Reaction (physics)

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In classical mechanics, Newton's third law states that forces occur in pairs, one called the action and the other the reaction (actio et reactio in Latin). Both forces are equal in magnitude and opposite in direction. The distinction between action and reaction is purely arbitrary: anyone of the two forces can be considered an action, in which case the other (corresponding) force automatically becomes its associated reaction.

Contents 1 Discussion 2 Examples of correct interpretations 3 Examples of common misunderstandings 4 References

[edit] Discussion

The reaction is one of the least understood of the basic physical concepts, perhaps because it is often poorly taught or incorrectly described in many publications (including in textbooks), or because Newton's laws of motion may appear counter-intuitive (see that article for a historical perspective or a statement of all three laws). Here is a modern statement (in words only) of the Third Law of motion:

If a force acts on a body, then an equal and opposite force must act upon another body

It is essential to understand that the reaction applies to another body than the one on which the action itself applies. For instance, in the context of gravitation, when object A attracts object B (action), then object B simultaneously attracts object A (with the same intensity and an opposite direction).

Another important point to keep in mind is that the physical nature of the reaction force is identical to that of the action itself: if the action is due to gravity, the reaction is also due to gravity. Hence, any discussion of this topic that amounts to a claim that an action results in a reaction of a different type (gravitational, electromagnetic, friction, spring, or whatever) is obviously wrong and should be discarded.

[edit] Examples of correct interpretations

1. The Earth orbits around the Sun because the gravitational force exerted by the Sun on the Earth (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 (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.
2. Consider a mass hanging at the end of a (non-stretchable) steel cable attached to the ceiling of the laboratory. The mass is pulled towards the Earth (action) by its weight. The corresponding reaction is the gravitational force that mass exerts on the planet: this has nothing to do with the steel cable; in fact, the reaction exists even in the absence of the cable. On the other hand, if the tension in the cable is pulling the mass upwards and preventing it from falling, then the mass is simultaneously pulling on the cable, with equal intensity and opposite direction. If this simple system is observed to be at rest (in particular not accelerated) with respect to the ceiling, Newton's first law implies that no net force is applied to the mass. Since we have just seen that two distinct forces do apply to the mass (the gravitational pull from the Earth and the tension from the cable), we conclude that these two forces are themselves equal and opposite, i.e., that they compensate each other. However, these latter two forces are not the action and the reaction of each other.
3. To verify the correct interpretation of these concepts, let's replace the cable by a spring, and consider the same system initially at rest (again with respect to the ceiling of the laboratory): the same considerations apply. 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 first law that a net force is responsible for the observed change in velocity. Yet, the gravitational action and reaction remain the same, since the masses involved have not changed, and the distance between the center of mass of the object and the center of mass of the Earth is modified so slightly that any variation in the gravitational force is immeasurably small. What has occurred is that we now have a dynamic system where the (constant) gravitational force on the mass is temporarily out of balance with the (variable) tension in the spring. The latter changes intensity and direction in time (at a frequency that is related to the strength of the spring), depending (in first approximation, and for small perturbations) on the deviation of the length of the spring with respect to its 'natural' length (i.e., in the absence of a mass).

[edit] Examples of common misunderstandings

• Newton's third law is frequently stated in a simplistic but incomplete or incorrect manner through statements such as

Action and reaction are equal and opposite

To every action there is an equal and opposite reaction

These statements fail to make it clear that the action and reaction apply to different bodies. Also, it is not because two forces happen to be equal in magnitude and opposite in direction that they automatically form an action-reaction pair in the sense of Newton's Third Law.

• Action and reaction are often confused with the issue of equilibrium. For example, consider the following statement:

A book standing still on a table is at rest because its weight, a force pulling it downwards, is balanced by the equal and opposite reaction of the table, a force pushing it upwards.

As stated, this is not an instance of the Third Law, nor an example of a reaction, since both forces invoked are applied to the book: one cannot be the reaction to the other, since they must apply to different bodies. In any case, the table and the book are not at rest (in any inertial frame of reference), and being at rest is irrelevant in the context of the Third Law. Note also that the concept of weight itself is often misunderstood.

• Another very common mistake is to state that

The centrifugal force is the reaction to the centripetal force.

Clearly, if an object were simultaneously subject to both a centripetal 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 pseudo force, to underscore the fact that such a force only appears when calculations or measurements are taking place in non-inertial reference frames.

[edit] 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.