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# Elasticity Dynamics

## power, lever, weight, prop, fulcrum, motion and produce

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DYNAMICS, ELASTICITY, Pones, TION?, MOTION, SE.C. will he found much relating to the doctrine of mechanics ; we shall therefore in this place chiefly treat of the mechanical powers, which are usually reckoned six in number : viz. the lever; the wheel and axis, or, as it is fre quently called, " the axis in peritrochio;" the pulley ; the inclined plane ; the wedge; and the screw. Some writers on this subject reduce the six to two, viz. the lever, and the inclined plane; the pulley, and wheel and axis being, in their estima tion, assemblages of the lever ; and the wedge and the screw being modifications of the inclined plane.

When two forces act against each other, by the intervention of a machine, the one is denominated the power, and the other the weight. The weight is the resistance to be overcome, or the ef feet to be produced. The power is the force, whether animate or inanimate, which is employd to overcome that resist ance, or to produce the required effect.

The power and weight are said to ba lance each other, or to be in equilibrio, when the effort of the one to produce motion in one direction, is equal to the effort of the other to produce it in the opposite direction; or when the weight opposes that degree of resistance which is precisely required to destroy the action of the power. The power of a machine is calculated when it is in a state of equilibri um. Having discovered what quantity of power will be requisite for this purpose, it will then be necessary to add so much more, viz, one-fourth, or, perhaps, one. third, to overcome the friction of the ma. chine, and give it motion.

The lever is the simplest of all ma Chines, and is a straight bar of iron, wood, or other material, supported on, and moveable about a prop called the fulcrum. In the lever, there are three circum stances to be principally attended to : 1. The fulcrum, or prop, by which it is sup ported, or on which it turns as a centre of motion : 2. The power to raise and sup port the weight • i. The resistance or weight to be raised or sustained._ The points of suspension are those points where the weights really are, or from which they hang freely. The power and

the weight are always supposed to act at right angles to the lever, except it be otherwise expressed. The lever is distin guished into three sorts, according to the different situations of the fulcrum, or prop, and the power, with respect to each other. 1. When the prop is placed between the power and the weight, as in steel-yards, scissars, pincers, &c. 2. When the prop is at one end of the lever, the power at the other, -and the weight. between them, as in cutting knives, List ened at, or near the point of the blade ; also in oars moving a boat, the water be ing the fulcrum. 3. When the prop is at one end, the weight at the other, and the power applied between them, as in tongs, sheers, &c.

The lever of the first kind is principally used for loosening large stones; or to raise great weights to small heights, in order to get ropes tinder them, or other means of raising them to still greater heights : it is the most common species of lever. A B C (Plate I. Mechanics, fig. 1.) is a lever of this kind, in which F is the ful crum, A the end at which the power is applied, and C the end where the weight acts. To find when an equilibrium will take place between the power and the weight, in this as well as in every other species of lever, we must observe, that when the momenta, or quantities of force, in two bodies are equal, they will balance each other. Now, let us consider when this will take place in the lever. Suppose the lever AB, fig. 2, to be turned on its axis, or fulcrum, so as to come into the situation DC; as the end .D is farthest from the centre of motion, and as it has moved through the arch AD in the same time as the endB moved through the arch BC, it is evident that the velocity of AB must have been greater than that of D. But the momenta being the products of the quantities of matter multiplied into the velocities, the greater the velocity, the less the quantity of matter to obtain the same product. Therefore, as the velocity of A is the greatest, it will require less matter to produce an equilibrium than 13.

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