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## Work, energy and power

Lesson for 16-19

For some students, this will be a revision topic on fairly well understood themes. For this reason you may want to state the basic physics with clarity and brevity at the beginning of the topic to allow the students as much time as possible performing the experiment.

## Episode 213: Preparation for work, energy and power topic

Teaching Guidance for 16-19

- Level Advanced

In these episodes, students can perform some useful experiments with *trolleys*, weights, pulleys etc. It will help if you familiarize yourself with this equipment in advance, and ensure that the wheels of trolleys and pulleys are as frictionless as possible.

Be prepared to cope with experiments where the results appear not to show that energy is conserved; this will be because of energy tranfers due to friction. Your students should appreciate that no practical system can be perfect; turn the situation to your advantage by opening up a discussion on the idea of energy efficiency.

Also in these episodes, you will find that there are opportunities for *datalogging* . It is impossible to provide experimental recipes which match each commercial variety of datalogger, so you will have to be prepared to adapt to the equipment available to you. Check the manufacturer’s supporting documentation for suggested experiments.

## Main aims of this topic

Students will:

- use the following equations:
- work done = force × distance moved in direction of force.
- change in gravitational energy =
*m**g**h* - power = work donetime taken, power = rate of energy transfer
- power = force × velocity
- efficiency = useful energy transferredtotal work done × 100 %
- understand changes in the way that energy is stored before and after an event: from energy stored gravitationally to energy stored kinetically
- equate work done in decelerating to rest with initial kinetic energy
- apply these ideas to situations in which vehicles and passengers are accelerated or decelerated
- understand and use the principle of conservation of energy (as applied to mechanical energy)

## Prior knowledge

Students are likely to have a simple understanding of energy, and how it is transferred by a force. They will have met the idea of conservation of energy. In these episodes, you can extend these ideas to make them more quantitative.

## Where this leads

A good grounding in ideas about mechanical energy is needed before going on to a consideration of momentum.

General ideas about energy and its conservation permeate the whole of physics (and, indeed, the whole of science). Many specific results in other areas of science turn out to be examples of energy conservation, e.g. Lenz’s law in electromagnetism, Bernoulli’s equation of fluid flow.

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### Work done by a force

## Episode 214: Work done by a force

Lesson for 16-19

- Activity time 65 minutes
- Level Advanced

In this episode, students have to learn to think of force as a mechanism by which energy is transferred from one body to another. This only occurs when the force moves in the direction of the force.

Lesson Summary

- Discussion: Introductory discussion (10 minutes)
- Student experiment: Efficiency of a ramp (25 minutes)
- Student questions: Calculations of work done (30 minutes)

## Discussion: Introductory discussion

For some students this will be a revision session. Others may be less familiar with the concepts. Use questions and answers to establish the knowledge of the group.

We say that work is done by a force when the object concerned moves in the direction of the force, and the force thereby transfers energy from one object to another. You can be a typical physics teacher and use a board rubber to illustrate your point about energy gain. Alternatively, use some other more interesting object such as a model Thunderbird One. The following questions should allow you to draw out the ideas used in the experiment which follows:

When you raise a mass (board rubber etc), how is the energy transferred stored? (Gravitationally)

What is the force acting against the movement? (mg) We say that the lifting force is doing work against gravity. Some students may feel that it takes a larger force than mg to raise the object; however, if the object is raised at a steady speed, it is in equilibrium and the lifting force will just balance weight. This of course ignores any air resistance etc

What is g? (You are looking for gravitational field strength here, not acceleration due to gravity; you may need to draw this point out.)

What two factors will determine how much energy you lose (and hence the energy transferred to the object)? (The size of the force and the distance h moved in the direction of the force.)

Can you state the equation which gives the energy gained? (*m**g**h*)

Hence how much energy is required to lift object height *h*? (*m**g**h*)

This suggests that
energy transferred = force × distance moved in direction of force.
This is known as the work done by the force. In fact, we have used the fact that students are familiar with the equation *E*_{g} = *m**g**h*
to lead them to the more general equation for work done. You should now point out that *m**g**h* is simply a particular case of work done.

You can now push the board rubber or thunderbird across the lab bench to show work being done against a frictional force. In this case, the energy transferred ends up in stored thermally as the bench surface has warmed up. A relatively cheap FLIR camera will show the warmer surface.

## Student experiment: Efficiency of a ramp

You may want to show the apparatus set up before the students attempt this experiment and show them how to get the block moving smoothly. The values of the masses to overcome friction depend on the apparatus you are using and therefore the experiment needs to be trialled before the lesson. Using a pulley system should allow the students to get reasonably consistent results.

This simple experiment is made more interesting by revising the resolution of forces and considering the total work done to be the sum of work against gravity and work against friction. This concept is reiterated in the questions (below).

Episode 214-1: Work done in raising a weight using a ramp (Word, 39 KB)

## Student questions: Calculations of work done

You may choose to use some of these in the class as discussion questions, or as worked examples.

Episode 214-2: Along the flat and up the hill (Word, 75 KB)

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### Forces on vehicles

## Episode 215: Forces on vehicles

Lesson for 16-19

- Activity time 35 minutes
- Level Advanced

This brief episode considers the forces on vehicles when accelerating/decelerating. It considers the effect of the distance over which the force acts rather than the time of action of the force. The latter requires an understanding of momentum.

Lesson Summary

- Discussion: Why wear seatbelts? (5 minutes)
- Demonstration: An analogy for seatbelts (15 minutes)
- Student questions: For discussion or homework (15 minutes)

## Discussion: Why wear seatbelts?

Why wear seatbelts? Students will happily suggest answers to this simple question. Let them. Then turn the discussion towards an answer framed in the physics of the situation. Be clear that they are, for the moment, considering the distance over which the force is acting. Many students will want to give answers in terms of the time over which the deceleration takes place. This is entirely reasonable and, of course, an equivalent argument. Nonetheless, it is a good discipline to limit the variables to force and distance.

It is unlikely that you will not, at some point in your career, teach a student who has been involved in a serious car crash or has had a relative that has suffered injury in this way. Be aware of this possibility when discussing this area and don’t treat it too lightly.

Students should be able to argue that work must be done to stop a person during a crash. Seatbelts stop the body over a greater distance and therefore reduce the average force on the body.

Ask: Can they think of other safety features which function similarly? Crumple zones and crash barriers do the same thing, as do egg boxes.

## Demonstration: Why wear seatbelts?

An analogy for seatbelts:

A diverting demonstration that highlights the issues raised in the discussion. It is worthwhile putting in a few numbers to get a feel for the force on the egg as it breaks. A scheme for such a calculation is suggested in the experimental description. This can be compared to the force required to crack an egg by adding newton weights to it. The force the egg experienced in the crash will have been many times the weight of the egg. Similarly, the force on a crash victim can be much higher than body weight.

Episode 215-1: Why wear seatbelts? (Word, 43 KB)

## Student questions: For discussion or homework

These questions cover similar ground to those in the previous episode but focus on the application of *W* = *F* × *s* to car safety.

Episode 215-2: Forces and car safety (Word, 26 KB)

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### Energy changes

## Episode 216: Energy changes

Lesson for 16-19

- Activity time 90 minutes
- Level Advanced

This episode extends the ideas from energy stored kinetically (and velocity) to braking distance and work. Two experiments are included, both of which connect work done in braking to the initial amount of energy stored in the decelerating body.

Lesson Summary

- Discussion: Work, force, distance (5 minutes)
- Student experiment: Moving a block along the bench (30 minutes)
- Demonstration or student experiment: Braking force and distance (15 minutes)
- Student questions: Energy changes (40 minutes)

## Discussion: Work, force, distance

You have established that work = force × distance. Before embarking on the practical work it may help to make the link between initial energy stored and work done in deceleration, as clear as possible.

A body has 1 MJ of energy stored kinetically and is decelerated to rest. How much energy is stored kinetically at the end? (0 J) Hence, how much work has been done on the body? (1 MJ)

This might be a good point to rehearse the SUVAT equation: *v*^{ 2} = *u*^{ 2} + 2*a**s*

Thus when a car is accelerated from *u* to *v* m s^{-1} , the change in
*E*_{K} = 12*m**v*^{ 2} − 12*m**u*^{ 2}

This just equals the work done by the accelerating force, *F**s*

using Newton’s Second Law: *F* = *m* × *a*
*m**a**s* = 12*m**v*^{ 2} − 12*m**u*^{ 2}

i.e.
*v*^{ 2} = *u*^{ 2} + 2*a**s*

## Student experiment: Moving a block along the bench

This is a very effective and simple experiment. A block is given an initial push so that it slides along the bench. It passes through a light gate, so that its velocity is measured; the distance travelled beyond the gate is then measured.

Students should be able to gather a very large number of results. If you have access to computers and spreadsheets in the lab you can combine all the results together and let Excel produce the graphs (scatter graphs with no lines drawn allow the students to practise interpreting points and scatter).

Using a circular mass means that the exact path it takes through the light gates is not important. With carefully set-up equipment you will find that the mass is tall enough to break the light beam as required.

It does not matter if the measuring apparatus calculates velocity for you or only measures a time period – the latter just gives the students another task.

You should emphasise the dependence of stopping distance on the square of the velocity. This ties in to the Highway Code data analysed below (in the Student Questions).

Episode 216-1: Braking distance and velocity (Word, 34 KB)

## Student questions: Energy changes

These questions, about a car running down the tracks of different shapes, require a good understanding of the energy changes involved.

Episode 216-2: A slide (Word, 24 KB)

Some further questions, concerning energy changes and work done, for a high jumper.

Episode 216-3: The high jump – energy changes (Word, 20 KB)

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### Conservation of energy

## Episode 217: Conservation of energy

Lesson for 16-19

- Activity time 30 minutes
- Level Advanced

The Principle of Conservation of Energy lies behind much of the physics studied at this level. Although we are concerned with conservation of mechanical energy in this episode it is useful to extend the principle to its wider context in order to give the students a full appreciation of the overarching nature of the principle when they meet it in different guises.

Lesson Summary

- Discussion: Examples of energy conservation (5 minutes)
- Demonstration: Energy transfers (10 minutes)
- Student questions: Including calculations (15 minutes)

## Discussion: Examples of energy conservation

Introduce different ways that energy can be stored, and discuss the physical process by which it is transferred. Concentrate on energy stored kinetically, gravitationally and thermally. Introduced power as energy transferred per second (measured in Watts). A Sankey diagram can be used to show where the energy is dissipated.

Note that some students may think that the conservation of energy is an idealized notion, and that in practical situations, energy is not conserved. This is an incorrect idea. Energy is always conserved; in practical situations, some energy may be dissipated, so stored thermally when we do not want it to be; however, correct accounting will show that the total amount of energy is still constant.

## Demonstration: Energy transfers

In transport systems, it is vital to minimize energy dissipated. This demonstration draws attention to transfers that result in dissipation.

An alternative approach would be to ask a group of students to prepare this as a presentation, which they could then make to the class.

Episode 217-2: Free transport? (Word, 136 KB)

## Student questions: Including calculations

These questions make use of the idea that, in a frictionless system, energy stored gravitationally is then stored kinetically when an object falls; i.e.
*m**g**h* = 12*m**v*^{ 2}.

Episode 217-3: Energy conservation (Word, 38 KB)

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### Mechanical power

## Episode 218: Mechanical power

Practical Activity for 16-19

- Activity time 60 minutes
- Level Advanced

Power is the rate at which work is done, i.e. the rate at which energy is transferred by a force. It is likely that your students will be familiar with this definition. They may also have studied power in an electrical context.

Lesson Summary

- Discussion: The meaning of power (10 minutes)
- Worked example: A sample calculation; power = force × velocity (10 minutes)
- Student experiment: Simple measurements of human power (20 minutes)
- Student questions: Practice calculations (20 minutes)

Many of the practical activities suggested earlier in this topic could readily be adapted to relate to power; simply measure the time during which a force acts, and calculate: power = work donetime taken.

## Discussion: The meaning of power

Give the definition of power – this will probably be revision for your students. Ask for the unit (watt, W) and its relationship to SI base units

(1 W = 1 kg m^{2} s^{-3}).

## Worked examples: A sample calculation; power = force × velocity.

A car engine provides a forward force of 1000 N. If the car is travelling at , what power is developed?

In 1 s, the car travels 20 m. Hence we can calculate:

work done in 1 s = force × distance

work done = 1000 N × 20 m

work done = 20 kJ

power = work donetime taken

power = 20 kJ1 s

power = 20 kW

From this example, you can point out that we could equally have used an alternative form of the equation for power:

power = force × velocity

e.g. power = work donetime taken

power = force × distance (in direction of the force)time taken,

so power = force × velocity.

(However, this only works if the velocity is steady, i.e. the force

is *not* the resultant force on the moving object.)

## Student experiment: Simple measurements of human power

Students can perform various physical activities, for example lifting measured weights, and deduce their useful output power, using a stop watch. (Note that the human body is not very efficient in these activities, so the actual power dissipated by the student will be considerably greater than deduced here.)

This is included as it is possible that some of your students are less than confident in this area. It is expected that the majority of students will have already covered this ground.

Episode 218-1: Power of a pupil – running upstairs (Word, 39 KB)

## Student questions: Practice calculations

The first questions are warm–up exercises which should give students confidence. Note that the first question makes the connection between power, force and velocity (power = force × velocity).

Episode 218-2: Mechanical power (Word, 26 KB)

Episode 218-3: Work out with a cycle (Word, 114 KB)