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40 multiplied by 12 furthest from the weight; and
20 feet cwt. on the support nearest to the weight.
WHEEL AND AXLE.
RULE.-As the radius of the wheel is to the radius of the axle, so is the effect to the power.
EXAMPLE.—A weight of 50 lbs. is exerted on the periphery of a wheel whose radius is 10 feet; requir. ed the weight raised at the extremity of a cord wound round the axle, the radius being 20 inches. 50 lbs. multiplied by 10 ft. ; by 12 inches.
300 lbs. 20 inches.
RULE.—Divide the weight to be raised by twice the number of pulleys in the lower block; the quotient will give the power necessary to raise the weight.
EXAMPLE.--What power is required to raise 600 lbs., when the lower block contains six pulleys ? 600
50 lbs., Ans. 6 multiplied by 2
RULE.-As the length of the plane is to its height, so is the weight to the power.
EXAMPLE.—Required the power necessary to raise 540 lbs. up an inclined plane, five feet long and two feet high.
As 5:2 :: 540 : 216 lbs., Ans.
Case 1.–When two bodies are forced from one another by means of a wedge, in a direction parallel to its Back.
RULE.-As the length of the wedge is to half its back or head, so is the resistance to the power.
EXAMPLE.-The breadth of the back or head of the wedge being three inches, and the length of either of its inclined sides 10 inches, required the power necessary to separate two substances with a force of 150 lbs.
As 10 : 1 1-2 :: 150 : 22 1-2 lbs., Ans. Case 2.—When only one of the bodies is inoveable.
RULE.—As the length of the wedge is to its back or head, so is the resistance to the power.
EXAMPLE.-The breadth, length, and force, the same as in the last example.
As 10 : 3 :: 150 : 45 lbs., Ans.
The screw is an inclined plane, and we may suppose it to be generated by wrapping a triangle, or an inclined plane, round the circumference of a cylinder.
The base of the triangle is the circumference of the cylinder; its height, the distance between two consecutive cords or threads; and the hypothenuse forms the spiral cord or inclined plane.
RULE.—To the square of the circumference of the screw, add the square of the distance between two threads; and extract the square root of the sum. This will give the length of the inclined plane; its height is the distance between two consecutive cords or threads.
When a winch or lever is applied to turn the screw, the
power of the screw is as the circle described by the handle of the winch, or lever, to the interval or distance between the spirals.
Velocity is gained at the expense of power by the lever, and the wheel and axle.
Case.- When the weight to be raised is at one end of the lever, the fulcrum at the other, and the power is applied between them.
RULE.—As the distance between the power and the fulcrum is to the length of the lever, so is the weight
to the power.
EXAMPLE.—The length of the lever being eight feet, and the weight at its extremity 60 lbs., required the power to be applied six feet from the fulcrum to raise it ?
As 6:8:: 60: 80 lbs., Ans.