英文科学读本 第六册·Lesson 23 Third Order of Levers

Lesson 23 Third Order of Levers

You see, boys, I have fitted up our model lever again for a lesson, began Mr. Wilson. "There is still another kind of lever calling for our attention; it differs in its arrangements from both the orders which we have already studied. We shall speak of it as a lever of the third order.

If you examine the model, you will see that it is arranged, so far as its fulcrum is concerned, in exactly the same way as we arranged it for the lever of the second order; that is to say, the fulcrum is placed at one end. Can you tell me the relative positions of the power and the weight in levers of the second order?"

Yes, sir, replied Will, "the power is always at the end of the lever, opposite the fulcrum, and the weight or resistance somewhere between the two."

Quite right, my lad, and in the third order the difference is that these relative positions of the power and weight are changed. In the third order of levers the weight is always at the end opposite the fulcrum, and the power acts between them. Turning now to our model, we will first get rid of the difficulty arising from the weight of the bar itself. If we support it, as we did before, over the grooved wheel with a cord and a sufficiently heavy weight, we shall have our lever ready for work. Let us begin, as before, by hanging our 1 lb. weight at the end of the lever. This time, however, we will attach the cord to the middle hole in the bar, and pass it over the grooved wheel above. This cord shall represent, as it did in the other case, the power, but it is acting now just half-way between the fulcrum and the weight.

Take the end of the cord in your hand, Fred, and support the lever, so as to keep it balanced in a horizontal position. What is the weight you are holding up?

The 1 lb. weight hanging at the end of the bar, sir, replied Fred.

Just so, my lad. Now let us see what force you are exerting on the cord to support this 1 lb. at the end of the lever. I will attach another 1 lb. weight to the cord, but now if you let go, the lever no longer rests horizontally— the two do not balance. We shall require 2 lbs. hanging from the cord to balance the 1 lb. at the end of the lever. That is to say, you had to exert just now a downward force of 2 lbs. to keep the bar horizontal. You ought to be able, from what we have already done, to tell me the reason for this. The weight-arm is twice as long as the power-arm; therefore, the power must be twice as great as the weight.

If we remove the cord for further experiments, we shall find that when we attach it to the second hole, i.e. at one-third the distance from the fulcrum, we shall require 3 lbs. at the end of it to balance the 1 lb.; and 6 lbs, weight will be necessary to preserve the balance, with the cord attached to the first hole, which is one-sixth of the distance from the fulcrum. It is now clear that, in levers of the third order, the power, being nearer the fulcrum than the weight, must always be greater than the weight. In other words, it takes a great power to raise a small weight. There is a loss of power. But the law of levers says that loss of power means gain in speed. Let us see whether this is true of the third order of levers as well as the others. Indeed, you shall see for yourselves. I will attach a very small additional weight to the cord, and leave the model to take its own course. The balance is at once upset; the weight at the end of the lever is carried rapidly upwards, and it moves through a much greater space than the weights at the end of the cord.

Hence we see that in levers of the third order there is no gain, but an actual loss of power; the mechanical advantage is a gain of speed. A shovel in the hands of a man, shovelling up coals, sand, or corn, will give a good illustration of the use of this kind of lever. The handle held in one hand becomes the fulcrum; the coal, sand, or corn to be lifted is the weight; and the power is applied by the other hand to some point in the shaft, between the weight and the fulcrum.

The man gains nothing in power—he actually loses power, for the force he expends is greater than the weight he lifts. When the weight is greater than usual, he shifts his power-hand down—nearer the weight. Why? What he loses in power, however, he gains in speed, and the heap of coals is rapidly moved.

A man with a pitchfork and a load of manure, hay, or straw is, of course, a similar illustration. A simple illustration of this kind of lever is also afforded by the treadle of a sewing-machine, a harmonium, a grindstone, or a lathe. The hinge of the treadle of course forms the fulcrum; the weight to be moved is attached to the opposite end, and the power is applied by the foot on the treadle itself.

There is no gain of power. The person using the machine expends greater force than is represented by the weight lifted. But speed is the thing desired here, not increase of power. Think of the sewing-machine. The movement of the foot on the treadle is slight as compared with the greater and more extended movement of the crank at the back of it, and of the wheels which it causes to fly round. There is a gain of speed. One other familiar illustration of these levers is presented when a man raises a long ladder with the lower end pressed close up to the wall. That lower end is, of course, the fulcrum. Think of the ladder as it lies on the ground. The man takes the opposite end in his hand and raises it, moving downwards from one round of the ladder to another. For a long time the weight is between him and the fulcrum, and the ladder is a lever of the second order. After a time, however, as he still moves on, he gets between the weight and the fulcrum, and the rest of the raising movement shows the work of a lever of the third order."