英文科学读本 第六册·Lesson 09 The Lever

Lesson 09 The Lever

Our lesson on the Forces of Nature showed us one important difference between civilized man and the untaught savage, said Mr. Wilson. "Both are surrounded by these wonderful forces. One makes a rough-and-ready use of some of the simplest of them; the other, by his ingenuity, has been able to subdue them all to his own will—change them, adapt them, and even magnify their intensity to an almost unlimited extent, so as to compel them to minister to his wants in thousands of ways. The contrivances which he has invented to assist him in this subjugation of the natural forces are known as the mechanical powers. They form the basis of every machine in use in the civilized world.

Our business this morning will be to consider the first and simplest of these mechanical powers. You shall come to the front and help us, Fred, by trying to raise this heavy cupboard off the floor.

Fred tried, but found it impossible to move the cupboard. Its weight offered too great a resistance to all the muscular force he was able to exert.

Now I will show you, continued Mr. Wilson, "how to raise the cupboard with the greatest ease, by calling in the help of this iron crow-bar. I will push one end of the bar under the cupboard, place this small block of wood a little distance off, and press the other end down. The cupboard moves easily. Try it for yourself, Fred. You now see that this simple bar of iron enables you, with the expenditure of a comparatively small muscular force, to raise that heavy body, which you were unable to move before by exerting all your strength.

The force which you applied at one end of the bar downwards was transmitted to the other end, and acted in an upward direction on the cupboard. Moreover, the small force which you applied was converted, by this bar, into a force sufficient to lift the heavy weight. This altering of the force is just what all mechanical contrivances are meant to do; hence the iron bar is a machine. It is the simplest of all machines. We call it a lever.

All that is necessary is that it must be perfectly rigid. A cane, or a bar of any yielding material, could never serve the purpose of a lever, because the force applied at one end, instead of being transmitted to the other, would be used up in bending the cane itself. The lever, from its simplicity, was, in all probability, the first of man's inventions in the mechanical powers. We must now learn the principles on which it works.

The first essential is that the bar shall be perfectly rigid. Here is a stout, flat lath, which will satisfy all the conditions in this respect. I have bored a number of holes in the lath, at exact distances apart, and I am going to fix it up to the edge of the table, by means of a large French nail through one of these holes. It is quite immaterial where we place the nail, as the bar is free to move in every position. This is the other essential in a lever. Besides being a rigid bar, it must be capable of moving about a fixed point. This fixed point about which the lever moves is called the fulcrum. Our lath then in its present position is a lever, and the nail which holds it to the edge of the table is its fulcrum. It is usual to call the parts of the bar on either side of the fulcrum the arms of the lever.

We will commence operations by placing the nail through the middle hole of the lever, so that the arms are of equal length. If now we hang a 2 lbs. weight at the end of each arm, they will balance. Now Fred shall remove the weight from one end, and still keep the bar balanced by holding it in his hand. How do you manage to keep it balanced, Fred?"

I am pressing down on the end of the bar, sir.

Can you tell me with what force you must be pressing?

With the force of the weight I removed, sir, I suppose, replied Fred.

Exactly. The two weights at first balanced, because they were both pulling downwards with equal force at the two ends of the bar; and you must now exert an equal amount of muscular force downwards, at the one end, to balance the weight hanging at the other. If you use the smallest amount of additional force now, you will raise the weight at the other end. We usually call the force which you have been exerting the power, and the heavy body whatever it may be at the other end is called the weight or the resistance. In like manner the two arms of the lever are known as the power-arm and the weight-arm.

Let us now alter the position of the lever, so as to make the power-arm twice the length of the weight-arm. If, with the lever so arranged, we hang a 2 lbs. weight at the end of the short arm, we shall easily find by experiment that a weight of 1 lb. at the end of the long arm is sufficient to balance it. The slightest extra pressure of the hand on the power-arm would then raise the 2 lbs. weight at the other end. By making fresh rearrangements of our lever, we may have the power-arm three, four, or six times as long as the weight-arm, and at every change our 1 lb. weight at the end of the long arm will balance a still heavier weight on the other. With the power-arm six times as long as the weight-arm, the 1 lb. weight would exactly balance 6 lbs. If we tried to balance the lever by holding the end of the power-arm, we should feel that very little muscular exertion would be necessary. We should press it down with only a force of 1 lb. to balance the 6 lbs. at the end of the weight-arm.

Here we have a machine which gives a distinct advantage. When we used the lever with equal arms, the only advantage gained was a change in the direction of the force. To raise the weight, the power pressed downwards instead of upwards. With the power-arm longer than the weight-arm, a small force will raise a heavy weight, and the longer the power-arm is, as compared with the weight-arm, the greater will be the weight which that small force can raise. This explains the ease with which you raised the heavy cupboard. The power-arm of your lever was very long compared with the weight-arm.