Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• draw on what pupils have learned about drawing arrows to represent forces
• reactivate their knowledge about resultant forces and natural motions

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How to:

• separate arrows representing force from arrows representing movement
• develop a good exposition of terminal speed
• describe situations where the resultant force is equal to 0

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

Preliminary ideas

Before looking at the relationship between forces and speed it is important for pupils to understand clearly that:

• Several forces can act on an object at the same time.
• Equal forces acting in opposite directions add to zero.
• Stationary objects (at rest) have a resultant force equal to zero.

These ideas were covered in the SPT: Forces topic.

Constant speed is a result of no resultant force

Wrong Track: It's obvious! I've got to push here to keep it going at a constant speed. That's all that's needed, my push at the back.

Right Lines: For an object to move with constant speed the forward force is opposed by the effects of retarding forces. There is no resultant force acting.

Explaining the role of friction

Thinking about the learning

The common line of thinking that takes pupils down the Wrong Track here is that a constant push is all that is needed to keep an object moving at a constant speed. In the world around us few objects move at a constant speed for any extended period of time. A pupil's everyday experience is more commonly of changing speed. We also live in a world where all motion is influenced by friction. However, pupils are so accustomed to the effects of friction that it is easy for them to take friction for granted, or to ignore it altogether.

Whether pupils are skateboarding, cycling or travelling in a car or bus, they know that when the driving force is removed the motion slows down and eventually stops. So it is natural and common sense to assume that a driving force must be present to act on any moving object to keep it moving. In the real world of friction this idea is correct, but the crucial point is that the driving force is not the only force acting. The driving force is opposed by the retarding forces.

Thinking about the teaching

When thinking about objects moving at constant speed it is very helpful to consider how they got to that speed in the first place. It is important to separate the initial force which started the motion from any subsequent forces which might be present to maintain the motion.

To start something moving there is the need for a force, acting for a period of time, which is often called an impulse. For example, you provide an impulse to a boat as you push it away from the jetty. The impulse lasts for just as long as you are in contact with the boat.

Once moving, if there is no friction, then the object will continue to move at a constant speed unaided. Where friction is present there will be a need for a driving force to maintain the motion. The driving force balances the effect of friction. When this happens, there is no resultant force acting on the object, but this doesn't mean that there are no forces at all.

Newton's first law

Imagine taking your worst enemy in a space craft to get rid of them in the farthest corner of the universe (way beyond Sunderland). On arrival at the farthest corner, you open the cargo-hold of the space craft, position your worst enemy on the edge of the decking and give them a gentle nudge out into space. The nudge is just sufficient to send them drifting away from the craft. As they travel away they neither speed up nor slow down, since there are no forces acting upon them. As they drift away into blissful eternity, never to be seen again, you muse on the fact that their motion is a stunning validation of Newton's first law.

Champion of constant speeds

A science teacher colleague, when talking about forces that add to zero and constant speed, always boasts to his class that he is a world champion in achieving constant speeds. The build-up to his claims of special expertise is so great that the pupils are soon clamouring to find out what he does to achieve these constant speeds, neither speeding up… nor slowing down.

And so the story goes:

Teacher: Well first of all I jump into my car and drive up onto the M62 motorway. Then I get into the outside lane and accelerate up to 70 miles per hour. Once at 70 mph, if the air resistance increases, and I start slowing, I gently press my foot down on the accelerator to increase the driving force. If I start speeding up, I think driving force greater than air resistance and I take my foot off the accelerator slightly to bring the forces back in line. It's such fun driving the car and keeping those forces in balance!

If my colleague is having a really good day, he goes further by claiming that he can also achieve constant speeds with pencil cases. With further great build-up he gets the class around a bench, borrows a pencil case and pushes the case at a constant speed across the surface.

Teacher: Ooops, just a little too much on the pushing side there, keep the push equal to the friction. Just look at that! Steady speed with no resultant force!

Amazingly his classes seem to enjoy these antics.

Just a little bigger

Wrong Track: If it's moving, the forward force must be just a little bit bigger than friction, to keep it going.

Right Lines: If an object is moving at constant speed the forward force must exactly equal the friction forces acting in the opposite direction.

Resultant forces for changing motion

Thinking about the learning

Pupils can sometimes hang onto inconsistencies when talking about constant speed. Thus some pupils may accept that the forces must add to zero for stationary objects, whilst arguing that in the case of objects moving at constant speed the driving force must be at least a little bit bigger than the friction forces. This line of thinking goes back to the idea that an object remains stationary if the forces acting on it add to zero. Intuitively then, since the object is moving, the force acting in one direction must, they argue, have an advantage.

Thinking about the teaching

When confronted with this kind of learning challenge go back to thinking about how the object got started moving in the first place. While initially the driving force must have been bigger than the retarding force in order to start the object moving in one direction (see episode 02), when the two forces add to zero the object travels at a constant speed, neither speeding up nor slowing down.

Drag forces and gravity forces add to zero

Wrong Track: As things fall they must keep speeding up because gravity pulls them down.

Right Lines: On Earth, all falling objects move through the atmosphere. The resulting movement through the air creates a frictional force which acts against the motion. Objects reach a constant speed when the upward force equals the downward force of gravity.

Demonstrating terminal speed

Thinking about the learning

The point here is for pupils to appreciate that objects speed up or accelerate as they fall under the influence of gravity, but also to recognise that they may achieve a constant terminal speed because of the effects of retarding forces.

Pupils know that you cannot take away or reduce the gravity force and therefore tend to assume that a falling object speeds up continuously. Furthermore, within the limits of pupil experience few falling objects reach a constant speed.

Thinking about the teaching

To move pupils onto the right lines you might set up some laboratory demonstrations to illustrate terminal speed. These might include objects falling in a tall column of water or low density objects such as polystyrene balls in free-fall.

There's a good chance you could improve your teaching if you were to:

Try these

• making stronger and continuous links to work on forces
• emphasising the counter-intuitive nature of Newtonian natural motion

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• drawing similar arrows for those representing forces and those representing movement
• speaking of balanced forces—prefer the resultant force is equal to 0

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.