A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 12
... reaction of the plane , and W the weight : from E , the intersection of W's direction . with the horizontal line through any point A of the plane , draw EF at right angles to the plane . Then , since P , W , R , produce equilibrium ...
... reaction of the plane , and W the weight : from E , the intersection of W's direction . with the horizontal line through any point A of the plane , draw EF at right angles to the plane . Then , since P , W , R , produce equilibrium ...
Page 16
... reaction R of the bowl , acting along MO , the force P , acting along MA , and the force W , acting vertically downwards : hence Р cos W Ꮎ ? COS 2 0 2 cos2 2 P 1 = COS W 2 ' Ꮎ P 0 cos2 COS = 2 0 2 = 2 W 2 P ± ( P2 + 8 W2 ) 4 W COS π 0 ...
... reaction R of the bowl , acting along MO , the force P , acting along MA , and the force W , acting vertically downwards : hence Р cos W Ꮎ ? COS 2 0 2 cos2 2 P 1 = COS W 2 ' Ꮎ P 0 cos2 COS = 2 0 2 = 2 W 2 P ± ( P2 + 8 W2 ) 4 W COS π 0 ...
Page 19
... 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 P2 + R2 + 2PR cos 60 ° - = P2 + PR + R2 . ( 3 ) Two weights P and Q hang at ...
... 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 P2 + R2 + 2PR cos 60 ° - = P2 + PR + R2 . ( 3 ) Two weights P and Q hang at ...
Page 25
... reaction of the circle , which takes place along PC , bisect the angle between PA and PQ . but Hence hence and therefore PCQ CAP + APC = = 2 APC = 24 CPQ : L 24 CPQ + 24 PCQ 180 ° : 1 34 PCQ = 180 ° , < PCQ = 60 ° , which determines the ...
... reaction of the circle , which takes place along PC , bisect the angle between PA and PQ . but Hence hence and therefore PCQ CAP + APC = = 2 APC = 24 CPQ : L 24 CPQ + 24 PCQ 180 ° : 1 34 PCQ = 180 ° , < PCQ = 60 ° , which determines the ...
Page 26
... reaction of the plane against the weight , and P = the sustaining force . Then , resolving forces along and perpendicularly to the in- clined plane , we have and √3 P. 2 2 W , or P : = √3 R + + / P = W W 3 ( 1 ) , .. ( 2 ) . From ( 1 ) ...
... reaction of the plane against the weight , and P = the sustaining force . Then , resolving forces along and perpendicularly to the in- clined plane , we have and √3 P. 2 2 W , or P : = √3 R + + / P = W W 3 ( 1 ) , .. ( 2 ) . From ( 1 ) ...
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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...
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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.