Our investigations into the nature and use of the lever led us to discover how it is that this simple machine is able to give such immense mechanical advantage. We know that we have only to make the power-arm very long as compared with the weight-arm, in order to overcome great resistance with the expenditure of a very small amount of force.
But we can go further than this. We can easily calculate the exact weight which any force is capable of raising by means of a lever, if we know also the respective lengths of the two arms of the lever. The power multiplied by the length of the power-arm is always the same as the weightmutiplied by the length of the weight-arm. If you go backto our trial experiments with the lever, you will find this absolutely true in every case ; the shorter the weight-arm, the greater the weight, and the longer the power-arm, the smaller the power.
It is important to remember that in every rearrangement we made with the lever the other day, we were careful to place the fulcrum each time between the power and the weight. Whenever levers are used in this way, they forma class by themselves, and are known as levers of the first order.
We will now enumerate a few practical examples of the use of this first order of levers, which you often meet with in everyday life.
To you the most familiar example of all will be the see-saw. The moment I mention the word you picture it in your mind"s eye, and are mentally pointing out to yourselves its fulcrum, and the two arms, one on each side of it. You know that, when the two boys are aboutthe same size you make the two arms equal by placing the fulcrum in the center of the plank. But how do you act when one boy is smaller than another? You give him the longer end of the plank-the long arm of the lever. You do this simply because you have seen other boys do it; nowyou know the reason for doing it.
It will be instructive to notice also how each boy on the see-saw in turn becomes first the weight and then the power. When either end of the plank is down, the boy at that end is the weight, and the one at the other end becomes the power which is to raise him, and so it goes on.
Among the other familiar illustrations of the use of this first order of levers are: (1) the poker in the act of stirring a fire; (2) a crowbar in the act of raising a paving stone;(3) the claw-hammer in drawing a nail; (4) the common pump-handle; (5) an ordinary pair of scales for weighinggoods; (6) a spade in the act of digging. Take each of these familiar examples one by one, and point out its fulcrum, power, and resistance, and you will see that it acts just as our model did.
In addition to the above we have the steelyard, a very useful instrument for weighing purposes. If we compare the steelyard with a pair of scales, we shall easily understand the principle on which it acts,In the scales the two arms are equal, and we use a great number of weights. In the steelyard the arms are unequal, the object to be weighed is hung from the short arm, and only one weight is used on the long arm. A little thought now will quickly tell you the reason for this.
A pair of scissors, pincers, and nippers are examples of double levers of the first order. Think for a moment, and try to explain why we bring hard, stiff material as close as possible to the rivet of the scissors when we wish to cut it.
Let us now go back to our see-saw. We will imagine two boys, a big one and a little one, riding on it. The little boy, as you know, sits on the long arm, the big boy on the short arm, and each, in turn, becomes the power and the weight.
When the big boy on the short arm is down, he is the weight, and the little boy on the long arm becomes the power to raise him. The little boy represents a very small power, but when that power acts at the end of the long arm, it increases, and he is able to raise the bigger boy.
When it becomes the turn of the big boy to act as power, that power is considerably greater than the weight to be raised, but it is acting at the end of the short arm of the lever. Now, consider for a moment. Which boy has the best ride? The little boy, of course, has the best ride. His end of the see-saw rises higher, and moves more quicklythan the other end.
Now I think you will be able to understand what I am going to say next. When the power acts at the end of the long arm it increases in magnitude, but the weight which it acts upon moves slowly, and through a short distance. When the power acts at the end of the short arm, the weight moves through a greater space and at a greater speed, but there is loss of power. It takes, that is to say, a great power to raise a little weight. This is a universal law as regards levers. Gain in power must mean loss in speed; and gain in speed must mean loss in power.