An Elementary Treatise on Mechanics

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Harper & brothers, 1845 - 432 Seiten
Looks at various topics of elementary mechanics.
 

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Seite 259 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
Seite 86 - ... of the base and at a distance from the base equal to one quarter of the height of the cone.
Seite 387 - We know now that the underlying principle is the same as in a mercurial barometer : it is the pressure of the atmosphere on the surface of the water in the well that pushes the water up into the pump.
Seite 127 - This proportion teaches us that, when in equilibrium, the power is to the weight as the height of the plane is to its length.
Seite 311 - ... be equal to the sum of the moments of those which tend to turn it in the opposite direction about the same axis.
Seite 264 - ... adjustment of the centripetal and centrifugal forces, so as exactly to balance each other, is a wonderful fact in nature. The planets all move in ellipses, not greatly removed from circles, having the sun in one of the foci. The general law or fact, in nature, so far as we can observe, is that all bodies attract each other in the direct ratio of their masses, and in the inverse ratio of the squares of the distances. It has, indeed, been asserted that this is a necessary fact. But we know too...
Seite 130 - ... consists of a screw combined with a wheel and axle in such a manner that the threads of the screw work into the teeth fixed on the periphery of the wheel. Suppose the power applied to the handle of the screw, and the weight attached to the axle of the wheel, then there will be equilibrium when the power is to the weight as the distance between the threads multiplied by the radius of the axle is to the circumference described by the power multiplied by the radius of the wheel.
Seite 379 - Ha measure; ratio of the weights of equal volumes of two bodies being always the same, if the unit of volume of each be taken, and one of the bodies become the standard, its weight will become the unit of weight. The term density denotes the degree of proximity...
Seite 331 - P, acting at G and in the same direction, and this produces translation only. The remaining \P at A combined with the remaining ^P at B, which acts in the opposite direction, form a couple which produces rotation about the centre G. Hence, when a body receives an impulse in a direction which does not pass through the centre of gravity, that centre will assume a motion of translation as though the impulse were applied immediately to it; and the body will have a motion of rotation about the centre...
Seite 320 - Hence the moment of inertia of a body with respect to any axis, is equal to its moment of inertia with respect to...

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