Bill's School and Mine: A Collection of Essays on Education

by William S. Franklin

Sucht erst den Geist heraus zu treiben.

Goethe

We must evidently direct our attention to something simpler than the wind. Let us, therefore, consider the drawing of a wagon or the propulsion of a boat. It is a familiar experience that effort is required to start a body moving and that continued effort is required to maintain the motion. Certain very simple facts as to the nature and effects of this effort were discovered by Sir Isaac Newton, and on the basis of these facts Newton formulated the laws of motion.

The effort required to start a body or to keep it moving is called force. Thus, if one starts a box sliding along a table one is said to exert a force on the box. The same effect might be accomplished by interposing a stick between the hand and the box, in which case one would exert a force on the stick and the stick in its turn would exert a force on the box. We thus arrive at the notion of force action between inanimate bodies, between the stick and the box in this case, and Newton pointed out that the force action between the two bodies A and B always consists of two equal and opposite forces, that is to say, if body A exerts a force on B, then B exerts an equal and opposite force on A, or, to use Newton's words, action is equal to reaction and in a contrary direction.

In leading up to this statement one might consider the force with which a person pushes on the box and the equal and opposite force with which the box pushes back on the person, but if one does not wish to introduce the stick as an intermediary, it is better to speak of the force with which the hand pushes on the box, and the equal and opposite force with which the box pushes back on the hand, because in discussing physical phenomena it is of the utmost importance to pay attention only to impersonal [42] things. Indeed our modern industrial life, in bringing men face to face with an entirely unprecedented array of intricate mechanical and physical problems, demands of every one a great and increasing amount of impersonal thinking, and the precise and rigorous modes of thought of the physical sciences are being forced upon widening circles of men with a relentless insistence—all of which it was intended to imply by referring to the "stress of dryness" which overtakes the little axolotl in his contented existence as a tadpole.

When we examine into the conditions under which a body starts to move and the conditions under which a body once started is kept in motion, we come across a very remarkable fact, if we are careful to consider every force which acts upon the body, and this remarkable fact is that the forces which act upon a body at rest are related to each other in precisely the same way as the forces which act upon a body moving steadily along a straight path. Therefore it is convenient to consider, first the relation between the forces which act upon a body at rest, or upon a body in uniform motion, and second the relation between the forces which act upon a body which is starting or stopping or changing the direction of its motion.

Suppose a person A were to hold a box in mid-air. To do so it would of course be necessary for him to push upwards on the box so as to balance the downward pull of the earth, the weight of the box as it is called. If another person B were to take hold of the box and pull upon it in any direction, A would have to exert an equal pull on the box in the opposite direction to keep it stationary. The forces which act upon a stationary body are always balanced.

Every one, perhaps, realizes that what is here said about the balanced relation of the forces which act upon a stationary box, is equally true of the forces which act on a box similarly held in a steadily moving railway car or boat. Therefore, the forces which act upon a body which moves steadily along a straight path are balanced.

This is evidently true when the moving body is surrounded on all sides by things which are moving along with it, as in a car or a boat; but how about a body which moves steadily along a straight path but which is surrounded by bodies which do not move along with it? Everyone knows that some active agent such as a horse or a steam engine must pull steadily upon such a body to keep it in motion. If left to itself such a moving body quickly comes to rest. Many have, no doubt, reached this further inference from experience, namely, that the tendency of moving bodies to come to rest is due to the dragging forces, or friction, with which surrounding bodies act upon a body in motion. Thus a moving boat is brought to rest by the drag of the water when the propelling force ceases to act; a train of cars is brought to rest because of the drag due to friction when the pull of the locomotive ceases; a box which is moving across a table comes to rest when left to itself, because of the drag due to friction between the box and the table.

We must, therefore, always consider two distinct forces when we are concerned with a body which is kept in motion, namely, the propelling force due to some active agent such as a horse or an engine, and the dragging force due to surrounding bodies. Newton pointed out that when a body is moving steadily along a straight path, the propelling force is always equal and opposite to the dragging force. Therefore, The forces which act upon a body which is stationary, or which is moving uniformly along a straight path, are balanced forces.