英文科學讀本 第六冊·Lesson 19 Second Order of Levers

Lesson 19 Second Order of Levers

We are going to talk about levers again this morning, said Mr. Wilson, "but we shall have to deal with levers of a different kind from those with which I have already made you familiar. Perhaps however, it would be better if I said that we are going to learn to use the lever in another way, rather than call it a different kind of lever; for every lever, of whatever kind, is simply a rigid bar, and the difference lies only in the manner in which we employ it.

As a proof of this, we shall use our lath, as before, for a model lever, but this time I shall put the fulcrum nail, not through the middle, but through a hole at one end. The levers we are now about to consider always have the fulcrum at one end. We call them the second order of levers, to distinguish them from those of the first order, in which the fulcrum lies somewhere between the two ends. Now that we have our lever-bar fixed at its fulcrum, you shall come and hold it horizontal, Fred. You at once find that it requires considerable exertion, for you are supporting the lever itself, which would otherwise fall by reason of its own weight. We must get rid of this difficulty before we can set the lever to work.

To do this I must call in the help of the little suspended wheel, with a grooved circumference, which we used in our first lesson on machines. We will fasten one end of a fine cord to the last hole (No. 6) in the bar, and pass the other end of it over the wheel. It will be easy now to attach to the free end of the cord something just heavy enough to keep the bar horizontal, and after that we may disregard its weight entirely. It is now merely a lever free to work on a fulcrum, placed at one extremity. We will commence operations by hanging a 1 lb. weight to the hole in the bar (No. 6) from which the cord passes over the wheel. This weight would cause the bar to fall, but I can at once bring it to rest in the horizontal position by attaching a similar 1 lb. weight to the cord itself. That is to say, a weight of 1 lb. at the end of the lever is supported by a power of 1 lb, acting also at the end of the lever.

This is just as we might have expected it to be, from what we already know. The weight-arm and the power-arm are the same length; hence the weight and power must be equal. Now, without interfering at all with the cord, or the weight attached to it, Fred shall remove the 1 lb. weight suspended from the end of the bar, and place it midway between the end and the fulcrum.

Does the lever assume the horizontal position now? No; the two forces do not balance. It requires a 2 lbs. weight at the middle of the lever to bring it to rest again in the horizontal position. In other words, the cord, with its power of 1 lb. acting at the end of the lever, can support a weight of 2 lbs. suspended from the middle. The power-arm is twice as long as the weight-arm. If we continue our experiments, we shall find that the same power of 1 lb. at the end of the lever will support a weight of 3 lbs. suspended at one-third of that distance from the fulcrum, or a weight of 4 lbs. at one-fourth of that distance. This, of course, is only repeating what we said about the other class of levers, except that with these we always have the fulcrum at one end and, consequently, the power-arm and the weight-arm are both on the same side of it.

The distinctive point about these levers of the second order is that the power always acts at one end, the fulcrum being at the other, and the weight somewhere between the two. The longer the power-arm is, as compared with the weight-arm, the greater will be the weight which a given power can raise; the power multiplied by the length of the power-arm is always the same as the weight multiplied by the length of the weight-arm. In this second order of levers the weight is always nearer the fulcrum than the power can be, for the power always acts at the opposite extremity of the bar. Hence the mechanical advantage gained by such a machine is an increase of power.

Our two boys on the see-saw illustrated a universal law in the science of levers—namely, that a gain in power must be accompanied by a loss in speed. Let us apply this to our lever of the second order to find how far it is true. We have seen that we do actually get an increase of power with these levers. Now think of the power acting at the end of the long arm, and the weight somewhere between it and the fulcrum. It is clear that the weight does not move so far or so quickly as the power.

The mechanical advantage therefore of levers of the second order is gain in power, and this means loss of speed. Let us now glance at a few practical examples of the use of this second order of levers. A crow-bar in the act of raising a block of stone becomes a lever of the second order. In this case the ground is the fulcrum, the weight of the stone rests on the bar between it and the power, which acts by forcing the lever upwards.

When the same crow-bar was used to raise the paving stone, the end of the lever was forced under it, the fulcrum was formed by the neighboring stone, which lay between the power and the weight, and the man overcame the resistance by pressing down on the power arm. We had then a lever of the first order. A wheel-barrow is a very familiar example of a lever of the second order. The fulcrum is placed at the axle of the wheel, the power is applied at the handles, and the weight lies between the two. A boatman's oar is another good example of the same order. Here the water is the fulcrum, the boat itself the weight, and the man applies the power at the handle of the oar.

A chopping-knife by its very action explains itself. You can have no difficulty in pointing out fulcrum and power. The work of the machine is to overcome the resistance offered by the substance to be chopped, which of course is placed between the fulcrum and the power. A pair of nut-crackers afford an illustration of a double lever of the second order, in which the fulcrum, power, and resistance are very apparent."