. 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 . elaw as regards velocity as those on inclined planes, i. e.,the terminal velocity is due only to the perpendicular faU. 274. The Brachystochrone (Greek hrachistos, shortest,and chronos, time,) or curve of quickest descent, is acurve somewhat greater than a circular curve, being whatmathematicians denominate a cycloi
. 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 . elaw as regards velocity as those on inclined planes, i. e.,the terminal velocity is due only to the perpendicular faU. 274. The Brachystochrone (Greek hrachistos, shortest,and chronos, time,) or curve of quickest descent, is acurve somewhat greater than a circular curve, being whatmathematicians denominate a cycloid, or that whicliTis de-scribed by a point in the circumference of a carriage wheelrolling along a plane. 275. Since Art. 270, the effect of gravity as an accelerating force on abody de.^cending an inclined piano is to the effect of gravity on a bodyIreely falling through the air as the height of the plane is to its length ;we have accelerating force of gravity on inclined plane ; and hence ghaccelerating force of gravity on inclined planes = —, Iwhere h = height of = length. g =z effect of gravity =32 Substitnting this value of the effect of gravity in the formulas in Art. 2fjf we get the foflowing formulas for the deecent of bodies on inclined planes. 126 DESCENT ON INCLINED PLANES. [Art. 276. FORMULAS FOR DESCENT OF BODIES ON INCLINEDPLANES. KO. GIVEJf. TO yoajtfULAs. CORRESPONDI5G FORMULA IN ART. 266. 1 23 g, h. I, t9, fi, I, V t. V S ght* 21 ^ 2gh s = iJv III in 456 s, t g. h, I, t g, h, I, s V 2s . VIIV V 78 9 S, V grh,i,vg,h,i,s t 2s ~ V Iv VI rvni IX 276. When the body is projected down an inclined plane with a given initial velocity V; and V ^ht ^f (10. ~ (11). When the body is projected up an inclined plane with a given initial velocity V; s = Vt?|f(12.) F-?ffa3.) Note.—When a body is thrown up an inclined plane, the attraction ofgravity acta as a uniformly retarding torce as when a body is projected Art. 276.] DESCENT ON INCLINED PLAN
Size: 1170px × 2135px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1860, booksubjectphysics, bookyear1867
