(fig. 5. plate 3.)

27. (Pg. 52) A cylinder of wood, may be made to rise to a small distance up an inclined plane. How may this be effected? (fig. 5. plate 3.)

28. (Pg. 53) When do we find the centres of gravity, and of magnitude in different points?

29. (Pg. 53) What influence will the density of the parts of a body exert upon its stability?

30. (Pg. 53) What other circ.u.mstance materially affects the firmness of position? (fig. 6. plate 3.)

31. (Pg. 53) Why is it more easy to carry a weight in each hand, than in one only?

32. (Pg. 53) What is said respecting two bodies united by an inflexible rod?

33. (Pg. 53) What is fig. 7, plate 3, intended to ill.u.s.trate? What fig.

8; what fig. 9?

CONVERSATION V.

ON THE MECHANICAL POWERS.

OF THE POWER OF MACHINES. OF THE LEVER IN GENERAL. OF THE LEVER OF THE FIRST KIND, HAVING THE FULCRUM BETWEEN THE POWER AND THE WEIGHT. OF THE LEVER OF THE SECOND KIND, HAVING THE WEIGHT BETWEEN THE POWER AND THE FULCRUM. OF THE LEVER OF THE THIRD KIND, HAVING THE POWER BETWEEN THE FULCRUM AND THE WEIGHT.

MRS. B.

We may now proceed to examine the mechanical powers; they are six in number: The _lever_, the _pulley_, the _wheel_ and _axle_, the _inclined plane_, the _wedge_ and the _screw_; one or more of which enters into the composition of every machine.

A mechanical power is an instrument by which the effect of a given force is increased, whilst the force remains the same.

In order to understand the power of a machine, there are four things to be considered. 1st. The power that acts: this consists in the effort of men or horses, of weights, springs, steam, &c.

2dly. The resistance which is to be overcome by the power: this is generally a weight to be moved. The power must always be superior to the resistance, otherwise the machine could not be put in motion.

_Caroline._ If for instance the resistance of a carriage was greater than the strength of the horses employed to draw it, they would not be able to make it move.

_Mrs. B._ 3dly. We are to consider the support or prop, or as it is termed in mechanics, the _fulcrum_; this you may recollect is the point upon which the body turns when in motion; and lastly, the respective velocities of the power, and of the resistance.

_Emily._ That must in general depend upon their respective distances from the fulcrum, or from the axis of motion; as we observed in the motion of the vanes of the windmill.

_Mrs. B._ We shall now examine the power of the lever. The _lever is an inflexible rod or bar, moveable about a fulcrum, and having forces applied to two or more points on it_. For instance, the steel rod to which these scales are suspended is a lever, and the point in which it is supported, the fulcrum, or centre of motion; now, can you tell me why the two scales are in equilibrium?

_Caroline._ Being both empty, and of the same weight, they balance each other.

_Emily._ Or, more correctly speaking, because the centre of gravity common to both, is supported.

_Mrs. B._ Very well; and where is the centre of gravity of this pair of scales? (fig. 1. plate 4.)

_Emily._ You have told us that when two bodies of equal weight were fastened together, the centre of gravity was in the middle of the line that connected them; the centre of gravity of the scales must therefore be supported by the fulcrum F of the lever which unites the two scales, and which is the centre of motion.

_Caroline._ But if the scales contained different weights, the centre of gravity would no longer be in the fulcrum of the lever, but remove towards that scale which contained the heaviest weight; and since that point would no longer be supported, the heavy scale would descend, and out-weigh the other.

_Mrs. B._ True; but tell me, can you imagine any mode by which bodies of different weights can be made to balance each other, either in a pair of scales, or simply suspended to the extremities of the lever? for the scales are not an essential part of the machine; they have no mechanical power, and are used merely for the convenience of containing the substance to be weighed.

_Caroline._ What! make a light body balance a heavy one? I cannot conceive that possible.

_Mrs. B._ The fulcrum of this pair of scales (fig. 2.) is moveable, you see; I can take it off the beam, and fasten it on again in another part; this part is now become the fulcrum, but it is no longer in the centre of the lever.

_Caroline._ And the scales are no longer true; for that which hangs on the longest side of the lever descends.

_Mrs. B._ The two parts of the lever divided by the fulcrum, are called its arms; you should therefore say the longest arm, not the longest side of the lever.

Your observation is true that the balance is now destroyed; but it will answer the purpose of enabling you to comprehend the power of a lever, when the fulcrum is not in the centre.

_Emily._ This would be an excellent contrivance for those who cheat in the weight of their goods; by making the fulcrum a little on one side, and placing the goods in the scale which is suspended to the longest arm of the lever, they would appear to weigh more than they do in reality.

_Mrs. B._ You do not consider how easily the fraud would be detected; for on the scales being emptied they would not hang in equilibrium. If indeed the scale on the shorter arm was made heavier, so as to balance that on the longer, they would appear to be true, whilst they were really false.

_Emily._ True; I did not think of that circ.u.mstance. But I do not understand why the longest arm of the lever should not be in equilibrium with the other?

_Caroline._ It is because the momentum in the longest, is greater than in the shortest arm; the centre of gravity, therefore, is no longer supported.

_Mrs. B._ You are right, the fulcrum is no longer in the centre of gravity; but if we can contrive to make the fulcrum in its present situation become the centre of gravity, the scales will again balance each other; for you recollect that the centre of gravity is that point about which every part of the body is in equilibrium.

_Emily._ It has just occurred to me how this may be accomplished; put a great weight into the scale suspended to the shortest arm of the lever, and a smaller one into that suspended to the longest arm. Yes, I have discovered it--look Mrs. B., the scale on the shortest arm will carry 3 lbs., and that on the longest arm only one, to restore the balance.

(fig. 3.)

_Mrs. B._ You see, therefore, that it is not so impracticable as you imagined, to make a heavy body balance a light one; and this is in fact the means by which you observed that an imposition in the weight of goods might be effected, as a weight of ten or twelve ounces, might thus be made to balance a pound of goods. If you measure both arms of the lever, you will find that the length of the longer arm, is three times that of the shorter; and that to produce an equilibrium, the weights must bear the same proportion to each other, and that the greater weight, must be on the shorter arm. Let us now take off the scales, that we may consider the lever simply; and in this state you see that the fulcrum is no longer the centre of gravity, because it has been removed from the middle of the lever; but it is, and must ever be, the centre of motion, as it is the only point which remains at rest, while the other parts move about it.

[Ill.u.s.tration: PLATE IV.]

_Caroline._ The arms of the lever being different in length, it now exactly resembles the steelyards, with which articles are so frequently weighed.

_Mrs. B._ It may in fact be considered as a pair of steelyards, by which the same power enables us to ascertain the weight of different articles, by simply increasing the distance of the power from the fulcrum; you know that the farther a body is from the axis of motion, the greater is its velocity.

_Caroline._ That I remember, and understand perfectly.

_Mrs. B._ You comprehend then, that the extremity of the longest arm of a lever, must move with greater velocity than that of the shortest arm, and that its momentum is greater in proportion.

_Emily._ No doubt, because it is farthest from the centre of motion. And pray, Mrs. B., when my brothers play at _see-saw_, is not the plank on which they ride, a kind of lever?

_Mrs. B._ Certainly; the log of wood which supports it from the ground is the fulcrum, and those who ride, represent the power and the resistance at the ends of the lever. And have you not observed that when those who ride are of equal weight, the plank must be supported in the middle, to make the two arms equal; whilst if the persons differ in weight, the plank must be drawn a little farther over the prop, to make the arms unequal, and the lightest person, who may be supposed to represent the power, must be placed at the extremity of the longest arm.

_Caroline._ That is always the case when I ride on a plank with my youngest brother; I have observed also that the lightest person has the best ride, as he moves both further and quicker; and I now understand that it is because he is more distant from the centre of motion.

_Mrs. B._ The greater velocity with which your little brother moves, renders his momentum equal to yours.