Newton's Third Law: Some explanations

None of Newton's three fundamental laws of dynamics is so perplexing as the famous third one―the law of action and reaction. Everybody knows it, and some even know how to apply it correctly in certain cases. However, few understand it fully.

Many, with whom the law is discussed, are prepared to admit it is right, however, making a few reservations. They willingly admit that it holds true for stationary objects, but cannot understand how it applies to the interaction of moving bodies. According to the law, for every action there is an equal and opposite reaction.

Consequently, when a horse pulls a cart, it means that the cart is pulling at the horse with the same force. In that case, the cart should stay where it is, isn't it? Nevertheless, it moves. Why don't these forces offset each other, since they are equal?

That is the usual argument raised when this law comes up. Does this mean that the law is wrong? Of course not. It is just that we don't understand it correctly. The forces do not offset each other, simply because they are applied to different bodies―one is applied to the cart and the other to the horse.

The forces are certainly equal, but do equal forces always produce the same action? Do equal forces impart an equal acceleration to all bodies? Does not the action of a force on a body depend on the body itself? And on the value of the 'reaction' which the body offers to the force?

Once you think about it, you will realize immediately why the horse pulls the cart along even though the cart is pulling the horse back with the same force.

The force acting on the cart and the force acting on the horse are of equal magnitude at every moment, but since the cart freely moves on the wheels, while the horse pushes away from the ground, the cart rolls in the direction in which the horse is pulling it.

Furthermore, one must realize that if the cart did not react to the horse's motive power, we would be able to dispense with the horse entirely, as the slightest push would already start the cart rolling. We need the horse to overcome the cart's reaction.

Perhaps, this point will be easily grasped if the law were expressed not so laconically as it usually is―'action is equal to reaction―but as the force of the reacting body is equal to the force of the acting body'.

After all, it is only the forces that are of equal magnitude―the actions of the forces if understood―as they are usually understood―as the translation of a body, are, on the other hand, different as a rule, because the forces are applied to different bodies.

In February 1934, the soviet ship Chelyuskin was crushed in the Arctic. Newton's third law easily explains why. When the ice pressed on the Chelyuskin's hull, the hull pressed back with an equal force.

The disaster occurred precisely because, while the thick ice was able to withstand the pressure without crumbling, the hollow hull succumbed to this force, and was crushed even though it was made of steel.

Even in falling, everybody strictly obeys the law of reaction. An apple falls because it is attracted by the earth's gravity. However, the apple itself attracts the whole planet with exactly the same force. Strictly speaking, the apple and the earth fall towards each other, but their speeds of falling are different.

The equal forces of mutual attraction impart to the apple an acceleration of 10 m/sec square, while to the earth, they impart an acceleration which is as many times less as many times the earth's mass is more than the mass of the apple. Naturally, the earth's mass is an incredible number times greater than that of the apple.

No wonder the earth's movement is so infinitesimally small, that for all practical purposes, it can be considered as nonexistent. Now, you know why we say that the apple falls on the earth, instead of saying that the 'apple and the earth fall towards each other'.