Compendium of Natural and Experimental Philosophy 6

Index

PREFACE TO THE REVISED AND ENLARGED EDITION 1871
INTRODUCTION
DIVISIONS OF THE SUBJECT
OF MATTER AND ITS PROPERTIES
OF GRAVITY
MECHANICS, on THE LAWS OF MOTION
THE MECHANICAL POWERS
REGULATORS OF MOTION
HYDROSTATICS
HYDRAULICS
PNEUMATICS
ACOUSTICS
PYRONOMICS
THE STEAM-ENGINE
OPTICS
ELECTRICITY
GALVANISM, OR VOLTAIC ELECTRICITY
MAGNETISM
ELECTRO MAGNETISM
THE ELECTROMAGNETIC TELEGRAPH
THE ELECTROTYPE PROCESS
MAGNETO-ELECTRICITY
THERMO-ELECTRICITY
ASTRONOMY

THE MECHANICAL POWERS

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What things in Mechanics require distinct consideration?

  1. THE MECHANICAL POWERS. — There are five things in mechanics which require a distinct consideration, namely:
    First, the power that acts.
    Secondly, the resistance which is to be overcome by the power.
    Thirdly, the centre of motion, or, as it is sometimes called, the fulcrum.*
    * The word fulcrum means a prop, or support.
    Fourthly, the respective velocities of the power and the resistance; and,
    Fifthly, the instruments employed in the construction of the machine.

 

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  1. (1.) The power that acts is the muscular strength of men or animals, the weight and momentum of solid bodies, the elastic force of steam, springs, the pressure of the air, the weight of water and its force when in motion, &c.

(2.) The resistance to be overcome is the attraction of gravity or of cohesion, the inertness of matter, friction, &c.

(3;) The centre of motion, or the fulcrum, is the point about which all the parts of the body move.

(4.) The velocity is the rapidity with which an effect is produced.

(5.) The instruments are the mechanical powers which enter into the construction of the machine.

What are the mechanical Powers?

  1. The powers which enter into the construction of a machine are called the Mechanical Powers. They are contrivances designed to increase or to diminish force, or to alter its direction.

What is the fundamental principle of Mechanics?

  1. All the Mechanical Powers are constructed on the principle that what is gained in power is lost in time. This is the fundamental law of Mechanics.
  2. If 1 lb. is required to overcome the resistance of 2 lbs., the 1 lb. must move over two feet in the same time that the resistance takes to move over one. Hence the resistance will move only half as fast as the power, or, in other words, the resistance requires double the time required by the power to move over a given space.

Fig. 26.

Explain Fig. 26.

  1. Fig. 26 illustrates the principle as applied to the lever. W represents the weight, F the fulcrum, P the power, and the bar W F P the lever. To raise the weight W to w, the power P must descend to p. But, as the radius of the circle in which the power P moves is double that of the radius of the circle in which the weight W moves, the arc P p is double the are W w; or, in other words, the distance P p is double the distance of W w.

 

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Now, as these distances are traversed in the same time by the power and the weight respectively, it follows that the velocity of the power must be double the velocity of the weight; that is, the power must move at the rate of two feet in a second, in order to move the weight one foot in the same time.

This principle applies not only to the lever, but to all the Mechanical Powers, and to all machines constructed on mechanical principles.

How many Mechanical Powers are there, and their names?

  1. There are six Mechanical Powers: * (* More properly called simple machines)
    the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge and the Screw.

All instruments and machines are constructed on the principle of one or more of the Mechanical Powers.

All the Mechanical Powers may be reduced to three classes, namely: 1st, a body revolving on an axis; 2d, a flexible cord; and, 3d, an inclined surface, smooth and hard. To the first belongs the lever, and the wheel and axle; to the second, the pulley; to the third, the- inclined plane, the wedge and the screw.

What is the Lever, and how is it used?

  1. The Lever is an inflexible bar, movable on a fulcrum or prop. It is used by making one part to rest on a fulcrum, applying the power to bear on another part, while a third part of the lever opposes its motion to the resistance which is to be overcome.
  2. In every lever, therefore, whatever be its form, there are three things to be distinctly considered, namely: the position of the fulcrum, of the power, and of the weight, respectively. It is the position of these which makes the distinction between the different kinds of levers.

How many kinds of levers are there?

  1. There are three kinds of levers, called the first, second and third, according to the respective position of the fulcrum, the power, and the weight.

These may be represented thus:

Power                     Fulcrum               Weight

Power                     Weight                Fulcrum

Weight                   Power                  Fulcrum

 

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What is the positon of the power, the weight, and the fulcrum respectively, in the three kinds of lever?

That is (1.) The power* is at one end, the weight at the other, and the fulcrum between them.

*It is to be understood, in the consideration of all instruments and machines, that some effect is to be produced by some power. The names power and weight are not always to be taken literally. They are terms used to express the cause and the effect. Thus, in the movement of a clock, the weight is the cause, the movement of the hands is the effect. The cause of motion, whether it be a weight or a resistance, is technically called the power; the effect, whether it be the raising-of a weight, the overcoming of resistance or of cohesion, the separation of the parts of a body, compression or expansion, is technically called the weight.

(2.) Power at one end, the fulcrum at the the fulcrum, other, and the weight between them.

(3) The weight is at one end, the fulcrum at the other, and the power between them.

Describe a lever of the first kind by figure 27, and tell the advantage gained by it.

  1. In a lever of the first kind the fulcrum is placed between the power and the weight.

Fig. 27.

Fig. 27 represents a lever of the first kind, resting on the fulcrum F, and movable upon it. W is the weight to be moved, and B

P is the power which moves it. The advantage gained in rising a weight, by the use of this kind of ever, is in proportion as the distance of the power from the fulcrum exceeds that of the weight from the fulcrum. Thus, in this figure, if the distance between P and F be double that between W and F, then a man, by the exertion of a force of 100 pounds with the lever, can move a weight of 200 pounds. From this it follows that the nearer the power is applied to the end of the lever, the greater is the advantage gained. Thus, a greater weight can be moved by the same power when applied at B than when it is exerted at P.

On what principle is the common steelyard constructed? Describe the steelyard.

  1. The common steelyard, an instrument for weighing articles, is constructed on the principle of the lever of the first kind. It consists of a rod or bar, marked with notches to designate the pounds and ounces, and a weight, which is movable along the notches.

 

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The bar is furnished with three hooks, on the longest of which the article to be weighed is always to be hung. The other two hooks serve for the handle of the instrument when in use.

Fig. 28.

The pivot of each of these two hooks serves for the fulcrum.

Of what use are the three hooks in the steelyard?

  1. When suspended by the hook C, as in Fig. 28, it is manifest that a pound weight at E will balance as many pounds at W as the distance between the pivot of D and the pivot of C is contained in the space between the pivot of C and the ring from which E is suspended.

The same instrument may be used to weigh heavy articles, by using the middle hook for a handle, where, as will be seen in Fig. 29, the space between the pivot of F (which in this case is the fulcrum) and the pivot of D (from which the weight is suspended) being lessened, is contained a greater number of times in the distance between the fulcrum and the notches on the bar. The steelyard is furnished with two sets of notches on opposite sides of the bar. An equilibrium * will always be produced when the product of the weights on the opposite sides of the fulcrum into their respective distances from it are equal to one another.

* Of Equilibrium. In the calculations of the powers of all machines it is necessary to have clearly in mind the difference between action and equilibrium. By equilibrium is meant an equality of forces; as, when one force is opposed by another force, if their respective momenta are equal, an equilibrium is produced, and the forces merely counterbalance each other. To produce any action, there must be inequality in the condition of one of the forces. Thus, a power of one pound on the longer arm of a lever will balance a weight of two pounds on the shorter arm, if the distance of the power from the fulcrum be exactly double the distance of the weight from the fulcrum; and the reason why they exactly balance is, because their momenta are equal. No motion can be produced or destroyed without a difference between the force and the resistance. In calculating the mechanical advantage of any machine, therefore, the condition of equilibrium must first be duly considered. After an equilibrium is produced, whatever is added upon the one side or taken away on the other destroys the equilibrium, and causes the machine to move.

 

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Fig. 29

A balance, or pair of scales, is a lever of the first kind, with equal arms. Steelyards, scissors, pincers, snuffers, and a poker used for stirring the fire, are all levers of the first kind. The longer the handles of scissors, pincers, &c., and the shorter the points, the more easily are they used.

  1. The lever is made in a great variety of forms and of many different materials, and is much used in almost every kind of mechanical operation. Sometimes it is detached from the fulcrum, but most generally the fulcrum is a pin or rivet by which the lever is permanently connected with the frame-work of other parts of the machinery.

 

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  1. When two weights are equal and the fulcrum is placed exactly in the centre of the lever between them, they will mutually balance each other; or, in other words, the centre of gravity being supported, neither of the weights will sink. This is the principle of the common scale for weighing.

How is power gained by the use of the lever?

  1. To gain power by the use of the lever, the fulcrum must be placed near the weight to be moved, and the power at the greater distance from it. The force of the lever, therefore, depends on its length, together with the power applied, and the distance of the weight from the fulcrum. *

* This being the case, it is evident that the shape of the lever will not influence its power, whether it be straight or bent. The direct distance between the fulcrum and the weight, compared with the same distance between the fulcrum and the power, being the only measure of the mechanical advantage which it affords.

What is a Compound Lever?

Fig. 30.

  1. A Compound Lever, represented in Fig. 30, consists of several levers, so arranged that the shorter arm of one may act on the longer arm of the other. Great power is obtained in this way, but its exercise is limited to a very small space.

Fig. 31.

Describe the Fig. 31.

  1. In a lever of the second kind, the fulcrum is at one end, the power at the other, and the weight between them.

(1.) Let Fig. 31 represent a lever of the second kind. F is the fulcrum, P the power, and W the weight. The advantage gained by a lever of this kind is in proportion as the distance of the power from the fulcrum exceeds that of the weight from the fulcrum. Thus, in this figure, if the distance from P to F is four times the distance from W to F, then a power of one pound at P will balance a weight of four pounds at W.

 

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(2.) On the principle of this kind of lever, two persons, carrying a heavy burden suspended on a bar, may be made to bear unequal portions of it; by placing it nearer to the one than the other.

  1. Two horses, also, may be made to draw unequal portions of a load, by dividing the bar attached to the carriage in such a manner that the weaker horse may draw upon the longer end of it.

Fig. 32.

  1. Oars, rudders of ships, doors turning on hinges, and cutting-knives, which are fixed at one end, are constructed upon the principle of levers of the second kind.*

* It is on the same principle that, in raising a window, the hand should be applied to the middle of the sash, as it will then be easily raised, whereas, if the hand be applied nearer to one side than the other, the centre of gravity being unsupported, will cause the further side to bear against the frame, and obstruct its free motion.

Describe the lever of the third kind by Fig. 33.

  1. In a lever of the third kind the fulcrum is at one end, the weight at the other, and the power is applied between them.

In levers of this kind the power must always exceed the weight in the same proportion as the distance of the weight from the fulcrum exceeds that of the power from the fulcrum.

Fig. 33.

In Fig. 33 F is the fulcrum, W the weight, and P the power between the fulcrum and the weight; and the power must exceed the weight in the same proportion that the distance between W and F exceeds the distance between P and F.

  1. A ladder, which is to be raised by the strength of a man’s arms, represents a lever of this kind, where the fulcrum is that end which is fixed against the wall; the weight may be considered as at the top part of the ladder, and the power is the strength applied in raising it.

 

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  1. The bones of a man’s arm, and most of the movable bones of animals, are levers of the third kind. But the loss of power in limbs of animals is compensated by the beauty and compactness of the limbs, as well as the increased velocity of their motion. The wheels in clock and watch work, and in various kinds of machinery, may be considered as levers of this kind, when the power that moves them acts on the pinion, near the centre of motion, and the resistance to be overcome acts on the teeth at the circumference. But here the advantage gained is the change of slow into rapid motion.
  2. PRACTICAL EXAMPLES OF LEVERAGE.

Questions for Solution

(1.) Suppose a lever, 6 feet in length, to be applied to raise a weight of 50 pounds, with a power of only 1 pound, where must the fulcrum be placed? Ans. 1.41 in. +

(2.) If a man wishes to move a stone weighing a ton with a crow-bar 6 feet in length, he himself being able, with his natural strength, to move a weight of 100 pounds only, what must be the greatest distance of the fulcrum from the stone? Ans. 3.42 n. +

(3.) If the distance of the power from the fulcrum be eighteen times greater than the distance of the weight from the fulcrum, what power would be required to lift a weight of 1000 pounds? Ans. 55.55 lb. +

(4.) If the distance of the weight from the fulcrum be only a tenth of the distance of the power from the fulcrum, what weight can be raised by a power of 170 pounds? Ans. 1700 lb.

(5.) In a pair of steelyards the distance between the hook on which the weight is hung and the hook by which the instrument is suspended is 2 inches; the length of the steelyards is 30 inches. How great a weight may be suspended on the hook to balance a weight of 2 pounds at the extremity of the longer arm. – Ans. 28 lb.

(6.) Archimedes boasted that, if he could have a place to stand upon, he could move the whole earth. Now, suppose that he had a fulcrum with a lever, and that his weight, compared with that of the earth, was as 1 to 270 millions. Suppose, also, that the fulcrum were a thousand miles from the earth; what must be his distance from the fulcrum? Ans. 270,000,000,000 mi.

(7.) Which will cut the more -easily, a pair of scissors 9 inches long, with the rivet 5 inches from the points, or a pair of scissors 6 inches long, with the rivet 4 inches from the points? Ans. The first.

(8.) Two persons, of unequal strength, carry a weight of 200 pounds suspended from a pole 10 feet long. One of them can carry only 75 pounds, the other must carry the rest of the Weight. How far from the end of the pole must the weight be suspended 2 Ans. 3.75 ft.

(9.) How must the whiffle-tree * of a carriage be attached, that one horse may draw but 3 cwt. of the load, while the other draws 5 cwt. 2 Ans. At 3/5.

* The whiffle-tree is generally attached to a carriage by a hook or leather band in the centre, so that the draft shall be equal on both sides. The hook or leather band thus becomes a fulcrum.

(10.) On the end of a steelyard, 3 feet long, hangs a weight of 4 pounds. Suppose the hook, to which articles to be weighed are attached, to be at the extremity of the other end, at the distance of 4 inches from the hook by which the steelyards are held up. How great a weight can be estimated by the steelyard 2 Ans. 32 lb.

What is the Wheel and Axle?

  1. THE WHEEL AND AXLE. – The Wheel and Axle consists of a cylinder with a wheel attached, both revolving around the same axis of motion.

 

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How are the power and the weight applied to the wheel and axle?

  1. The weight is supported by a rope or chain wound around the cylinder; the power is applied to another rope or chain wound around the circumference of the cylinder. Sometimes projecting spokes from the wheel supply the place of the chain.*

* A cylinder is a long circular body of uniform diameter, with extremities forming equal and parallel circles.

  1. The place of the cylinder is sometimes supplied by a small wheel.

Explain the construction of the wheel and axle by Fig. 34.

  1. The wheel and axle, though made in many forms, will easily be understood by inspecting Figs. 34 and 35. In Fig. 34 P represents the larger wheel, where the power is applied; C the smaller wheel, or cylinder, which is the axle; and W the weight to be raised.

What is the the advantage gained by the use of the wheel and axle?

The advantage gained is in proportion as the circumference of the wheel is greater than that of the axle. That is, if the circumference of the wheel be six times the circumference of the axle, then a power of one pound applied at the wheel will balance a power of six pounds on the axle.

Fig. 35

How does the wheel and axle described in Fig. 35 differ from that described in Fig. 34?

  1. Sometimes the axle is constructed with a winch or handle, as in Fig. 35, and sometimes the wheel has projecting spokes, as in Fig. 34.

 

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On what principle is the wheel and axle constructed?

  1. The principle upon which the wheel and axle is constructed is the same with that of the other Mechanical Powers, the want of power being compensated by velocity. It is evident (from the Figs. 34: and 35) that the velocity of the circumference of the wheel is as much greater than that of the axle as it is further from the centre of motion; for the wheel describes a great circle in the same time that the axle describes a small one; therefore the power is increased in the same proportion as the circumference of the wheel is greater than that of the axle. If the velocity of the wheel be twelve times greater than that of the axle, a power of one pound on the wheel will support a weight of twelve pounds on the axle.
  2. The wheel and axle are sometimes called “the perpetual lever,” the diameter of the wheel representing the longer arm, the diameter of the axle representing the shorter arm, the fulcrum being at the common centre.
  3. The capstan,* on board of ships and other vessels, is constructed on the principle of the wheel and axle. It consists of an axle placed uprightly, with a head a(r drum, pierced with holes for the lever, or levers, which supply the place of the wheel.

* The difference between a capstan and a windlass lies only in the position of the wheel. If the wheel turn horizontally, it is called a capstan; if vertically, a windlass.

  1. Windmills, lathes, the common windlass, used for drawing water from wells, and the large wheels in mills, are all constructed on the principle of the wheel and axle.
  2. Wheels are a very essential part to most machines. They are applied in different ways, but, when affixed to the axle, their mechanical power is always in the same proportion; that is, as the circumference of the wheel exceeds that of the axle, so much will the power be increased. Therefore, the larger the wheel, and the smaller the axle, the greater will be the power obtained.

What are Cranks, and how are they made?

  1. CRANKS. – Cranks are sometimes connected with the axle of a wheel, either to give or to receive its motion. They are made by bending the axle in such a manner as to form four right angles facing in different directions, as is represented in Fig. 36.

Fig. 36

They are, in fact, nothing more than a double winch.

 

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  1. A rod connects the crank with other parts of the machinery, either to communicate motion to or from a wheel. When the rod which communicates the motion stands perpendicular to the crank, which is the case twice during each revolution, it is at what is commonly called the dead point, and the crank loses all its power. But, when the rod stands obliquely to the crank, the crank is then effective, and turns or is turned by the wheel.
  2. Cranks are used in the common foot-lathe to turn the wheel. They are also common in other machinery, and are very convenient for changing rectilinear to circular motion, or circular to rectilinear.
  3. When they communicate motion to the wheel they operate like the shorter arm of a lever; and, on the contrary, when they communicate the motion from the wheel they act like the longer arm.

What are Flywheels, and what is their use?

  1. FLY-WHEELS are heavy rims of metal secured by light spokes to an axle. They are used to accumulate power, and distribute it equally among all the parts of a machine. They are caused to revolve by a force applied to the axle, and, when once set in motion, continue by their inertia to move for a long time. As their motion is steady, and without sudden jerks, they serve to steady the power, and cause a machine to work with regularity.
  2. Fly-wheels are particularly useful in connexion with cranks, especially when at the dead points, as the momentum of the flywheel, received from the cranks when they acted with most advantage, immediately carries the crank out of the neighbourhood of the dead points, and enables it to again act with advantage.
  3. There are two ways in which the wheel and axle is supported, namely, first on pointed pivots, projecting into the extremities of the axle,* and, secondly, with the extremities of the axle resting on gudgeons. As by the former mode a less extensive area is subjected to friction, it is in many cases to be preferred.

* The terms axle, axis, arbor and shaft, are synonymously used by mechanics to express the bar or rod which passes through the centre of a wheel. The terminations of a horizontal arbor are called gudgeons, and of an upright one frequently pivots; but gudgeons more frequently denote the beds on which the extremities of the axle revolve, and pivots are either the pointed extremities of an axle, or short pins in the frame of a machine which receive the extremities of the axle. The term axis, in a more exact sense, may mean merely the longest central diameter, or a diameter about which motion takes place.

 

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How many kinds of Water-wheels are there?

  1. WATER-WHEELS. – There are four kinds of Water-wheels called, respectively, the Overshot, the Undershot, the Breast and the Turbine. [See Par. 1440 to 1450]
  2. The Overshot Wheel receives its motion from the weight of the water flowing in at the top. [See Par 1441]

Fig. 37

Describe the Overshot Wheel

Fig. 37 represents the Overshot Wheel. It consists of a wheel turning on an axis (not represented in the figure), with compartments called buckets, a b c d, &c., at the circumference, which are successively filled with water from the stream S. The weight of the water in the buckets causes the wheel to turn, and the buckets, being gradually inverted, are emptied as they descend. It will be seen, from an inspection of the figure, that the buckets in the descending side of the wheel are always filled, or partly filled, while those in the opposite or ascending part are always empty until they are again presented to the stream. This kind of wheel is the most powerful of all the water-wheels.

  1. The Undershot Wheel is a wheel which is moved by the motion of the water. It receives its impulse at the bottom. [See Par. 1443]

Describe the Undershot Wheel

Fig. 38

Fig. 38 represents the Undershot Wheel. Instead of buckets at the circumference, it is furnished with plane surfaces, called float-boards, a b c d, &c., which receive the impulse of the water, and cause the wheel to revolve.

 

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Describe the Breast Wheel

  1. The Breast Wheel is a wheel which receives the water at about half its own height, or at the level of its own axis. It is moved both by the weight and the motion of the water.

Fig. 39

Fig. 39 represents a Breast Wheel. It is furnished either with buckets, or with float-boards, fitting the water-course, receiving the weight of the water with its force, while in motion it turns with the stream.

  1. In the water-wheels which have now been described, the motion is given to the circumference of the larger wheel, either by the weight of the water or by its force when in motion.
  2. All wheels used in machinery are connected with the different parts of the machine by other parts, called gearing. Sometimes they are turned by the friction of endless bands or cords, and sometimes by cogs, teeth, or pinions. When turned by bands, the motion may be direct or reversed by attaching the band with one or two centres of motion respectively.

Fig. 40.

Fig. 41.

  1. When the wheel is intended to revolve in the same direction with the one from which it receives its motion, the band is attached as in Fig. 40; but when it is to revolve in a contrary direction, it is crossed as in Fig. 41. In Fig. 40 the band has but one centre of motion; in Fig. 41 it has two.
  2. Instead of the friction of bands, the rough surfaces of the wheels themselves are made to communicate their motion. The wheels and axles thus rubbing together are sometimes coated with rough leather, which, by increasing the friction, prevents their slipping over one another without communicating motion.
  3. Figure 42 represents such a combination of wheels. As the wheel a is turned by the weight S, its axle presses against the circumference of the wheel b, causing it to turn; and, as it turns, its axle rubs against the circumference of the wheel c, which in like manner communicates its motion to d. Now, as the circumference of the wheel a is equal to six times the circumference of its axle, it is evident that when the wheel a has made one revolution b will have performed only one-sixth of a revolution. The wheel a must therefore turn round six times to cause b to turn once. In like manner b must perform six revolutions to cause c to turn once, and c must turn as many times to cause d to revolve once.- Hence it follows that while d revolves once on its axis c must revolve six times, b thirty-six times, and a two hundred and sixteen times.

 

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  1. If, on the contrary, the power be applied at F, the conditions will all be reversed, and c will revolve six times, b thirty-six, and a two hundred and sixteen times. Thus it appears that we may obtain rapid or slow motion by the same combination of wheels.

How may rapid or slow motion be obtained at pleasure by a combination of wheels with their axles?

  1. To obtain rapid motion, the power must be applied to the axle; to obtain slow motion, the power must be applied to the circumference of the wheel.
  2. Wheels are sometimes moved by means of cogs or teeth articulating one with another, on the circumference of the wheel and the axle. The cogs on the surface of the wheels are generally called teeth, and those on the surface of the axle are called leaves. The axle itself, when furnished with leaves, is called a pinion.

Fig. 43.

  1. Fig. 43 represents a connexion of cogged wheels. The wheel B, being moved by a string around its circumference, is a simple wheel, without teeth. Its axle, being furnished with cogs or leaves, to which the teeth of the wheel D are fitted, communicates its motion to D, which, in like manner, moves the wheel C. The power P and the weight W must be attached to the circumference of the wheel or P of the axle, according as a slow or a rapid motion is desired.
  2. Wheels with teeth or cogs are of three kinds, according to the position of the teeth.

Fig. 44. Fig. 45.

When the teeth are raised perpendicular to the axis, they are called spur wheels, or spur gear. When the teeth are parallel with the axis, they are called crown wheels.

 

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When they are raised on a surface inclined to the axis, they are called bevelled wheels. In Fig. 43 the wheels are spur wheels. In Figs. 44 and 45 the wheels are bevelled wheels.

  1. Different directions may be given to the motion produced by wheels, by varying the position of their axles, and causing them to revolve in different planes, as in Fig. 44; or by altering the shape and position of the cogs, as in Fig. 45.

How may the the power of toothed wheels may be estimated?

  1. The power of toothed wheels may be estimated by substituting the number of teeth in the wheel and the number of leaves in the pinion for the diameter or the circumference of the wheel and axle respectively.
  2. SUSPENSION OF ACTION. – In the arrangement of machinery, it is often necessary to cut off the action of the moving power from some parts, while the rest continues in motion. This is done by causing a toothed wheel to slide aside in the direction of its axis to and from the cogs or leaves into which it articulates, or, when the motion is communicated by a band, by causing the band to slip aside from the wheel to another wheel, which revolves freely around the axle, without communicating its motion.
  3. Wheels are used on vehicles to diminish the friction of the road. The larger the circumference of the wheel, the more readily it will overcome- obstacles, such as stones or inequalities in the surface of the road.
  4. A large wheel is also attended with two additional advantages; namely, first, in passing over holes, ruts and excavations, a large wheel sinks less than a small one, and consequently causes less jolting and expenditure of power; and, secondly, the wear of large wheels is less than that of small ones, for, if we suppose a wheel six feet in diameter, it will turn round but once while a wheel three feet in diameter will turn round twice, its tire will come twice as often to the ground, and its spokes will twice as often have to bear the weight of the load.
  5. But wheels must be limited in size by two considerations: first, the strength of the materials; and secondly, the centre of the wheel should never be higher than the breast of the horse, or other animal by which the vehicle is drawn; for otherwise the animal would have to draw obliquely downward, as well as forward, and thus expend part of his strength in drawing against the ground.*

* In descending a steep hill, the wheels of a carriage are often locked (as it is called), that is, fastened in such a manner as to prevent their turning; and thus the rolling is converted into the sliding friction, and the vehicle descends more safely.

Castors are put on the legs of tables and other articles of furniture, to facilitate the moving of them; and thus the sliding is converted into the rolling friction.

 

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  1. PRACTICAL EXAMPLES OF POWER APPLIED TO THE WHEEL AND AXLE.

Questions for Solution.

(1.) With a wheel 5 feet in diameter and a power of 6 pounds, what must be the diameter of the axle to support 3 cwt.. Ans. 1.2 in.

(2.) How large must be the diameter of the wheel to support with 10 lbs. a weight of 5 cwt. on an axle 9 inches in diameter? Ans. 3T.5ft.

(3.) A wheel has a diameter of 4 feet, an axle of 6 inches. What power must be applied to the wheel to balance 2 cwt. on the axle? A??s. 25 lb,

(4.) There is a connexion of cogged wheels having 6 leaves on the pinion and 36 cogs on the wheel. What is the proportion of the power to the weight in equilibrium? Anas. As 1 to 6.

(5.) Suppose a lever of six feet inserted in a capstan 2 feet in diameter, and six men whose united strength is represented by e of a ton at the capstan, how heavy an anchor can they draw up, allowing the loss of I of their power from friction? A s. 2 T.

(6.) What must be the proportion of the axle to the wheel, to sustain a weight 30 cwt. with a power of 3 cwt.? Ans. As 1 to 10.

(7.) The weight is to the power in the proportion of six to one. What must be the proportion of the wheel to the axle? Ans. 6 to 1.

(8.) The power is represented by 10, the axle by 2. How can you represent the wheel and axle. Ans. 10: weight:: 2:,wheel.

(9.) The weight is expressed by 15, the power by 3. What will represent the wheel and axle? Ans. 5 and 1.

(10.) The axle is represented by 16, the power by 4. Required the proportion of the wheel and axle. Ans. 4: weight:: 16: wheel.

(11.) What is the weight of an anchor requiring 6 men to weigh it, by means of a capstan 2 feet in diameter, with a lever 8 feet long, 2 feet of its length being inserted in the capstan; supposing the power of each man to be represented by 2 cwt., and a loss of ~ the power by friction? Ans. 56 cwt.

(12.) A stone weighing 2 tons is to be raised by a windlass with spokes 2 feet in length, projecting from an axle 9 inches in diameter. How many men must be employed, supposing each man’s power equal to 2 cwt., including the loss by friction 1 Ans. 2.5 ment.

What is a Pulley

  1. THE PULLEY. – The Pulley is a small wheel turning on an axis, with a string or rope in a groove running around it.

How many kinds of pulleys are there?

There are two kinds of pulleys – the fixed and the movable. The fixed pulley is a pulley that has no other motion than a revolution on its axis, and it is -used only for changing the direction of motion.

Explain Fig. 46.

  1. Fig. 46 represents a fixed pulley. P is a small wheel turning on its axis, with a string running round it in a groove. W is a weight to be raised, F is the force or power applied. It is evident that, by pulling the string at F, the weight must rise just as much as the string is drawn down.

 

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Fig. 46.

As, therefore, the velocity of the weight and the power is precisely the same, it is manifest that they balance each other, and that no mechanical advantage is gained.*

* Although the fixed pulley gives no direct mechanical advantage, a man may advantageously use his own strength by the use of it. Thus, if he seat himself on a chair suspended from one end of a rope passing over a fixed pulley, he may draw himself up by the other end of the rope by exerting a force equal only to one-half of his own weight. One half of his weight is supported by the chair and the other half by his hands, and the effect is the same as if he drew only one half of himself at a time; for, the rope being doubled across the pulley, two feet of the rope must pass through his hands before he can raise himself one foot. In this manner laborers and others frequently descend into wells, and from the upper floors of stores, by means of a rope passing over a fixed wheel or pulley.

But this pulley is very useful for changing the direction of motion. If, for instance, we wish to raise a weight to the top of a high building, it can be done with the assistance of a fixed pulley, by a man standing below. A curtain, or a sail, also, can be raised by means of a fixed pulley, without ascending with it, by drawing down a string running over the pulley.

On what principle does the fixed Pulley act?

  1. The fixed pulley operates on the same principle as a lever of the first kind with equal arms, where the fulcrum being in the centre of gravity, the power and the weight are equally distant from it, and no mechanical advantage is gained.

How does the movable pulley differ from the fixed?

  1. The movable pulley differs from the fixed pulley by being attached to the weight; it therefore rises and falls with the weight.

Fig. 47.

Explain Fig. 47.

  1. Fig. 47 represents a movable pulley, with the weight W attached to it by a hook below. One end of the rope is fastened at F; and, as the power P draws the weight upwards, the pulley rises with the weight. Now, in order to raise the weight one inch, it is evident that both sides of the string must be shortened; in order to do which, the power P must pass over two inches.

 

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As the velocity of the power is double that of the weight, it follows that a power of one pound will balance a weight on the movable pulley of two pounds.*

* Thus, it is seen that pulleys act on the same principle with the lever and the wheel and axle, the deficiency of the strength of the power being compensated by superior velocity. Now, as we cannot increase our natural strength, but can increase the velocity of motion, it is evident that we are enabled, by pulleys, and other mechanical powers, to reduce the resistance or weight of any body to the level of our strength.

 

What is the advantage gained in the use of the movable pulley?

  1. The power gained by the use of pulleys is ascertained by multiplying the number of movable pulleys by 2. **

** This rule applies only to the movable pulleys in the same block, or when the parts of the rope which sustains the weight are parallel to each other. The mechanical advantage, however, which the pulley seems to possess in theory, is considerably diminished in practice by the stiffness of the ropes and the friction of the wheels and blocks. When the parts of the cord, also, are not parallel, the pulley becomes less efficacious; and when the

parts of the cord which supports the weight very widely depart from parallelism, the pulley becomes wholly useless. There are certain arrangements of the cord and the pulley by which the effective power of the pulley may be augmented in a three-fold instead of a two-fold proportion. But, when such an advantage is secured, it must be by contriving to make the power pass over three times the space of the weight.

  1. A weight of 72 pounds may be balanced by a power of 9 pounds with four pulleys, by a power of 18 pounds with two pulleys, or by a power of 36 pounds with one pulley. But in each case the space passed over by the power must be double the space passed over by the weight, multiplied by the number of movable pulleys. That is, to raise the weight one foot, with one pulley, the power must pass over two feet, with two pulleys four feet, with four pulleys eight feet.

Fig. 48.

Explain Fig. 48.

  1. Fig. 48 represents a system of fixed and movable pulleys. In the block F there are four fixed pulleys, and in the block M there are four movable pulleys, all turning on their common axis, and rising and falling with the weight W. The movable pulleys are connected with the fixed ones by a string attached to the hook H, passing over the alternate grooves of the pulleys in each block, forming eight cords, and terminating at the power P. Now, to raise the weight one foot, it is evident that each of the eight cords must be shortened one foot, and, consequently, that the power P must descend eight times that distance.

 

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The power, therefore, must pass over eight times the distance that the weight moves.

  1. The movable pulley, as well as the fixed, acts on the same principle with the lever, the deficiency of the strength of the power with the movable pulley being compensated by its superior velocity.

On what principle is the movable pulley constructed?

  1. The fixed pulley acts on the principle of a lever with equal arms. [See No. 313.] The movable pulley, on the contrary, by giving a superior velocity to the power, operates like a lever with unequal arms.
  2. Practical use of Pulleys. Pulleys are used to raise goods into warehouses, and in ships, &c., to draw up the sails. Both kinds of pulleys are in these cases advantageously applied: for the sails are raised up to the masts by the sailors on deck by means of the fixed pulleys, while the labor is facilitated by the mechanical power of the movable ones.
  3. Both fixed and movable pulleys are constructed in a great variety of forms, but the principle on which all kinds are constructed is the same. What is generally called a tackle and fall, or a block and tackle, is nothing more than a pulley. Pulleys have likewise lately been attached to the harness of a horse, to enable the driver to govern the animal with less exertion of strength.

What law applies to all the Mechanical* Powers? (*See Appendix)

  1. It may be observed, in relation to the Mechanical Powers in general, that power is always gained at the expense of time and velocity; that is, the same power which will raise one pound in one minute will raise two pounds in two minutes, six pounds in six minutes, sixty pounds in sixty minutes, &c.: and that the same quantity of force used to raise two pounds one foot will raise one pound two feet, &c.: And, further, it may be stated that the product of the weight multiplied by the velocity of the weight will always be equal to the product of the power multiplied by the velocity of the power.

 

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In what proportion is the power to the weight when the movable pulley is used?

Hence we have the following rule: The power is in the same proportion to the weight as the velocity of the weight is to the velocity of the power.*

* The stiffness of the cords and the friction of the blocks frequently require large deduction to be made from the effective power of pulleys. The loss thus occasioned will sometimes amount to two-thirds of the power.

  1. PRACTICAL EXAMPLES OF APPLICATION OF THE PULLEY.

Questions for Solution.

(1) Suppose a power of 9 lbs. applied to a set of 3 movable pulleys. Allowing I loss for friction, what weight can be sustained by them 1 A. 36 lb.

(2.) Six movable pulleys are attached to a weight of 1800 lbs.; what power will support them, allowing a loss of two-thirds of the power from friction? Ans. 450 lb.

(3.) Six men, with a block and tackle containing nine movable pulleys, are required to raise a sail. Suppose each man’s strength to be represented by two cwt. and two-thirds of the power lost by friction, what is the weight of the sail, with its appendages? Ans. 72 cwt.

(4.) If a stone weighing 3 tons is to be raised by horse power to the wall of a building in process of erection, by means of a derrick from which are suspended 3 movable pulleys, how many horses must be employed, supposing each horse capable of drawing as much as eight men, each of whom can lift 2 cwt., making an allowance of two-thirds for friction? Ans. 1.

(5.) A block contains 5 movable pulleys, connected with a beam containing 5 fixed pulleys. A weight of half a ton is to be raised. Allowing a loss of two-thirds for friction, what power -must be applied to raise it? A. 8 cwt.

(7.) The power is 3, the weight is 27; how many pulleys must be used, if friction requires an allowance of two-thirds? Ans. 27.

(8.) Friction one-third of the power, power 6, weight 72, – how many pulleys? Ans. 18.

(9;) Weight 84, friction nothing, pulleys, 3 fixed, 3 movable; required the power. Ans. 14.

(10.) Power 12, friction 8, four pulleys, two of them fixed; required the.weight. Ans. 16.

(11.) Six movable and six fixed pulleys. The weight is raised 3 feet. How far has the power moved Ans. 36 ft.

(12.) The power has moved 12 feet; how far has the weight moved under two pulleys, one fixed, the other movable. Ans. 6ft.

(13.) The weight, suspended from a fixed pulley, has moved 6 feet. How far has the power moved. Ans. 6ft.

(14.) The power has moved 20 feet under a fixed pulley; how far has the weight moved. Ans. 20ft.

What is the Inclined Plane?

  1. THE INCLINED PLANE. The Inclined Plane consists of a hard plain surface, inclined to the horizon.
  2. The principle on which the inclined plane acts as a mechanical power is simply the fact that it supports part of the weight. If a body be placed on a horizontal plane, its whole weight will be supported; but, if the plane be elevated at one end, by degrees, it will support less of the weight in proportion to the elevation. until the plane becomes at right angles to the horizon, when it will support no part of the weight, and the body will fall perpendicularly.

 

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  1. A body, in ascending or descending an inclined plane, will have a greater space to traverse than if it should rise or fall perpendicularly. The time, therefore, of its ascent or descent will be longer, and thus it will oppose less resistance, and thus, also, a less force will be required to cause its ascent. Hence, we see that the fundamental principle of Mechanics, “What is gained in power is lost in time,” applies to the Inclined Plane as well as to the Mechanical Powers that have already been described.

What is the advantage gained by the use of the inclined plane?

  1. The advantage gained by the use of the inclined plane is in proportion as the length of the plane exceeds its perpendicular height.

Fig. 49.

Fig. 49 represents an inclined plane. C A its height, C B its length, and W a weight which is to be moved on it. If the length C B be four times the height C A, then a power of one pound at C will balance a weight of four pounds on the inclined plane C B.

  1. The greater the inclination of the plane, the greater must be its perpendicular height, compared with its length; and, of course, the greater must be the power to elevate a weight along its surface.
  2. Instances of the application of the inclined plane are very common. Sloping planks or pieces of timber leading into a cellar, and on which casks are rolled up and down; a plank or board with one end elevated on a step, for the convenience of trundling wheelbarrows, or rolling barrels into a store, &c., are inclined planes.
  3. Chisels and other cutting instruments, which are chlamfered, or sloped only on one side, are constructed on the principle of the inclined plane.*

* Chisels for cutting wood should have their edges at an angle of about 30°; for cutting iron from 50° to 60°, and for cutting brass at about 80° or 90°. Tools urged by pressure may be sharper than those which, like the wedge, are driven by percussion.

  1. Roads which are not level may be considered as inclined planes, and the inclination of the road is estimated by the height corresponding to some proposed length.

 

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To raise a load up an inclined plane requires a power sufficient to carry it along the whole distance of the length of the base, and then to lift it up to the elevation; but in the inclined plane a feebler force will accomplish the desired object, because the resistance is spread equally over the whole distance.*

* Mention has already been made of the sagacity of animals in a former page [see No. 541], and a sort of intuitive knowledge which they appear to possess of philosophical principles. In ascending a steep hill, a common dray-horse will drag his load from side to side, as if he were conscious that he thus made the plane longer in proportion to its height, and thereby made his load the lighter.

What is the Wedge?

  1. THE: WEDGE.- The Wedge consists of two inclined planes united at their bases.

What is the advantage gained by the use of the wedge?

  1. The advantage gained by the wedge is in proportion as its length exceeds the thickness between the converging sides.

In what proportion is the proportion of the wedge?

It follows that the power of the wedge is in power to its sharpness.

Fig. 50.

  1. Fig. 50 represents a wedge. The line a b represents the base of each of the inclined planes

of which it is composed, and at which they are united.

  1. The wedge is a very important mechanical power, used to split rocks, timber, &c., which could not be effected by any other power. **

** The wedge is an instrument of exceedingly effective power, and is frequently used in presses for extracting the juice of seeds, fruits, &c. It is used especially in the oil mill, by which the oil is extracted from seeds. The seeds are placed in hair bags, between planes of hard wood, which are pressed together by wedges. The pressure thus exerted is so intense that the seeds, after the extraction of the oil, are converted, into masses as hard and compact as the most dense woods.

Wedges are used also in the launching of vessels, and also for restoring buildings to the perpendicular which have been inclined by the sinking of the foundation.

  1. Axes, hatchets, knives, and all other cutting instruments, chamfered, or sloped on both sides, are constructed on the principle of the wedge; also pins, needles, nails, and all piercing instruments.

On what does the effective power of the wedge depend?

  1. The effective power of the wedge depends on friction; for, if there were no friction, the wedge would fly back after every stroke.

 

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  1. The wedge derives much of its power from the force of percussion, which in its nature is so different from continued force, such as the pressure of weights, the force of springs, &c., that it would be difficult to submit it to numerical calculation; and, therefore, we cannot properly represent the proportion which a blow bears to the weight.

What is the Screw?

  1. THE SCREW. – The Screw is an inclined plane wound around a cylinder, thus producing a circular inclined plane, forming what is called the threads of the screw.
  2. Cut a piece of paper in the shape of an inclined plane, as represented by Fig. 49, and, beginning, with the end represented by the, height C A, in that Figure, wind it around a pencil, or a round ruler. The edge of the paper will be a circular inclined plane, and will represent the threads of the screw. The distance between any two threads on the same side of the rule will represent the perpendicular height of the inclined plane that extends once around the cylinder, and the advantage gained in the use of the; screw (when used without a lever) will be the same as in the inclined plane; namely, as the length of the plane exceeds the perpendicular height. But the screw is seldom used alone. A lever is generally attached to the screw, and it is with this attachment the screw will now be considered.

What appendage generally attends the Screw?

  1. The Screw is generally accompanied by an appendage called the nut, which consists of a concave cylinder or block, with a hollow spiral cavity cut so as to correspond exactly with the threads of the screw. When thus fitted together, the screw and the nut form two inclined’ planes, the one resting on the other.

Is the screw, or the nut movable?

  1. Sometimes the screw is movable and the nut is stationary, and sometimes the screw is stationary and the nut is movable.
  2. At every revolution the screw or the nut advances or retreats through a space equal to the distance between the threads of the screw.

In what manner does the power applied to a screw move?

  1. The power applied to a screw generally describes a circle around the screw, perpendicular to the direction in which the screw or nut moves.

 

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What is the advantage gained by the screw?

  1. The advantage gained by the screw is in proportion as the circumference described by the power exceeds the distance between the threads of the screw.

What is meant by the Convex and the Concave Screw?

  1. The cylinder with its threads is called the Convex Screw, and the nut is called the Concave Screw. The lever is sometimes attached to the screw, and sometimes to the nut.

Fig. 51.

Explain Fig. 51.

  1. Fig. 51 represents a fixed screw S, with a movable nut N, to which is attached the lever L. By turning the lever in one direction the nut descends, aid by turning it in the opposite direction the nut ascends, at every revolution of the lever, through a space equal to the distance between the threads of the screw; to accomplish which, the hand or power applied to the end of the lever L will describe a circle around the screw S, of which the radius is L S. The power thus passes over a space represented by the circumference of this circle, and the advantage gained is in the same proportion as the space exceeds the distance between each thread of the screw.

Fig. 52.

Explain Fig. 52.

  1. Fig. 52 represents a movable screw, with a nut fixed in a frame, and L consequently immovable. As the lever L is turned, the screw ascends or descends at every revolution of the lever through a space equal to the distance between the threads of the screw, and the advantage gained is in the same proportion as in the case of the movable nut in Fig. 51.
  2. It will thus be seen that, although the screw is usually considered distinctly as a mechanical power, it is in fact a compound power, consisting of two circular inclined planes, moved by a lever.
  3. The power of the screw being estimated by the distance between the threads, it follows that the closer the threads are together, the greater will be the power, but the slower will be the motion produced; for, every revolution of the lever advances the screw or the nut only through a space as great as the distance of the threads from each other.

 

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  1. The screw is applied to presses and engines of all kinds where great power is to be applied, without percussion, through small distances. It is used in bookbinders’ presses, in cider and wine presses, in raising buildings.

Fig. 53.

It is also used for coining, and for punching square or circular holes through thick plates of metal.

Fig. 54.

When used for this purpose, the lever passes through the head of the screw and terminates at both ends with heavy balls or weights, the momentum of which adds to the force of the screw, and invests it with immense power.

  1. HUNTER’S SCREW. —The ingenious contrivance known by the name of Hunter’s Screw consists of two screws of different threads playing one within the other; and such will be the effect, that while one is advancing forward the other will retreat, and the resistance will be urged forward through a distance equal only to the difference between the threads of the two screws. An indefinite increase in the power is thus obtained, without diminishing the thread of the screw.*

* From what has been stated with regard to the Mechanical Powers, it appears that by their aid a man is enabled to perform works to which his unassisted natural strength is wholly inadequate. But the power of all machines is limited by the strength of the materials of which they are composed. Iron, which is the strongest of all substances, will not resist a strain beyond a certain limit. Its cohesive attraction may be destroyed, and it can withstand no resistance which is stronger than its cohesive attraction. Besides the strength of the materials, it is necessary, also, to consider the time which is expended in the application of mechanical assistance. Archimedes is said to have boasted to Hiero, King of Syracuse, that, if he would give him a place to stand upon, he would move the whole world. In order to do this, Archimedes must himself have moved over as much more space than he moved the world as the weight of the world exceeded his own weight; and it has been computed that he must have moved with the velocity of a cannon-ball for a million of years, in order to move the earth the twenty seven millionth part of an inch.

 

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  1. PRACTICAL EXAMPLES OF THE APPLICATION OP THE INCLINED PLANE AND THE SCREW.

Questions for Solution.

(1.) With an inclined plane the power moves 16 feet, the power is to the weight as 6 to 24. How far does the weight move? Ans. 4ft.

(2.) The length of an inclined plane is 5 feet, the proportion of the power to the weight is as 2 to 10. What is the height of the plane? A. 1ft.

(3.) An inclined plane is 4 feet high, a power of 6 lbs. draws up 30 lbs. What is the length of the plane? Ans. 20ft.

(4.) The length of a plane is 12 feet, the height is 3 feet. What is the proportion of the power to the weight to be raised? Ans. As 1 to 4.

(5 ) The distance between the threads of a screw is 1 inch, the length of the lever is 2 feet. What is the proportion Ants. 1 to 150.79 +

(6.) Which will exert the greater force, a lever 3 feet long with the fulcrum 6 inches from one end, or a screw with a distance of 1 inch between the threads and a lever one foot long I Anzs. The screuw.

(7.) A screw with the threads 2 inches apart, and a lever 6 feet long, draws a ship of 200 tons up an inclined plane whose length is to the height in the proportion of 1 to 16. What power must be applied to the lever of the screw. Avs. 11.05 lb. +

(8.) If a man can lift a weight of 150 lbs., how much can he draw up an inclined plane whose length is to its height as 24 to 3? AAns. 1200 lb.

(9.) A Hunter’s screw has a lever four feet long. The distance between the threads of the larger screw is 1 inch, between those of the smaller i of an inch. How much weight can a man whose power is represented by 175 lbs. move with such a screw? Ans. 211115.52 lb.

(10.) A screw with a lever of 2 feet in length, and a distance of k of an inch between its threads, acts on the teeth or cogs of a wheel whose diameter is to that of the axle as 4 to 1. Fastened to the axle is a rope, one end of which is attached to a weight at the bottom of an inclined plane, the length of which is to the height as 12 to 3. Suppose this weight to require the strength of a man who can lift 200 lbs. to be applied to the lever of the screw to move it. What is the weight? Ans. 9650995200 lb.

What is the Toggle Joint?

  1. THE KNEE JOINT, OR TOGGLE JOINT.- The Toggle Joint, or Knee Joint, consists of two bars united by a hinge or ball and socket, which, being urged by a power perpendicular to the resistance, acts with rapidly increasing force, until the bars form a straight line.

The toggle (or knee) joint affords a very useful mode of converting velocity into power, the motion produced being very nearly at right angles with the direction of the force. It is a combination of levers, and the same law applies to it as to all machinery, namely, that the power is to the resistance inversely as the space of the power is to the space of the resistance.

 

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Fig 55.

Explain Fig. 55.

  1. Fig 55 represents a toggle joint, A C and B C are the two rods connected by a joint at C. A moving force applied at C, in the direction C D, acts with great and constantly increasing power to separate the parts A and B.

Fig. 56.

  1. The operation of the toggle joint is seen in the iron joints which are used to uphold the tops of chaises. It is also used in various kinds of printing presses to obtain the greatest power at the moment of impression.*

* A similar effect, but with a reversed action, is produced when a long rope tightly strained between two points, is forcibly pulled in the middle.

  1. MEDIA.- The motion of all bodies is affected by the substance or element which they move, and by which they are on all sides surrounded. Thus the bird flies in the air, the fish swims in the water. Air therefore is the medium in which the foirmer moves, while water is the medium in which the motion of the latter is made.

What is a Medium?

  1. A Medium is the substance, solid or fluid, Medium which surrounds a body, and which the body must displace as it moves.
  2. – When the fish swims or the bird flies, each must force its way through the air or the water; and the element thus displaced must rush into the spot vacated by the body in its progress. It has already been stated that the body of the fish or of the bird is propelled in its motion in the one case by the reaction of the air on the wings of the bird, and in the other of the water on the fins of a fish. The fish moves in the denser medium and needs therefore to present a less surface for the reaction of the water; while the bird, living in a comparatively rare medium, presents in his wings a much larger extent of surface to receive the reaction of the air. In making the fins of a fish, therefore, so much smaller, in proportion to its size, than the wings of a bird, nature herself has taught us that,

In what proportion is the resistance of a medium?

  1. The resistance of a medium is in exact proportion to its density.

 

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  1. A body falling’ through water will move more slowly than one falling in the air, because it meets with more resistance from the inertia of the water, on account of the greater density of the water.

What is a Vacuum?

  1. A VACUUM. — A Vacuum is unoccupied space; that is, a space which contains absolutely nothing.
  2. From this definition of a vacuum, it appears that it does not mean a space which to our eyes appears empty: What we call an empty bottle is, in fact, full of air, or some other invisible fluid.

If we sink an empty bottle in water or any other liquid, neither the water nor any other liquid can enter until some portion of the air is expelled. A small portion of water enters- the bottle immersed, and the air issues in bubbles from the mouth of the bottle. Other portions of water then enter the bottle, expelling the air in similar manner, until the water entirely fills the bottle, and then the air bubbles cease to rise.

  1. From this statement of the meaning of the term “a vacuum,” it will be seen that if a machine be worked in a vacuum (or, as it is more commonly expressed in Latin, “in vacuo”) its motion will be rendered easier, because the parts receive no resistance from a surrounding medium.

What is Friction, and how many kinds of friction are there? Describe each.

  1. FRICTION. — Friction is the resistance which bodies meet with in rubbing against each other.

There are two kinds of friction, namely, the rolling and the sliding friction. The rolling friction is caused by the rolling of a circular body.

  1. The sliding friction is produced by the sliding or dragging of one surface over another.
  2. Friction is caused by the unevenness of the surfaces which come into contact.*

*All bodies, how well soever they may be polished, have inequalities in their surfaces, which may be perceived by a microscope. When, therefore, the surfaces of two bodies come into -contact, the prominent parts of the one will: often fall into’ the hollow partsof:the other, and cause more or less resistance to motion.

It is diminished in proportion as the surfaces are smoothed and well polished. The sliding friction is overcome with more difficulty than the rolling.

 

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What portion of the power of a machine is lost by friction?

  1. Friction destroys, but never can generate, motion. It is usually computed that friction destroys one third of the power of a machine. In calculating the power of a machine, therefore, an allowance of one-third must be made for loss by friction.*

* When finely polished iron is made to rub on bell-metal, the friction is said to be reduced to about one-eighth. Mr. Babbit, of Boston, has propared a composition for the wheel-boxes of locomotive engines and other machinery, which, it is said, has still further reduced the amount of friction. This composition is now much in use. As the friction between rolling bodies is much less than in those that drag, the axle of large wheels is sometimes made to move on small wheels or rollers. These are called friction wheels, or friction rollers. They turn round their own centre as the wheel continues its motion.

What is used to lessen friction? and why?

  1. Oil, grease, black lead or powdered soap – stone, is used to lessen friction, because they act as a polish by filling up the cavities of the rubbing surfaces, and thus make them slide more easily over each other.

How does friction increase?

  1. Friction increases:

(1.) As the weight or pressure is increased.

(2.) As the extent of the surfaces in contact is increased.

(3.) As the roughness of the surface is increased.

How may friction be diminished?

  1. Friction may be diminished:

(1.) By lessening the weight of the body in motion.

(2.) By mechanically reducing the asperities of the sliding surfaces.

(3.) By lessening the amount of surface of homogeneous bodies in contact with each other.

(4.) By converting a sliding into a rolling motion.

(5.) By applying some suitable unguent. **

** From the experiments made by Coulomb, it appears that the friction of heterogeneous; bodies is. generally less than that of homogenous that is, that if a body rub against another composed of the same kind of wood or metal, the friction is greater than that of different kinds of metal, or of wood.

Ferguson’s experiments go to prove that the friction of polished steel against polished steel is greater than that of polished steel on copper or on brass. In a combination where gun-metal rubs against steel, the same weight may be moved with a force of fifteen and a half pounds that it would require twenty-two pounds to move when cast-iron moves against steel.

 

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What are the uses of friction?

  1. Friction, although it retards the motion of machines, and causes a great loss of power, performs important benefits in full compensation. Were there no friction, all bodies on the surface of the earth would be clashing against each other. Rivers would dash with unbounded velocity, and’we should see little but motion and collision. But, whenever a body acquires a great velocity, it soon loses it by friction against the surface of the earth.
  2. The friction of water against the surfaces it runs over soon reduces the rapid torrent to a gentle stream; the fury of the tempest is lessened by the friction of the air on the face of the earth; and the violence of the ocean is soon subdued by the attrition of its own waters. Our garments, also, owe their strength to friction; and the strength of ropes, cords, sails and various other things, depends on the same cause, for they are all made of short fibres pressed together by twisting, and this pressure causes a sufficient degree of friction to prevent the fibres sliding one upon another. Without friction it would be impossible to make a rope of the fibres of hemp, or a sheet of the fibres of flax; neither could the short fibres of cotton have ever been made into such an infinite variety of forms as they have received from the hands of ingenious workmen. Wool also, has been converted into a thousand textures of comfort and luxury, and all these are constituted of fibres united by friction.

 

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…. fibres united by friction.