The Wedge.

445. The wedge is composed of two inclined planes, united

together along their bases, and forming a solid ACB. It is used to cleave masses of wood or stone. The resistance which it overcomes is the attraction of cohesion of the body which it is employed to separate. The wedge acts, principally, by being struck with a hammer, or mallet, on

A

B

its head, and very little effect can be produced with it, by mere pressure.

All cutting instruments are constructed on the principle of the inclined plane or wedge. Such as have but one sloping edge, like the chisel, may be referred to the inclined plane; and such as have two, like the ax and the knife, to the wedge.

Rule.-Half the thickness of the head of the wedge, is to the length of one of its sides, as the power which acts against its head to the effect produced at its side.

Examples.

1. If the head of a wedge is 4 inches thick, and the length of one of its sides 12 inches, what will measure the effect of a force denoted by 96 pounds?

2. If the head of a wedge is 6 inches thick, the length of the side 27 inches, and the force applied measures 250 pounds, what will be the measure of the effect?

3. If the head of a wedge is 9 inches, and the length of the side 2 feet, what will be the effect of a blow denoted by 200 pounds?

4. If the head of a wedge is 10 inches, and the length of the side 30 inches, what will measure the effect of a blow noted by 500?

The Screw.

446. The screw is composed of two parts-the screw, S, and the nut, N.

The screw, S, is a cylinder with a spiral projection winding around it. The nut, N, is perforated to admit the screw, and within it is a grove into which the thread of the screw fits closely.

The handle, D, which projects from the nut, is a lever which works the nut upon the screw.

The power of the screw depends on the distance between the threads. The closer the threads of the screw, the greater will be the power; but then the number of revolutions made by the handle, D, will also be proportionably increased: so that we return to the general principle-what is gained in power is lost in time. The power of the screw may also be increased by lengthening the lever, D, attached to the nut.

The screw is used for compression, and to raise heavy weights. It is used in cider and wine presses, in coining, and for a variety of other purposes.

Rule. As the distance between the threads of a screw, is to the circumference of the circle described by the power, so is the power employed to the weight raised.

Examples.

1. If the distance between the threads of a screw is half an inch, and the circumference described by the handle 15 feet, what weight can be raised by a power denoted by 720 pounds?

2. If the threads of a screw are one-third of an inch apart, and the handle is 12 feet long, what power must be applied to sustain 2 tons?

3. What force applied to the handle of a screw 10 feet long, with threads one inch apart, working on a wedge whose head is 5 inches, and length of side 30 inches, will produce an effect measured by 10000 lb. ?

4. If a power of 300 pounds applied at the end of a lever 15 feet long will sustain a weight of 282744 lb., what is the listance between the threads of the screw?

QUESTIONS IN NATURAL PHILOSOPHY.

UNIFORM MOTION.

447. If a moving body passes over equal spaces in equal portions of time, it is said to move with uniform motion, or uniformly.

448. The velocity of a moving body is measured by the space passed over in a second of time.

449. The space passed over in any time is equal to the product of the velocity multiplied by the number of seconds in the time.

If we denote the velocity by V, the space passed over by S, and the time by T, we have

S = V X T.

LAWS OF FALLING BODIES.

450. A body falling vertically downward in a vacuum, falls through 16 ft. during the first second after leaving its place of rest, 481 ft. during the second second, 805 ft. the third second, and so on: the spaces forming an arithmetical progression of which the common difference is 321 ft., or double the space fallen through during the first second. This number is called the measure of the force of gravity, and is denoted by g.

451. It is seen from the above, that the velocity of a body

is continually increasing. If H denote the height fallen through, T, the time, V, the velocity acquired, and g, the force of gravity, the following formulas have been found to express the relations between these quantities:

1st. That the velocity acquired at the end of any time, is equal to the force of gravity (321) multiplied by the time.

2d. That the square of the velocity is equal to twice the force of gravity multiplied by the height; or, the velocity is equal to the square root of that quantity.

3d. That the space fallen through is equal to one-half the velocity multiplied by the time.

4th. That the space fallen through is equal to one-half the force of gravity multiplied by the square of the time.

452. If a body is thrown vertically upward in a vacuum, its motion will be continually retarded by the action of gravitation. It will finally reach the highest point of its ascent, and then begin to descend. The height to which it will rise may be found by the second formula in the preceding paragraph, when the velocity with which it is projected upward is known; for the times of ascent and descent will be equal.

453. The above laws are only approximately true for bodies falling through the air, in consequence of its resistance. We may measure the depths of wells or mines, and the heights of elevated objects approximately, by using dense bodies, as leaden bullets or stones, which present small surfaces to the air.

Examples.

1. A body has been falling 12 seconds: what space did it describe in the last second, and what in the whole time?

2. A body has been falling 15 seconds: find the space described and the velocity acquired.

3. How far must a body fall to acquire a velocity of 120 feet?

4. How many seconds will it take a body to fall through a space of 100 feet?

5. Find the space through which a heavy body falls in 1 seconds, and the velocity acquired.

6. How far must a body fall to acquire a velocity of 1000 feet?

7. A stone is dropped into a well, and strikes the water in 3.2 seconds: what is the depth of the well?

8. A stone is dropped from the top of a bridge, and strikes the water in 2.5 seconds: what is the height of the bridge?

9. A body is thrown vertically upward with a velocity of 160 feet what height will it reach, and what will be the time of ascent ?

10. An arrow shot perpendicularly upward, returned again in 10 seconds. Required the velocity with which it was shot, and the height to which it rose.

11. A ball is let fall from the top of a steeple, and reaches the ground in three seconds and a half: what is the height of the steeple?

12. What time will be necessary for a body falling freely, to acquire a velocity of 2500 feet per second?

13. If a ball be thrown vertically upward with a velocity of 350 feet per second, how far will it ascend, and what will be the time of ascent and descent?

14. How long must a body fall freely to acquire a velocity of 3040 feet per second?

15. If a body falls freely in a vacuum, what will be its velocity after 45 seconds of fall?