The Principles and Practice of Statics and Dynamics: Embracing a Clear Development of Hydrostatics, Hydrodynamics, and Pneumatics: With Central Forces and Super-Elevation of Exterior Rail
The Principles and Practice of Statics and Dynamics: Embracing a Clear Development of Hydrostatics, Hydrodynamics, and Pneumatics: With Central Forces and Super-Elevation of Exterior Rail
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. 1851 Excerpt: ...2 P + p, the velocity as p, the weight that puts the whole system in motion; and if p be constant, the velocity is inversely as 2 P + p which is the whole mass or weight moved. Since, then, the velocity is proportional to P T, it follows that p is proportional to (2 P + p) x velocity, and therefore is proportional to ...
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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. 1851 Excerpt: ...2 P + p, the velocity as p, the weight that puts the whole system in motion; and if p be constant, the velocity is inversely as 2 P + p which is the whole mass or weight moved. Since, then, the velocity is proportional to P T, it follows that p is proportional to (2 P + p) x velocity, and therefore is proportional to the momentum generated in a given time, or varies as the moving force. This establishes the truth of Newton's third law of motion in a most satisfactory manner. 143. Prop.--When two unequal bodies are connected by a cord hanging over a fixed pulley, to determine the nature of their motion, the cord and pulley being considered without weight. Let P and Q be the two bodies; then it is evident that the moving force is in this case proportional to the excess of P over Q, that is, to P--Q; but the accelerating force is as the moving force divided by the quantity of matter moved, by the P--Q third law of motion, and is therefore as _ When Q = 0, the body falls freely, and the accelerating force is the force of gravity g; hence the accelerating force in this case P--Q is/=----pr g. This value of the accelerating force being r X y substituted for g in the formulae Art. 140, will shew the relation between the space, velocity, and time of the two bodies. 144. Pkop.--To find the accelerating force when one body draws another along an inclined plane. Let a body P descend down the inclined plane, and draw the body Q up another inclined plane, (see fig. Art. 77); and let a and 0 be the respective angles of elevation of the planes, on which P and Q are in motion; then the force of P in the direction of its plane is equal to P sin a, and the force of Q in the direction of its plane is equal to Q sin 0. Now, if these forces be equal, the bodies P and Q will be ...
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