. Whence P — Wy.\dR PxR Wx\d ^^ PxR—p—, and d = -j^. Example 36.—In a differential wheel and axle the radius ofthe larger axle is 4^ inches, the radius of the smaller axle is 4^inches, the radius of the wheel is 70 inches. What power willbalance a weight of 1000 lbs. SOLniOH. Here d = difference of radii = i — ^, = J^, IF= 1000 lbs., £ = 10 in. men/--. ^ _ ^^ -gr ^5^ = ^,«. Example 37.—In a differential wheel and axle the radii of theaxles are 2\ and 2^ inches, the radius of the wheel is 100 power will balance a weight of 7234 lbs. ? • The radii l>eine proportional to tlie circumferences. ] THE ^VHEEL AND AXLE. 20 SOLUTIOK. Here d — .\^ ^3^-=^«-
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Keywords: ., bookcentury1800, bookdecade1860, booksubjectphysics, bookyear1861
