## 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)