Analytical mechanics for students of physics and engineering . of the string, the reaction at the joint, and the reaction of the a slighl displacement to be given to the system by pressing down-ward at the joint. The work done by the force which produced the dis-placement equals the sum of the work done by the other forces which actupon the rods during the displace-ment. Bui since both the force ap-plied and the displacement producedare very small their product is negli-gible. Therefore the sum of the workdone by all the other forces is zero. The reactions at the ends of therod-
Analytical mechanics for students of physics and engineering . of the string, the reaction at the joint, and the reaction of the a slighl displacement to be given to the system by pressing down-ward at the joint. The work done by the force which produced the dis-placement equals the sum of the work done by the other forces which actupon the rods during the displace-ment. Bui since both the force ap-plied and the displacement producedare very small their product is negli-gible. Therefore the sum of the workdone by all the other forces is zero. The reactions at the ends of therod- do not contribute to the virtualwork because each of the reactions is perpendicular to the corresponding surface of contact along which the displacement takes place. Thereforethe weights and the tensile force of the string contribute all the virtualwork. If // and <lh denote, respectively, the increase in length of the Btring and the distance through which the centers of mass of the rods areI during the virtual displacement the virtual work takes the form. »( f + Wdfc) 0. But from the liirure /and <//< = — aobtain a Bin 0, and h = (i cos 0. Therefore dl = a cos OddMaking these substitutions and simplifying we T = Jirtane1. WORK \s:\ 3. Find the mechanical advantage of the jack-screw. Let / be the pitch of the screw, I the length of the lever arm, F the forceapplied and P the force derived. Thensince at any instant the system is supposedto be in equilibrium the virtual work, due ^to a small displacement, must vanish. Let /dd denote a small angular displacement l\and dh the corresponding rise of the if G denotes the torque applied thevirtual work takes the formGdB-Pdh = 0. But G = F • I and dh Fide Ppdd 2tt p. Therefore
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Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyo, bookyear1913
