. A text book of elementary mechanics, for the use of colleges and schools. upon itssurface is exerted in the direction of lines drawn to thecentre. For the particles of the same body, or of neigh-boring bodies, these lines may be regarded as a given body the resultant of all these parallel forceswill act, whatever its position, at a certain point, calledthe centre of gravity. Hence Tlie centre of gravity of a tody is that point at whichthe whole weight of the body may he considered as concen-tratal; or— It is a point at which the body, if supported there andif acted upon only by
. A text book of elementary mechanics, for the use of colleges and schools. upon itssurface is exerted in the direction of lines drawn to thecentre. For the particles of the same body, or of neigh-boring bodies, these lines may be regarded as a given body the resultant of all these parallel forceswill act, whatever its position, at a certain point, calledthe centre of gravity. Hence Tlie centre of gravity of a tody is that point at whichthe whole weight of the body may he considered as concen-tratal; or— It is a point at which the body, if supported there andif acted upon only by gravity, will balance in everyposition. The definition may be extended to the case of a systemof bodies if we suppose them and their centre of gravityto be rigidly connected. 160. The Centre of Gravity of Two Bodies. Let P and Q (Fig. 91) be any twobodies of known weight. Itis required to find the posi-tion of their centre of grav-ity. The weights may beconsidered as two like paral-lel forces whose resultant (144)will be equal to their sum and will act at a point which. 170 STATICS. [161. shall divide the distance between them in the inverseratio of the forces. Therefore, if the straight line ABbe drawn and the point G taken on it, so that AGBG 9P G will be the centre of gravity of P and Q. If thispoint be rigidly connected with the two bodies, the sys-tem, supported there, will balance in every position. 161. The Centre of Gravity of any Number of Bodies. Let P, Q, S, and T (Fig. 92) be four bodies of knownweight and occupying certain positions with refer-ence to each other. It isrequired to find their com-mon centre of gravity. Onthe straight lineal? join-ing the positions of P andQ take E, so thatAE _Q mEB ~ P;then, by 160, E will be thecentre of gravity of P and Q. Again, suppose P -f- Qto act at E, and on the line EC take F\ so that EF _ SFC~~P+Q; then Pis the centre of gravity of P, Q, and 8. Again,suppose P -(- Q -f- Sto act at F> and on the line DFtakeG, so that FG
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectmechanics, bookyear18
