Lesson 34 The Wheel and Axle

We have seen before, said Mr. Wilson, at the commencement of the next lesson, "how one machine gradually suggested another. I want to show you this morning how a very important machine grew out of the fixed pulley, just as the pulley itself grew out of the lever.

I have here two circular wooden discs, with grooved circumferences, similar to the one I used before. The smaller of two is, as you see, only about half the size of that; the other is much larger. I will fix both discs to the edge of the table, by means of a large nail, or a screw, in the usual way, placing the smaller one in front. I want both discs to revolve together, so I will fix them to each other with a peg. Now, on the right of the large disc or wheel, and the left of the small one, I will fix separate cords. Each cord shall be passed under its own disc, and round the grooved circumference, so that the end may hang from the outer side in each case. Notice that, when I pull the cord of either wheel downwards, the other rises upwards. In other words, our new machine is a lever of the first order. We want to see how it differs from the single wheel or disc. You will see this best if I draw with the chalk a horizontal diameter across the small front disc. The two radii of this diameter form the two equal arms of a lever, which act on the center as their fulcrum. The cord of this wheel hangs and acts at the extremity of the left arm.

I will now produce the chalk-line, towards the right, across the larger wheel. As the large wheel moves with the small one, the chalk line drawn across from the center to the circumference represents a radius of the large circle. It is really the right arm of a long lever, and at its extremity, on the circumference of the wheel, the cord of that wheel hangs and acts. Now you shall pull the cord hanging from the larger wheel, and watch the chalk-line while you do it. The pulling of the cord depresses the line on that side of the center, and, of course, raises the shorter line on the other side, because both wheels move together. We have, in fact, a lever of the first order, with arms of unequal length.

Each wheel, as we have already seen, may be regarded as composed of a great number of levers, all acting on the center, as their fulcrum; the combination of the two wheels—a large and a small one—gives the advantage of unequal arms to each lever. We know, from the principle of levers of the first order, that a small weight acting at the extremity of the long arm will balance a large weight at the end of the short arm, and that the slightest additional weight on either will cause the other to move upwards. This is the whole secret of the wheel and axle.

The radius of our large wheel is twice that of the small one; a power of 1 lb. will therefore support a weight of 2 lbs.; if it were ten times as long, the same power would support a weight of 10 lbs., and so on. Hence, the greater the difference between the size of the wheels, the greater the mechanical advantage. By making one wheel very small and the other very large, we get very great advantage of power.

Now, before we leave our model, I want you to watch its working once more. We will first attach our 1 lb. and 2 lbs. weights to their respective cords, and so get a balance; and then I will add a very small weight to the cord on the larger wheel. The 2 lbs weight at once begins to move upwards and the other down. But you notice that the former moves very slowly as compared with the latter, and it moves, moreover, through a smaller space. Here we have again an illustration of the principle that gain of power means loss of speed; loss of power, gain of speed. The simplest and most familiar application of the wheel and axle is the windlass for raising the bucket in a well. The axle, on which the rope attached to the bucket is wound, represents the small wheel of our model. The power is applied either to the ends of the spokes of a large wheel, or to a long handle attached to the center of the axle. When the handle makes a revolution, it describes a large circle. The advantage, as regards gain of power, depends upon the size of this circle as compared with the axle.

The capstan for heaving the anchor on board ship, opening and closing lock-gates, etc., is another application of the wheel and axle. In order to increase the power, the men work at the end of long spokes, which are fixed into the axis. The longer the spokes, the greater the mechanical advantage of the machine.