Weight (force)

“ An unsupported weight will fall, and even when supported will exert a pressure downward. And this tendency is no mere directed force in the physical sense, but an impulse, in the personal sense. For when with hand or shoulder we support a weight, we inevitably interpret it in terms of our own voluntary muscular exertion in resisting it; even as we strive to resist it, so it seems to strive to fall. Although this force is exerted downward, it shows itself in the horizontal lines of a building, in string courses, parapets, cornices, friezes ”

“ A raised weight can produce work, but in doing so it must necessarily sink from its height, and, when it has fallen as deep as it can fall, its gravity remains as before, but it can no longer do work. ”

“ The piece of iron or other substance which is attracted to the earth with this force in London, is attracted to the earth with a greater force at the pole and a less force at the equator; hence, in order to define the standard force, we have to mention the locality in which the pressure of the weight is exerted.
It is easy to conceive how the magnitude of a pushing or a pulling force may be described as equivalent to so many pounds. The force which the muscles of a man’s arm can exert is measured by the weight which he can lift. ”

“ But if the power should be applied at only four times the distance from the fulcrum at which the weight is, then it would require a force of 18 pounds to balance the 72 pounds on the short arm. Similar variations can be made by altering the length of the short arm. The power and the weight will balance each other if the weight multiplied by the length of the short arm, and the power multiplied by the length of the long arm, give equal products. ”

“ In order to study the question exactly, we shall ascertain what weight suspended from the hook b will suffice to raise a. I find that in order to raise 14 lbs. on a no less than 47 lbs. is necessary on b, consequently there is an enormous loss of force: more than two-thirds of the force which is exerted is expended uselessly. If instead of the 14 lbs. weight I substitute any other weight, I find the same result, viz. that more than three times its amount is necessary to raise it by means of the rope passing over the studs. ”

“ So in every calculation, where power is to be calculated, first find out how many foot pounds are developed, and then use the unit of measure, 33,000, as the divisor to get the horse-power, if you wish to express it in that way.
It must be understood, therefore, that horse-power is a simple unit of work, whereas a foot pound is a compound unit formed of a foot paired with the weight of a pound.
Energy.—Now work and energy are two different things. Work is the overcoming of resistance of any kind, either by causing or changing motion, or maintaining it against the action of some other force. ”

“ 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. ”

“ Weight has been defined as the measure of the earth's attraction. A body weighing one pound attracts the earth and is attracted by it with a force of one pound, but the same body at the sun's surface would attract the mass of the sun with a force of twenty-seven pounds, since its weight has been increased twenty-seven times by the sun's attraction. ”

“ If a one-pound weight could raise a two-pound weight without thus moving through twice as much space we might then say that there is an actual gain of power in the lever. But it evidently makes no difference whether one pound moves through two feet or two pounds through one foot; the force is the same in both cases. For the momentum or force of a moving body is in proportion to its weight and velocity, § 201; and therefore the pound weight, moving through two feet, has as much momentum as the two-pound weight moving through one foot in the same time. ”

“ A child can lift his own weight against the attraction of the mighty earth; and by combined strength as many children as would have a weight equal to the earth's would easily bear a weight exceeding the earth's, if the force could be wholly and directly applied to such work. ”

“ And what can assure us that it is not so, except removal of one or other force, and consequent tilting of the lever? The other fundamental axiom of statics, that the pressure on the point of support is the sum of the weights ... is merely a scientific transformation and more refined mode of stating a coarse and obvious result of universal experience, viz. that the weight of a rigid body is the same, handle it or suspend it in what position or by what point we will, and that whatever sustains it sustains its total weight. ”

“ All power is expressed in foot pounds. Suppose a cannon ball of sufficient weight and speed strikes an object. If the impact should indicate 33,000 pounds it would not mean that the force employed was one horse-power, but that many foot pounds. ”

“ The cases in which a force is apparently increased or diminished, as well as those in which it seems to disappear, are all found, on examination, to be illusive. For example, the apparent increase of a man's power by the use of a lever is really no increase at all. It is true that, by pressing upon the outer arm with his own weight, he can cause the much greater weight of the stone to rise ”

“ If the heart should expend its entire force lifting its own weight, it would raise itself nearly twenty thousand feet an hour, ten times as high as a pedestrian can lift himself in ascending a mountain. ”

“ Because the force of the stroke is greater than the weight of the bird, and it therefore rises with the difference of these two forces; were the stroke less than its weight, then would it sink with the difference. Suppose, for example, a bird weighs twelve ounces, and it strikes the air with a force equal to sixteen, is it not clear that it must rise with a force equal to four? ”

“ And with 215 such a collection of heavy bodies, or weights, we can readily measure all other forces; for the same principle of the equality of action and reaction leads at once to this maxim, that any statical force is measured by the weight which it would support. ”

“ 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. ”

“ In the familiar instance of a body whirled round by a string, the breaking of the string no more implies that an active force has pulled away the body, than the breaking of a rope by which a weight is pulled implies that the weight has exerted an active resistance. ”

“ These weights are at first each 14 lbs. I raise a up to the pulley, leaving b upon the ground; I then let go the rope, and down falls a: it first pulls the slack rope through, and then, when a is about 3' from the ground, the rope becomes tight, [Pg 253] b gets a violent chuck and is lifted into the air. What has raised B? It cannot be the mere weight of a, because that being equal to b, could only just balance b, and is insufficient to raise it. It must have been a force which raised b ”

“ If a weight be suspended from an india-rubber spring, it is evident the spring will stretch so that the weight pulls the spring and the spring pulls the weight; hence the number of pounds in the weight is the measure of the force the spring is exerting. ”

“ 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. ”

“ You must exercise a force of 100 pounds over 12 feet of space in order to raise a weight of 200 pounds a distance of 6 feet. When we raise 100 pounds through 12 feet or 200 pounds through 6 feet the total work done is the same; but the pulley enables those who cannot furnish a force of 200 pounds for the space of 6 feet to accomplish the task by furnishing 100 pounds for the space of 12 feet. ”

“ We had, let us say, always seen heavy bodies sink when their support was taken away; we had also seen, perhaps, that the sinking of heavier bodies forced lighter bodies upwards. But now we see a lever in action, and we are suddenly struck with the fact that a lighter body is lifting another of much greater weight. ”

“ If, for example, the balance is attached two inches from the fulcrum and the weight twelve inches, the pull on the balance is found to be six times greater than the weight that is being lifted. If other positions are tried, it is found that the power exerted in each case is as many times greater than the weight as the weight-arm is times longer than the power-arm. ”

“ You observe a little catch on the edge of the wheel, which keeps the wheel from going in the opposite way during the relaxation of the muscle. Consequently the muscle, as you see, winds up the weight. Now if we multiply the weight by the height through which the muscle has lifted it we get a measure of the work done. We speak of a foot pound, that is one pound weight lifted one foot in height, or we speak of a kilogrammetre, that is one kilogram lifted one metre in height. ”

“ No one wants to be fat and heavy of body—then why of head? For some clumsy reason we have come to confuse strength with weight. The crude methods of early building undoubtedly had much to do with this. The old ox-cart weighed a ton—and it had so much weight that it was weak! ”

“ Any figure bearing an additional weight out of the central line, must throw as much natural or accidental weight on the opposite side as is sufficient to form a counterpoise round that line, which passes from the pit of the neck, through the whole mass of weight, to that part of the foot which rests upon the ground. We observe, that when a man lifts a weight with one arm, he naturally throws out the opposite arm; and if that be not enough to form an equipoise, he will add as much of his own weight, by bending his body, as will enable him to resist such accidental load. ”

“ In all cases the arms must be quite inflexible. A balance made by Ramsden for the Royal Society, is capable of weighing ten pounds, and turns with one hundredth of a grain, which is the seven-millionth part of the weight. ”

“ Then weighing what they had borne, whether we should find it to be ten or thirty pounds—I cannot guess how much it might be at this distance—one might safely say, without fear of mistake, "The strength of this young lady is equal to ten, twenty, or thirty pounds"—in other words, "she represents a weight of ten, twenty, or thirty pounds" and by a similar plan people have ascertained the strength of the air—that is, the weight which it represents. They have weighed what it is capable of carrying. ”

“ If now you either pull or push the empty scale downwards, the beam may be brought into the horizontal position again, and the effort required to bring it into the horizontal position will be the greater, the greater the weight of the body in the opposite scale. An ounce in the one scale is easily raised by the pressure of a finger in the other. A pound requires more effort; ten pounds needs putting out the strength of the arm; to raise fifty pounds involves still more exertion; while a couple of hundredweight will not be stirred by the strongest push or pull upon the empty scale. ”

“ Men may apply their strength several ways in working a machine. A man of ordinary strength, turning a roller by the handle, can act for a whole day against a resistance equal to 30 pounds weight; and if he works ten hours in a day, he will raise a weight 30lb. ”

“ Imagine, if you can, a man weighing all of three hundred pounds, not more than five feet ten-and-one-half inches in height and yet of so lithesome a build that he gave not the least sense of either undue weight or lethargy. ”

“ Nevertheless that which excels in size shows greater powers, since it seizes greater weights and has a wider orbe of virtue. For a loadstone weighing one ounce does not lift a large nail as does one weighing a pound, nor does it rule so widely, nor extend its forces; and if from a loadstone of a pound weight a portion is taken away, something of its power will be seen to go also ”

“ Sometimes, for a difference, these light-weights are men of tremendous pluck and quality of muscle, able to thrash a burly bargee twice their weight and development with as much ease as a steel sword can cut through one of pith. ”

“ When, for example, we speak of a pound weight on the long end of a lever balancing a ten-pound weight on the short end, it is equally appropriate to speak of the ten-pound weight as balancing the one-pound weight. ”

“ If you wanted to measure your strength, one way of doing so would be to fasten a heavy weight to one end of a rope and pass the rope over a pulley. Then you might take hold at the other end of the rope and pull as hard and steadily as you could, marking the place to which you raised the weight. ”

“ For instance, if we drop a pound weight a foot on to a scale balance, the work it does is equal to one foot-pound. But if we place it on the scale gently, it will just balance one pound on the other side. ”