Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . ne or more forces, inview of the foregoing, and of Newtons second law, given theinitial velocity in amount and direction, the starting-point,the initial amounts and directions of the acting forces and the 74 MECHANICS OF ENGINEERING. laws of their variation if they are not constant, we can resolvethem into a single X and a single Y force at any instant,determine the Xand Amotions independently, and afterwards
Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . ne or more forces, inview of the foregoing, and of Newtons second law, given theinitial velocity in amount and direction, the starting-point,the initial amounts and directions of the acting forces and the 74 MECHANICS OF ENGINEERING. laws of their variation if they are not constant, we can resolvethem into a single X and a single Y force at any instant,determine the Xand Amotions independently, and afterwardsthe resultant motion. The resultant force is never in the direc-tion of the tangent to the path (except at a point of inflection).The relations which its amount and direction at any instantbear to the velocity, the rate of change of that velocity, andthe radius of curvature of the path will appear in the nextparagraph. y\i 74. General Equations for the curvilinear motion of a ma-terial point in a plane.—The motion will be considered result-ing from the composition ofindependent X and Y motions,.Xand Y being perpendicular toeach other. Fig. 79. In twoconsecutive equal times (each. = dt), let dx and dx = smallspaces due to the X motion;and dy and CK = dy, due tothe Y motion. Then ds andds are two consecutive elementsfig. 79. of the curvilinear motion. Pro- long ds, making BE = ds; then EE = d*x, CE= d*y, andCO = d*s {EO being perpendicular to BE). Also draw CLperpendicular to BG and call CL d2n. Call the velocity ofthe X motion vx, its acceleration px; those of the Y motion^Vy and py. Then, v„ = d*xdf A dVV dx dy dv, dt> Vy = ~di; Px = ~dtFor the velocity along the curve (, tangent)v = ds -— dt, we shall have, since ds* = dx2 -f- dy*,, (dsV fdxV . (dy\ a *=U = [dt) + KdiJ = v*+v* df* CO Hence v is the diagonal formed on vx and vv (as in § 71).Let j^ = the acceleration of v, , the tangential acceleration^. CURVILINEAR MOTION OF A MATERIAL POINT. 75 then^?e = d2s
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
