A Collection of Problems in Illustration of the Principles of Theoretical MechanicsW.P. Grant, 1842 - 451 páginas |
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Términos y frases comunes
absolute force acted angular velocity assigned law axes axis beam body catenary centre of force centre of gravity circle co-ordinates collision constant quantity cos² curve cylinder D'Alembert's Principle denote density determine differential distance dt dt dt² dx dy dx² elasticity equal equation Euler formula friction given velocity hence horizontal plane inclined plane initial value integrating James Bernoulli John Bernoulli length ma² mk² moment of inertia motion moving oscillation parabola particle Petrop position of equilibrium pressure Principle problem radius of gyration right angles Sciences de Paris SECT sin² smooth sphere straight line string supposed tangent tension tube uniform unit of mass vertical plane virtual velocities Vis Viva weight zero δε
Pasajes populares
Página 167 - F— ka line, V the velocity of projection, and k the resistance for a unit of velocity. (8) A particle acted on by gravity falls from a given altitude in an uniform medium of which the resistance varies as the square of the velocity ; on arriving at the lowest point of its descent it is reflected upwards with the velocity which it has acquired in its fall, after reaching its greatest altitude it again descends and is again reflected, and so on perpetually ; to determine the altitude of ascent after...
Página 32 - Find the centre of gravity of the surface of a hemisphere when the density at each point of the surface varies as its perpendicular distance from the base of the hemisphere.
Página 15 - Find the centre of gravit\- of the solid formed by the revolution of the sector of a circle about one of its extreme radii. Ans. x = J« cosH/2, where ft is the angle of the sector.
Página 105 - A, and the other end to a weight which is placed on a rough horizontal plane passing through A, and the chain hangs through a slit in the horizontal plane. Shew that if I be the length of the chain...
Página 300 - Soit donné un système de Corps disposés les uns par rapport aux autres d'une manière quelconque ; et supposons qu'on imprime à chacun de ces Corps un Mouvement particulier, qu'il ne puisse suivre à cause de l'action des autres Corps : trouver le Mouvement que chaque Corps doit prendre.
Página 73 - V ; shew that if 0 be the limiting value of the angle of inclination of the beam to the horizon at which it will rest, W its weight, and R, R
Página 154 - A particle is attracted by a force to a fixed point varying inversely as the «th power of the distance ; if the velocity acquired by it in falling from an infinite distance to a distance a from the centre is equal to the velocity that would be acquired by it in falling from rest at a distance a to a distance -, shew that »='„-. 11.
Página 83 - CB, are connected by a smooth hinge at C, and are placed in a vertical plane with their lower extremities, A and B, resting on a rough horizontal plane ; from observing the greatest value of the angle...
Página 17 - M be the arithmetic mean of all transverse sections of the solid generated by the revolution, about the axis of x, of the portion of the latter curve between the limits x = a6lt x - aO, ; shew that 6.
Página 296 - The moment of inertia of the irregular volume about any axis is equal to the sum of the moments of inertia about that axis of the various partial volumes into which it is divided.