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 1 inch apart, working on a wedge whose head is 5 inches, and length of side 30. inches, will produce an effect measured by 10000lbs. ?

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

QUESTIONS IN NATURAL PHILOSOPHY.

UNIFORM MOTION.

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

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

384. 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.

382. What is a uniform motion ?

383. What is the velocity of a moving body?

384. To what is the space passed over in a unit of time equal? What is the space passed over equal to, in uniform motion?

EXAMPLES.

1. A steamboat moves with a velocity of 23 feet: what space does it pass over in 1 hours?

2. A locomotive is moving with a velocity of 32 feet: what distance will it travel in 3 minutes?

3. A horse travels uniformly a distance of 12 miles with a velocity of 6 feet: what time does he require to perform the journey?

4. A carriage performs a journey of 15 miles in 23 hours: with what velocity does it move?

5. The hammer of a pile-driver is moved upward a distance of 35 feet with a velocity of 1 feet: what time is required to raise it?

6. A ton of coal is raised from a mine 1000 feet deep in 33 minutes with what velocity does it move?

7. A vessel containing a criminal, after leaving a port, sailed with a daily speed of 170 miles; four days after, a clipper was dispatched in pursuit, and sailed at a daily rate of 275 miles: in what time did the clipper overtake the vessel?

8. A bird flew a distance of 100 miles in 11 hours: with what velocity did it travel?

9. Sound moves with a velocity of 1127 feet. If the report of a gun was heard 31.3 seconds after the flash was seen, what distance was the gun from the observer?

10. A hurricane moves with a velocity of 95 feet: what time does it take to move through 3 degrees of latitude, the degree being estimated at 691 miles?

11. The velocity of light has been found, by astronomical observations, and by experiments made in France, to be 191,300 miles what time will it occupy to traverse the mean distance of the earth from the sun, or 95000000 of miles?

12. If a message sent by electro-magnetic telegraph 2300 miles requires 14 seconds for its transmission, what is the velocity of the magnetic current in this telegraph line?

LAWS OF FALLING BODIES.

12.

385. A body falling vertically downward in a vacuum, falls through 16ft. during the first second after leaving its place of rest, 481 ft. during the second second, 80 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.

386. 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.

385. If a body falls vertically, in a vacuum, how far will it fall in the first second of time? How far on the second second second? In the third? What is the common difference of the spaces? What is the measure of the force of gravity?

386. How does the velocity of a falling body change? What is the velocity acquired at the end of any time equal to ? What is the space fallen through equal to ?

387. If a body is thrown vertically upwards 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.

388. The above laws are only approximately true for bodies falling through the air, in consequence to 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 surface to the air.

EXAMPLES.

1. A body has been falling 12 seconds: what space has it described 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 10 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 32 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?

387. How far will a body ascend when projected upwards? 388. Are the above laws perfectly or only approximately true?

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

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

12. During how many seconds must a body fall in a vacuum to acquire a velocity of 1970 feet, which is that of a cannon ball? 13. What time is required for a body to fall in a vacuum, from an elevation of 3280 feet?

14. From what height must a body fall to acquire a velocity of 984 feet?

15. A rocket is projected vertically upward with a velocity of 386 feet after what time will it begin to fall, and to what height will it rise?

SPECIFIC GRAVITY.

389. The SPECIFIC GRAVITY of a body is the weight of a unit of volume. Distilled rain water is the standard for measuring the specific gravity of bodies. Thus, 1 cubic foot of distilled rain water weighs 1000 ounces avoirdupois. If a piece of stone, of the same volume, weighs 2500 ounces, its specific gravity is 2.5; that is, the stone is 2.5 times as heavy as water.

If, then, we denote the standard by 1, the specific gravity of all other bodies will be expressed in terms of this standard; and if we multiply the number denoting the specific gravity of any body by 1000, the product will be the weight in ounces of 1 cubic foot of that body.

If any body be weighed in air and then in water, it will weigh less in water than in air. The difference of the weights will be equal to the sustaining force of the water, which is found to be equal to the weight of an equal volume of water: hence,

389. What is the specific gravity of a body? What is the standard for measuring the specific gravity of a body? What is the numerical value of the cubic foot of a body? How do you find the specific gravity of a body?