Theoretical Mechanics; An Elementary Text-Book

Theoretical Mechanics; An Elementary Text-Book

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 edition. Excerpt: ...that their vector sum is equal to the given resultant. 263. Resolution Into Simultaneous Motions an Arbitrary Process.--Obviously a particle cannot at the same time describe two different paths; neither can it have, at the same instant, two different velocities or accelerations. The motion has at every instant a definite direction and a definite speed, and the actual velocity is represented by a definite vector. This may be expressed as the sum of several component vectors, but it is only by an arbitrary use of language that these component vectors can be said to represent velocities actually possessed by the particle at the same instant. 264. Effects of Simultaneous Forces May Be Estimated Separately.--One case in which it may be advantageous to regard the actual motion of a particle as the resultant of two or more simultaneous motions is that in which the particle is acted upon by two or more forces such that the effect of each acting alone admits of simple determination. From the law of composition of forces (Art. 255) the actual acceleration is the vector sum of the accelerations which would result from the several forces acting singly. Hence these component accelerations may be computed separately and then combined. This method may be carried further, and applied to the computation of the velocity-increment and the displacement due to the simultaneous action of several forces, constant or variable, during any interval. 265. Velocity-Increment Due to Several Forces Acting Simultaneously.--Since acceleration is by definition (Art. 247) the increment of velocity per unit time, and since, by the law of composition of forces, the acceleration at each instant is the vector sum of the accelerations which would result from the separate action of the...
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Product details

  • Paperback | 144 pages
  • 189 x 246 x 8mm | 268g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236601890
  • 9781236601896