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 . s considered) which are normalto the rubbing surfaces at any instant will cancel out, whiletheir components tangential to the rubbing surfaces (, fric-tion, since if the surfaces are perfectly smooth there can beno tangential action) will appear in the algebraic addition asresistances multiplied by the distances rubbed through, meas-ured on the rubbing surfaces. For example, Fig. 155, where-one rotating p
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 . s considered) which are normalto the rubbing surfaces at any instant will cancel out, whiletheir components tangential to the rubbing surfaces (, fric-tion, since if the surfaces are perfectly smooth there can beno tangential action) will appear in the algebraic addition asresistances multiplied by the distances rubbed through, meas-ured on the rubbing surfaces. For example, Fig. 155, where-one rotating piece both presses and rubs on another. Let the-normal pressure between them at A be i?2 = B2 ; it is a work-ing force for the body of mass M, but a resistance for M,hence the separate symbols for the numerically equal forces(action and reaction). Similarly, the friction at A is B3 = Bs; a resistance for M,a working-force for M. (In some cases, of course, frictionmay be a resistance for both bodies.) For a small motion, Adescribes the small arc AA about 0 in dealing with M, butfor M it describes the arc AA about O1, AA beingparallel to the surface of contact AD, while AB is perpen-. Fig. 156. Fig. 157. Fig. 155. dicular to AA. In Figs. 156 and 157 we see W and Mfree, and their corresponding small rotations indicated. Duringthese motions the kinetic energy (K. E.) of each mass haschanged by amounts d(K. E.)^/ and d(K. ~E.)m respectively, andhence eq. (XV.) gives, for each free body in turn, P~a~ti - B,AB - = d(K. • (1> - BbW7 + + P,A^B = d(K. (2) WORK, ENERGY, AND POWER. 149 [Now add (1) and (2), member to member, remembering thatjP2 = i?2 and P3 = Rz — Fz = friction, and we have Pxaa - FZAA - R$b = d(K. E.)M, + d(K. E.)M„, (3) in which the mutual actions of M and 1£ do not appear,except the friction, the work done in overcoming which, whenthe two todies are thus considered collectively, is the productof the friction by the distance A A of actual rub
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
