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### Efficiency and calculations - Teaching and learning issues

## Efficiency and calculations - Teaching and learning issues

Teaching Guidance for 16-19

The **Teaching and Learning Issues** presented here explain the challenges faced in teaching a particular topic. The evidence for these challenges are based on: research carried out on the ways children think about the topic; analyses of thinking and learning research; research carried out into the teaching of the topics; and, good reflective practice.

The challenges are presented with suggested solutions. There are also teaching tips which seek to distil some of the accumulated wisdom.

## Things you'll need to decide on as you plan: Efficiency and Calculations

Teaching Guidance for 14-16

#### Bringing together two sets of constraints

**Focusing on the learners:**

Distinguishing–eliciting–connecting. How to:

- bring calculations back to the lived-in word
- relate very abstracted descriptions to very practical concerns
- keep power and energy separate, yet related
- keep calculations linked to physical concerns, showing what cannot happen

**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:

- deal with power as that which accumulates energy
- separate descriptions that link snapshot to snapshot from descriptions of processes
- construct explanations in careful, explicit steps

**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.

### Up next

### Questions that can be answered

#### Practical concerns are the focus of this episode

The focus of this episode is on putting electricity to work in different kinds of electrical appliances. We see how it's possible to get students thinking about questions such as How long will the job take?

and How efficient is the electrical appliance being used?

.

Working out how to make a process better often involves cutting down on waste. When tracking energy or power, you'll be looking for energy dissipation or power switched to pathways that the designers of the system did not plan on.

### Up next

### How long will it take? - a matter of power

#### Power is connected to duration

Suppose an electric motor is being used to lift a heavy load: it might, for example, be a fork-lift truck lifting up a heavy box in a warehouse. If the warehouse is busy, it's not difficult to imagine that it would be useful to know how long it takes to lift each box – too slow and the warehouse is likely to grind to a halt as lots of packages arrive.

This kind of problem is one that can be tackled in terms of energy or, more specifically, in terms of power. If the power supply (in watts) to the electric motor is known, then this gives the maximum rate at which energy can be shifted to lift the box.

For example, supposing that the power supply to the fork-lift lifting motor is 4 kilowatt and that a 200 kilogram box needs to be lifted through 4 metre.

The total energy needed to lift the box through 4 metre: energy = force × distance. Here this is gravity force × height, so (*m* × *g*) × *h*. Put the numbers in, to get: (200 kilogram × 10 newton inverse kilogram) × 4 m, and do the calculation to get energy as 8000 J.

The lifting motor can supply 4000 joule second^{-1}.

So, the job of lifting the 200 kilogram box will take: 8000 joule4000 joule *second*^{ -1}, which is 2 s.

This kind of calculation raises a number of interesting points.

It assumes that all of the power supplied to the motor is made available for lifting the box. In other words, the assumption being made is that the motor is 100 % efficient. This, in practice, won't be the case and, bearing this in mind, the figure of 2 seconds must be the minimum possible time for lifting the box. In practice, the job will take a little longer because some power is switched to heating pathways while the motor is working.

This is a good example of the way in which energy ideas can be used to find out what is possible without getting into the details of the underlying working. Here we have learned that the job can't possibly be done in less than 2 seconds and have arrived at this result without having to consider the detailed mechanism of how the lifting electric motor works. This is one of the strengths of using energy or power ideas in calculations.

### Up next

### How efficient is that?

#### Bringing precision to a term that is also used more widely

**Wrong Track: **Electrical transformers are very efficient because they work well and never break down.

**Right Lines: ** Electrical transformers are very efficient devices because little energy is dissipated through heating. They are very efficient devices because all the power remains in the electrical working pathway: almost none is switched to other pathways.

#### Keeping a term for a particular use

**Thinking about the teaching**

The concept of efficiency has a precise meaning in physics, which is likely to be different from everyday

understandings of what is meant by efficiency. The efficiency of any device is defined as: efficiency = energy_{out}energy_{in} × 100 %.

This relationship assumes that the energy output and input are measured over the same period of time. An equivalent form for the relationship is: efficiency = power_{out}power_{in} × 100 %.

Here we are comparing the energy out and in per second.

Supposing we think about a domestic filament bulb. For every 100 watt of power supplied to the bulb, about 5 watt goes to lighting the surroundings whilst the remaining 95 watt goes to heating the bulb and surroundings. The efficiency of the bulb can be calculated easily(using the relationship quoted above, efficiency = power_{out}power_{in} × 100 % and put the values in: 5 watt100 watt × 100 % to get an efficiency of 5 %.

In this case the power_{out} is taken as being the useful energy output per second. The job of an electric light bulb is to provide light. As can be seen from the calculation, it doesn't do this very efficiently because more power is switched to heating than to lighting.

### Up next

### Why do car headlamps go dim when starting a car?

## Why do car headlamps go dim when starting a car?

Teaching Guidance for 14-16

#### A selection of answers to an on-line question

**Wrong Track: **Because the starter motor uses a lot of electricity. There's only so much to go around and so your headlights dim.

**Wrong Track: **The car needs electrical power to start, therefore the car dumps the power going to the headlights. That's why.

**Wrong Track: **It's the current or power drain from the battery when you turn the ignition.

**Wrong Track: **When you start the car you are using only battery power and the battery can only deliver so many amps to the starter motor to turn the flywheel.

**Right Lines: ** When the car engine is started, there's a very large current in the starter motor. So there's a very large current in the battery and a significant potential difference is produced across the internal resistance of the battery.

#### Building up an explanation: avoiding short cuts

**Thinking about the learning**

This question was posed on a web forum and gave rise to some interesting answers, which were more often than not going down the wrong track. The wrong track statements (which were presumably written by people with some interest or expertise in these matters) are interesting for the way in which they include the same kinds of vague

or incorrect ideas as those reported in episode 01 from 11–14-year-old students.

So, we have:

- The ideas of
current

andpower

being used interchangeably. - The idea that the battery is the source of current (or power), which can be
drained

. - Reference to
electricity

andelectrical power

, andbattery power

. - The battery as a source of
amps

.

Each of these statements suffers from a lack of clarity (from a scientific point of view) caused by the incorrect usage of technical terms such as current and power.

### Up next

### Thinking about actions to take

## Thinking about actions to take: Efficiency and Calculations

Teaching Guidance for 14-16

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

**Try these**

- using
efficiency

as a technical term, perhaps reservingeffectiveness

for the more general idea of getting stuff done well - using apparatus, words and diagrams together to develop accounts
- developing physical descriptions before accounts that use energy and power
- emphasising the practical consequences of calculations with power and energy

**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**

- calculating without sharing the purpose of the calculations
- running together different steps of multi-step arguments
- confusing snapshots with processes

**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.