A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 6
... portion CA of the string , in the direction CA , and by the tension . P of the portion CP of the string vertically downwards . : Let ACB a : then the angle between the two equal forces P , P , acting at C , is equal to + a : hence the ...
... portion CA of the string , in the direction CA , and by the tension . P of the portion CP of the string vertically downwards . : Let ACB a : then the angle between the two equal forces P , P , acting at C , is equal to + a : hence the ...
Page 14
... portions of the string cannot be all equal . ( 8 ) Two small rings slide on the arc of a smooth vertical circle ; a ... portion between the rings ; to find the position of the rings when they are in equilibrium . If A , B , be the two ...
... portions of the string cannot be all equal . ( 8 ) Two small rings slide on the arc of a smooth vertical circle ; a ... portion between the rings ; to find the position of the rings when they are in equilibrium . If A , B , be the two ...
Page 18
... portions of the string , supposing AH , HK , KB , to be all equal . If AB = c , and 1 = the whole length of the string , the ten- sion of HK is equal to P ( 3c - 1 ) { 4l2 — ( 3c — 1 ) 2 } 1 ' and that of AH or BK to 2 Pl - { 41o — ( 3c ...
... portions of the string , supposing AH , HK , KB , to be all equal . If AB = c , and 1 = the whole length of the string , the ten- sion of HK is equal to P ( 3c - 1 ) { 4l2 — ( 3c — 1 ) 2 } 1 ' and that of AH or BK to 2 Pl - { 41o — ( 3c ...
Page 34
... portion BDC of the string being sup- posed to be equal to the portion BAC . to The pressure on A is equal to W , and that on B or C W √3 ( 21 ) A string , of length c , passes over four tacks forming a square ABCD , fig . ( 34 ) , of ...
... portion BDC of the string being sup- posed to be equal to the portion BAC . to The pressure on A is equal to W , and that on B or C W √3 ( 21 ) A string , of length c , passes over four tacks forming a square ABCD , fig . ( 34 ) , of ...
Page 50
... portions a , b , c , and these are formed into a triangle ; when the triangle is placed in unstable equilibrium , resting with its plane vertical , one of its angular points being supported upon a smooth hori- zontal plane , to find the ...
... portions a , b , c , and these are formed into a triangle ; when the triangle is placed in unstable equilibrium , resting with its plane vertical , one of its angular points being supported upon a smooth hori- zontal plane , to find the ...
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attached axle beam bisect the angle centre of gravity chord coefficient of friction collision component cos² cylinder denote determine distance equal forces equation feet find the inclination find the position find the pressure fixed point forces act fulcrum geometrical given circle given point hangs hence highest point horizontal plane impact impinges inclined plane intersection join latus rectum length lever line of quickest magnitude and direction middle point motion moveable parabola parallel parallelogram particle perpendicular point of projection position of equilibrium pound weight pounds prove pully quickest descent radii radius ratio reaction respectively rest resultant right angles SECT shew sides sin² sliding sphere straight line string passing supposing suspended tan¹ three forces uniform rod University of Cambridge velocity of projection vertical plane wheel
Popular passages
Page 145 - OUT of childhood into manhood Now had grown my Hiawatha, Skilled in all the craft of hunters, Learned in all the lore of old men, In all youthful sports and pastimes, In all manly arts and labors. Swift of foot was Hiawatha ; He could shoot an arrow from him, And run forward with such fleetness, That the arrow fell behind him...