Units for speed

Wrong Track: 60 km/h is faster than 40 mph 'cos it's bigger.

Right Lines: A speed has two parts, a value and a unit. Speeds are much easier to compare if they have the same unit.

Converting units

Thinking about the learning

A car travelling at 60 must be going faster than a car travelling at 40.

This kind of statement is very common and reflects what we see around us. Speed limit signs are 30 or 50 with no attention paid to units.

Of course bigger numbers give a bigger message. A younger child offered the choice between 100 pence or one pound might be seduced by the larger number of pence into thinking that it was somehow worth more. In this example, pence and pounds are examples of two different units of measurement. There is a conversion factor between them (100 p is £1).

And so it is with speed. However, in the 60 kilometre / hour and 40 mph example it is not altogether obvious which of the two speeds mentioned above is greater. In fact they are almost the same speed, quoted in different ways.

Thinking about the teaching

A car travelling at 60 kilometre / hour will be going faster than a car travelling at 40 kilometre / hour.

However, a car travelling at 60 kilometre / hour is not going faster than a car travelling at 40 mph. It is important that pupils realise from the outset the importance of specifying units, so that comparisons can be made. Numbers on their own are meaningless.

To illustrate this in another context, imagine that you were told that John is 1420, Max is 150 and Ian is 1.6 tall. Is John the tallest?

Including the units we see that if John is 1420 millimetre, Max is 150 centimetre and Ian is 1.6 metre tall, then Ian is the tallest. Mathematics often concentrates on numbers and relationships between numbers. Science rarely deals with pure numbers but with quantities. A quantity is a number multiplied by a unit. For example 56 is a number but 56 metre / second is a quantity. An education in science must make this distinction in a formal sense. This will not be the first time that pupils have met the challenge of different units. One approach is to ensure that most examples given to pupils are quoted in metres and seconds in the first instance. Hence try to avoid early questions which have objects moving at speeds such as 22 millimetre / second or 47 kilometre / hour. It is far better to use examples such as people walking at 3 metre / second or cars travelling at 12 metre / second or sound travelling at 330 metre / second.

Thinking about units

Here are some careful thoughts on choosing particular ways of writing the units for speed.

It is common for people (adults and children) to think of speeds as being measured in miles per hour. Pupils may also meet speeds measured in kilometre per hour and metre per second.

It is possible to convert between different units. However, the conversion from millimetre / second to centimetre / second or metre / second should be avoided if it is likely to get in the way of pupils' understanding of the basic concept. There is limited value in expecting pupils at this stage to convert between different unit systems (for example between kilometre / hour and mph). If necessary, a conversion table can be provided.

At this level the most commonly used units for speed will be metres per second, often written as metre / second and sometimes metre second^-1. While these all have the same meaning, they will not be equally accessible to pupils.

The notation itself may cause a problem, and it is useful to liaise with the maths department to establish consistency on this issue. The notation metre / second is probably the most straightforward to use, since it is easy to see how the unit metres divided by seconds comes directly from the formula used to calculate speed and can act as a link to it. You might even choose to write metresecond.

Teacher Tip: Choose notation wisely, and liaise with maths colleagues.

Average speed

Wrong Track: If it takes Bill an hour to travel the 40 miles from Glasgow to Edinburgh he must be travelling at 40 mph.

Right Lines: For any journey, the total time and total distance allow us to calculate an average speed.

Describing real journeys

Thinking about the learning

The child's point of view sounds very sensible. However on a journey of 40 miles it is unlikely that Bill would be moving at the same speed throughout. He might need to take a bus to the train station. He'll probably spend some time waiting for the train. On the train he'll probably keep up a high speed but the train might make several stops during which time Bill's speed will reduce to zero and then pick up again. So in effect, Bill might never have maintained a speed of exactly 40 mph during his journey. The value 40 mph is his average speed.

Thinking about the teaching

The journey described above is a real life story of a real journey. It's a journey travelled daily by hundreds of commuters between two of Scotland's great cities.

It is helpful to try to place physics calculations in real life contexts such as this in order to illustrate the complexity of speed calculations. In a laboratory it might just be possible to consider an object moving at a constant speed but in most scenarios all that is possible is a calculation of an average speed.

We'd suggest that whenever you're after a calculation of an average speed you use data from a journey that has taken place (even if that journey is only in the imagination).

A fly past

Wrong Track: Everyone agrees – it's on the aeroplane speedometer. We're doing 500 kilometres per hour.

Right Lines: Alice and Bob are sitting next to each other for the whole flight. Alice does not record any change of distance between her and Bob. But Charlie, in a fighter jet, records Alice and Bob's speed as 300 kilometre / hour as he overtakes, putting an extra 300 kilometre between himself and Alice for each hour of flying time.

Speed is always from someone's point of view

Thinking about the learning

Most pupils are comfortable with the concept of speed, though they may not have a neat definition for it. However, comparisons and calculations of speed may raise difficulties.

So can under-defined questions. Speed is always with respect to a point of view, and sometimes we need to carefully state the point of view to avoid ambiguity.

Thinking about the teaching

Take care to specify a point of view when you ask for a speed. The speed specifies the rate at which one object moves away from another.

So you need to locate yourself – perhaps you're moving along with one of the objects.

If you report something as at rest, all we can work out from that is that you and it are moving along together – the distance between you and the object is not changing. We don't know of absolute point of view against which we can all agree that something is stationary.

The main challenges

The main teaching and learning challenges in introducing the idea of force are:

The use of familiar terms, such as force, in unfamiliar, specialist contexts The use of common sense ideas which may be incorrect from the scientific point of view The fact that you can't see forces – they require an abstract construction

The key is that we're after a simple, tractable description – a usable model. Make it simple enough and no simpler. The tendency is to add the not-needed and not-useful: often impairing complexity persists.

The model consists of one thing, and cunningly selected arrows, representing forces acting on that isolated thing.

To think about – who do you agree with here?

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Falling because of gravity

Wrong Track: When you drop a ball it just falls. It falls to the ground 'cause it's heavy.

Right Lines: When you release a ball from your hand it accelerates to the ground because of the gravitational force of the Earth pulling on it.

Objects fall because of the gravitational pull of the Earth

Thinking about the learning

A key step on the journey is to move away from thinking that objects fall because they are heavy. In other words, believing that it's something within the object (its heaviness) that makes it fall. The Newtonian view is that objects fall because of the action of the external gravitational pull of the Earth.

Thinking about the teaching

A possible activity is to set the pupils the challenge of battling the pull of gravity. This involves taking the class to the school gymnasium and getting volunteers (there's never a shortage) to hang from a horizontal bar so that their feet are just clear of the ground. You can then time how long each can withstand the pull of gravity.

The idea here is to set up a situation where the pupils can get the idea (and feel) that gravity is pulling them down towards the centre of the Earth. It is always a memorable lesson as you encourage the pupils to battle against the pull of gravity and ask can you feel the pull of the Earth?.

Interestingly, its often the little, thin pupils who can withstand the pull of gravity the longest, with the more likely stronger boys struggling against the larger gravitational pull on their greater masses.

Tables pushing

Wrong Track: How can the table push up on the book? It's not alive is it?

Right Lines: A force can be exerted by any object whether living, dead or never lived.

Identifying forces

Thinking about the learning

Pupils are often unable to associate a force with an inanimate object. People can apply a force to objects – they make a decision to lift a bag of shopping or to push a motor car. However what about a book resting on a table? How can the table be forcing the book? The table is not alive. This is indeed a tricky situation. There is no easy practical activity which can immediately unravel this dilemma. However, a useful way of thinking about and explaining support forces is presented at the start of episode 02.

Here are some children trying to identify forces. These clips are worth watching several times. Particularly interesting, at this stage, is to think about how you can put them in a position where they can work out how to identify the forces, rather than just telling them the answers.

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A force is what is known in science as a vector quantity. To communicate the idea of forces, learners are expected to annotate diagrams using arrows. To build confidence in doing this it is important to offer learners an experience with a number of force-related situations. Invite learners to explore the language of forces, and experiment using force arrows. There are teaching activities here designed to support such learning.

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Thinking about the teaching

Being able to see that a force is acting and also where a force is acting is a skill to be developed. Being able to identify, describe and label forces is part of being able to model the real world as a scientist might. Learners need to be given the key to a language which will help them to describe forces. Here are three guiding principles:

• The first is that in every situation they meet, the vertical force due to gravity is present. Many start their description with this force.
• Secondly, look carefully at the selected object. It will be interacting with local things in its environment, and perhaps with other things not so close. Each of these kinds of interaction will be replaced with a force arrow. Use the kinds of interactions to identify the force arrows.
• Finally, the phrases acts on and exerted by are critical to talking about forces. For example: a force exerted by that thing acts on this object.

There is gravity in space

Wrong Track: There is no gravity in space or on the Moon because there is no air there.

Right Lines: The gravitational force does not depend upon the presence of an atmosphere.

Atmosphere and gravity

Thinking about the learning

Orbiting astronauts are seen to float about in their spacecraft. This is often attributed, incorrectly, to there being no gravity up there in space. This is one of the most common misconceptions about space. A reason often given for this assertion is that the space craft is above the Earth's atmosphere. Therefore, because there is no atmosphere there is no gravity. The same logic is used to explain the fact that lunar astronauts must wear large heavy boots because there is no gravity on the Moon, because there is no atmosphere.

These clips are worth watching and listening to carefully:

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Thinking about the teaching

This misunderstanding, which involves making a direct link between gravity and atmosphere, is a regular visitor to science classrooms.

A video clip of Apollo 15 astronaut Dave Scott dropping a feather and hammer on the surface of the Moon in 1971 is evidence that things do fall on the Moon – there is plenty of gravity there, but no atmosphere.

Falling freely – at the same rate

Wrong Track: It's obvious. If I drop a cannonball and a cricket ball, the cannonball will fall faster.

Right Lines: All objects fall freely at the same rate irrespective of mass (provided the effects of air resistance can be ignored).

Forces, mass and acceleration

Thinking about the learning

This is held as being so obvious that most people wouldn't even bother to check it out. A heavy block of wood, mass 2 kilogram, is clearly being pulled down with a greater force of gravity (about 20 newton) than a lighter piece of wood, mass 1 kilogram (about 10 newton). It seems clear to most that this larger force will make the heavy object fall faster.

Thinking about the teaching

The fact that a larger block of wood is subject to a greater force from gravity is indeed true. However, the greater mass of this wood requires a greater force to maintain its accelerated motion. Overall, the effect of a small force on a small mass is the same as that of a large force on a large mass. The net effect is the same – they fall together. They have the same force to mass ratio. (There is more on this argument in the Gravity and Space episode in the SPT: Earth in space topic.) The most important strategy for teaching is to set up a simple and effective dropping objects practical activity. Pupils should drop the objects themselves and also watch objects dropped by others. It is important to use objects that will not damage the floor or feet.

Gravity acts between all objects

Wrong Track: If the book falls off the table, it's because of gravity pulling it. If the book is on the table, it's just sitting there, gravity doesn't come into it.

Right Lines: Gravity is a universal force that acts between all objects with mass in the universe. An object does not need to be falling to be under the influence of gravity. If you are asleep in bed you are being pulled down onto the bed by the Earth's gravitational force. The bed springs push back up on you and you stay in your sleeping position.

Gravity is always acting

Thinking about the learning

Some pupils only associate gravity with situations where something is falling.

Thinking about the teaching

It is worth considering a range of objects in a whole variety of situations and asking whether or not gravity is acting on them. The answer is always yes.

For example, try water at the top of a waterfall compared with water in the pool at the bottom of the waterfall.

Forces on stationary objects

Wrong Track: It's just stood there. There are no forces acting.

Right Lines: Stationary objects that appear to be affected by no force might have several forces acting on them which all add to zero.

Forces in equilibrium

Thinking about the learning

Early introductions to forces in equilibrium will be via static situations. However, rather than identifying forces which sum to zero, pupils often describe such static situations as having no forces. This is an understandable conclusion and one that is almost correct. In equilibrium there is no resultant force.

Thinking about the teaching

You can subvert this natural tendency by identifying the forces acting from looking at the physical situation – an approach that is built into this SPT: Forces topic. We'd suggest not using equilibrium as a means of identifying forces. However it may be useful, in tricky situations, as a backup, and as a means of nudging individuals towards looking again at the situation because you believe that there is another force yet to be identified.

Moving and forces

Wrong Track: The ball has a force which keeps it moving through the air. If it's moving it must carry a force.

Right Lines: No constant force is needed to keep an object moving at a steady speed.

Giving forces to things

Thinking about the learning

That moving things need a force to keep them going is a very common misconception. When questioned, a child might typically argue:

Sandra: The trolley is carrying the force you gave it when you pushed it to start it off.

Objects moving with a steady speed are often labelled by pupils with force arrows in the direction of motion. A child might say:

Naz: It will stop when its force is used up.

The idea that a moving object carries a force, usually traced back to the force that was originally applied, is common sense and it is almost correct. A moving object might indeed have been forced to start its motion. However this force was involved in the initial action, the starting push. Once the pushing agent, perhaps a hand or an elastic band, is removed the force is no longer there. The object continues to move but does not carry a force. But the energy in a kinetic store does increase (see the SPT: Energy topic) as a result of the action of the force.

Here are some children talking about moving objects:

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Thinking about the teaching

The big challenge here is to try to eliminate the problems associated with friction. Everyday experience tells us that to keep something moving we need to keep pushing it. This continued application of a force is required simply to overcome the retarding effect of friction. In a world without friction there would be no need to keep pushing. Objects, once in motion, would carry on moving. Pupils don't live in a world without friction. Their experience tells them you need to push to keep things moving.