A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 1
... SECT . 1. Geometrical Method . IF two forces P , Q , act upon a point 0 , fig . ( 1 ) , in the directions OA , OB , respectively , and if OA OB :: P : Q , then OC , the diagonal of the parallelogram OA CB , will coincide with the ...
... SECT . 1. Geometrical Method . IF two forces P , Q , act upon a point 0 , fig . ( 1 ) , in the directions OA , OB , respectively , and if OA OB :: P : Q , then OC , the diagonal of the parallelogram OA CB , will coincide with the ...
Page 5
... SECT . 2. Trigonometrical Method . Let two forces P , Q , act upon a point , and let a be the angle between their directions : then , if R be their resultant , and if R's direction be inclined to the directions of P , Q , at angles 4 ...
... SECT . 2. Trigonometrical Method . Let two forces P , Q , act upon a point , and let a be the angle between their directions : then , if R be their resultant , and if R's direction be inclined to the directions of P , Q , at angles 4 ...
Page 12
William Walton. CHAPTER II . EQUILIBRIUM OF THREE FORCES ACTING ON A POINT . SECT . 1. Triangle of forces . If three forces , the magnitudes of which are proportional to the sides BC , CA , AB , of a triangle ABC , and of which the ...
William Walton. CHAPTER II . EQUILIBRIUM OF THREE FORCES ACTING ON A POINT . SECT . 1. Triangle of forces . If three forces , the magnitudes of which are proportional to the sides BC , CA , AB , of a triangle ABC , and of which the ...
Page 14
... at three points of the circumference : shew that the forces are as the sides of the cir- cumscribing triangle which touches the disc at those points . SECT . 2. P Q R :: sin Q , 14 EQUILIBRIUM OF THREE FORCES ACTING ON A POINT .
... at three points of the circumference : shew that the forces are as the sides of the cir- cumscribing triangle which touches the disc at those points . SECT . 2. P Q R :: sin Q , 14 EQUILIBRIUM OF THREE FORCES ACTING ON A POINT .
Page 15
William Walton. SECT . 2. P Q R :: sin Q , R : sin R , P : sin P , Q. If three forces P , Q , R , act on a point , and Q , R , R , P , P , Q , denote the respective angles between Q , R ; R , P ; P , Q ; the sufficient and necessary ...
William Walton. SECT . 2. P Q R :: sin Q , R : sin R , P : sin P , Q. If three forces P , Q , R , act on a point , and Q , R , R , P , P , Q , denote the respective angles between Q , R ; R , P ; P , Q ; the sufficient and necessary ...
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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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