Force is the action of objects on objects, so forces appear in pairs.There are force objects and force objects.Two objects interact in different forms, such as attractionrelative motionThe force generated by deformation is called force.
Newton's Third Law(Newton's third law), inclassical mechanicsWhen two objects interact, the force exerted on each other is equal in magnitude and opposite in direction.powerIt will appear in pairs: one of the forces is called "force";The other force is called "reaction force"（LatinActio and reactio), also known as "resistance";The two forces are equal in magnitude and opposite in direction.The distinction between them is purely arbitrary;Any force can be considered as a force, and its corresponding force naturally becomes the accompanying reaction force.The paired force and reaction force are called "pairing force".
The third law is expressed as
Among them,
Is the force exerted by object B on object A,
Is the force exerted by object A on object B.[1]
Two versions
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The law of action and reaction can be divided into two versions: the strong version and the weak version.Here, the third law describes the "weak version of the law of action and reaction".The "strong version of the law of action and reaction", in addition to the requirements of the weak version of the law of action and reaction, also requires that the force and reaction act on the samestraight lineOn.Universal gravitationAndstatic electricityAll forces obey the strong law of action and reaction.However, in some cases, the force and reaction force are not the same line (the line connecting the two action points).For example, twoTranslational motionOfchargeThe translation speed is the same, but it is not perpendicular to the line of two chargesBiot Savart point charge lawAndLorentz forceThe force and reaction force calculated by the law are not in the same line.This force only obeys the weak version of the law of action and reaction.For example, suppose twoTranslational motionIf the moving speed of the charges is perpendicular to each other, the electromagnetic forces they feel do not comply with the weak version of the law of action and reaction.[1]
Newton's exposition
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Each force corresponds to a reaction force of equal resistance: that is, the force exerted by two objects on each other is always equal in magnitude and opposite in direction.
Figure 1. Schematic diagram of Mala stone case
Newton used the example of horse pulling stone to explain.If the stone is dragged by a horse, the horse will be dragged by the stone in the same way, because the tension imposed on the horse by the rope that ties the horse and the stone at both ends
Dragging from the stone tends to pull the horse towards the stone, just like the tension it exerts on the stone
The drag from the horse tends to pull the stone towards the horse
It will hinder the horse's dragging, just like force
It will push the stone forward.
Since the horse and stone drag each other equally, why do the horse and stone move in the direction of the horse (called the front), rather than the direction of the stone (called the rear)?This is because the horse and stone have moved forward at a uniform speed, and the stone feels the tension from the horse
It happens to offset the friction encountered by the stone
(towards the rear), i.e
There is no resultant force to accelerate or decelerate, and the horse feels the tension from the stone
It also happens to offset the friction force exerted by the ground on the horse
(towards the front),
The resultant force is also zero, so the horse and the stone will still move at a uniform speed in the direction of the horse.be aware
And
Not a pair of forces and reactions;
Friction force imposed on the ground by the horse
It is a pair of force and reaction force.similarly,
And
Not a pair of forces and reactions;
Friction force imposed on the ground by the horse
It is a pair of force and reaction force.
Assume that at the beginning, the horse and the stone are in a static state, and the stone feels the tension from the horse
Greater than the friction force encountered by the stone
, i.e
, the resultant force felt by the stone
Will make the stoneAcceleration motion。The relationship between the inertial force generated by this acceleration movement and the resultant force is equal in magnitude and opposite in direction.
Newton then talked aboutcollisionQuestion.Suppose that object A collides with object B and changes the motion of object B, then object A will also change its motion in the opposite direction.The corresponding motion changes of the two objects caused by the collision, assuming that no other external force is involved, the change of their momentum is equal, rather than the change of their speed.Since the momentum of two objects changes, their size is equal and their direction is opposite, so the speed change of each object is inversely proportional to the mass.
Newton deduced from the third lawMomentum conservation。However, according to the theory of advanced physics, the conservation of momentum is more fundamental than the third law (applicationNott's theorem, the conservation of momentum can be derived from the Galilean invariance).The more general conservation of momentum does not depend on Newton's laws.
In order to prove the correctness of the third law, Newton came up with an experiment.Suppose a spacer C is placed between two objects A and B that attract each other to prevent objects A and B from gathering together.If any one of object A or object B feels a greater attraction, for example, if the attraction felt by object A is greater than that felt by object B, object A will exert a greater pressure on isolator C than the pressure exerted by object B on isolator C.Therefore, the isolator C will not be in equilibrium. It will move together with objects A and B in the direction of object B, and will always move with acceleration.This result violates the first law.According to the first law, if no external force is applied, the motion speed of the object will not change.Therefore, the pressure exerted by objects A and B on isolator C should be equal in size and opposite in direction;The attraction that objects A and B exert on each other should also be equal in size and opposite in direction.
It is not difficult to do the experiment.Newton willMagnetiteAnd iron blocks were put into two boats floating on the water.Due to the attraction between the magnet and the iron block, the two boats attract each other and collide with each other to reach a balanced static state.In this way, Newton confirmed the correctness of the third law.[2]
Pairing power
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According to the third law, force is the interaction between objects,powerIt must appear in pairs: one of the forces is called "force";The other force is called "reaction force"（LatinactioAndreactio), also known as "resistance";The two forces are equal in magnitude and opposite in direction.The distinction between them is purely arbitrary;Any force can be considered as a force, and its corresponding force naturally becomes the accompanying reaction force.The paired force and reaction force are called "pairing force" or "third law pairing force".The third law is also called "the law of action and reaction".[3]
Wrong and correct basic physical concepts
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When two objects interact, the force exerted on each other is equal in magnitude and opposite in direction.
Here, it must be clear that the reaction force is applied to another object, not to the object that feels the force.For example, suppose that objects A and B impose on each otherUniversal gravitationOn the other side, when object A exerts an attraction on object B (force), object B also exerts an attraction on object A (reaction force of equal size and opposite direction).
Another point: the physical essence of the reaction force and the action force is identical.If the essence of force is gravity, then the essence of reaction force is also gravity.If the physical nature of force and reaction is different, this analysis must be incorrect;This incorrect analysis cannot be accepted.
Correctly analyze examples
Aroundsunlight，earthFollow the track.This is because the earth feels the universal gravitation (force) of the sun.Here, the role of the force iscentripetal force, attracting the earth near the sun.At the same time, the sun feels the gravity (reaction force) of the earth, which is equal to the force and opposite to the direction (here, it attracts the sun to move towards the earth).Because of the sunqualityIt is larger than the earth, and it seems that the attraction of the earth has no effect on the sun;In fact, the sun is affected by the earth.A correct description of the common motion of these two celestial bodies (ignoring all other celestial bodies) is that they all follow orbits around the center of mass of the whole system.
Think of a shot put, suspended at the end of a (inextensible) wire rope.The other end of the cable is fastened to the ceiling of the laboratory.Because of gravitation, the shot is attracted by the earth.The corresponding reaction force is the gravity exerted by the shot put on the earth: this has nothing to do with the steel cable;In fact, even in the absence of wire rope, the reaction force still exists.On the other hand, if thetensionPull the shot up to prevent it from falling, and the shot will also pull the wire rope with tension, which is equal in size and opposite in direction.If, for the ceiling, this simple system is static (absolutely no acceleration), according toNewton's first law, felt by shot putResultant external forceIt is equal to zero, and this external force is the vector sum of two different forces (the gravity of the earth and the tension of the steel cable).These two forces are equal in magnitude and opposite in direction;In other words, they complement each other.However, this does not mean that they are a pair of forces and reactions, they are not a pair of forces and reactions.
In order to check whether the interpretation of these concepts is correct, the wire rope can be changed toSpring。If the new system is initially static (relative to the laboratory reference system).The previous analysis is also suitable.But if the system feelsPerturbation(For example, if the shot is pushed or pulled slightly), the shot will start to vibrate up and down.Due to the acceleration, according toNewton's first law, the resultant external force is not equal to zero.However, the quality of shot put and the earth has not changed;The distance between the shot and the earth's center of mass is almost the same.Therefore, the force and reaction force derived from gravity remain unchanged.The difference is that the system has becomepowerSystem, the universal gravitation felt by the shot temporarily andelastic forceOut of balance.The magnitude and direction of the elastic force change with time (the vibration frequency law is related to the spring constant of the spring).The elastic force is linear with the change of spring length.[4]
Example of error analysis
The third law is often stated in a simple, incomplete or incorrect sentence:
These sentences do not clearly state that,ForceAndReaction forceIt is applied to different objects.It is not because the two forces happen to be equal in size and opposite in direction that they can automatically form a "force reaction" force pair that conforms to the third law.
