The motion of all macroscopic objects surrounding us is described using the so-called three Newton laws. In this article we will not say anything about the first two of them, but consider in detail the third Newton's law and examples of its manifestation in life.
The wording of the law
Each of us noticed that when jumping on any surface, she seemed to “hit” our legs, or if we take the wheel of a bicycle, it begins to put pressure on our hands. These are all examples of Newton’s third law. In a physics course in secondary schools, it is formulated as follows: any body that exerts a force on some other body experiences a similar effect from the latter, directed in the opposite direction.
Mathematically, this law can be written as follows:
F 12 ¯ = -F 21 ¯
On the left side of the equation is written the force with which the first body acts on the second, on the right side there is a similar modulo force with which the second body acts on the first, but in the opposite direction (therefore, a minus sign appears).
The equality of the modules and the opposite direction of the considered forces led to the fact that this law is often called the interaction, or the principle of influence-reaction.
The action on various bodies is a key point of the law in question.
Looking at the above formula, one might think that since the forces are equal in absolute value and opposite in direction, then why should they be considered at all, because they cancel each other out? This judgment is erroneous. The proof of this is a huge number of examples of Newton’s third law from life. For example, a horse pulls a cart. According to the law under consideration, the horse acts on the cart, but with the same force, the horse acts in the opposite direction on the animal. Nevertheless, the entire system (horse and cart) does not stand still, but moves.
The above example shows that the principle of action-reaction under consideration is not as simple as it seems at first glance. The forces F 12 ¯ and -F 21 ¯ are not canceled, since they are applied to different bodies. The horse does not stand still, although the cart prevents this, only because another force acts on its hooves, which seeks to convey acceleration to the animal - this is the effect of the earth's surface (support reaction).
Thus, when solving problems on the 3rd Newtonian principle, one should always consider the forces that act on individual specific bodies, and not on the entire system at once.
Connection with the law of conservation of momentum
The third Newtonian law is essentially the reason for maintaining the momentum of the system. Indeed, let us consider one interesting example of Newton’s third law - the motion of a rocket in outer space. Everyone knows that it is carried out due to jet propulsion. But where does this craving come from? A missile carries tanks with fuel, such as kerosene and oxygen, on board. During combustion, the fuel leaves the rocket and flies at high speed into outer space. This process is characterized by the effect of burnt gases on the rocket body, the latter has an effect on gases with a similar force. The result is the acceleration of gases in one direction, and rockets in the other.
But this problem can also be considered in terms of conservation of momentum. If we take into account the signs of gas and rocket velocities, then the total momentum will be equal to zero (it was like that before the fuel was burned). The impulse is preserved only because the forces acting according to the principle of action-reaction are internal, existing between the parts of the system (rocket and gases).
How is the principle under consideration related to the acceleration of the entire system?
In other words, how will the forces F 12 ¯ and -F 21 ¯ change if the system in which they arise moves faster? Consider the example of a horse and cart. Suppose the whole system began to increase its speed, but the forces F 12 ¯ and -F 21 ¯ remain unchanged. Acceleration occurs due to an increase in the force with which the surface of the earth acts on the hooves of the animal, and not due to a decrease in the reaction force of the cart -F 21 ¯.
Thus, the interactions within the system are independent of its external state.
Some life examples
“Give examples of Newton’s third law” - this task can often be heard from school teachers. The examples with a rocket and a horse have already been given above. In the list below, we list a few more:
- pushing the swimmer away from the pool wall: the swimmer gains acceleration because the wall affects him;
- bird flight: pushing the air down and back with each flap of the wing, the bird receives a push from the air up and forward;
- rebound of a soccer ball from the wall: manifestation of counteraction of the reaction force of the wall;
- Earth's attraction: with what force our planet pulls us down, with exactly the same we act on it upward (for the planet it’s a tiny force, it “does not notice” it, and we do).
All these examples lead to an important conclusion: any force interactions in nature always arise as a pair of opposing forces. It is impossible to influence an object without having experienced its opposition.