Of the Mechanical Powers.

resistance exactly balances the power, in which case all the parts of the machine are at rest.

We shall first examine the lever.

4. The Lever, is a straight bar of wood or metal, which moves around a fixed point, called the fulcrum. There are three kinds of levers.

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

QUEST.-4. What is a lever? How many kinds of levers are there? Describe the first kind. Where is the weight placed in the second kind? Where is the power placed, in the third kind?

Of the Mechanical Powers.

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

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

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 lbs.

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

Ans. 20 lbs.

5. In a lever of the first kind, that is 6 feet long, a

QUEST.-5. When is an equilibrium produced in all the levers? What is then the proportion between the weight and power?

Of the Mechanical Powers.

weight of 200 lbs. is placed at 1 foot from the fulcrum: what power will balance it?

Ans. 40 lbs.

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 1 lb? A weight of 14 lbs? Of 2 lbs? Of 4 lbs?

7. In a lever of the third kind, the distance from the fulcrum to the power is 5 feet, and from the fulcrum to the weight 8 feet: what power is necessary to sustain a weight of 40 lbs?

Ans. 64 lbs.

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 lbs?

Ans. 150 lbs.

6. 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

QUEST.-6. Has the weight been considered in determining the equilibrium of the levers? In a lever of the first kind, will the weight increase or diminish the power? How will it be in the two other kinds?

Of the Mechanical Powers.

the powers, 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 all the other machines.

OF THE PULLEY.

1. 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 pully turns around its axis, which is generally supported by being attached to a beam above.

2. Pulleys are divided into two kinds, fixed pulleys and moveable 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.

QUEST.-1. What is a pulley? 2. How many kinds of pulleys are there? Does a fixed pulley give any increase of power?

Of the Mechanical Powers.

3. A moveable pulley gives a mechanical advantage. Thus, in the moveable pulley, the hand which sustains the cask does not actually support but one half the weight of it-the other half is supported by the hook to which the other end of the cord is attached.

4. If we have several moveable 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

QUEST.-3. Does a moveable pulley give any mechanical advantage? In a single moveable pulley how much less is the power than the weight? 4. Will an advantage be gained by several moveable pulleys? State the general principle in machines. What does the actual loss of power arise from? What is this rubbing called? Does this vary in different machines?