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 33
... ΣΧ ( Art . 31 ) , and R. OK = Σ ( Xy – Yx ) , OT = Σ ( Χy – Yx ) - • ΣΧ Consequently in this case the resultant is a single force R acting at the point just found . 66. When the forces are reducible to a single result- ant , to find the ...
... ΣΧ ( Art . 31 ) , and R. OK = Σ ( Xy – Yx ) , OT = Σ ( Χy – Yx ) - • ΣΧ Consequently in this case the resultant is a single force R acting at the point just found . 66. When the forces are reducible to a single result- ant , to find the ...
Page 34
... ΣΧ = ΣΥ .x ' , ΣΧ or y ́ΣΧ – α'ΣΥ = Σ ( Xy – Yx ) . 67. Any number of forces act in one plane at dif- ferent points of a rigid body ; to find the conditions that they may balance each other . Let the system of forces be that of Art . 64 ...
... ΣΧ = ΣΥ .x ' , ΣΧ or y ́ΣΧ – α'ΣΥ = Σ ( Xy – Yx ) . 67. Any number of forces act in one plane at dif- ferent points of a rigid body ; to find the conditions that they may balance each other . Let the system of forces be that of Art . 64 ...
Page 43
... ΣΧ , ΣΥ , ΣΖ acting at 0 ; and the three couples - Σ ( Υ ) – Σ ( Χy ) = ∑ ( Yx – Xy ) in the plane xy , Σ ( ΧΧ ) ... ΣΧ , R cos β = ΣΥ , R cos y = ΣΖ , 2 R2 = ( ΣΧ ) 2 + ( ΣΥ ) 2 + ( ΣΖ ) * : and G cos a ' = 2 ( Zy – Yx ) = L ...
... ΣΧ , ΣΥ , ΣΖ acting at 0 ; and the three couples - Σ ( Υ ) – Σ ( Χy ) = ∑ ( Yx – Xy ) in the plane xy , Σ ( ΧΧ ) ... ΣΧ , R cos β = ΣΥ , R cos y = ΣΖ , 2 R2 = ( ΣΧ ) 2 + ( ΣΥ ) 2 + ( ΣΖ ) * : and G cos a ' = 2 ( Zy – Yx ) = L ...
Page 45
... ΣΧ – α'ΣΖ = ∑ ( Xx – Zx ) = M , - α'ΣΥ – γ ́ΣΧ = ∑ ( Yx – Xy ) = N , - x ' , y ' , x ' are the co - ordinates of any point in the line in which R " acts . There being three equations between these quan- tities , it would seem as if ...
... ΣΧ – α'ΣΖ = ∑ ( Xx – Zx ) = M , - α'ΣΥ – γ ́ΣΧ = ∑ ( Yx – Xy ) = N , - x ' , y ' , x ' are the co - ordinates of any point in the line in which R " acts . There being three equations between these quan- tities , it would seem as if ...
Page 46
... ΣΧ ΣΥ ΣΖ ́ 00 = , Again , we may suppose the plane of G to pass through the origin . And since a ' , β ' , γ ' are the angles which a perpen- dicular upon it makes with the co - ordinate axes , its equation is x ' cos a ' + y ' cos β ...
... ΣΧ ΣΥ ΣΖ ́ 00 = , Again , we may suppose the plane of G to pass through the origin . And since a ' , β ' , γ ' are the angles which a perpen- dicular upon it makes with the co - ordinate axes , its equation is x ' cos a ' + y ' cos β ...
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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