OF THE MECHANICAL POWERS.

432. There are six simple machines, which are called Mechanical powers. They are, the Lever, the Pulley, the Wheel and Axle, the Inclined Plane, the Wedge, and the Screw.

433. To understand the nature of a machine, four things must be considered.

1st. The power or force which acts. This consists in the efforts of men or horses, of weights, springs, steam, &c.:

2d. The resistance which is to be overcome by the power. This generally is a weight to be moved:

3d. The center of motion, called a fulcrum or prop. The prop or fulcrum is the point about which all the parts of the machine move:

4th. The respective velocities of the power and resistance.

434. A machine is said to be in equilibrium when the resistance exactly balances the power; in which case all the parts of the machine are at rest, or in uniform motion, and in the same direction.

Lever.

435. THE LEVER is a bar of wood or metal, which moves around the fulcrum. There are three kinds of levers.

1st. When the fulcrum is between the weight and the

ower:

2d. When the weight is between the power and the fulcrum :

3d. When the power is between the fulcrum and the weight:

The perpendicular distance from the fulcrum to the di

rections of the weight and power, are called the arms of the lever.

436. An equilibrium is produced in all the levers, when the weight, multiplied by its distance from the fulcrum, is equal to the power multiplied by its distance from the fulcrum. That is,

Rule. The weight is to the power, as the distance from the power to the fulcrum, is to the distance from the weight to the fulcrum.

Examples.

1. In a lever of the first kind, the fulcrum is placed at the middle point: what power will be necessary to balance a weight of 40 pounds?

2. In a lever of the second kind, the weight is placed at the middle point: what power will be necessary to sustain a weight of 50 lb. ?

3. In a lever of the third kind, the power is placed at the middle point: what power will be necessary to sustain a weight of 25 lb. ?

4. A lever of the first kind is 8 feet long, and a weight of 60 lb. is at a distance of 2 feet from the fulcrum: what power will be necessary to balance it ?

5. In a lever of the first kind, that is 6 feet long, a weight of 200 lb. is placed at 1 foot from the fulcrum: what power I will balance it?

6. In a lever of the first kind, like the common steelyard, the distance from the weight to the fulcrum is one inch; at what distance from the fulcrum must the poise of 1 lb. be

placed, to balance a weight of 1lb? A weight of 14 lb.? Of 2 lb.? Of 4 lb.?

7. In a lever of the third kind, the distance from the fulpower is 5 feet, and from the fulcrum to the

crum to the weight 8 feet 40 lb. ?

what power is necessary to sustain a weight of

8. In a lever of the third kind, the distance from the fulcrum to the weight is 12 feet, and to the power 8 feet: what power will be necessary to sustain a weight of 100 lb.?

437. REMARKS.-In determining the equilibrium of the lever, we have not considered its weight. In levers of the first kind, the weight of the lever generally adds to the power, but in the second and third kinds, the weight goes to diminish the effect of the power.

In the previous examples, we have stated the circumstances under which the power will exactly sustain the weight. In order that the power may overcome the resistance, it must of course be somewhat increased. The lever is a very important mechanical power, being much used, and entering, indeed, into most other machines.

Of the Pulley.

438. THE PULLEY is a wheel, having a groove cut in its circumference, for the purpose of receiving a cord which passes over it. When motion is imparted to the cord, the pulley turns around its axis, which is generally supported by being attached to a beam above.

B

439. Pulleys are divided into two kinds, fixed pulleys and movable pulleys. When the pulley is fixed, it does not increase the power which is applied to raise the weight, but merely changes the direction in which it acts.

440. A movable pulley gives a mechanical advantage. Thus, in the movable pulley, the hand which sustains the cask actually supports but onehalf of the weight of it; the other half is supported by the hook to which the other end of the cord is attached.

441. If we have several movable pulleys, the advantage gained is still greater, and a very heavy weight may be raised by a small power. A longer time, however, will be required, than with the single pulley. It is, indeed, a general principle in machines, that what is gained in power, is lost in time; and this is true for all machines. There is also an actual loss of power, viz., the resistance of the machine to motion, arising from the rubbing of the parts against each other, which is called the friction of the machine. This varies in the different machines, but must always be allowed for, in calculating the power necessary to do a given work. It would be wrong, however, to suppose that the loss was equivalent to the gain, and that no advantage is derived from the mechanical powers. We are unable to augment our strength, but by the aid of science we so divide the resistance, that by a continued exertion of power, we accomplish that

which it would be impossible to effect by a single effort.

If, in attaining this result, we sacrifice time, we cannot but see that it is most advantageously exchanged for power.

442. It is plain, that in the movable pulley, all the parts of the cord will be equally stretched; and hence, each cord run

ning from pulley to pulley, will bear an equal part of the weight; consequently,

Rule. The power will always be equal to the weight divided by the number of cords which reach from pulley to pulley.

Examples.

1. In a single immovable pulley, what power will support a weight of 60 lb.?

2. In a single movable pulley, what power will support a weight of 80 lb. ?

3. In two movable pulleys, with 4 cords (see last fig.), what power will support a weight of 100 lb. ?

Rule.-The power to the weight, as the radius of the uxle, to the length of the crank, or radius of the wheel.

Examples.

1. What must be the length of a crank or radius of a wheel, in order that a power of 40 lb. may balance a weight of 600 lb. suspended from an axle of 6 inches radius?