英文科學讀本 第六冊·Lesson 27 The Pulley

Lesson 27 The Pulley

If you please, sir, began Fred one morning, "I have been thinking a good deal lately, first about the levers, and then about that grooved wheel, which the workman uses to raise his materials from the ground to the scaffold where he is working. I pictured to myself a large block of stone lying on the ground ready for the workman to use, if he could only manage to raise it. I purposely forgot all about the wheel, and began to wonder whether he could raise the stone with no other help than the lever."

Well, my lad, replied Mr. Wilson, "and what conclusion did you arrive at?"

I think he could do it, sir, but it would be done with tremendous expenditure of force and time. The lever would only succeed in raising the stone a little way. Then he would have to prop it up in that position, take another fulcrum, and raise it a little higher. All this would have to be repeated again and again many, many times before he could raise the stone where he wanted it.

Yes, Fred, you are right, said Mr. Wilson, "or he might fix his lever and its fulcrum on the scaffold itself, and connect one end of it, by means of a rope or a chain, with the block of stone below. The rope or the chain, as we have already seen, would transmit to one end any force which is applied to it at the other. The man, by applying force to the lever at the top, would thus be enabled to raise the block a short distance, as your man did with the lever on the ground. Then it would have to be propped up and lifted, as before, little by little.

But your plan as well as mine, Fred, would be exceedingly tedious, and wasteful as regards the expenditure of force. Now let us see how this use of the lever first suggested the idea of another machine— the pulley. I have here a short wooden bar or lath, similar to the one we used for our model lever, except that it is only about a foot in length. I have drilled a hole through its center and we will fix it to the edge of the table as before, leaving it free to move on a nail. The nail thus becomes the fulcrum, and the bar is a lever of the first order, with equal arms. We will next attach a cord to the end of each arm, and you, Fred, shall hold one of the cords in your hand, while I hang a weight to the extremity of the other.

Pull your cord down now, Fred, and you will find that, as the arm of the lever on that side is lowered, the other rises on the fulcrum, and with it the cord and the weight attached to it. Continue the pulling and let us see how far you can raise it. You see at once that you can bring the lever into a vertical position, and so raise the weight a short distance, but beyond that it will not move. Now, instead of a single lever, I am going to show you a little contrivance, which consists really of several levers, all of the same length, and so arranged as to cross each other at the same point—the center of each. Through this centre I have drilled a hole as before. Our contrivance looks very much like the spokes of awheel. Let us now fix our wheel up to the table edge by means of a nail through its centre. The nail thus becomes the fulcrum of each of these separate levers. They are all free to move on this point.

Before we proceed further, I want you to notice that I have cut a groove in the extremities of each lever. This groove shall receive the cord which is going to help us to do our work. Hold one end of the cord in your hand, Fred, as before, while I hang a weight to the other end. Now pull your end of the cord down, and you will easily raise the weight at the opposite extremity. Each spoke of the wheel in turn takes its share of the work, and acts as a separate lever.

We are now in a position to pass to another little contrivance. Here is a circular wooden disc, with a groove cut round the circumference, and a hole drilled through its center. On the face of the disc I have marked plainly in chalk a number of diameters, to represent as many levers all crossing at the center. If we fix the disc to the edge of the table in the usual way, and pass a cord with its weight round the grooved circumference, the principle of action will be at once made quite clear. This revolving wheel is nothing but a succession of levers of the first order. Your mind goes back, of course, to the grooved wheel which the workman used on the scaffold, and you are quite right, although we are now going to give it a better name. The weight at one end of the cord is raised by the person pulling at the other end. Hence we call this grooved wheel a pulley. We also call it a fixed pulley, because it is fixed, and works on some kind of pivot at its center.

Suppose we next think for a moment, not of the wheel itself, but of some one of its imaginary levers. These are all of the same length; they are diameters of the same circle. Each one has two equal arms. Now, if I wish to raise a stone weighing 50 lbs. with a lever of the first order, having equal arms, what force must I use?"

The force or power must be equal to the weight, sir, replied Fred, "because the arms of the lever are equal."

Then are we to understand that such a lever gives no mechanical advantage?

It does give an advantage, sir, although not in the amount of force required, but in the direction in which the force is applied. We raise the weight by applying the power downwards, not by lifting it.

Quite right, Fred, and what is true of a single lever ought to be true of a number, and hence also of the pulley. We have seen that it is true of the pulley as regards direction. Let us next see whether it is also true with respect to the amount of force required.

If I hang a cord over the pulley, with equal weights at its extremities, they will balance, and the smallest addition to either will cause the other to rise. Hence we see that the forces on either side of such a pulley must be equal if they are to balance. There is no mechanical advantage so far as the amount of force is concerned.