英文科学读本 第六册·Lesson 39 The Inclined Plane

Lesson 39 The Inclined Plane

This morning on my way to school, said Mr. Wilson, "I saw some brewer's draymen unloading great heavy barrels from their wagon, by sliding them down a sort of slanting ladder to the ground. When they had got them to the ground they lowered them into the cellar in the same way. Besides this I saw them raise other barrels, first from the cellar to the ground, and then from the ground to the wagon, by rolling them up the same ladder. This slanting ladder is a machine—very simple, and at the same time very useful. By means of it the men were able to move those heavy bodies with ease from their awkward positions. We call it the inclined plane. Let us see what we can learn about it.

Here is a smooth, polished board. We will lay it on the table, so that it rests in a horizontal position, and then place on it one or two objects, also having a smooth, polished surface. The objects, whatever they are, rest on this horizontal plane, showing no tendency to move. Now we will rest one end of the board on this block of wood. It is a plane still, but, instead of being horizontal, it slopes; it is, in fact, an inclined plane. I want you to notice how the same smooth objects act when we place them on the board now. They, one and all, roll quickly down the slope. We will next change the smooth polished board for one made of rough deal, incline it at the same angle, and place the same smooth objects on it as before. They do not move as quickly now; some of them, indeed, do not move at all, but remain at rest on the slope.

The rough inequalities on the surface cause a rubbing or friction between the objects and the board, and it is this friction that retards the movement of the objects, and actually brings some of them to a standstill. The same things rolled rapidly down the smooth board, because there was less friction. Indeed, in considering the inclined plane, we must for the present think of the surface as being perfectly smooth, so as to cause no friction, although practically this is never quite true. Let us glance for a moment in another direction. The slope of a hill is, of course, an inclined plane. Now, suppose I set one of you boys the task of taking to the top of a hill a load too heavy for you to lift, how would you act? I think, if it were a round body that would roll, you would roll it up the hill; if it were something with a flat surface, such as a box, you would probably attach a rope to it, and drag it up. What kind of hill would present the easier task—one with a steep slope, or one with a gentle slope? You would find it much easier to roll or drag the load up the gentle slope than up the steep one.

I want to show you now the reason for this, and to make clear to you what mechanical advantage the inclined plane gives. Let us return to our smooth, polished plane. I will adjust the plane so as to make its height exactly half the length of its slope, and that will give us an incline of 30°. To the top of the slope a small pulley shall be fixed, and I will attach one end of the cord which passes over the pulley to some smooth object standing on the plane. I have chosen for our object this little toy truck, which runs on smooth, polished wheels; and I have loaded the truck to make it weigh exactly 2 lbs. Now, Fred, you shall hold the cord, while I attach to the other end of it a 1 lb. weight. When that is done we will leave the truck to take care of itself, and we see that the 1 lb. weight is sufficient to balance it on the slope. A half-ounce weight more hung on the cord will make the truck travel up the inclined plane.

We may alter the inclination of the plane now, and we shall find that as we vary the slope so the power will vary. The little truck will not be supported by the same power on different slopes. Thus, if we make the height one-third the length of the slope, the truck will be supported by one-third its weight; if the height be one-fourth the length, it will require only one-fourth its weight to support it. In other words, the longer we make the slope as compared with the height, the greater is the mechanical advantage. It is important to remember that we have made use of the pulley only to enable us to measure the force required. Whether the body be pushed upwards from behind, or pulled up by means of a cord, the force necessary to accomplish it is the same in each case.

We will next glance at a few practical applications of the inclined plane. We have already had something to say about the drayman's ladder. Next time you see one, notice how smooth its working surfaces are. You are now prepared, of course, to tell what kind of ladder is most advantageous to him—a long or a short one—and to give your reasons for what you say.

We often see an inclined plane used for transferring a great block of stone into a cart. The rough surface of the stone, in addition to its weight, would, however, prevent it from moving even on the inclined plane. Hence, in order to overcome some of the friction, three or four rollers are placed under the block, and, as these roll forward, they carry the block with them, the hindmost one being transferred to the front from time to time, as it is disengaged. In the construction of bridges a great deal of thought and care must be given to the length of the approaches on either side. These approaches slope upwards towards the middle of the bridge, and the slope must be made sufficiently long in comparison with the height, so as not to cause too great a strain on the horses which will have to draw heavy loads over the bridge.

The horse travels with its burden along a level road with comparative ease, because the weight rests upon the wheels of the cart, and it has only to overcome the friction between the wheels and the rough surface of the road. As soon, however, as it begins to mount a hill, the weight is thrown behind the wheels, and there is now, in addition to the friction, another force to contend against, namely, the force of gravity, due to the weight of the load, and it is plain that this must increase with the increase of the slope. The road up a steep hill is, for the same reason, usually made to wind round and round the hill, in order to give a longer slope, and so render the ascent easy."