Weight (physics)

“ What kind of a quantity is that which now weighs more, and now weighs less, so to speak? But this apparent deviation from the method of determination commonly used in practical life, that by weight, is, closely considered, an agreement. On a high mountain a heavy mass also is less powerfully attracted to the earth than at the level of the sea, and if it is permitted us in our determinations to neglect the consideration of level, it is only because the comparison of a body with fixed conventional weights is invariably effected at the same level. ”

“ The attraction of the earth on masses of matter that are not free to move gives rise to forces which are called weights. Thus the attraction of gravitation on a mass of one pound produces a pressure equal to a weight of one pound. ”

“ As the moon is much smaller than the earth, what weighs a pound with us would weigh much less than a pound in the moon. And as the sun is much larger than the earth, what is a pound with us would be much more than a pound there. If we knew the exact densities of the sun and the moon and the earth, as well as their size, we could estimate exactly the difference in the weights which any body would have in them; for the attraction which causes the pressure that we call weight is as the quantity of matter, and the quantity of matter depends on both density and size. ”

“ Now, the force of gravity in a body is greater, in proportion as its quantity of matter is greater. Consequently, we might suppose, that the weight of a body (weight being nothing else than the measure of the force of gravity) would be increased in the same proportion; or, that a body, which weighs only one pound at the surface of the earth, would weigh three hundred and fifty thousand pounds at the sun. But we must consider, that the attraction exerted by any body is the same as though all the matter were concentrated in the centre. ”

“ On the other hand, when a body is situated in the gravitational field of the earth, the gravitational force which acts upon it and which is commonly known as the weight of the body not only depends on the mass of the earth but likewise varies with the mass of the body. ”

“ We know that if the bodies in the scale-pans were formed, one of brass and the other of iron, and there were a magnet concealed under the table on which the operator placed his balance, the masses would not be equal when there was equilibrium. But that the law is true, and that, accordingly, weight is a true measure of mass, follows with the highest probability from the third of Kepler's laws, and was proved experimentally by Newton, by experiments with pendulums. ”

“ The mass of bodies varies according to their size; if you have the same nature of material, then for a double size you have a double mass. Some bodies are more concentrated than others, that is to say, more dense; it is as though they were more tightly squeezed together. Thus a ball of lead of an inch in diameter contains forty-eight times as much mass as a ball of cork an inch in diameter. In order to know the weight of a certain mass of matter, we should have to multiply the mass by a figure representing the attractive force or pull of the earth. ”

“ Masses are compared by the Balance (q.v.) , which may be made to indicate a 100,000,000th of the mass. They may also be estimated, not by their attractive force being balanced by an equal mass, but by the elasticity of a spring; this, which is the only true weighing-machine showing weight and not mass, is useful for rough purposes, owing to its quick indication ”

“ But the proportion of the resistance to the weight is augmented, when either the specific gravity is made less, the magnitude remaining equal, or when the density of the medium is made greater, or when, by diminishing the magnitude, the resistance becomes diminished in a less ratio than the weight. ”

“ And similarly with mechanical forces, the unhesitating assumption is that if one unit of force acting in a given direction produces a certain result, two units will produce twice the result. Every process of measurement in a physical experiment takes this for granted; as we see in one of the simplest of them—the process of weighing. If a measured quantity of metal, gravitating towards the Earth, counterbalances a quantity of some other substance, the truth postulated in every act {301} of weighing is, that any multiple of such weight will counterbalance an equi-multiple of such substance. ”

“ The weight of a body is the force it exerts in consequence of its gravity, and is measured by its mechanical effects, such as bending a spring. We weigh a body by ascertaining the force required to hold it up, or to keep it from descending. Hence, weights are nothing more than measures of the force of gravity in different bodies. ”

“ It is an essential part of the theory of gravitation that the proximity of other attracting particles is without effect upon the attraction existing between any two molecules. Two pound weights weigh as much together as they do separately. Every pair of molecules in the world have, as it were, a private communication, apart from their relations to all other molecules. Another undoubted result of experience pointed out by Newton‍323 is that the weight of a body does not in the least depend upon its form or texture. ”

“ When you go a journey and your luggage is weighed, it is not put on scales, but on a spring; the weight depresses the spring a certain amount, and the result is indicated by a needle on a dial. The same principle is used in automatic machines for finding your weight. The spring balance shows weight, but scales show mass. So long as you stay in one part of the world, the difference does not matter ”

“ Newton’s conception of the earth’s gravitation as extending as far as the moon gave further importance to the distinction between mass and weight; for if a body were removed from the earth to the moon, then its mass would be unchanged, but the acceleration due to the earth’s attraction would be 60 × 60 times less, and its weight diminished in the same proportion. ”

“ The fact that all bodies fall at the same rate (when the resistance of the air is eliminated) , proves that weight is proportional to mass; or more explicitly, that the gravitative attraction of the earth on matter near its surface depends on the amount of that matter, as estimated by its inertia, and on nothing else. ”

“ All units must be assumed to be equal in that other respect; and this is never practically true, for one actual pound weight is not exactly equal to another, nor one mile's length to another; a nicer balance, or more accurate measuring instruments, would always detect some difference. ”

“ This shows that the quantity of matter existing in those bodies implies “a constant of mass” independent of the intensity of gravitation, and that the ratio of the two masses is the ratio of two “absolute” quantities—that is, of two numbers of primitive material units.
It is not true, therefore, that the weight is not “the presentation of an absolute substantive entity,” as the author pretends. Weight implies mass and gravitation, and presents the one as subject to the other. Now, the mass is an “absolute substantive entity,” as we have shown. ”

“ To express mechanical force or power, the foot pound is the unit employed—that is, the mechanical energy necessary to raise a weight of one pound to a height of one foot. On the Continent, where the units of length and weight are the metre and the gramme, the unit of mechanical energy is the metre gramme. ”

“ We can readily calculate from the formula how much power will be required to raise a given weight; for example, suppose 200 lbs. be attached to the moveable pulley, we find that 111 lbs. must be applied as the power. But in order to raise 200 lbs. one foot, the power exerted must act over two feet; hence the number of foot-pounds required is 2 × 111 = 222. The quantity of energy that is lost is 22 foot-pounds. Out of every 222 foot-pounds applied, 200 are usefully employed; that is to say, about 90 per cent. of the applied energy is utilized, while the remaining 10 per cent. ”

“ As the balances are pulled downwards by the bar when it is loaded, so they will react to pull the bar upwards. This will be evident if we think of a weight—say 14 lbs.—suspended from one of these balances: it hangs at rest; therefore its weight, which is constantly urging it downwards, must be counteracted by an equal force pulling it upwards. The balance of course shows 14 lbs.; thus the spring exerts in an [Pg 43] upward pull a force which is precisely equal to that by which it is itself pulled downwards. ”

“ The cause of Weight: Attraction: Force. We know nothing whatever of the reason why bodies possess weight. Bodies do not fall on account of the law of gravitation (§ 9) ; nor does their gravity explain why they fall. Gravity, as we have seen, is only a name for weight, and the law of gravitation is only a statement of how bodies approach one another, not why they do so. ”

“ We are in the habit of estimating mass by its weight, and we do so rightly, for at any place on the earth, as London, the weights of masses are always proportioned to the masses, and if you want to find out what mass of tea you have got, you weigh it, and you know for certain. Hence in our minds we confuse mass with weight. ”

“ Any force may be compared with gravity, considered as a standard. Weight is the action of gravity on a given mass. Whatever therefore is proved concerning the weights of bodies will be true in like circumstances of other forces.
Weights are supposed to act in lines of direction parallel to each other. In fact, these lines are directed to the centre of the earth, but the angle formed between any two of them within the space occupied by a mechanical engine is so small, that the largest and most accurate astronomical instruments are scarcely capable of exhibiting it. ”

“ As a gramme mass acquires through the action of gravity a velocity-increment of about 981 centimetres in a second, accordingly, a gramme is attracted to the earth with 981, or, in round numbers, 1000 units of force of the centimetre-gramme-second system, while a milligramme-weight would strive to fall to the earth with approximately the unit force of this system. ”