A Treatise on Dynamics

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Сторінка 32 - NEWTON was able to formulate his great law of universal gravitation in these comprehensive words: "Every particle of matter in the universe attracts every other particle with a force directly as the masses of the two particles, and, inversely as the square of the distance which separates them." To show the nature of the attractive forces among these various particles, let us represent by m and m' the masses of two attracting bodies. We may conceive the body m to be composed of m particles, and the...
Сторінка 52 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Сторінка 21 - MASS AND WEIGHT.— The mass of a body is the quantity of matter in it ; the weight of a body is due to the force of gravity acting upon this matter.
Сторінка 32 - GRAVITATION.* — Every particle of matter in the universe attracts every other particle of matter with a force directly proportional to its mass, and decreasing as the square of the distance Fig.
Сторінка 15 - If two forces acting at a point be represented in magnitude and direction by the sides of a parallelogram, the resultant of these two forces will be represented in magnitude and direction by the diagonal of the parallelogram passing through this point.
Сторінка 91 - Remembering that the resistance of the air varies as the square of the velocity, it might easily be shown that the strength should be at least eight times, instead of twice, as great. Passing to the question of power. The soaring of birds is a most important fact, of which no one who has taken the trouble to make observations has any doubt. Though it was lately the subject of a...
Сторінка 150 - That is, if the resultant of all the external forces applied to a body is zero, the center of gravity will move in a straight line with uniform velocity. This is a generalization of Newton's First Law of Motion. REMARK. — It will be noticed that the above reasoning applies also to a non-rigid system of particles if the internal forces are in equilibrium among themselves. For example, so far as...
Сторінка 172 - OA of the smaller circle to represent the direction of the incident ray, and let NAB be the direction of the normal to the surface at the point of incidence, so that 0 AN is the angle of incidence.
Сторінка 136 - The motion about the center of gravity is the same as if the center of gravity were fixed in space and the actual forces were unchanged in magnitude, direction, and point of application.
Сторінка 53 - ... substituted in (a), gives y*=4hx, (62) the equation of a parabola referred to the oblique axes AX, AY ; and, since 4A is the parameter to the diameter through A, h is the distance from A, the point of projection to the focus F, or to the directrix. COR. The velocity of the body at any point of its path is that which the body would acquire in falling vertically from the directrix to that point. For if the body were projected from any point of its path in the direction, and with the velocity it...

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