# Reaction (physics)

w: Reaction (physics)

As described by the third of Newton's laws of motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first.[1] The third law is also more generally stated as: "To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."[2] The attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can be considered the action, while the other is its associated reaction.

## Examples

### Interaction with ground

When something is exerting force on the ground, the ground will push back with equal force in the opposite direction. In certain fields of applied physics, such as biomechanics, this force by the ground is called 'ground reaction force'; the force by the object on the ground is viewed as the 'action'.

When someone wants to jump, he or she exerts additional downward force on the ground ('action'). Simultaneously, the ground exerts upward force on the person ('reaction'). If this upward force is greater than the person's weight, this will result in upward acceleration. When these forces are perpendicular to the ground, they are also called a normal force.

Likewise, the spinning wheels of a vehicle attempt to slide backward across the ground. If the ground is not too slippery, this results in a pair of friction forces: the 'action' by the wheel on the ground in backward direction, and the 'reaction' by the ground on the wheel in forward direction. This forward force propels the vehicle.

### Gravitational forces

The Earth orbits around the Sun because the gravitational force exerted by the Sun on the Earth, the action, serves as the centripetal force that maintains the planet in the neighborhood of the Sun. Simultaneously, the Earth exerts a gravitational attraction on the Sun, the reaction, which has the same amplitude as the action and an opposite direction (in this case, pulling the Sun towards the Earth). Since the Sun's mass is very much larger than the Earth's, it does not appear to be reacting to the pull of the Earth, but in fact it does. A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass of the combined system.

### Supported mass

Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight. The corresponding 'reaction' is the gravitational force that mass exerts on the planet.

If the object is supported so that it remains at rest, for instance by a cable from which it is hanging, or by a surface underneath, or by a liquid on which it is floating, there is also a support force in upward direction (tension force, normal force, buoyant force, respectively). This support force is an 'equal and opposite' force; we know this not because of Newton's Third Law, but because the object remains at rest, so that the forces must be balanced.

To this support force there is also a 'reaction': the object pulls down on the supporting cable, or pushes down on the supporting surface or liquid. In this case, there are therefore four forces of equal magnitude:

• F1. gravitational force by earth on object (downward)
• F2. gravitational force by object on earth (upward)
• F3. force by support on object (upward)
• F4. force by object on support (downward)

Forces F1 and F2 are equal because of Newton's Third Law; the same is true for forces F3 and F4. Forces F1 and F3 are only equal if the object is in equilibrium, and no other forces are applied. This has nothing to do with Newton's Third Law.

### Mass on a spring

If a mass is hanging from a spring, the same considerations apply as before. However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's second law that a net force is responsible for the observed change in velocity. The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F1 and F3 are no longer equal.

However, it is still true that F1 = F2 and F3 = F4, as this is required by Newton's Third Law.

### Causal misinterpretation

The terms 'action' and 'reaction' have the unfortunate suggestion of causality, as if the 'action' is the cause and 'reaction' is the effect. It is therefore easy to think of the second force as being there because of the first, and even happening some time after the first. This is incorrect; the forces are perfectly simultaneous, and are there for the same reason.

When the forces are caused by a person's volition (e.g. a soccer player kicks a ball), this volitional cause often leads to an asymmetric interpretation, where the force by the player on the ball is considered the 'action' and the force by the ball on the player, the 'reaction'. But physically, the situation is symmetric. The forces on ball and player are both explained by their nearness, which results in a pair of contact forces (ultimately due to electric repulsion). That this nearness is caused by a decision of the player has no bearing on the physical analysis. As far as the physics is concerned, the labels 'action' and 'reaction' can be flipped.

### 'Equal and opposite'

One problem frequently observed by physics educators is that students tend to apply Newton's Third Law to pairs of 'equal and opposite' forces acting on the same object.[3][4] This is incorrect; the Third Law refers to forces on two different objects. [ha 1] For example, a book lying on a table is subject to a downward gravitational force (exerted by the earth) and to an upward normal force by the table. Since the book is not accelerating, these forces must be exactly balanced, according to Newton's First or Second law. They are therefore 'equal and opposite'. However, these forces are not always equally strong; they will be different if the book is pushed down by a third force, or if the table is slanted, or if the table-and-book system is in an accelerating elevator. The case of three or more forces is covered by considering the sum of all forces.

A possible cause of this problem is that the Third Law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, without the details, namely that these forces act on two different objects. Moreover, there is a causal connection between the weight of something and the normal force: if an object had no weight, it would not experience support force from the table, and the weight dictates how strong the support force will be. This causal relationship is not due to the Third Law but to other physical relations in the system.

### Centripetal and centrifugal force

Another common mistake[original research?]

is to state that

The centrifugal force that an object experiences is the reaction to the centripetal force on that object.

If an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force, the resultant force would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames.

## Proverbs

영어 속담 문장 형식
A bad workman always blames his tools.
서툰 일꾼이 늘 탓한다 / 자기 연장을
SVO
A bird in the hand is worth two in the bush.
한마리 새는 [손안의] 가치가 있다 / 두마리 [숲속의]
SVC
A chain is no stronger than its weakest link.
사슬은 더 튼튼하지 않다 / 가장 약한 고리보다
SVC
Actions speak louder than words.
행동은 말한다 [더 큰소리로 / 언어보다]
SVC

No news is good news.
무소식이 희소식
SVC
Pride comes before a fall.
자랑은 온다 / 망신 전에
SV

Strike while the iron is hot.
때려라 (쇠를) / 쇠가 뜨거울 때
SVO SVC
Talk is cheap.
말은 값싸다.
SVC
The pen is mightier than the sword.
펜은 더 강하다 / 칼보다
SVC
The spirit is willing but the flesh is weak.
정신은 의욕적이지만 육체는 약하다
SVC SVC
The squeaky wheel gets the grease.
삐걱거리는 바퀴가 먹는다 / 그리스를
SVO

When in Rome do as the Romans do.
로마에 있을 때는 하거라 / 로마 사람들이 하듯
SV SV SV
You can't teach an old dog new tricks.
너는 가르칠 수 없다 / 늙은 개에게 새 재주를
SVOO
You can lead (take) a horse to water but you can't make it drink.
그대는 데려갈 수는 있다 [말을 물가로] 그러나 그대는 할 수 없다 [그것이 물을 마시게는]
SVO SVOC
You scratch my back and I'll scratch yours.
그대가 긁으면 [내 등을] 나는 긁으리 [그대 등을]
SVO SVO

## References

• Feynman, R. P., Leighton and Sands (1970) The Feynman Lectures on Physics, Volume 1, Addison Wesley Longman, ISBN 0-201-02115-3.
• Resnick, R. and D. Halliday (1966) Physics, Part 1, John Wiley & Sons, New York, 646 pp + Appendices.
• Warren, J. W. (1965) The Teaching of Physics, Butterworths, London,130 pp.

# Footnotes

1. Suppose you either elongate or compress a coil spring with two hands. Then a pair of two 'equal and opposite' forces act on just one thing by your hands, one of which should be 'action' while the other 'reaction', regardless of which is first. In this very case of not 'two things' but 'one thing', acted and reacted upon, should we never subscribe to Newton's 3rd law, as originally built on 'two things'?

Although the resulting 'net force' may be zero-sum, cancelling each other, the said pair of forces did work indeed anyway by making the spring either longer or shorter, while innately building up a definite elasticity, that is, restoring force or energy hidden within, as hard to prove as Yin. Yet zero-sum games work!

Perhaps more fortunate is the above case that there is anyway something to be acted and reacted upon. In contrast, suppose a rocket flying in a gravity-free state. There is nothing to be acted and reacted upon. The rocket acts on nothing, but just flies opposite to its jet.

Who pushes it? No one but just the reaction (as Yin) to its jet action (as Yang)!

References
1. Taylor, John R. (2005). Classical Mechanics. University Science Books. pp. 17–18. ISBN 9781891389221.
2. This translation of the third law and the commentary following it can be found in the "Principia" on page 20 of volume 1 of the 1729 translation.
3. Colin Terry and George Jones (1986). "Alternative frameworks: Newton's third law and conceptual change". European Journal of Science Education 8 (3): 291–298. doi:10.1080/0140528860080305. Retrieved 2013-10-26. "This report highlights some of the difficulties that children experience with Newton's third law."
4. Cornelis Hellingman (1992). "Newton's Third Law Revisited". Physics Education 27: 112–115. doi:10.1088/0031-9120/27/2/011. Retrieved 2013-10-26. "... following question in writing: Newton’s third law speaks about ‘action’ and ‘reaction’. Imagine a bottle of wine standing on a table. If the gravitational force that attracts the bottle is called the action, what force is the reaction to this force according to Newton’s third law? The answer most frequently given was: ‘The normal force the table exerts on the bottle’."