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which impels a body to fly from the centre, is called the centrifugal force. In circular motion these two forces balance each other.
If a ball be thrown in a horizontal direction, it is acted upon by three forces, viz. the force of projection; the resistance of the air through which it passes ; and the force of gravity which finally brings it to the ground. Bodies thus projected describe a curve line in their descent. If the forces of projection and of gravity both produced uniform motion, the ball would move in the diagonal of a parallelogram: but the motion produced by the force of projection alone is uniform, that produced by gravity is accelerated; and it is this acceleration which makes it fall in a curve instead of a straight line. The curve line which a ball describes, if the resistance of the air be not taken into consideration, is called in geometry a parabola.
The middle point of a body is called its centre of magnitude, that is, the centre of its mass or bulk.
The centre of gravity is the point about which all the parts of a body exactly balance each other, in every position of the body; if therefore this point is supported, the body will not fall. When a boat is in danger of being upset, it is dangerous for the passengers to rise suddenly; this is owing to their raising the centre of gravity. When a man stands upright, the centre of gravity of his body is supported by the feet. If he lean to one side he will no longer stand firm. A rope-dancer performs all his feats of agility, by dexterously supporting his centre of gravity ; whenever he finds himself in danger of losing his balance, he shifts the heavy pole which he holds in his hands, in order to throw the weight towards the side that is deficient ; and thus by changing the situation of the centre of gravity, restores his equilibrium. A person carries a single pail of water with great difficulty, owing to the centre of gravity being thrown on one side : but two pails, one hanging on each arm, are carried with much greater facility, because they balance each other.
When two bodies are fastened together, they are to
be considered as forming but one body. If the two bodies
be of equal weight, the centre of gravity will be in the middle of the line which unites
them ; but if one be heavier than the other, the centre of gravity will be proportionably nearer the heavy body than the light one.
ON THE MECHANICAL POWERS.
There are six mechanical powers, viz. the lever, the pulley, the wheel and axle, the inclined plane, the wedge and the screw. One or more of these enters into the composition of every machine.
In order to understand the power of a machine, there are four things to be considered. Firstly, the power that acts ; this consists in the effort of men or horses, of weights, springs, steam, &c. Secondly, the resistance which is to be overcome by the power. The effect of the power must always be superior to the resistance, otherwise the machine could not be put in motion. For instance, were the resistance of a carriage equal to the strength of the horses employed to draw it, they would not be able to draw it.' Thirdly, we are to consider the centre of motion, or, as it is termed in mechanics, the fulcrum, which means prop. And lastly, the respective velocities of the power, and of the resistance.
The lever is an inflexible rod or beam, that is to say, one which will not bend in any direction. For
instance, the steel rod, to which a pair of scales is suspended, is a lever, and the point by which it is suspended, called the prop or fulcrum, is also the centre of motion. The two parts of a lever, divided by the fulcrum, are called its arms. Now, both scales being empty, they are of the same weight, and consequently balance each other. We have stated that if two bodies of equal weight are fastened together, the centre of gravity will be in the || middle of the line that connects them; the centre of gravity of the scales must, therefore, be in the middle between them, as the fulcrum is, and, this being supported, the scales balance each other.
You recollect, that if a body be suspended by that point in which the centre of gravity is situated, it will remain at rest in any position indifferently; which is not the case with this pair of scales, for when we hold them inclined, they instantly regain their equilibrium. The reason of this is, that the centre of suspension, instead of exactly coinciding with that of gravity, is a little above it. If, therefore, the equilibrium of the scales be disturbed, the centre of gravity moves in a small circle round the point of suspension, and is therefore forced to rise; and the instant it is restored to liberty, it descends and resumes its situation immediately below the point of suspension, when the equilibrium is restored. It is this property which renders the balance so accurate an instrument for weighing goods. If the scales contain different weights, the centre of gravity will be removed towards the scale which is heavier, and being no longer supported, the heaviest scale will descend. If the lever be taken off the prop, and fastened on in another point, that other point then becomes the fulcrum. In this case the equilibrium is destroyed; the longer
the lever is heaviest, and descends. The centre of gravity is not supported, because it is no longer immediately below the point of suspension. But if we can bring the centre of gravity immediately below that point, as it is now situated, the scales will again balance each other.
Thus . if a heavy weight be placed in the scale suspended to the shorter arm of the lever, and a lighter one into that suspended to
the longer arm,
the equilibrium will be restored. It is not, there. fore, impracticable to make a heavy body balance a light one; and by this means position in the weight of goods is sometimes effected. An ingenious
balance, called a steel. yard, has been invented, on the principle that a weight increases in effect in proportion to its distance from the fulcrum.
When a lever is put in motion, the longer arm, or acting part of the lever, must move with greater velocity than the shorter arm, or resisting part of the lever, because it is further from the centre of motion. When two boys ride on a plank drawn over a log of wood, the plank becomes a lever, the log which supports it the fulcrum, and the two boys, the the resistance at each end of the lever. When the boys are of equal weight, the plank must be supported in the middle to make the two arms equal; if they differ in weight, the plank must be drawn over the prop, so as to make the arms unequal, and the lighter
boy must be placed at the extremity of the longer arm, in order that the greater velocity of his motion may compensate for the superior gravity of his companion, so as to render their momentums equal. But we know, that the action of the power must be greater than the resistance in order to put a machine in motion. For this purpose each boy at his descent touches the ground with his feet; and the support he receives from it diminishes his weight, and enables his companion to raise him; thus each boy alternately represents the power and the weight, and the two arms alternately perform the function of the acting and the resisting part of the lever.
A lever in moving, describes the arc of a circle, for it can move only around the fulcrum or centre of mo
tion. It would be impossible for one child to rise perpendicularly to the point A, or for the other to descend in a straight line to B; they each describe arcs of their respective circles ; and it may be judged from the different dimensions of the circle how much greater the