This episode concerns Newton’s second law. Your students will probably have met the second law in the form F = ma; many will have performed experiments to demonstrate the law. It is therefore useful to approach the experimental demonstration of the law as an exercise in data gathering and analysis. Using a simple set of apparatus should allow students to work individually or in pairs and critically consider the limits of the experiment as well as re-familiarizing themselves with the second law.

Lesson Summary

• Discussion: Revision of kinematics (10 minutes)
• Student investigation: Relationship between acceleration and force (30 minutes)
• Discussion: Looking at the results (10 minutes)
• Student questions: Using Newton’s second law (30 minutes)

Discussion: Revision of kinematics

Before embarking on the main activity it is useful to run through the equations of motion (the SUVAT equations) once again so that students will understand the recipe they use to calculate acceleration. You want to establish that by referring to the equation s = ut + 12at² the acceleration of a body travelling distance from rest is given by a = 2 st²

Student experiment: Relationship between acceleration and force

In this experiment, a trolley is accelerated by weights which are hanging on the end of a string which passes over a pulley.

It is important to note that the mass which is being accelerated includes the mass of the weights on the end of the string.

After the preliminary discussion the students should be able to tackle this without too many difficulties. The questions at the end of the section are best attempted after the apparatus is cleared away and the students have drawn the graphs. You can use their responses as a basis for a plenary session in which further discussion of sources of error (timing – more difficult for shorter time intervals, non-uniform acceleration etc).

Episode 211-1: Effect of force & mass on acceleration of an object (Word, 45 KB)

Discussion: Looking at the results

Discuss your students’ results:

Do they find that acceleration is proportional to force, and inversely proportional to mass?

Numerically, are their results consistent with the equation F = m × a?

You may wish to point out that the experiment can only show proportionality. In other words, we can only conclude that

F = k  ×  m × a , where k is a constant. In the SI system of units, we choose k = 1. This defines the Newton: 1 N = 1 kg m s^-2.

Student questions: Using Newton’s second law

Make a selection from these questions: cut out those you think may be too trivial for some, and others (using resolved forces) which may confuse weaker students even though the concepts have already been covered. You may wish to reserve some of the questions for later use.

Episode 211-2: Newton’s second law (Word, 25 KB)

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!

Lesson 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

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.

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.)

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)