SIMPLE MACHINES,

OFTEN CALLED

MECHANICAL POWERS.

LESSON 194.

There are usually reckoned six simple machines; the lever, the wheel and axle, the pulley, the inclined plane, the screw, and the wedge.

1

The force that raises a weight, or overcomes a resistance, is called the power. The power is usually the force of men, oxen, horses, moving water, wind, &c.

THE LEVER.

The support or prop round which the lever moves, is called the fulcrum.

Figure 22.

Figure 23.

There are three kinds of levers. In the first kind the fulcrum is between the power and the weight, as in figure

22.

In the second kind the weight is between the power and the fulcrum, as in figure 23.

How many simple machines are there usually reckoned? Name them.

What is called the power? What is usually the power?

What is called the fulcrum?

How many kinds of levers are there? Explain them?

Figure 24.

In the third kind the power is between the weight and fulcrum, as in figure 24.

When these levers are extremely light, experiment shows that in order to sustain a weight with either of them,

The power must be to the weight in the same proportion as the distance from the fulcrum to the weight is to the distance from the fulcrum to the power.

To be performed in the mind.

1. In what proportion must the power be to the weight with the first kind of lever, in order to balance the weight, if the fulcrum is placed in the centre of the lever? If the weight be 10 lbs., how many pounds must the power be equal to ?

2. A lever of the second kind is 6 ft. long, and the weight is placed 3 ft. from the fulcrum; in what proportion_must the power be to the weight in order to sustain it? If the weight be 12 lbs., how much must the power lift?

3. A lever of the third kind is 8 ft. long, and the power is applied 4 ft. from the fulcrum; in what proportion must the power be to the weight to sustain it? If the weight be 13 lbs., how much must the power lift?

4. A lever of the first kind is 7 ft. long, and the fulcrum is 2 ft. from the weight; what proportion must the power bear to the weight to balance it?

5. A lever of the second kind is 10 ft. long, and the weight is placed 3 ft. from the fulcrum; in what proportion must the power be to the weight in order to sustain it?

6. A lever of the third kind is 9 ft. long, and the power is applied 4 ft. from the fulcrum ; in what proportion must the power be to the weight in order to sustain it?

LESSON 195.

To be performed in the mind.

1. A lever of the first kind is 6 ft. long, and the fulcrum is 2 ft. from the weight; what proportion must the power

When these levers are extremely light, what does experiment show?

bear to the weight in order to balance it? What part of the weight must the power be ? If the weight be 42 lbs., how many pounds must the power be equal to ? If the power be 9 pounds, what weight will it balance?

2. A lever of the second kind is 15 ft. long, and the weight is 5 ft. from the power; in what proportion must the power be to the weight to sustain it? What part of the weight must the power be? If the weight be 60 lbs., how many pounds must the power lift? If the power lift 12 lbs., how many pounds will it sustain ?

3. A lever of the third kind is 12 ft. long, and the power is 9 ft. from the fulcrum; what proportion must the power bear to the weight in order to sustain it ? What part of the weight must the power be? If the weight be 72 lbs., how many pounds must the power lift? If the power be 12 lbs., what weight will it sustain ?

4. There is a lever of the first kind, 8 ft. long; what weight will 12 lbs. as a power, on the end of it, balance, if the fulcrum be placed 2 ft. from the weight?

5. A lever of the second kind is 9 ft. long, and a power can be applied that will lift 10 lbs. ; what weight, placed 3 ft. from the fulcrum, will the power sustain ?

6. A lever of the third kind is 7 ft. long, and a power can be applied 4 ft. from the fulcrum, that will lift 14 lbs.; what weight placed at the end of the lever will it sustain ?

7. There is a lever of the first kind 6 ft. long, the power is equal to 10 lbs., and the weight is 30 lbs. ; where must the fulcrum be placed, so that the power shall balance the weight?

8. A lever of the second kind is 12 ft. long, the power amounts to 7 lbs., and the weight is 28 lbs. ; where must the weight be placed, so that the power shall sustain it?

9. A lever of the third kind is 8 ft. long, the power amounts to 16 lbs., and the weight is 14 lbs. ; where must the power be placed, so as to sustain the weight?

10. If the weight is suspended 1 inch from the fulcrum in a steelyard, at what distance from the fulcrum must a poise weighing 1 lb. be placed, to balance a weight of 1 Îb.? A weight of 2 lbs. ? 21 lbs. ? 3 lbs. ? 11 lbs. ?

If the first notch is 1 inch from the fulcrum, and the notches are of an inch apart, how many pounds and ounces will the poise balance, when placed in the 2d notch? 3d notch? 4th notch? 5th notch? 8th notch? 16th notch? 64th notch? 72d notch? 80th notch?

LESSON 196.

For the Slate.

1. A weight of 2,000 lbs. is on the end of a lever of the first kind, 1 ft. from the fulcrum; how many pounds as a power must be placed 10 ft. from the fulcrum to balance the weight? Ans. 200.

2. A lever of the second kind being 12 ft. long, where must a weight of 720 lbs. be placed, so that a power capable of lifting 50 lbs. shall sustain it?

Ans. 10 in. from the fulcrum.

3. A lever of the third kind is 15 ft. long, with a weight at the end of 90 lbs.; if a power be applied 1 ft. from the weight, how many pounds must it be capable of lifting in order to sustain the weight? Ans. 100.

4. A lever of the first kind, 11 ft. long, has a weight of 1,500 lbs. at one end, and a power equal to 150 lbs. can be applied at the other; where must the fulcrum be placed so that the power shall balance the weight?

Ans. 1 ft. from the end. 5. I wish to sustain 933 lbs. on a lever of the second kind, 14 ft. long, the fulcrum of which is 3 ft. from the weight; what power must I employ ?

Ans. a power capable of raising 200 lbs 6. If you have a lever of the third kind 10 ft. long, with a weight at the end of 145 lbs., where must you apply a power equal to 900 lbs. to sustain the weight?

Ans. 1 ft. 7 in. from the fulcrum. 7. If the place of suspending the weight in a steelyard be 2 inches from the fulcrum, what weight will a poise weighing 4 lbs. balance, if placed 3 ft. from the fulcrum ? Ans. 72 lbs.

8. The place of suspending the weight in a steelyard being 14 inches from the fulcrum, at what distance from the fulcrum must a poise weighing 4 lbs. be placed, so as to balance a weight of 56 lbs. ? Ans. 1 ft. 9 in.

Observations on the Lever. We have regarded the lever as very light; the weight of it, however, in practice, will increase or diminish the power a little. By examining figures 22, 23, and 24, lesson 194, we see that the weight of the lever of the first kind, will generally increase the

What will the weight of the lever do in practice? What do we see by examining figures 22, 23, and 24, lesson 194?

power, and that the weight of the levers of the second and third kinds, will generally diminish the power.

When the power and weight balance each other, the power must be increased a little in order to raise the weight, as there is some rubbing or friction on the fulcrum.

The lever is a very important instrument, and is used in a great many different forms; when you employ your weight on the end of an iron bar to overturn a log, the bar is a lever of the first kind; but if you place your shoulder beneath the bar to roll over the log, the bar is a lever of the second kind. A man who loads hay with a pitchfork, employs a lever of the third kind, one hand being the fulcrum, and the other the power. Common tongs are double levers of the third kind; blacksmiths' tongs are double levers of the first kind, the fulcrum being at the pivot.

The power must be to the weight as the radius of the axle is to the radius of the wheel.

When the power and weight balance each other, what must be done in order to move the weight? Why?

What is an example of a lever of the first kind? Second kind? Third kind? What are common tongs? Blacksmith's tongs; and where is the fulcrum?

What principle is employed in the wheel and axle? Explain how. How must the power be to the weight in order to balance it?