# Making sense of Newton’s Laws

You know those moments when something suddenly makes sense, but you’d never known it didn’t until you got it? I guess we could call it an ‘apple insight’! I had one of those with Newton’s Laws a few years back. At that point I don’t think I’d ever read an edublog, let alone written one myself, so it didn’t occur to me to write about and share the new clarity I had gained. I also felt a bit silly that I’d only just really grasped this (given that I studied some degree level physics modules…).  Sitting down to think about teaching Newton’s Laws again, I found myself reliving that moment. This time, I thought I’d share. I hope you find it useful.

I imagine if you’re reading this, you’re probably familiar with Newton’s Laws, certainly in as far as there are three of them and they’re to do with forces. When discussing Newton’s Laws and forces there are some phrases we often use – balanced forces, equal and opposite forces, pairs of forces – but when used loosely and interchangeably across a discussion of Newton’s Laws, confusion can result. I think the key take-away is that “equal and opposite” (Newton’s Third Law) is not the same as “balanced” (Newton’s First Law).

The question which revealed my misunderstanding was this:

My immediate response was, “The reaction force from the table.” However, this is not the answer. My experience in asking others (students and teachers) this question, is that I’m not alone in getting this wrong. In case you answered the same as I did, I will return to this question a bit later.

First, I want to explore the First and Third Laws in turn and think about some of the nuances of the language we use to describe them, and the ‘rules’ I teach students to help them to identify different situations correctly.

Newton’s First Law

An object will remain stationary or continue to move at a constant velocity if the resultant force acting on it is 0 N.

Newton’s First Law considers the forces acting on a single object. In the language we often use – if there is no resultant force, or the forces acting on the object are ‘balanced’, an object will remain stationary or continue to move at a constant velocity. We can break this down into two scenarios which make identifying whether or not we expect an object to move (given the forces acting on it) or to have a non-zero resultant force acting on it (given its motion).

• An object with zero acceleration (stationary or moving at constant speed) will have a resultant force of 0 N acting on it. Put the other way about, an object with a resultant force of 0 N acting on it will be either stationary or moving at a constant speed.
• An object which is accelerating (speeding up, slowing down or changing direction) will have a non-zero resultant force acting on in. Or, if an object has a non-zero resultant force acting on it, it will be accelerating.

Elaborating on this law with these two scenarios gives a framework in which to think about any example of an object and the forces which act up on it. Students can be asked to calculate resultant forces and state whether or not the object would be accelerating, or to identify the forces acting on an object given the knowledge of whether it is moving or at rest. In the latter problems, determining whether a zero or non-zero resultant force is expected before thinking about what forces are present can be helpful.

For example, you might ask students to identify the forces acting on a boat travelling at constant speed. Many will immediately identify the driving force and draw an arrow pointing forward on their diagram, but they stop there. The thought process being, ‘the boat is moving forwards, so the force must be forwards’.

If we have set out the criteria above before giving students this example to think about, we can then question them – Does the boat in your diagram have a resultant force of 0 N? What does this mean the boat must be doing? What does the question say about the boat’s motion? What does this tell you about the resultant force acting on the boat? Think about what other force must be acting (against the driving force) to make the resultant force equal to zero? A series of questions, applying the rules which fall out of Newton’s First Law can really help in developing students’ thinking. It has certainly helped me to think through this type of problem more systematically.

Many examples can be used to draw out and challenge different misconceptions about forces and moving objects. Another one I always explore is that of an object, which has been thrown, as it travels through the air. It’s moving horizontally in one direction, but the only horizontal force acting on it is opposing the motion – this is counterintuitive to most students and they will need to think through the forces very carefully, in stages, to be convinced of it! Read Carole Kenrick’s excellent blog (and watch her @ChatPhysics video) for a full explanation of this example. Gethyn Jones has written about another way of tackling this misconception, through Galileo’s thought experiment, which I think is also really helpful.

Returning to the box on the table…

Imagine I lifted up the box which was sitting on the table, in the problem mentioned earlier, and dropped it. It would fall through the air, accelerating as it fell … until it hit the table. Why did it fall? Why did it accelerate? Why did it stop when it hit the table? Newton’s First Law can answer all of these questions:

The box stops falling when it hits the table because the normal contact force (sometimes described as the reaction force) of the table upwards on the box is the same size and in the opposite direction to the weight of the box which acts downwards. These two forces both acting on the box are equal in size, but opposite in direction so they are ‘balanced’ and the net resultant force acting on the box is zero. The box is stationary. So, the force I identified in the question about Newton’s Third Law force pairs was actually an example of balanced Newton’s First Law forces.

Should we talk about ‘balanced’ forces?

I know I do use this language, and I think it has a place in helping students to grasp the concept, but I’m not sure it’s always helpful. I prefer to talk about a resultant force of zero. My main reason for this is that ‘balanced’ implies a one dimensional scenario with forces of equal size acting in opposite directions, but when we move into two dimensions, diagrams in which the resultant force is 0 N do not always appear that way. A common example is a box on an inclined plane. This situation is often drawn showing the weight, the normal contact force and the frictional force – no two forces are acting along the same line, so seeing that they are ‘balanced’ is more complex. If we use the language of resultant forces, students are more likely to recognise the need to calculate this by resolving forces, rather than concluding (wrongly) that the forces are not ‘balanced’ because the arrows are not equal and opposite.

Newton’s Third Law

When two objects interact with one another they exert equal and opposite forces on each other.

In this case it’s important to notice straight away that the forces are:

• of equal size
• in opposite directions
• acting on different objects
• of the same type

Consider the box falling through the air, it falls because the weight force (acting downwards) is bigger than the air resistance force (acting upwards), resulting in a non-zero downwards resultant force.  Let’s consider the weight. What causes that weight force? It’s due to the gravitational pull of the Earth acting on the mass of the material making up the box. So one object here is the box, the second object interacting with it is the Earth. The Newton’s Third Law pair of forces is in this interaction between these two objects. The Earth pulls the box downwards and the box pulls the earth upwards – both of these forces are due to gravitational attraction.

The magnitude of these forces is equal, they act in opposite directions and on different objects. This is counterintuitive because we see the box falling to earth, but we don’t see the effect of this force on the earth due to it’s much greater mass (a manifestation of Newton’s Second Law, F = ma, which I’m not tackling in this post).

It’s really important to bring these examples involving non-contact forces into our discussion of Newton’s Third Law as it emphasises the point that the forces are acting on different objects – this is very clear from the force diagram. Examples involving contact forces are often used to illustrate this law, and should be for completeness. However, I think misconceptions can be avoided when these are used later, rather than as initial examples. The problem with diagrams involving objects in contact is that it’s often less clear that the ‘equal and opposite’ forces are acting on different objects. For example, the contact force between the box and the table is equal and opposite to that between the table and the box, but the diagram can be ambiguous in making clear that one force acts on the table and the other on the box:

Using two bar magnets can be a helpful way to demonstrate the action of both forces in a pair. If one magnet is held still, it appears to be pulling the other magnet towards itself. But if both magnets are free, it is clear that they are being pulled towards one another as they both move.

In the example above, it’s important to note that the normal contact forces between the box and the table is because of the weight and has the same magnitude as the weight, but in considering Newton’s Third Law force pairs, the weight is paired with the box’s pull on the earth, and the contact force on the table with that of the table on the box. The contact force from the table opposes the weight, resulting in a zero resultant force on the box so that it is stationary (Newton’s First Law), but these are not a Third Law force pair due to acting on the same object (the box) and being of different types.

My favourite example to bring it all together

One problem I like to think through with students is that of a person leaning against a wall. I ask students to identify all the forces acting on the person, and the Third Law paired force for each one. Very often, the force students struggle to identify is the frictional forces between the feet and the ground. However, if that wasn’t present, the wall would ‘push’ the person away – imagine the person standing on a skateboard… This is often another ‘apple insight’ moment in developing students’ understanding. Top: Person leaning on wall, Middle: Forces on person (1st Law – balanced in the first example, but not with the skateboard), Bottom: Third Law Force Pairs (red arrows paired with black ones)

I write this as a non-specialist and am keen to learn from those who know more – if you have any thoughts about what I’ve written – alternative useful examples, suggestions to make the distinction between these laws clearer, different views about when we should use ‘equal and opposite’ and ‘balanced’ to describe forces, or anything which I’ve got wrong, please let me know.

My thanks goes to James de Winter for teaching the excellent SKE Physics course which I completed in 2015 – this was when I first really grasped a lot of the Physics I had previously studied, including Newton’s Third Law.