A text-book of physics, largely experimentalOn the Harvard college "Descriptive list of elementary physical experiments." . edded part may be repre-sented, as in the figure, by a number of horizontal horizontal forces directed toward the left have a singleresultant, those directed toward the right an equal result-ant. These two resultants are equivalent to a negativecouple, and thus the positive couple WW is balanced. Limit of Strength of the Bar. Influence of length.—The parts of the bar at the sectionab can bear a certain amount of stretching and compression, TWO SETS OF FORCES AT
A text-book of physics, largely experimentalOn the Harvard college "Descriptive list of elementary physical experiments." . edded part may be repre-sented, as in the figure, by a number of horizontal horizontal forces directed toward the left have a singleresultant, those directed toward the right an equal result-ant. These two resultants are equivalent to a negativecouple, and thus the positive couple WW is balanced. Limit of Strength of the Bar. Influence of length.—The parts of the bar at the sectionab can bear a certain amount of stretching and compression, TWO SETS OF FORCES AT RIGHT ANGLES. 125 and no more. The moment of the couple they can exerthas a certain limit. If the moment of WW becomesgreater than this limit, the bar breaks. The moment ofWW is WX bP. Evidently, the greatest load, W, whichthe bar can bear without breaking is inversely proportionalto the length bP, the horizontal distance from ab to P.(See § 202.) Influence of thickness.—If the bar is made twice asthick, as in Fig. 85, we may draw twice as many arrows torepresent the molecular forces, but the outside arrows have. FIG. 85. the same limit of length as before; for the limit of stretch-ing or compression of the substance is the same as in thesmaller bar. The average length of the arrows is thesame, at the breaking condition, in the thick bar as inthe thin one. The right-hand and the left-hand resultants are twiceas great as in the thin bar, and the points of applicationof these resultants are twice as far apart as in the thinbar. Hence the moment of the molecular couple justbefore breaking is four times as great in the thick bar asin the other. Doubling the thickness multiplies thestrength by four (see § 202). Influence of width.—Doubling the width of the barwould double the resultants of the molecular forces, but 126 PHYSICS. would leave the lever-arm of the couple unchanged in length. Hence it would merely double the strength of the bar. Example 2. In Fig. 86 the incline
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishe, booksubjectphysics
