Elements of mechanics: for the use of colleges, academies, and high schools (1859)
Peck, William G. (William Guy), 1820-1892 · New York, A. S. Barnes & Burr · leaf 77
^ _ fydx x, = I ydx and 7/j J ydx (34.) Centre of Gravity of a parabolic area, 6§a Let A OB represent the area,having its chord at right angles to theaxis. Let 0 be the origin of co-ordinates,taken at the vertex, and let the axis of Xcoincide with the axis of the curve; thevalue of yr will, as… … fV^P fx3dx CENTRE OF GRAVITY. 75 Integrating between the limits x = 0, and x = ay wehave, and, hence, / x2dxo 5. x2dx = |aJ That is, the centre of gravity of a segment of a parabolais on its axis, and at a distance from the vertex equal tothree-fifths of the altitude of the segment. Application to…
Mechanics
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