A Collection of Problems in Illustration of the Principles of Theoretical MechanicsW.P. Grant, 1842 - 451 من الصفحات |
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absolute force angular velocity axes axis beam body centre of force centre of gravity circle co-ordinates collision constant quantity cos² curve cylinder D'Alembert's Principle denote descends distance do² dt dt dt² dt2 dt2 dx dy dx² elasticity equal equation Euler find the centre formula friction geometry given velocity hence horizontal plane inclined plane initial value integrating James Bernoulli John Bernoulli length ma² mass mk² moment of inertia oscillation parabola parallel particle Petrop position of equilibrium pressure Principle problem radius of gyration resolving forces right angles Sciences de Paris SECT sin² smooth sphere straight line string supposed surface tension tube uniform varies vertical plane virtual velocities Vis Viva weight zero δε аф
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الصفحة 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...
الصفحة 202 - ... purely elliptical, and in order to simplify the pro-blem still more he assumes that the orbit is circular. By dividing any interval of time into a great number of small intervals the well-known method of mechanical quadratures enables us to find the co-ordinates of a body which starts from a given point with a given velocity and in a given direction, and is acted on by known forces, without its being necessary to integrate the equations of motion. This process is attended with the advantage that...
الصفحة 2 - A Selection of GEOMETRICAL PROBLEMS ; containing some of the most Useful Deductions from Euclid ; and calculated to assist the Student in the solutions of Deductions in general. 8vo. 2s.
الصفحة 238 - Troy, Indiana. 14. Two equal particles attracting each other with forces varying inversely as the square of the distance, are constrained to move in two straight lines at right angles to each other; supposing their motions to commence from rest, to find the time in which each of them will arrive at the intersection of the two straight lines. — Communicated by PBOF. J. M
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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...
الصفحة 3 - THE design of these Conversations is to direct attention to the following facts, — namely, that the Church of England is scriptural in her doctrines, charitable in her spirit, primitive in her government ; that in her the pure Word of God is preached, and the Sacraments administered according to Christ's...
الصفحة 158 - A body not affected by gravity falls down the axis of a thin cylindrical tube infinite in length, the particles of which attract with a force which varies inversely as the square of the distance. Find the velocity acquired in falling through a given space.