英文科學讀本 第六冊·Lesson 30 The Movable Pulley

Lesson 30 The Movable Pulley

I saw some men yesterday, sir, raising chests of tea to a loft in a warehouse by means of the pulley, said Fred. "But I have been very much puzzled ever since about that pulley; it was not fixed to a beam, as ours was the other day, but moved up and down the rope. There was a hook fixed to the pulley itself, and this held the chests which had to be raised.''

Ah, Fred, said Mr. Wilson, "your puzzle is nothing more than a block-pulley. Here is one; see, it answers in every way to your description, and it has a hook at one end of it. Let me explain how it is used.

I will pass this cord round it, and fasten one end of the cord to the cross-beam of our stand. Now we will hook a 2 lbs. weight to the pulley, and you shall mount on the table, and support it by holding the other end of the cord. Try and keep the two parts of the cord parallel, while we examine the working. Pull the cord upwards, and watch what happens. As you pull, the block rises and carries with it the weight which is attached to it.

This pulley, you see, instead of being a fixture like the one in our former lesson, moves upwards when force is applied to the cord. We call it a movable pulley.

Now the entire weight supported by the block is 2 lbs. The block, that is to say, is being pulled downwards, with a force of 2 lbs., the force of gravity due to the weight of the body itself, and this weight of 2 lbs. is supported by two cords. Now I want you to notice that there is a strain or tightness about the two cords. We call this strain the tension of the cord. In the present case, as the 2 lbs. weight is supported by two cords, each one (or rather each part of the cord) ought to bear half the strain or tension. That is to say, you ought to be supporting the 2 lbs. weight with the expenditure of a force of 1 lb. at your end of the cord.

If this be true, the movable pulley gives a distinct mechanical advantage, as far as power and weight are concerned. Any given power will raise a weight of twice its value. But what have you to say about direction? Is there any advantage in the direction in which the power is applied?"

I don't think there is, sir, replied Fred, "and I ought to know, for I have been supporting the weight all this time by pulling the cord upwards."

You are quite right, Fred; the single movable pulley gives no advantage in direction. At the same time it gives us no means of testing the truth of our statement with respect to the tension in the cord. But we will test it, for all that. You shall pass the free end of the cord over the fixed pulley, suspended from the beam, and after taking care to see that the two parts of the cord are parallel, we will then hang a 1 lb. weight at that end, and leave the machine to take care of itself. The result is proof at once. The 1 lb. force at the end of the cord balances the 2 lbs. weight hanging from the block.

We have already learned that the fixed pulley, from its very nature, gives no advantage in power—a certain weight on one side requires an equal weight on the other to balance it. In other words, the tension of the cord on both sides is the same. But our pulley tells us that the tension of the cord on one side is 1 lb. Therefore the tension of that on the other side is 1 lb. also. The movable pulley gives a mechanical advantage in power. It divides the weight equally between the two parts of the cord. Hence, by using a fixed pulley with a movable pulley we get a double advantage. The movable pulley divides the weight between the two cords, so that only half the force is necessary, and the fixed pulley effects a change in direction downwards. Just one thought more. We will first lower the 2 lbs. weight, and then you shall raise it by pulling the opposite end of the cord down over the fixed pulley. Notice that the distance through which the power end of the cord moves is twice that through which the weight moves. In other words, the weight moves at only half the speed and through half the distance travelled by the power. We see once more that gain in power means loss in speed."