## Episode 211: Newton’s second law of motion

Lesson for 16-19

- Activity time 80 minutes
- Level Advanced

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* = *u**t* + 12*a**t*^{ 2} the acceleration of a body travelling distance from rest is given by
*a* = 2 *s**t*^{ 2}

#### 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)