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 26
... transposed so as to make all their equal arms exactly coincide ; in which position the system of couples is reduced to one couple , the arm of which is b , and the forces of which are equal to P1 + P2 + P3 + ... + P. Hence the moment of ...
... transposed so as to make all their equal arms exactly coincide ; in which position the system of couples is reduced to one couple , the arm of which is b , and the forces of which are equal to P1 + P2 + P3 + ... + P. Hence the moment of ...
Page 31
... transposed to that point , without altering the direction in which it acts . 64. Any number of forces act , in one plane , at dif- ferent points of a rigid body : to find their resultant . .... Let F1 , F2 , F be the forces PARALLEL ...
... transposed to that point , without altering the direction in which it acts . 64. Any number of forces act , in one plane , at dif- ferent points of a rigid body : to find their resultant . .... Let F1 , F2 , F be the forces PARALLEL ...
Page 32
... transposed to O without altering its di- rection , if at the same time we also apply to the body a couple whose moment = - F1 . OQ = - F1 . ( ON – QN ) 1 = - F1 . ( x1 cos MON – y1 sin MPQ ) - = - F1 . ( 1 sin a1 - Y1 cos a1 ) 1 ...
... transposed to O without altering its di- rection , if at the same time we also apply to the body a couple whose moment = - F1 . OQ = - F1 . ( ON – QN ) 1 = - F1 . ( x1 cos MON – y1 sin MPQ ) - = - F1 . ( 1 sin a1 - Y1 cos a1 ) 1 ...
Page 35
... point is the same as if all the forces which act on the body were transposed to the fixed point without altering their direc- tions . CHAPTER IV . ON FORCES , NOT IN ONE PLANE D2 NON - PARALLEL FORCES IN A PLANE . 35.
... point is the same as if all the forces which act on the body were transposed to the fixed point without altering their direc- tions . CHAPTER IV . ON FORCES , NOT IN ONE PLANE D2 NON - PARALLEL FORCES IN A PLANE . 35.
Page 37
... transposed the force Z1 to O , retaining its proper direction , and have introduced the couples - Z11 , + Z1y in the planes x , yz respectively . Proceeding in the same manner with the re- maining forces Z2 , Z3 .... Zn we shall have ...
... transposed the force Z1 to O , retaining its proper direction , and have introduced the couples - Z11 , + Z1y in the planes x , yz respectively . Proceeding in the same manner with the re- maining forces Z2 , Z3 .... Zn we shall have ...
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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