Episode 212: Newton’s third law of motion

Newton’s third law of motion causes problems to physicists at many levels and it is worthwhile spending a little time developing a clear approach to the concept to avoid confusion in later work.

There are a number of difficulties in teaching this concept:

  • the pervasiveness of its application
  • misconceptions from previous experience
  • the difficulty of a convincing demonstration
  • use of the concept is either trivial or mathematical
  • recognising these difficulties is half the battle; the other half is ensuring that your own understanding is sound!

Summary

  • Discussion: Newton’s third law (15 minutes)
  • Demonstration: The third law (10 minutes)
  • Questions: For discussion or homework (15 minutes)

Discussion: Newton’s third law
Ask the class to state Newton’s third law. Hope that you get the archaic answer: ‘Every action has an equal and opposite reaction’. If you do you can proceed to ask what that statement actually means and ask the students to give examples. This discussion is likely to reveal a number of misconceptions.

Give the law in the form:

‘If body A exerts a force on body B then body B will exert the same force on body A but the force will be in the opposite direction.’ This could be thought of as a ‘law of conservation of force’.

Make sure that the students are clear about the following aspects of a ‘Newton’s third-law pair of forces’:

The two forces act on two different bodies.

  • Both forces are always of the same type (i.e. both gravitational, both electrostatic, etc.)
  • The forces are equal in magnitude
  • The forces are opposite in direction
Book on a table

The example of a book on a table is useful at this point.

Ask about the two forces acting on the book; this will often elicit the response, ‘the weight of the book and the reaction force of the table’. These forces are present but are not a Newton’s third-law pair – they are not the same type of force, and they act on the same object. When you take away the table the weight of the book remains.

There are two Newton pairs here: (i) The pull of the Earth on the book and the pull of the book on the Earth (gravitational forces) and (ii) the push of the book on the table and the push of the table on the book (contact forces). Notice that in each case removing one force makes the other vanish.

The situation may be clarified with the use of a suitable diagram.

It may help to draw up a table of typical Newton pair situations as shown here:

SituationBody ABody BType of force
Satellite in orbit around EarthSatelliteEarthgravitational

Of course, many situations involve more than one Newton pair.

Demonstration: The third law
A very basic demonstration – but how many Newton pairs are there here?

Episode 212-1: Newton’s third law (Word, 39 KB)

Another demonstration might be to show two bar magnets. Choose one that is stronger than the other; demonstrate this by showing that one can lift a greater iron weight than the other.

Ask: If the two magnets attract one another, will one pull more strongly than the other? The answer is, no. You can feel that they pull each other equally. (This is because the force is proportional to the strength of each.)

Car and two magnets

If magnet A pulled magnet B more strongly than B pulled A, you could attach B to the front of your car and lean out, holding A in front. Your car would move effortlessly!

Questions: For discussion or homework
Question 1 is one of the oldest brain teasers in physics and is certainly worth discussing. If your students are competent mathematicians they will enjoy the other question, if not you may prefer to go through them with the class.

Note that some students decide for themselves that Newton’s Third Law is an idealized notion, and that the two forces may not be exactly equal and opposite – this is wrong!

Episode 212-2: Questions on Newton’s third law (Word, 529 KB)

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Episode 212: Newton’s third law of motion (Word, 585 KB)