A Treatise on Statics: Containing the Theory of the Equilibrium of Forces; and Numerous Examples Illustrative of the General Principles of the Science |
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Page 17
... co - ordinates of any point P in it . Then if OP be taken to represent R , the co - ordinates will represent the components , and therefore by Art . 25 , X y Σ . F cos a Σ . F cos β Σ . F cos γ ' which are the equations required . C If ...
... co - ordinates of any point P in it . Then if OP be taken to represent R , the co - ordinates will represent the components , and therefore by Art . 25 , X y Σ . F cos a Σ . F cos β Σ . F cos γ ' which are the equations required . C If ...
Page 18
... co - ordinates , let its co - ordinates be a , b , c ; then since the line whose equations are required passes through this point , x - a y - b 0-2 = Σ . F cos a Σ . F cos β Σ . F cos y are the equations of it in this case . 38. To find ...
... co - ordinates , let its co - ordinates be a , b , c ; then since the line whose equations are required passes through this point , x - a y - b 0-2 = Σ . F cos a Σ . F cos β Σ . F cos y are the equations of it in this case . 38. To find ...
Page 32
... co - ordinate axes refer the given forces and their points of application . ( fig . 15. ) 16 Let a1 , a2 .... a , be the inclinations of the lines in which the forces act to Ox ; X1 Y1 , X2 Y2 , .... XnYn the co - ordinates of the ...
... co - ordinate axes refer the given forces and their points of application . ( fig . 15. ) 16 Let a1 , a2 .... a , be the inclinations of the lines in which the forces act to Ox ; X1 Y1 , X2 Y2 , .... XnYn the co - ordinates of the ...
Page 33
... co - ordinates of any point in the line R'K ( fig . 16 ) in which the resultant acts . Then because D this line passes through the point T and , being NON - PARALLEL FORCES IN A PLANE . 33.
... co - ordinates of any point in the line R'K ( fig . 16 ) in which the resultant acts . Then because D this line passes through the point T and , being NON - PARALLEL FORCES IN A PLANE . 33.
Page 36
... co - ordinates . It is necessary therefore only to observe that when a couple acts in a co - ordinate plane , it will be con- sidered a positive couple when its axis stands on the positive side of that plane . Thus a positive couple in ...
... co - ordinates . It is necessary therefore only to observe that when a couple acts in a co - ordinate plane , it will be con- sidered a positive couple when its axis stands on the positive side of that plane . Thus a positive couple in ...
Common terms and phrases
a₁ axle balance beam Cambridge catenary centre of gravity College components conditions of equilibrium consequently cos² curve cylinder density direction distance draw dx)² equal to zero equation equi exerts F₁ F₂ find the centre find the conditions find the position fixed axis fixed point forces acting forces F forces which act friction frustum fulcrum Hence horizontal plane inclined plane John Deighton length lever librium m₁ machine magnitude motion parallelogram particle passing perpendicular position of equilibrium pressure proportional pulley pyramid radius represent resolved respectively rest resultant couple right angles rigid body screw shew single force smooth string suppose surface suspended Taylor's theorem tension three forces transposed triangle Trinity College University of Cambridge virtual velocities wheel Wherefore ΣΖ ΣΥ ΣΧ
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