A Collection of Problems in Illustration of the Principles of Theoretical MechanicsDeighton, Bell, 1876 - 667 páginas |
Dentro del libro
Resultados 1-5 de 48
Página 17
... Taking Ax , Ay , as the axes of x , y , the equation to the curve will be x2 = 4my . Let AC - a , BC = b ; then a [ [ xy da dy [ ( a ' - y ) ada b a ffy de dy dx W. S. b ( ay ) de S " dx 2 == 2m + = 2m2 a [ * ( a2 CENTRE OF GRAVITY . 17.
... Taking Ax , Ay , as the axes of x , y , the equation to the curve will be x2 = 4my . Let AC - a , BC = b ; then a [ [ xy da dy [ ( a ' - y ) ada b a ffy de dy dx W. S. b ( ay ) de S " dx 2 == 2m + = 2m2 a [ * ( a2 CENTRE OF GRAVITY . 17.
Página 58
... ) ; R. 2a sina + Wa cos a- R ' . 2a cos a = = 0 , 2R sin a + W cos a = 2R ' cos a . ( 3 ) . and , taking moments about the point C , or From ( 1 ) , ( 2 ) , ( 58 EQUILIBRIUM OF A SINGLE BODY . No Friction II Friction.
... ) ; R. 2a sina + Wa cos a- R ' . 2a cos a = = 0 , 2R sin a + W cos a = 2R ' cos a . ( 3 ) . and , taking moments about the point C , or From ( 1 ) , ( 2 ) , ( 58 EQUILIBRIUM OF A SINGLE BODY . No Friction II Friction.
Página 60
... taking moments about A , and therefore , by ( 2 ) , whence R " . AA " - R ' . AA'- Wa cos a = 0 , R'b Wa cosa ; = R ' = R " : = Wa cos a b ( 2 ) . ( 3 ) A rigid rod AB , ( fig . 28 ) , rests upon a fixed point E , while its lower ...
... taking moments about A , and therefore , by ( 2 ) , whence R " . AA " - R ' . AA'- Wa cos a = 0 , R'b Wa cosa ; = R ' = R " : = Wa cos a b ( 2 ) . ( 3 ) A rigid rod AB , ( fig . 28 ) , rests upon a fixed point E , while its lower ...
Página 61
... taking moments about A , P.AE = W.AF , P ( a + b ) sin ( p − 0 ) = Wa cos 0 ........ again , from the geometry , - ( 1 ) ; ( a + b ) sin + BC sin & = 1 , ( a + b ) cos + BC cos = k , and therefore , eliminating BC , ( a + b EQUILIBRIUM ...
... taking moments about A , P.AE = W.AF , P ( a + b ) sin ( p − 0 ) = Wa cos 0 ........ again , from the geometry , - ( 1 ) ; ( a + b ) sin + BC sin & = 1 , ( a + b ) cos + BC cos = k , and therefore , eliminating BC , ( a + b EQUILIBRIUM ...
Página 62
... taking moments about H , ( Y + W ) . BE . cos 30 ° = X. BE . sin 30 ° , or From ( 1 ) and ( 2 ) , W + Y = X √3 . ( 2 ) . X = √3W , Y = - } W : whence , if R denote the resultant action of the hinge on the rod , R = ( X2 + Y2 ) 3 = W ...
... taking moments about H , ( Y + W ) . BE . cos 30 ° = X. BE . sin 30 ° , or From ( 1 ) and ( 2 ) , W + Y = X √3 . ( 2 ) . X = √3W , Y = - } W : whence , if R denote the resultant action of the hinge on the rod , R = ( X2 + Y2 ) 3 = W ...
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Términos y frases comunes
absolute force acted angular velocity attraction axes axis beam body catenary centre of force centre of gravity circle co-ordinates coefficient of friction cos² curve cycloid cylinder denote density descends determine distance dt dt dt² dx dy dx² elastic ellipse equal equation Euler find the centre fixed point hence horizontal plane inclined plane inertia integrating James Bernoulli John Bernoulli lamina mass middle point moment of inertia motion natural length oscillation parabola perpendicular position of equilibrium pressure radius of gyration radius vector resolving forces rest right angles SECT sin² smooth sphere square straight line string supposing surface taking moments tangent tension triangle tube uniform rod varying inversely vertex vertical plane Vis Viva weight
Pasajes populares
Página 203 - A centre of force attracting inversely as the square of the distance is at the centre of a spherical cavity within an infinite mass of liquid, the pressure on which at an infinite distance is...