A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 8
... supposing the resultant to be √7 . The required angle is 60 ° . ( 15 ) Apply two pressures of P pounds and P / 3 pounds so as to produce the same effect as a pressure of 2P pounds applied in a given direction . The two forces P and P ...
... supposing the resultant to be √7 . The required angle is 60 ° . ( 15 ) Apply two pressures of P pounds and P / 3 pounds so as to produce the same effect as a pressure of 2P pounds applied in a given direction . The two forces P and P ...
Page 17
... supposing the angle between P's direction and R's to be , and that between Q's and R's to be , to com- pare the magnitudes of the forces . P , Q , R , are to each other respectively as 2 , √3 , 1 . ( 5 ) A sphere rests upon two ...
... supposing the angle between P's direction and R's to be , and that between Q's and R's to be , to com- pare the magnitudes of the forces . P , Q , R , are to each other respectively as 2 , √3 , 1 . ( 5 ) A sphere rests upon two ...
Page 18
... supposing AH , HK , KB , to be all equal . If AB = c , and 7 = 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 { 4l2 — ( 3c − 1 ) 2 ) 1 - ( 11 ) Two ...
... supposing AH , HK , KB , to be all equal . If AB = c , and 7 = 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 { 4l2 — ( 3c − 1 ) 2 ) 1 - ( 11 ) Two ...
Page 19
... supposing R to be the pressure on the plane , to prove that W2 = P2 + PR + R2 . The reaction of .the inclined plane against the weight is equal to R , and the angle between this reaction and P's direc- tion is equal to 60 ° : hence W2 ...
... supposing R to be the pressure on the plane , to prove that W2 = P2 + PR + R2 . The reaction of .the inclined plane against the weight is equal to R , and the angle between this reaction and P's direc- tion is equal to 60 ° : hence W2 ...
Page 24
... Supposing the particle to be moved through a certain space towards one of the angular points , and there fixed ; and that the resultant force exerted upon it by the strings is then equal to half of each of the weights , to find the ...
... Supposing the particle to be moved through a certain space towards one of the angular points , and there fixed ; and that the resultant force exerted upon it by the strings is then equal to half of each of the weights , to find the ...
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Common terms and phrases
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...
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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.