. The elements of railroad engineering . Fig. 149 is shown an arrangement called a dif-ferential pulley. It will be seen that if a force be appliedat P, so as to pull the point Pdown to Z?, therope or chain will wind up on the large pulley^, and unwind from the smaller pulley i?,and since (T is a movable pulley, the weight Wwill move an amount equal to one-half thedifference between the amount of windingon A and unwinding on B. Let the radius of A be represented by /v,and of ^ by r; then, when P is pulled downto Z>, a point E on the pulley A will movethrough a certain angle, EOF, the length
. The elements of railroad engineering . Fig. 149 is shown an arrangement called a dif-ferential pulley. It will be seen that if a force be appliedat P, so as to pull the point Pdown to Z?, therope or chain will wind up on the large pulley^, and unwind from the smaller pulley i?,and since (T is a movable pulley, the weight Wwill move an amount equal to one-half thedifference between the amount of windingon A and unwinding on B. Let the radius of A be represented by /v,and of ^ by r; then, when P is pulled downto Z>, a point E on the pulley A will movethrough a certain angle, EOF, the length ofthe arc E /^ being equal to the distance P point on the pulley B, which is fastened toA., will turn through the same angle; and thedifference between the arc KL, through whichthis point turns, and the arc E /^ will be pro-portional to the difference of the radii R and r. When Pmoves down to Z>, the point //onthe other side will move up through the same distance to//.The point/will move up to /, a distance equal to the length. Fig. 149. 344 ELEMENTARY MECHANICS. of the arc AA, and ;;/ will fall through the same distanceto ///, thus causing the weight /J to be raised one half theliifferenee betxceen in ni and P J^. The ratio between thedistances through which /Kand /^move will be arc R F — arc KL ,, ,, R — r „ : /: /, or —;:— : R. Ilencc, J/x 2 R-r 2 C^i.) Example.—If /? = 7 inches, and r = 6i inches, how much weight canbe raised at IV with a force of 50 pounds at i ? _ ... IPR 2 X50 X7 , ,^ Solution.— // =-7^ - = —^—:;^i^—= 1,400 pounds. Ans. R-r 1-U THE INCLINED PLANE. 940. An inclined plane is a slope or a flat surface,making an angle with a horizontal line. Three cases may arise in practice witli the inclined plane: I. When the power acts parallel to the plane, as in II. When the power acts parallel to the base, as in III. When the power acts at an angle to the plane, orto the base, as in Fig. 152. Ciisc I.—In Fig. 150, the
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectrailroadengineering
