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2. Definition of FORCE.
Whatever the cause be which produces, or prevents, motion, or which tends to produce, or to prevent, motion, in a body, it is called a FORCE.
If a heavy body, as a stone, be laid on the open hand, experience shews that, to prevent the stone from falling, the hand must make some effort. Again, to set a ball rolling along the ground requires some exertion. The effort, or exertion, is called in either case a FORCE ; and although the effect produced be not great enough to prevent entirely the fall of the stone, or to communicate motion to the ball, yet it is still called a FORCE.
From the definition of STATICS given in Art. 1, it will readily be understood, that in that branch of MECHANICS the conditions are investigated which are fulfilled by those Forces only, which keep a body at rest.
3. Definition of WEIGHT.
All bodies, if left to themselves, fall, or tend to fall, towards the earth's centre, through a power, which resides in the earth, of constantly drawing all substances towards it, called THE FORCE OF GRAVITY. Consequently, if any body be reduced to a state of rest, it exerts a certain presdownwards
that which sustains it. And the precise amount of this pressure for any particular body is called the WEIGHT of that body.
4. The WEIGHTS of different bodies may be compared thus :-Let two bodies be successively attached in the same manner to a spring, so that they may act upon it by their weights in the same way. If they produce the same effects, (by bending the spring to the same extent,) the weights of the bodies are equal. Any other body, which produces the same effect on the spring by its weight as both the former bodies when applied together do by their weights, has its weight double of that of either of them. And by means of such a contrivance as this spring, bodies might be shewn to be three, four, or any number of, times the weight of a given body.
5. The WEIGHT of any body is measured thus :—The weight of a certain bulk of some particular substance is first fixed upon as :: standard. Thus the weight of a piece of lead of a certain size being called a pound, any other body, which by the force of gravity only, produces the same effect as four, or six, or ten, such pieces of
lead, will be four, or six, or ten, pounds in weight, as the case
6. Definition of QUANTITY OF MATTER.
The substance, material, or stuff, of which any body is made, is called MATTER. And since all bodies have Weight, the property of having Weight is to be considered as necessarily belonging to Matter. Hence in the same ratio, or degree, that one body has more weight than another, it is concluded, that it contains more matter; that is, the Quantity of Matter in a body is proportional to its Weight.
Thus, if a body A weigh one pound, and another body B weigh three pounds, the quantity of matter contained in A is said to be to the quantity contained in B as 1 to 3 ; or B is said to contain three times as much matter as A does.
7. The exact quantity of matter contained in any body may be measured by comparing its weight with the weight of some particular body, which has been fixed upon for a standard. Thus, if a cubic inch of water be previously taken as the body by which to measure the quantities of matter contained in all other bodies, and the quantity of matter in this cubic inch of water be called 1, then the quantity of matter in any other body would properly be said to be 5, if the weight of that body were five times as great as the weight of the cubic inch of water.
8. Definition of Density.
The Density of a substance, or body, is the degree of closeness, with which the matter composing it is, as it were, packed; which closeness is measured, or compared in manner following:
Let equal bulks of two different substances be taken, suppose Water and Lead. Then, if the bulk of water which is taken weigh one pound, it will be found, that the piece of lead of equal size with it will weigh 11% pounds. There is evidently, therefore, 114 times as much heavy matter in a piece of lead as there is in an equal bulk of water; and this fact is expressed, or described, by saying, that “The DENSITY of Lead is to the DENSITY of Water, as 114 is to 1”; or by saying, “The DENSITY of Lead is 114 times that of Water.
If the Density of water be called 1, that is, if water be taken as a standard, to measure Density, then the Density of lead will be properly called 11%, or 11:4.
In the same manner as it has been explained how the Density of lead is estimated with respect to the Density of water, the Densities of
any other substances, whether solid or fluid, may be determined with respect to that of water.
9. Definition of “MEASURE OF FORCE”.
In Statics a FORCE is measured by the weight which it would support. In other words, the amount of a Statical Force is expressed by stating the number of pounds it would support, if the Force were made to act directly opposite to the Force of Gravity.
Thus, if the weight of a body were P pounds, and it were pre- . vented from moving towards the earth's surface by a hand placed beneath it, the resistance offered by the hand to the communication of motion (that is, the force exerted by the hand), would be P pounds ; and if this same pressure were produced by the hand in any other direction, it would be described in the same manner, by saying that it was “equal to P pounds", or that it was “P pounds”. If, therefore, a Force be represented by P, it is meant that P is the number of pounds which the Force would support, on the supposition that the Force is made to act directly opposite to the Force of Gravity. In other words, P is the number of pounds, which the Force is just able to lift.
FORCES, in STATICS, also called PRESSURES. 10. In whatever direction a Force tends to produce motion, its magnitude, as has already been stated, is measured by the weight of the body which would exert the same effect to produce motion downwards, as the Force under consideration exerts in the line in which it endeavours to produce motion. And that such a method of measuring Forces is allowable appears from this consideration, viz., that the effect produced by the weight of a heavy body* may be made to take place in any direction whatever ; horizontally, as in the case of a string being attached to an object lying on a table and kept stretched by a heavy body (W), which hangs over the edge o
* By' a heavy body', in MECHANICS, is simply meant a body acted on by the Force of Gravity.
the table, as in fig. (1); or vertically upwards, by passing the string over a peg A, and at
A taching the end to a ring B, so that BA may
(1) be vertical, as in fig. (2); or in any other direc
(3) tion, as in fig. (3), by TV
W making the heavy body pull the string in the line BA, which is inclined at any angle to that (AW) in which it acts itself.
11. Definitions with respect to the action of FORCES.
(1) The point at which a Force acts upon a body is called the "point of application" of the Force.
(2) The line in which a Force, acting alone, produces, or tends to produce, motion, is called “the line of the Force's action"; and any line which is parallel to the line of a Force's action is said to be “in the direction of the Force's action", or“ in the direction of the Force”.
When the direction of a Force's action, (or, as it is generally called, “the direction of the Force”,) is indicated by a line, either the very line is given in which the Force acts, or some line which is parallel to it. “ The line of a Force's action”, and “the direction of the Force”, must by no means be confounded together. If the former be known, the latter is necessarily known also; but if only the latter be given, the precise line in which the Force produces, or tends to produce, motion, is uncertain; and all that can be said respecting it is, that the line of action of the Force is either that given line, or some other line which is parallel to it.
(3) If two or more Forces be applied to a body, or at some point, and no motion is produced, they are said to “counteract", or to "balance”, one another, or to be “in equilibrium”.
12. Forces properly represented by geometrical straight lines.
Since lines may be drawn of any length, and in any direction, from a point, the lines in which Forces act, and the ratios which the Forces bear to one another, may be represented by drawing lines, which coincide with the lines in which the Forces act, and whose lengths bear to one another the same ratios that the Forces themselves bear to one another.
Among other advantages which attend this method of expressing the magnitudes and directions of Forces, the addition and subtraction of such Forces as act at a point in the same straight line are easily effected. Thus, if a certain Force act at A in the line AH, and AB be taken to represent it, and another Force, half as great as the former, act at A in the same direction, and also tend to move the body from A towards H, then, by taking BC equal to the half of AB, the line AC will represent the whole pressure at A, both with re- A D
C spect to the magnitude of that pressure, and to the line in which it acts. And, in like manner, if a Force equal to half the original Force AB act at A in the line AH, but tends to move the body at A from A towards K, half the pressure of the former Force will be counteracted by this new Force. Cutting off from the line AB, therefore, a part BD equal to the half of AB, the effective pressure still remaining will be properly represented by AD, with respect both to its magnitude, and to its line of action.
13. N.B. It will be gathered from the above, that a Force AB applied to A has not the same effect as a force BA applied at that point; for a Force AB would tend to move a body at A in the line KH towards H, but a Force BA would tend to move a body at A in the line KH from A towards K. It is not, therefore, indifferent whether the words “a Force AB”, or “a Force BA”, be used; since, though the two Forces represented by AB, and BA, are the same in magnitude, and also act in the same straight line, yet they tend to produce motions directly opposite to one another, the Force AB tending to move the body at A towards H, and the force BA tending to move the body at A towards K.
14. The effect produced at a point by any Force is the same at whatever point in its line of action the Force is applied, provided the latter point be supposed rigidly connected with the former.
Thus, if a body P be suspended by a string CP, the Force necessary to prevent P falling to the earth is found to be the same whether that Force be applied at A, or B, B or C;-the weight of the string being either neglected, or the weight of that portion of it which is supported along
A with the heavy body P, being counterbalanced. And although, in this case, the points A, B, C, are not, in fact, rigidly connected with one another, and with P, the result PO