A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 27
... radius of the sphere : then and T = Psin , R = Pcos . r ( 4 ) The ends of a fine cord of given length are tied to two given points in the same horizontal line , and a smooth ring , sliding on the cord , sustains a given weight : to find ...
... radius of the sphere : then and T = Psin , R = Pcos . r ( 4 ) The ends of a fine cord of given length are tied to two given points in the same horizontal line , and a smooth ring , sliding on the cord , sustains a given weight : to find ...
Page 37
... radius through P to the horizon . The required inclination = П 4 ( 5 ) A given horizontal force Pjust supports a weight Won a rough plane inclined to the horizon at an angle : the same weight will just rest without support on a plane of ...
... radius through P to the horizon . The required inclination = П 4 ( 5 ) A given horizontal force Pjust supports a weight Won a rough plane inclined to the horizon at an angle : the same weight will just rest without support on a plane of ...
Page 44
... radius CD to bisect the angle ACB . Join CE . Let ‹ ACD = α = ‹ BCD , and ‹ ECD = 0 . Taking moments about E , as a fulcrum , we have , for the equilibrium of the lever , P. AC sin ( a - 0 ) = Q. BC . sin ( a + 0 ) , and therefore P ...
... radius CD to bisect the angle ACB . Join CE . Let ‹ ACD = α = ‹ BCD , and ‹ ECD = 0 . Taking moments about E , as a fulcrum , we have , for the equilibrium of the lever , P. AC sin ( a - 0 ) = Q. BC . sin ( a + 0 ) , and therefore P ...
Page 64
... radius of the circle . Let x , y , be the co - ordinates of the centre of gravity of the remaining portion of the board . Then and therefore Similarly ab . α = πr2 . r + ( ab − πr2 ) x , x = -- ab - πr2 · + b2a — πr3 - ba - Tr2 - ( 5 ) ...
... radius of the circle . Let x , y , be the co - ordinates of the centre of gravity of the remaining portion of the board . Then and therefore Similarly ab . α = πr2 . r + ( ab − πr2 ) x , x = -- ab - πr2 · + b2a — πr3 - ba - Tr2 - ( 5 ) ...
Page 65
... of remainder of triangle . But , r denoting the radius of the circle , r ( 3 + 4 + 5 ) = 3 × 4 , and therefore , r = 1 . Our two equations accordingly become 6 = + ( 6 ) x , x = 1 ; W. S. 9 and 3 × 6 = π + ( 6 − CENTRE OF GRAVITY , 65.
... of remainder of triangle . But , r denoting the radius of the circle , r ( 3 + 4 + 5 ) = 3 × 4 , and therefore , r = 1 . Our two equations accordingly become 6 = + ( 6 ) x , x = 1 ; W. S. 9 and 3 × 6 = π + ( 6 − CENTRE OF GRAVITY , 65.
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body is projected centre of gravity chord coefficient of friction collision component cos² cylinder denote described determine directrix distance equal forces equation feet find the position find the pressure fixed point forces act fulcrum geometrical progression given circle given point hangs hence highest point horizontal plane impact impinges inclined plane intersection join latus rectum lever line of quickest lowest point magnitude and direction mass middle point motion moveable parabola parallel parallelogram particle perfectly elastic ball 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 smooth sphere straight line string passing supposing suspended tan¹ tangent three forces uniform rod velocity of projection vertex vertical circle vertical plane
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Page 255 - Classics, so far as they have been published, will be adopted. These editions have taken their place amongst scholars as valuable contributions to the Classical Literature of this country, and are admitted to be good examples of the judicious and practical nature of English scholarship ; and as the editors have formed their texts from a careful examination of the best editions extant, it is believed that no texts better for general use can be found. The volumes will be well printed at the Cambridge...
Page 257 - Progressive Exercises in Greek Tragic Senarii, followed by a Selection from the Greek Verses of Shrewsbury School, and prefaced by a short Account of the Iambic Metre and Style of Greek Tragedy. For the use of Schools and Private Students. Second Edition, altered and revised. 8vo. 8*.
Page 141 - 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...
Page 255 - THIS series is intended to supply for the use of Schools and Students cheap and accurate editions of the Classics, which shall be superior in mechanical execution to the small German editions now current in this country, and more convenient in form. The texts of the " Bibliotheca Classica" and " GrammarSchool Classics,'" so far as they have been published, will be adopted.