14. How far would a body fall in 1 hour?

Ans. 39,272 miles 1280 yards.

15. How far would a body fall in 9 days?

Ans. 1,832,308,363 miles 1120 yards.

PROBLEM VI.

The velocity given, to find the space fallen through to acquire that velocity.

RULE.

-

· Divide the velocity by 8, and the square of the quotient will be the distance fallen through to acquire that velocity.

16. The velocity of a cannon-ball is 660 feet per second. From what height must it fall to acquire that velocity?

Ans. 6806 feet.

17. At what distance must a body have fallen to acquire the velocity of 1000 feet per second? Ans. 2 miles 5065 feet.

PROBLEM VII.

The velocity given per second, to find the time.

RULE. Divide the velocity by 8, and a fourth part of the quotient will be the time in seconds.

18. How long must a body be falling to acquire a velocity of 200 feet per second? Ans. 6 seconds. 19. How long must a body be falling to acquire a velocity of 320 feet per second? Ans. 10 seconds.

PROBLEM VIII.

The space through which a body has fallen given, to find the time it has been falling.

RULE. Divide the square root of the space in feet fallen through by 4, and the quotient will be the time in seconds in which it was falling. 20. How long would a body be falling through the space of 40,000 feet? Ans. 50 seconds. 21. How long would a ball be falling from the top of a tower, that was 400 feet high, to the earth? Ans. 5 seconds.

PROBLEM IX.

The weight of a body and the space fallen through given, to find the force with which it will strike.

RULE.

Multiply the space fallen through by 64, then multiply the square root of this product by the weight, and the product is the momentum, or force with which it will strike.

22. If the rammer for driving the piles of Warren Bridge weighed 1000 pounds, and fell through a space of 16 feet, with what force did it strike the pile ?

16 x 64 32

32 × 1000= 32,000lbs. Answer.

23. Bunker Hill Monument is 220 feet in height; what would be the momentum of a stone, weighing 4 tons, falling from the top to the ground? Ans. 1,063,184.6+ lbs.

SECTION LXXX.

MECHANICAL POWERS.

THAT body which communicates motion to another is called the power.

The body which receives motion from another is called the weight.

The mechanical powers are six, the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw, and the Wedge.

THE LEVER.

The lever is a bar, movable about a fixed point, called its fulcrum or prop. It is in theory considered as an inflexible line, without weight. It is of three kinds; the first, when the prop

is between the weight and the power; the second, when the weight is between the prop and the power; the third, when the power is between the prop and the weight.

A power and weight acting upon the arms of a lever will balance each other, when the distance of the point at which the power is applied to the lever from the prop is to the distance of the point at which the weight is applied as the weight is to the power.

Therefore, to find what weight may be raised by a given power, we adopt the following

RULE. - As the distance between the body to be raised, or balanced, and the fulcrum or prop, is to the distance between the prop and the point where the power is applied, so is the power to the weight which it will balance.

1. If a man weighing 170 pounds be resting upon a lever 10 feet long, what weight will he balance on the other end, the prop being one foot from the weight? Ans. 1530lbs.

2. If a weight of 1530 pounds were to be raised by a lever 10 feet long, and the prop fixed one foot from the weight, what power applied to the other end of the lever would balance it? Ans. 170lbs.

3. If a weight of 1530 pounds be placed one foot from the prop, at what distance from the prop must a power of 170 pounds be applied to balance it? Ans. 9 feet. 4. At what distance from a weight of 1530 pounds must a prop be placed, so that a power of 170 pounds, applied 9 feet from the prop, may balance it? Ans. 1 foot.

5. Supposing the earth to contain 4,000,000,000,000,000,000,000 cubic feet, each foot weighing 100 pounds, and that the earth was suspended at one end of a lever, its centre being 6000 miles from the fulcrum or prop, and that a man at the other end of the lever was able to pull, or press with a force of 200 pounds; what must be the distance between the man and the fulcrum, that he might be able to move the earth?

Ans. 12,000,000,000,000,000,000,000,000 miles. 6. Supposing the man in the last question to be able to move his end of the lever 100 feet per second, how long would it take him to raise the earth one inch?

Ans. 52,813,479,690y. 17d. 14h. 57m. 46 sec.

THE WHEEL AND AXLE.

The wheel and axle is a wheel turning round together with its axle; the power is applied to the circumference of the wheel, and the weight to that of the axle by means of cords.

An equilibrium is produced in the wheel and axle, when the weight is to the power as the diameter of the wheel to the diameter of its axle.

To find, therefore, how large a power must be applied to the wheel to raise a given weight on the axle, we adopt the following

RULE. As the diameter of the wheel is to the diameter of the axle, so is the weight to be raised by the axle to the power that must be applied to the wheel.

7. If the diameter of the axle be 6 inches, and the diameter of the wheel 4 feet, what power must be applied to the wheel to raise 960 pounds at the axle ? Ans. 120lbs.

8. If the diameter of the axle be 6 inches, and the diameter of the wheel 4 feet, what power must be applied to the axle to raise 120 pounds at the wheel? Ans. 960lbs. 9. If the diameter of the axle be 6 inches, and 120 pounds applied to the wheel raise 960 pounds at the axle, what is the diameter of the wheel?

Ans. 4 feet. 10. If the diameter of the wheel be 4 feet, and 120 pounds applied to the wheel raise 960 pounds at the axle, what is the diameter of the axle? Ans. 6 inches.

THE PULLEY.

The pulley is a small wheel, movable about its axis by means of a cord, which passes over it.

When the axis of a pulley is fixed, the pulley only changes the direction of the power; if movable pulleys are used, an equilibrium is produced when the power is to the weight as one to the number of ropes applied to them. If each movable pulley has its own rope, each pulley will be double the power.

To find the weight that may be raised by a given power. RULE. Multiply the power by the number of cords that support the weight, and the product is the weight.

11. What power must be applied to a rope, that passes over one movable pulley, to balance a weight of 400 pounds?

Ans. 200lbs. 12. What weight will be balanced by a power of 10 pounds, attached to a cord that passes over 3 movable pulleys?

Ans. 60lbs.

13. What weight will be balanced by a power of 144 pounds, attached to a cord that passes over 2 movable pulleys?

Ans. 576lbs. 14. If a cord, that passes over two movable pulleys, be attached to an axle 6 inches in diameter, whose wheel is 60 inches in diameter, what weight may be raised by the pulley, by applying 144 pounds to the wheel? Ans. 5760lbs.

THE INCLINED PLANE.

An inclined plane is a plane which makes an acute angle with the horizon.

The motion of a body descending an inclined plane is uniformly accelerated.

The force with which a body descends an inclined plane, by the force of attraction, is to that with which it would descend freely, as the elevation of the plane to its length; or, as the size of its angle of inclination to radius.

To find the power that will draw a weight up an inclined plane.

RULE. Multiply the weight by the perpendicular height of the plane, and divide this product by the length.

15. An inclined plane is 50 feet in length, and 10 feet in perpendicular height; what power is sufficient to draw up a weight of 1000 pounds? Ans. 200lbs.

16. What weight, applied to a cord passing over a single pulley at the elevated part of an inclined plane, will be able to sustain a weight of 1728 pounds, provided the plane was 600 feet long, and its perpendicular height 5 feet? Ans. 142lbs.

17. A certain railroad, one mile in length, has a perpendic ular elevation of 50ft.; what power is sufficient to draw up this elevation a train of cars weighing 20,000lbs. ? Ans. 1893.

18. An inclined plane is 300 feet in length, and 30 feet in perpendicular height; what power is sufficient to draw up a weight of 2000 pounds? Ans. 200lbs. 19. An inclined plane is 1000 feet in length, and 100 feet in perpendicular height; what power is sufficient to draw up this elevation a weight of 5000 pounds? Ans. 500lbs.

20. What weight applied to and passing over a single pulley, at the elevated part of an inclined plane, will be able to sustain a weight of 7000lbs., provided the plane is 300 feet long and its perpendicular height 30 feet? Ans. 700lbs.