. An elementary treatise of mechanical philosophy, wirtten for the use of the undergraduate students of the University of Dublin. quation (11), or t infinite in equation(12), there is ^ m This, therefore, is the limit to which the velocity of the de-scending body always approaches, without ever attaining tothat value. When the body thrown upwards with the velocity v,returns to the point from which it was projected, it is evi-dent that it does not regain the whole of this velocity, inas- OF FORCES PRODUCING RECTILINEAR MOTION. 301 much as in each point of the space, the force which acce-lerates
. An elementary treatise of mechanical philosophy, wirtten for the use of the undergraduate students of the University of Dublin. quation (11), or t infinite in equation(12), there is ^ m This, therefore, is the limit to which the velocity of the de-scending body always approaches, without ever attaining tothat value. When the body thrown upwards with the velocity v,returns to the point from which it was projected, it is evi-dent that it does not regain the whole of this velocity, inas- OF FORCES PRODUCING RECTILINEAR MOTION. 301 much as in each point of the space, the force which acce-lerates the motion in the descent, is less than that by whichthe motion upwards was retarded. These velocities arecompared by equating the values of x and x, as given forthe body in its ascent and descent. This gives €±^=-^. and .=-£2^,. g g—mv g + mv^ Wherein mv~ is the resistance encountered by the bodymoving with the velocity of projection. The same state-ment will serve for comparing the velocities of ascent anddescent at any point, by putting in place of v, the velocityof ascent at that point. 302 DYNAMICS,—SECT. CTION III. OF FORCES PRODUCING CURVILINEAR MOTION. 1. When a body moves in a curve of any kind, the direc-tion of its motion is continually changed, which cannot be,unless the body is under the influence of a force or forcesacting in directions different from that of the motion. Nowit is the business of mechanical philosophy to connect theseforces and movements, so that each may be ascertained, asto its intensity, direction, and laws, when the other is those who first cultivated this branch of mechanics, suchquestions were managed by resorting to the indefinitelysmall movements successively compounded, and the forcesby which they were produced. Thus, if ac (Fig. 139.) isthe path of the body; am the portion of the tangent at a,which would have been described in a unit of time with thevelocity at that point; and ao, the line actually describedin that
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Keywords: ., bookcentury1800, bookide00leme, booksubjectdynamics, bookyear1835
